/sci/ - Science & Math

http://www.youtube.com/watch?v=uQSoaiubuA0

The comparison is probably not 100% accurate, because of open system vs. closed system inaccuracies, but I'd still give this video as a pretty 'it probably won't hurt' recommendation for someone who hasn't heard of statistical mechanics before.

>>5174555
what is the advantage of looking at sheaves, really?
While I like topoi, I have not seen an interesting result.

Also, physics is not just applied math. There is just the impression that it is like that, because once some framework/axioms stands, it's really just math in a way. But coming up with a way of representing what we observe in terms of a new theory is more than applying combinatorincs to descrete things, or importing data from a surface or sound signal and do established geometrics. Physics is applied math only when the methods you use are established. Otherwise, it borders more to onthology.

also
>this thread
why is it even up, still?

>>4889021
Beaz and Haag. Physical insigh is ensured.
>his face when after reading 3 books on QFT, he doesn't know a single QED cross section, or what a cross section is for that matter.

I like both autors, but at which point does he want to read these books??

>>4851837
The Kuratowski definition is the standard definition.
http://en.wikipedia.org/wiki/Ordered_pair#Kuratowski_definition
(notice the decision to distribute the brackets)

This, together with the standard definition of the natural numbers
http://en.wikipedia.org/wiki/Peano_arithmetic#Set-theoretic_models
leads to this faux pas. The 1 is modelt to be the bracketed zero, which is the empty set.
So in the ordered pair <0,a>, where a is some set, the first entry is of <,> takes as a set is not 0 but 1.

There is no absolute ordered pair
http://en.wikipedia.org/wiki/Absoluteness

even worse is probably
en.wikipedia.org/wiki/Skolem_paradox

>>4182988
Well, I disagree on that with the pov, that if a theory works in the sense that if a theory can predict result for unmeasured stuff, then its a perfectly nice theory. It's not the fault of the theory side, that the only questions we can't really answer (except for computational problems in macroscopic physics) are the cosmological problems that dark matter/energy tries to explain.
Also, I'd not missuse the word metaphysics, it's a specific field, which is not related to string theory in any sense I can make out.

>>4171117
If this is your face, then I really want to know what feeling you associate with that expression.

>>3508763
ya, I'm comparing one quantized and one unquantized version of a field (say classical phi^4 and quantized phi^4). On the one hand you have (difficult to compute) classical propagation of field and on the other you have (even more difficult to compute) 2-point function.

If someone would ask you: "what is the difference between them?" what would you possibly answer?

>>3301474
http://www.wolframalpha.com/input/?i=Sum[%281%2F6%29%285%2F6%29^%282n%29%2C{n%2C0%2Cinf}]

>>3009891

oh look, mommy, that huge faggot is still bitter about failing out of his engineering curriculum, and now he works at Best Buy

axiomatization in contrast to what?
like you can't do set theory without axioms.

Elaborate

>>2852917
I'm talking about D's with D^2=∆
and the Leibnitz rule
D(f·v)=Df·v+f·Dv=dªf·v+f·Dv,
where dª is some derivative of a calculus, so that
(dªf)(v) = f·Dv - D(f·v) = [f,D]v
i.e., some Dirac operator, which generates a calculus.
(Like the gamma-Matric Dirac operators which describes the calculus of spinors in Yang Mills theory)

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

more generally

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

>1) Find some concept where any definition has certain setbacks.
>Examples:
>Definition of decimal expansions
>Definition of square roots
>Definition of 0^0, 0!, or any empty product
>Definition of log on the complex plane

>.<

why not just save the variable you're interested in as the output of the function itself?
Otherwise be more specific.

>>2794770
well, ...mhm...but since you need to use u=4 as a boundary while the one x in the integrand is still untouched I think you do have to integrate it eventually.

>>2752897
living person, child prodigy and mayor contributions to math:

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

>>2752902
It's difficult, since you don't get told if someone wasn't clever at young age, you only get to read about it if they are. So one can only guess. I donno, Heißenberg made big contributions but he isn't famous for being a genius. I wrote his autobography and he tells how he went to school, listended to nazi music, etc. Nothing interesting there, so I guess that would be an example.
Also, nowadays you don't really get to know the names of the big contributers too good, if the inovations are done @IBM or Nasa.

>>2731446
Das sind alles Lie Ableitungen :)

I'd also deny that
>physicists are notorious for not liking formal math.

>>2689464
I don't understand.
and
>the domain its valid for
what does that mean?

"I remember once going to see him when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways." "

one of my favorite tales of Ramanujan.
There are also Dirac stories of the same fashion

http://en.wikipedia.org/wiki/Ramanujan
http://en.wikipedia.org/wiki/Taxicab_number

>>2676507
hey, hallo ;)