/sci/ - Science & Math

>>15394236
i) Let T = A*A. T* = T
Tv = av
v*Tv = a(v*v)
(v*Tv)* = a*(v*v)
v*v > 0
a = a*
ii) Tv = av
0<= (Av)*(Av) = v*A*Av = v*Tv = a (v*v)
and since v*v > 0, a >= 0
iiI) Clearly Av = 0 => Tv =0

Assume A*Av = 0. Then v*A*Av = 0, so (Av)*(Av) = |Av|^2 = 0, so Av =0.
QED

>>15291196
The people who make the "you are actually motivated by emotions and not logic and here's why" are invariably the least self-aware and least objective people. When one is not capable of arguing their positions in cold logic, they choose to appeal to armchair-psychological explanations. Happens all the time.

>>15265755
Here are some kind of obvious thoughts that I had that surprisingly little normies and pop philosophers agree with:
1. Voting doesn't matter. You might just as well go play the lottery. The odds of your individual vote changing the outcome of whatever the vote's trying to decide are usually microscopic. What's more, this is the correct lens through which to analyze the individual decision for voting. The critique "what if everyone thought the same way" doesn't apply, since they don't. If nobody voted, your chances to actually influence the outcome would be much higher.
2. People have free will, like actual libertarian free will. In a lot of decisions they make, they could have done otherwise, and the determinist argument is a basically a fantasy that people make up in their heads that's not real (the usual story about causal chains and factors). Many philosophers admit that physics as we currently understand it is not deterministic, but still cannot let go of the usual fantasy of non-physical (as in not currently studied by physics) causal chains etc. for which they have no justification.
3. The importance of sources and transparency. Most people are just happy to hear a claim without the justification for it and move on. They say just look it up or just think about it without providing proof. So many things in the world would become better with just a little bit of epistemic rigor. "It's common sense" shouldn't cut it.
4. "The laws of physics" concept as it exists in most people's heads is nonsensical and extremely damaging. There are only the laws of physics that physicists write down and study, which are almost always inaccurate to some extent. There are no "actually real but hidden" laws of physics that physicists try to get at, this is solely a fantasy that exists in people's heads because people like to think the universe is simpler than it actually is.

>>15230467
>, a mathematician knows he must prove it to be true, beyond all doubt.
Mathematicians nowadays don't believe in proofs as demonstrations beyond all doubts. Instead, they believe in something called formalism, where proofs are merely syntactic manipulations of formulas and hold no epistemic significance beyond that. Propositions are not true/false, they are only provable/disprovable and to them math holds no connection to the real world (a demonstrably false belief, but a very common one nonetheless). In this way, math is worse than science, it's a schizophrenic theological system.
There are however people (usually called constructivists/finitists) who still hold a sober view of mathematics.