Archived threads in /sci/ - Science & Math - 942. page

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Music is often hypnotic because of beats and rhythms and shit
Most visual media is not

>>8618894
Wait, how does the Mandelbrot set relate to the logistic map?

>>8618898
i have no fucking idea i'm just an idiot who saves cool pictures

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Phonepost because lazy...

Put the question in google. You're welcome.

>>8618819
This is what Ive come up with:
>The light hits the first border, and the different wavelengths get separated.
>They then hit the second border, and get partially reflected at the same angle as the angle of incident.
>They hit the first border from the other side, and get refracted again.

But now they are all at the same angle as they were before,except on the other side of the normal.
All wavelengths are at 45°, but they are spaced apart slightly.

The angle is thus not related to the thickness of the layer, and I cant find the answer.

What am I missing? Does it have to do with total reflection upon hitting the first barrier the second time or something? I dont get it.

>evolutionary purpose
Quite the memester, aren't you...
Evolution has no purpose, tons of good, bad and neutral variations occur, good and neutral ones survive, bad ones don't. This doesn't happen via a guided mechanism, it is random.
There is no way to suggest emotional stress is beneficial to survival or reproduction yet. I might just have no effect

>>8618802
I agree that effects of emotional stress isn't something connected to the prior benefits, it's probably a random consequence

But I'm getting tired of this "purpose of evolution" semantical nazism
Of course evolution doesn't have a purpose, fucking duh
But it is much more convenient to word it that way than saying "how was that mechanism beneficial for this organism to he point that it is still here/widespread/bla bla"

>>8618823
it doesn't have to be beneficial for it to be widespread

your rewording is still as retarded as
>What's the evolutionary purpose of this?

>>8618790
yeah

any field extension of R by adding a root of a polynomial must be of degree 2 (only degree 2 polynomials are irreducible and don't give R as an extension), and any finite field extension is of this form (otherwise for a new element c there's an infinite subbasis basis c, c^2, c^3, ...). so all we need to see is how R extends by roots of quadratic equations

for an irreducible polynomial x^2 + bx + c, we add sqrt(b^2 - 4c), a root of a negative number. but sqrt(4c-b^2) is positive so dividing we get i. and R[i] = C

that means we have C inside all of them, what about other copies of C? C only has two automorphisms, the trivial one and the one that goes i -> -i. I'd say that's all

so yes, it's always C, and even if you don't consider it up to isomorphism, there are only two ways to extend it

>>8618812

I didn't fully understand the post. Could you at least tell me where I could look that stuff up?

>>8618812
OP is talking about making R2 a field, not making it complete.

So consider the operation (a,b) + (c,d) = (a+c,b+d) and (a,b)*(c,d) = (ac,bd)

Proof of associativity:
((a,b) + (c,d)) + (e,f) = (a+c,b+d) + (e,f) = (a+c+e,b+d+f)

And
(a+b) + ((c,d) + (e,f)) = (a+b) + (c+e,d+f) = (a+c+e,b+d+f) = (a+c+e,b+d+f)

The proof for multiplication is the same.

The proof of commutativity for both operations follow from the properties of operations of real numbers.

The additive identity of obviously (0,0) and the multiplicative one is (1,1).

The additive inverse of (a,b) exists and is (-a,-b). The same goes for multiplication.

The big one: Distributivity

(a,b)*( (c,d) + (e,f))) = (a,b)*(c+e,d+f) = (ac + ae, db + fb)

But also
(a,b)*(c,d) + (a,b)*(e,f) = (ac,bd) + (ae,bf) = (ac + ae,bd + bf)

This completes the proof.

Reminder that the operation induced by C is (a,b)*(c,d) = (ac - bd, ad + cb) so the operation described above is clearly different.

Exercise: Find another operation that makes R2 a field and prove that it is.

>>8618641
>French math-fag here.
Kek.

It's pushed heavily by French academia because your state and industry sank a lot of money into it's development, there is no good reason to use it besides politics.

It's not a bad language per se, there as some interesting and big projects in it, but you rely A LOT on libraries written by (french) PhD students who no longer care about it and abandoned them. Also less tool support and libraries and support via community than Scala, Haskell or even LISP.

>>8618641
i had to learn and use it a few years ago, its a shit one, really annoying language, its useless since its only used for education, and has no real practical application, just do it, and do worry, in a few years you'll be doing real programming with java or C++

>>8618754
do not* worry

>>8618078
what the fuck you start.

>>8618078
>Central Limit Theorem
>Law of Large Numbers

What's the point of this thread?

>>8619698
What's the point of anything

I dont get why philosophy and science hate each other, specially hard sciences.

They are both needed

>>8617841

I've never taken a science or math class in which the professor mentioned philosophy

>>8618303
But here in /sci/ every talks shit about all social/human sciences in general and act like they are superior for studying STEM.

Also I met a engineering professor who every class talked shit about law school.

yes, become his acolyte, op

Yes, and when you publish your thesis on rational approximations to Sqrt[2] with decimal expansions consisting of less than 10^21 digits, you will land some really prestigious professor gigs the like of Harvard, Yale etc

>>8617677
I would.

When I graduate I will unironically apply to go gradschool there. If I get accepted to somewhere better then I won't go but if I don't then... time for my PhD thesis in rational analysis.

>>8617556
>big space habitat
>realistic
why live where there is nothing?

>>8617578
>wanting to live in a gravity well
Good goy.

>>8617556
Yes. Bernal sphere is more efficient though

Badly.

Goodly

Okayly.

>>8617419
One time a young student at Cambridge was studying Algebraic Geometry and stuck on a particularly difficult problem assigned to him. Meanwhile, the great A Grothendieck was to give a talk at the university and the student was not to miss it. After the talk, he sheepishly approached the wizard and asked him about the homework problem. Grothendieck mumbled "EGA Section whatever paragraph number" and the student walked away. Sure enough, upon finding the tome in the library, there was the solution to his problem, laid out in the text. The student relaid this tale to his professor, JG Thompson, for he could not now honestly write up the solution. Thompson remarked "I don't know if I should give you an F for looking it up, or an A for having the balls to ask him about it."

That students name? Richard Foote.

>>8617451
Cool, where did you get that anecdote? Also isn't Foote a (finite?) group theorist? lol

Have you read EGA? Are you basically telling me that I should be able to quote it chapter and verse like the bible?

>>8617419
I'm 95% sure reading EGA is a waste of your time. If you had a professor fluent in algebraic geometry nearby, you wouldn't be asking a board full of undergrads what to read. You probably don't have a nearby algebraic geometer so you probably aren't planning to do research in algebraic geometry, which is the only good reason to be reading EGA instead of something more accessible/less time-consuming.

Trying to filter down EGA into a barebones graduate-introduction course is stupid, especially since you'll need another book anyway to find problems.

Pretty sure it was about madness not drugs

>>8617181
>he thought they were insane
How can complex numbers be insane if they aren't people?

>not reading Euclid and His Modern Rivals
Alice in wonderland a shit

>>8616845
>you have to go back
>>>/x/

Before you go back to >>>/x/, can you tell me what you mean?

>>8616993
https://www.google.com.co/amp/s/www.wired.com/2013/04/gov-secrecy-orders-on-patents/amp/

>>8616579
Precalc

>>8616579
>Physics: Mechanics
>Methods of Lagrange and Hamilton
>Continuous media using Fourier series
>Mathematical formulation of the dynamics of a particle and systems of particles, including applications to atomic physics

>Civil engineering major

>>8616579
Pre-algebra

>>8615812
is this a real question ?

>>8615812
a bowling ball is sitting on the fabric of space time if its in earths gravity

Obviously because gravity is a hoax OP