/sci/ - Science & Math

[Anonymous No.6779516]

>physicist wants to be mathematical physicist
>has to learn hard as shit maths

>mathematician wants to be mathematical physicist
>has to learn "intuition"
>i.e. "gravity points down", wow so hard

What is even the point of doing a physics degree if it all eventually becomes maths?

[Anonymous No.6779529]

For me at least, the intuition IS the hard part. Everyone can (after enough practice) learn to follow mathematical algorithms and such. The intuition part of physics is what challenges me (I am in fact a physics student, wanting to become a theoretical physicist eventually)

[Anonymous No.6779555]

Mathematician here, was watching a General Relativity lecture, and I don't think high level physics is exactly 'intuitive' unless you're referring to low level physics.

[Anonymous No.6779589]

>>6779516
Theoretical physics is constantly learning math on the fly, using it to capture the ideas behind theory you work on, and then forgetting about the math at the right moment, so you actually end up with some new directions.
Meanwhile, in mathematics, seven generations of PhD students will write about the exact same topic.
(In both fields, the names which people remember are the guys who work in the first generation, and the people who end the subject. Related: The initial pages of chapter 6 here are a good read:
http://arxiv.org/pdf/math.ho/9404236.pdf))

I believe the dividing of math and theoretical physics is just a self-fulfilling prophecy. It's not the subject as such that's different, it's different just from having being academically split into two broad working collectives which developed different content-producing- and results-judging habits out of their different emphasis on the sub-part of problem they work out.
This is a viewpoint I only take for some years no - at one point I was completely opposed to Arnolds (extreme) point of view
http://pauli.uni-muenster.de/~munsteg/arnold.html

[Anonymous No.6779597]

>>6779529
>mathematics is following algorithms
>math is easy after practice

????? what the fuck have you seen any higher level math

[Anonymous No.6779603]

Well "gravity points down" is just one of many very simplified ideas, as you delve deeper it becomes much more complex.

[Anonymous No.6779608]

>>6779603
it's usually special cases of math

for example, the whole classical E&M is just application of stoke's theorem

[Anonymous No.6779646]

>>6779608
I'd say he speaks of the physical concepts, not the math which is used to describe it. The subject of Electrodynamics isn't the same as the theory of Maxwell equations. Otherwise, there would not be much motivation to learn it.

I also think general relativity and gravity in general is a pretty bad example in >>6779555. You can formally learn Riemannian geometry and you'll have an easy time to learn the maths of it. But in that subject in particular, you have to think lots of "physical thoughts" to discard the point of view you got used to. At least I spent hours thinking about roller coasters and people falling through clouds, while learning it.

Another "physical" example for me is brownian motion. If you learn set theory, topology, measure theory, probability theory, partial differential equations and statistics to understand the last proofs in stochastic processes formally, you'll still be unhappy if you don't picture the process with real things tumbling through some space.
Developing an intuition for why after t time, the distance a drunken walker will be from it's starting point is \sqrt{t} is gained "physically".

[Anonymous No.6779700]

>the physicists stuff becomes math
>the mathematicians stuff becomes philosophy
Gee I wonder which I want to deal with the rest of my life

[Anonymous No.6779714]

>>6779700
you state that as rhetorical question, but without knowing your agenda, I don't know what you're saying here

[Anonymous No.6779733]

>>6779700
math doesnt become philosophy at any point, math is the end

philosophy is mostly senseless mind-masturbation for people who can't do actual science and people too tired to do science

[Anonymous No.6779753]

>>6779608
And Gauss's Theorem. Can't forget Gauss.

[Anonymous No.6779779]

>>6779753
Stoke's theorem isn't what you think it is. It's much, much more general than real 3d spaces and it's really called Newton-leibniz-gauss-green-ostrogradsky-stokes-poincaré theorem.

The divergence theorem is a special case of it

[Anonymous No.6779782]

>>6779646
Undergrad physics major here, and I spent some time on Brownian Motion and Diffusion in Statistical Thermodynamics as a project last semester. I don't particularly have a super rigorous maths background to understand the process formally as far as mathematical proofs go. In the case of Brownian Motion, isn't the distance a drunk walker will be from it's starting point more like the distance of the probability (Gaussian) curve? And in the case of Diffusion, I just thought of it as a bunch of drunken walkers and the probability curve would be the actual percentage of the total number of walkers at each point?
Sorry if this is either nit picky or nonsense. I just want to see if I understood this subject as well as I thought I did.

[Anonymous No.6779790]

>>6779779
Well crud. Griffiths is really casual in his writing, so I guess I shouldn't have expected all the information. Would this be in an advanced Calculus course?

[Anonymous No.6779802]

>>6779790
not quite, it's on chapter 10 of baby rudin
you can start reading it, and get ready for your mind to expand

[Anonymous No.6780209]

>>6779802
Stop recommending this book, please, it sucks as an introductory material because it's way harder than it needs to be and it is supposed to be an introduction so it won't cover advanced subjects at all! For that Papa Rudin is actually good.
Also, he doesn't even name the Arzelà-Ascoli theorem, that's how much it sucks.

[Anonymous No.6780258]

intuition isn't "gravity points down". Intuition is "These higher order terms can be discarded to drastically simplify the model of a system at little cost of precision." Approximations are essential in physics, and reasoning about them can be a rigorous subject on its own. The foundational principles are still mathematical, i.e. Taylor expansions, order of magnitude estimation, etc.

[Anonymous No.6780260]

>>6779779
That's the one that says that the integral of a k-form field over the boundary of a set is the same as the integral of the exterior derivative of that form over the interior of the set?

[Anonymous No.6780261]

>>6780258
this isn't inherent to physics at all

order of error, convergence and stability are all mathematical subjects more than physical ones, imo. you see it a LOT in numerical analysis, for instance

[Anonymous No.6780264]

>>6780209
i've heard the opposite, that papa rudin actually sucks. i havent got to it yet.

baby rudin is terse, but i see that as a plus

[Anonymous No.6780279]

>>6779733
This can people explain to me why I been seeing people on here saying it turns into philosophy? Honest question

[Anonymous No.6780308]

>>6780264
Why would that be a plus for your first book on analysis and formalism in mathematics? It's ok if you like it and for some people it will be a good book, but Rudin shouldn't be the standard book on analysis, there are others much better that are easier and cover more material.

Also, it might give the wrong impression to new students and make them think math is all about formalism and no intuition. People never tell you that the deal with intuition is that you have to develop your own.

[Anonymous No.6780554]

>>6779782
Yes, in the frequentest interpretation of probability you get the distribution by having a walker for each possible case, and then for each endpoint, the probability is the number of walked ending up there over the total numbers of walkers. What's your question again?

>>6780279
Philosophical question almost only arise in foundations of math - not when you work on "hands on" stuff like differential equations.
My personal opinions are too strong to make an objective judgement, so at least for the range of topics maybe this helps
http://plato.stanford.edu/entries/philosophy-mathematics/

[Anonymous No.6780561]

>>6780260
My wife's gonna kill me.

[Anonymous No.6780583]

>>6779589
>Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
>Implying mathematics is a part of physics.
>Implying mathematics uses the scientific method.
>Implying one performs experiments in mathematics.
>Implying evidence counts for shit in mathematics unless you're proving existence or counterexample.
>etc...

So many retarded things right off the bat. Glad I didn't waste my time reading that shit.

[Anonymous No.6780589]

>>6780583
Me again.

The Arxiv article is wrong as well. It approaches mathematics from a pop-sci understanding of it. It's clear the author hasn't actually worked through the construction of an axiomatic system by beginning with a formal language.

It's unfortunate that so many people like to handwave away foundations and then go on to make wrong general statements on the topic in spite of that.

[Anonymous No.6780600]

>>6780583
>>6780589
Yeah, your platitudinous, pseudo-intellectual, and prepubescent understanding is surely more accurate than the well-cited descriptions of a Fields medalist and one of the world's best mathematical physicists... both of which you mistakenly believe to have comprehended. You're full of shit, kid.

[Anonymous No.6780603]

Engineering major here. I don't have to delve deep into either subject yaaaay for skirting by

[Anonymous No.6780605]

>>6780600
Being a field medalist doesn't imply you're knowledgeable in every field of mathematics. Foundations is also considered one of the more esoteric fields of mathematics that most working mathematicians just hand wave away.

[Anonymous No.6780608]

>>6779516
I know this mathematician who used to claim, that mathematics is all you really need, and if you know maths, physics is really easy to learn. So he started to sit in my physics lectures.

Eventually he capitulated during the thermodynamics lectures.

[Anonymous No.6780610]

>>6780605
>Being a field medalist doesn't imply you're knowledgeable in every field of mathematics.
It implies having at minimum an elementary undergraduate-level understanding of the spectrum of mathematics, something you clearly haven't obtained.

> that most working mathematicians just hand wave away
You should really go see a psychiatrist and get those delusions of persecution in check.

[Anonymous No.6780618]

>>6780610
>Spectrum of mathematics
What a very pop-sci description.

http://ncatlab.org/nlab/show/foundation+of+mathematics

[Anonymous No.6780626]

>>6780618
Wow, you linked a page giving some monotonous philosophical overview of categorical foundations subconsciously tainted by the authors with new-age CS bullshit. Was this supposed to prove how deep and insightful you are? Something routinely covered in every mandatory undergrad "philosophy of math 101" class?

[Anonymous No.6780629]

>>6780626
no, just a quick overview of several different foundations so that you can look into them yourself.

Here is the intro chapter from a text on second order arithmetic.
http://www.personal.psu.edu/t20/sosoa/chapter1.pdf

[Anonymous No.6780634]

>>6780629
>muh reverse mathematics
>so logical, so intellectual xDDDDDDD
Is there some way to flip the pages around without printing it out? The blank backsides are probably more interesting than your toddler tier scribblings.

[Anonymous No.6780642]

>>6780634
First and second order arithmetic are the logic systems that one typically works in when they state the Peano axioms and do the constructions necessary to do Analysis.

Again, it was an example. The ZFC axioms are also expressed as sentences of a predicate logic.

You're missing the point here. One first begins with a formal language, then they give it the expressive power of a logic (by associating to it semantics, a truth function, and a derivation system), and then they choose a set of sentences in the system and proceed to explore what other sentences are entailed inside the system (via the derivation system). All of this is typically done by maintaining the principle of compositionality (or part of it at least).

To dumb this down a lot. When one says A=>B in mathematics, we are not making an assertion or a derivation, we are simply making a statement and asserting that it evaluates to true. If you have {A=>B, A} then those two sentences entail a third sentence, B. A mathematician doesn't simply "assume some axioms are true" and proceed to prove things about them. A mathematician choose a set of statements inside a logic system and proceeds to use all of the expressive power of the logic system to find out what other statements are entailed by that set. Semantics is entirely separate from the truth function and one doesn't actually care about "what A means in the real world".

Writing a proof explicitly in a logic system using it's derivation system is often very long winded, tedious, and pedantic. For this reason most working mathematicians don't write proofs at that level of rigor. The idea is that one writes a hand wavy [less] formal proof with the intention that it convinces the reader that a truly formal proof can be written.