/sci/ - Science & Math

>>7259506
>0^2 = -2
>you retard
no U

Literally every second person alive is above average intelligence.

No to the rest.

Literally every second person is above average intelligence.
No to the rest.

>>7090404
>advanced probabilities
>odds
no

>>6883300
>heat expands
no-1.gif

>>6759031
>I should have made it more clear, but by "quadratic" I specifically mean "quadratic form", so there are no linear velocity terms in the Lagrangian. This is always the case in classical mechanics.
No
Consider
http://en.wikipedia.org/wiki/Lorentz_force#Lorentz_force_and_analytical_mechanics
or the Landau problem, or any expansion of non-polynomial dispersion relations in solid state physics.

>No, C must be there
You parsed that sentence differently, than I intended, for C=0 the geodesics are an example.
And "term" meant name, as in new name for that kind of equation.

>I really just want some stability theorems to do with this equation, or any sort of qualitative analysis.
There is certainly much literature.. I don't really know but since you want to talk about a broad class of systems, the answer will be broad. Do you know of stuff like KAM theory, or ergodicity stuff. If not, maybe that leads somewhere
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold%E2%80%93Moser_theorem

>1)Life in Academia,
>all you do is research your subject as much as you can all day long every day
Except writing unending proposals for your institute etc.
Also, I don't want to learn only one thing.
>(excluding weekends and holidays).
Do you think Terrence Tao takes a day off?
Why would you want to take a day off anyway.
>Your salary will be average, you will have your own little office space and most importantly you will be a doctor.
Yeah, the doctor isn't the problem, you get that with 30. But then there is 3++ years of postdock and then trying to get a stable position, and maybe one day you'll be a full professor.
>You may have a chance at the nobel prize
That's mostly politics
>you may contribute to society in a significant way.
Was never my aim, but I see some are motivated by that. Noble.

I want to the one negative guy, saying that all is circle-jerking, that many many big things have started in academic circles. The logicist program of Wittgenstein/Russel etc. and co is most academic goal to set and work for, but Gödel and later Turing were working exactly on those problems - we don't have the computer because someone needed to program excel. Turings discovery of the possibility of universal computation is a major brainfuck, in fact, and not to be expected by anyone. Thx academia.

>2)Life in the the private sector, very high salary,
If you make it
>lots of off days,
why lots, compared to other jobs?
>company car,
I don't drive, but okay.
>all travel expenses paid.
Academics go to conferences more, I think.
>Your work is repetitive,
all jobs are, I think.
>boring and mundane
then don't do it
>but the salary makes up for it. You may NOT have a chance at the nobel prize, you may NOT contribute to society in a significant way. You WILL however be able to retire early in the 40s.
wut.

I'd say, find something you love and fuck around.

>>6593606
Will depend on the logic used for decomposition and what decomposition really means. Many logics don't even have equality.
In the example
>>6593648
if all terms are countable x1,x2,...xN, then one can write a=b+c as
(a=b+x1 and c=x1) or ... or (a=b+xN and c=xN)
and consider each a=b+xi as predicate P_xi(a,b).

At least in propositional logic, I suspect that the answer is no as e.g. there is a famous trick to reduce n-ary "or"-chain predicate to a long "and"-chain of 2-ary ones predicates:
http://en.wikipedia.org/wiki/Boolean_satisfiability_problem#3-satisfiability
The statement is that the new formula is the same from a proof theoretical perspective (equisatisfiable) but not logically the same formula anymore.

What is
>my_ternary_equality_operator(a,b,c)
supposed to express?
If a equals b, then usually a=b. You want to involve a third term, because...? The only way I could read it is that you want to make it say "a=b and b=c and c=a", but you require that actually not just two are equal, and you also maybe don't want to use "=" to define it. In homotopy type theory it requires three terms to participate. Funky example: Equality is an operation (a dependent type, really) and if "a" and "b" are of type X (written a:X, b:X), then "a=b" is a type which might a priori be empty. Only when there is a third term c of type a=b, i.e. c:a=b, then equality between a and b holds.
(The terms c is considered a proof of the relation. One axiom of the theory is that for all terms a, the type a=a is never empty and its inhabitant is called "refl_a". So refl_a:a=a. Proving a=b is done by finding a deformation from the identity path refl_a to c. Similarly, when you have two proofs c and d of a=b, then you might find a path from c to d, showing how the proofs are related. That's the whole homotopy business.)
http://en.wikipedia.org/wiki/Homotopy_type_theory#Interpretation