/sci/ - Science & Math

I, for one, want to have an impact on the world.
Trying to learn different stuff, reading a lot, enjoying life at the moment. yo.

>>5266458
Wir sind Helden, haha.

On a somewhat related not, there is this phenomenon that good mathematicans often report that an idea/reuslt/trick just suddently comes to them, after learning and trying to understand for a long long while. That seems to be how the brain often works. You think about stuff alot and then, under the shower, it's there.
I think being clever is good, but it seems hard work and dedication is what makes it. I don't really think that it's not possible to be better than the genius people, at least if you work more than them.
Also related, I like this paper, where someone asked great mathematicans to give general advice
http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf
and, I see, everyone interprets the question quite differently.

>>4873643
that's a nice tautology you got there.

I specialize in a very specific type of information:
useless information

http://en.wikipedia.org/wiki/Arithmetic_derivative

Theoretical physics papers related to the topic:

http://arxiv.org/abs/hep-ph/0103051
http://arxiv.org/abs/hep-th/0201077
http://arxiv.org/abs/hep-ph/0203060
http://arxiv.org/abs/hep-ph/0306028

http://arxiv.org/abs/hep-ph/9810355
http://arxiv.org/abs/hep-ph/9607477
http://arxiv.org/abs/hep-th/9411230

http://www.sciencedirect.com/science/article/pii/0370269385904605

http://www.sciencedirect.com/science/article/pii/0370269386904806

http://arxiv.org/abs/hep-ph/0009291

http://motls.blogspot.com/2011/09/superluminal-neutrinos-from.html

http://arxiv.org/abs/hep-ph/9812418
http://arxiv.org/abs/hep-ph/9809521
http://arxiv.org/abs/0801.0287
http://arxiv.org/abs/hep-ph/0610324

http://arxiv.org/abs/1109.5687

http://en.wikipedia.org/wiki/Starfish_Prime

The differential d is a map of the function space over M to N into the space of functionals of the tangential space over M to the tangential space over N.

Any questions?

okay, here some Mathematica code:

ops = {?????????};

Permutations@%;
Table[Take[#, n], {n, Length@ops}] & /@ %;
Flatten[%, 1];
Join[#, {"2", "2", "2", "2"}] & /@ %;
Permutations /@ %;
strings = Flatten[%, 1];

ToExpression[RowBox[#]] & /@ %;
sols = DeleteDuplicates@%;
depending on your computing power, you can find all possible solutions...

http://room538ccpp.files.wordpress.com/2009/01/penrose.png?w=460&h=415

>mfw

>>3256660
If time itself stated when the big bang happened, then the expression "caused the Big Bang" or "what existed before it" doesn't make no sense. It's like asking "which color had the wall in your yard before it was build?".

Think of a hight dimensional blobb consisting of all time frames of the univers (The spacetime as a whole). Then the big bang is just one end of it and for some reason our consciousness is always only perceiving one moment of it. And for us, these moments are moving away from the spacetime-area where the big bang is located

http://en.wikipedia.org/wiki/Arrow_of_time
http://en.wikipedia.org/wiki/Entropy_%28arrow_of_time%29

>>3251673
ah okay, then the questions probably refers to
http://en.wikipedia.org/wiki/Hund%27s_rules
and you have your "answer".

however, electrons having different spin would fuck up the rest of the univers - the consequences wouldn't just turn up when it comes to chemisty

>>3213935
The word photon is a bit difficult if you talk about classical general relativity, since there the electromagnetic field is not quantized: You would be talking about a plane wave or so. However, if the momentum is fixed, like with a photon, then the plane wave exp(ikx) is pretty much non-localized.

Anyway, I don't know the solutions by heart, but if you really have only photons/electromagnetic field and no currents or charge densities, then

http://upload.wikimedia.org/math/1/1/c/11cca0c5c0d7949ff9a6ce0dbfdf597a.png

this is "obviously" traceless

T^\mu_\mu=0

therefore, plugging that into

http://upload.wikimedia.org/math/3/f/5/3f50fd206f2fe543a6a8a3e687cf74c3.png

you see that R (curvature tensor, here R is rather R_\mu\nu but I was sloppy above) is traceless, i.e. R=0 (ricci scalar is zero), and so light alone doesn't really change spacetime too much. There is a reason why all the black hole solutions, high curvature, have mass in the middle.

don't know if you know what a trace is though, so this might not help

>>3168017
God.

>>3138035
there is no continous section like H(p,q)=E, but a special set of basis vectors, namely the eigenstates of H, which correspond to a specific Energy value/frequency.

The state, let's call it S, is a composition of those eigenvectors and therefore a wild weighted ensemble of frequecies. Every eigenvector changes (in time) acording to his Energy/freqeuncy and if the eigenvectors change then S does too, because S is composed of them.

the seperate eigenvectors might be represented in a q-space or in the p-space, but they themself aren't really related to H anymore.

>>3138060
ich schick dir jetzt das pdf, k

>>3054473
oi, mein schöner deutsch is wundervoll

?/4

It's a running eater of overal factors (I was bored)

>>3012137
I think there is pretty much no mathematical aspect of life which hasn't been studied for ages by someone.
I always like to say that there are tons of papers on this little fucker:
http://en.wikipedia.org/wiki/Petersen_graph

and concerning paper-folding etc.:
there's this graph theory/combinatorics/computer science/group theory professor who works for wolfram who also has a pretty much private website with lots of crazy shit:

http://www.mathpuzzle.com/

you're welcome

>>2929641
anything is too vague.
you know it's a fucking huge topic as one would guess from this page
http://en.wikipedia.org/wiki/List_of_group_theory_topics

okay random fact
<span class="math">Sp(1) \cong SO(4)/SO(3) \cong SU(2) \cong Spin(3)[/spoiler]
these are all well known Lie Groups and they turn out to be the same. "SU(2)" is probably the most commonly used name for it.
Moreover, topologically this group is equal to S^3, the threedimensional Sphere. It can easily be made to be a Riemannian manifold (this is also "obvious from the fact that the group is compact").
Moreover, there is a nice construction of this sphere
http://en.wikipedia.org/wiki/Hopf_fibration
The group is also the symmetry groups of spin 1/2 fermions (electrons).
Note that "all compact groups" (not technically) can be represented unitary (they leave some Hilbert Space product/expectation value (in Quantum Theory) invariant)

What is preasure?
What is temperature?
What is more complicated?