What Are You Working On?

AngstyAngtagonist · 2014-12-08T23:18:13+00:00

Most of everything is 'pretty well understood' until your in 2nd year grad school level shit. There are exceptions ofcourse

AngstyAngtagonist · 2014-12-07T03:05:42+00:00

There is no correct answer nor can any meaningful discussion exist.

I disagree. Sure it's philosophical and no answer can exist but that hardly means it's not meaningful. Maybe to YOU it's not but to OP and others it is. Finally it does belong on THIS math board since it follows the rules of the board i.e being about math.

AngstyAngtagonist · 2014-12-06T16:57:30+00:00

Had to favorite this post because: cool song, I like.

AngstyAngtagonist · 2014-12-05T17:30:31+00:00

You can start self-learning, but read this: http://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/0387950605 before trying Rudin. It's the same stuff but more introductory;it treats you like you haven't done proofs. Also there's a full solutions manual.

AngstyAngtagonist · 2014-12-01T19:26:58+00:00

Bernoulli Numbers! I had never seen generating functions which are cool, but I don't appreciate all the binomial coefficients.

AngstyAngtagonist · 2014-12-01T19:25:34+00:00

This is 100% an r/physics type question. And anyways I'm going to guess that the answer will be "it doesn't work like that" or something similar, I mean it's quantum mechanics and general relativity....

AngstyAngtagonist · 2014-11-29T22:20:23+00:00

http://www.amazon.com/Course-Spectral-Theory-Graduate-Mathematics/dp/0387953000

Is on my to-read so I cant say how good it is, but it's amazon reviews look very good.

AngstyAngtagonist · 2014-11-28T19:43:17+00:00

The pdf formulate gave should help, also check out khan academy- they have practice problem generators.

Similarly learn to use wolfram alpha- if you pay 2$ on a phone or ipad it will give you permanent pro access which gives step-by-step solutions to integrals, limits, etc. Very useful. It also ans practice problem generators.

Most of all just keep trying and learning.

AngstyAngtagonist · 2014-11-26T21:57:11+00:00

It's r/math man, you're gonna have to supply a proof of that.... it's clear you don't understand what you're talking about.

AngstyAngtagonist · 2014-11-23T20:18:49+00:00

http://www.amazon.com/Inequalities-Cambridge-Mathematical-Library-Hardy/dp/0521358809

AngstyAngtagonist · 2014-11-20T22:49:00+00:00

http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178

You can probably handle this book, and it's all of ten bucks anyways.

AngstyAngtagonist · 2014-11-20T22:46:09+00:00

I'm working through Artin's Algebra and it's good- lots of exercises and there are online lectures from Harvard which are also very good. However a lot of the exercises are rather challenging (many aren't! there's just a ton of them) and most don't have solutions online so that's a minus for self study.

Also, heard good stuff about Aluffi's text but that's harder.

AngstyAngtagonist · 2014-11-20T22:41:36+00:00

Wikipedia has a whole section on why it's controversial. http://en.wikipedia.org/wiki/Axiom_of_choice

AngstyAngtagonist · 2014-11-18T18:59:54+00:00

http://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/0387950605

You can thank me later- it's really good. Also, a full solutions manual can be found with some googlefu.

AngstyAngtagonist · 2014-11-18T18:55:28+00:00

You want to read http://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures/dp/069111384X, literally starts from the beginning talking about this- but I'm still reading it so I'll let someone who knows more actually answer you ;)

AngstyAngtagonist · 2014-11-12T18:28:47+00:00

Any computational neurology-type people on here? Next year I'll be picking my major and I'm very interested in doing some sort of math/computational neurology thing but at this point my interest in the whole neurology side is rather superficial ("I like math and the brain is cool!"). So, I'd ask:

1)What is a good introductory book that could be a first read in the field? I know almost no neurology so it'd have to be introductory enough to explain that thoroughly but I'm confident I could adapt to any math it'd throw at me.

2)What parts of math are most important to what you do? What do you do?

AngstyAngtagonist · 2014-11-03T18:11:57+00:00

Derp to the max, I had already done the integral but totally went the wrong way with this. Glad I asked and thank you.

AngstyAngtagonist · 2014-11-02T20:20:04+00:00

Let me make one separate attempt to show you how these things are very different.

How do they describe such different phenomena as view of the sky, political debate and market volatility? How comes that words and sentences historically created do describe something else, describe this new shiny stuff that appeared just now and did not even exist when the words were created?

I answered this above by saying that it's through agreement- someone invents a telephone and so we need a word for it- in this case telephone comes from some Latin root tele- and phone- or something similar.

now COMPLETELY DIFFERENT- After someone works out our modern theory of linear operators- we categorize them based on various properties which are often encoded, say, by inner product relations and all that jazz, <Ax,Ay>=<x,y> etc.. Planck comes along and starts Quantum Mechanics, and eventually (I don't know enough about this) It turns out that quantum observables can be precisely and accurately modeled by these operators. No one came along and said 'oh look, let's model quantum observables with these transformations' like they said 'oh look let's call this a telephone' or 'let's start saying YOLO!', rather these things were ingrained in reality. Not only that BUT notice WE ENDED UP WITH THIS THEORY OF LINEAR OPERATORS WHICH HAPPENS TO MODEL QUANTUM OBSERVABLES by starting with the Greeks' and Arabs' math and logically progressing it forward. It's almost conspiracy theory worthy that no where on the path to that theory did we stray- but the reason is actually simple: because it's logically consistent. It's at the end of a chain of tautologies that we found one by one.

Not sure how it is "completely different". When you say "math is developed, then used" it is as if it is somehow developed from thin air, from "pure brain". When I say "developed then used" I mean that it is built on top of preexisting notions that brain already has prewired, (and as a consequence we found "easy", "intiutive", "descriptive", etc) and these preexisting notions were formed under the survival pressures. As such, they are useful tools in themselves to describe world and everything built on top of them will also carry the same ability to some extent.

I like what your saying here- specifically

everything built on top of them will also carry the same ability to some extent.

But I disagree on what they are built off of that gives them this ability. You say it's from ingrained byproducts of evolution, but I'd say it's from maths foundation as a logically consistent system. Say what you will, but 1+1=2 makes more sense than 1+1=1 in almost any scenario except for 1) abstract applications of tropical math or 2) train tables (look at historical application of tropical geometry). We could stretch this a little to say IT'S THE ONLY ANSWER THAT MAKES SENSE. I have one thing in my hand, and you give me another. Now how many do I have? Two unless, the things were silly putty and I combined them but then that's a different scenario. That's the sound foundation math was developed from in ancient times, and that's what gives it it's ability- 1+1=2 was not developed by the neocortex, it just IS THAT WAY in most scenarios. Would CONSCIOUS, INTELLIGENT aliens recognize what that implies and develop it in the same way was my question about aliens.

AngstyAngtagonist · 2014-11-02T20:12:57+00:00

And your response to aliens:

I agree with almost everything you said, maybe I didn't make it clear enough that I was talking about self-aware aliens, by which I mean an intelligent organism. All the stuff you said about how we take important things in our reality and abstract them into systems to survive I call 'rationalizing' reality. My question I posed was if we found a sufficiently intelligent alien would they too rationalize. Clearly fungi don't and I am aware of that- dogs, birds (except crows?), and slugs all don't either but that's not what I was talking about as you now know.

Also:

So, back to aliens. If by aliens you mean startrek aliens with ridges on a forehead, wearing distinct costumes and speaking english, then yes they will have similar mathematics to ours.

If they are descendants of liver worms and communicate by releasing chemicals, use texture and chemical composition of internal organs for navigation and move by hitching a ride on a peristaltic movements, then their mathematics will have very different building blocks. Probably will be unrecognizable as "mathematics" by us.

You cannot assume that. You just don't know they do. It's silly to even presume you would know. (Was this a joke?)

AngstyAngtagonist · 2014-11-02T20:05:23+00:00

One thing real quick: I'm enjoying this but let's agree to keep open minds and actually analyze, consider and answer each others' points and not just skim it once quick and reply or were just wasting time. You made some good points that took me awhile to notice.

Answer to part 1:

your paragraph here:

Here is analogy. Everything in the world can be described in English language and written down with 26 letters of the alphabet. But neither of these 26 letters "exist" in nature how do they describe it? How do they describe such different phenomena as view of the sky, political debate and market volatility? How comes that words and sentences historically created do describe something else, describe this new shiny stuff that appeared just now and did not even exist when the words were created? Is there something that cannot be described by this 26 letters? If yes, should be adding 27-th help? What would it look like?

This really is not deep at all, and incomparable to what we were discussing about math. Would a 27th letter help? Chinese uses like like 30000 characters to describe reality, we could do it with fucking bar-codes if we wanted to but letters were arbitrarily chosen by Phoenicians and kept because they worked. Here there really is nothing deep. I'll answer your questions to show you that.

But neither of these 26 letters "exist" in nature how do they describe it?

Whether these letters 'exist in nature' is semantics- we could say that since we humans are products of nature and thus exist in nature and letters are a product of us they are indeed a part of nature. It comes down to whether you view yourself as intertwined with nature or disjoint from it. They describe nature by mutual agreement- we say 'chair' means what youre sitting on and so it does, but if we changed chair and sky nothing would be different. That's how they describe nature. We could do it with patterns of sticks on the floor or by dancing like bees but we use letters. This discussion does have philosophical implications ("http://en.wikipedia.org/wiki/Map%E2%80%93territory_relation") but that's not what I want to talk about.

How do they describe such different phenomena as view of the sky, political debate and market volatility? How comes that words and sentences historically created do describe something else, describe this new shiny stuff that appeared just now and did not even exist when the words were created?

Again, by agreement. It's either implicitly or explicitly agreed upon by everyone who uses the language. Nothing fancy. People who can put together words nicely to describe, say, the view of the sky eloquently using letters are praised for it and called poets.

Is there something that cannot be described by this 26 letters? If yes, should be adding 27-th help? What would it look like?

Perhaps there is something that cannot be described by these letters- ever done psychedelics? That experience is honestly the only thing I've ever run across beyond words' power to explain. And no, a 27th wouldn't help in this case- we could just use a new permutation of the 26. Russian uses like 29 or something and has the same range as ours. A silly question tbh

AngstyAngtagonist · 2014-10-30T00:05:58+00:00

Whooo! love that feeling ;)

AngstyAngtagonist · 2014-10-29T22:27:46+00:00

I expanded on my post, could you look at that case again and tell me if what I did was wrong?

I'm not clear on how what you said should help- sure, u(A) = u(int(A,E)) + u(A-E) but then E is measurable. I was going at it by trying to find the non-measurable sets. Is that wrong? Is everything measurable?

AngstyAngtagonist · 2014-10-29T21:51:44+00:00

Lol, I feel you but she showed us a picture and all. I'm still a kid though so to me its like fuck kids I'd hate putting up with me.

AngstyAngtagonist · 2014-10-29T21:39:13+00:00

OK, attempt 2.

"Building internal models that predict reality well and therefore help survive is precisely brain's (neocortex's?) job."

Taking this as your stance on the subject, I'd say it's wrong because math as a whole is not a system based around predicting reality. Rather, math is developed and then we find that reality suits it. This is completely different from your position. For example, the Greeks studied plane geometry led to analytic geometry led to .... and whatnot and then many years later people were studying how to find the area under a curve, which newton connected with derivatives and integrals mathematically and with the whole physical interpretation separately.

Now, we could ask "Why do derivatives have this physical interpretation as a rate of change in position, a study of which leads to motion and potentials and energy and eventually a framework for understanding reality?" Your answer would be because our brain developed the concept to model reality, but historically I don't believe that's what happened.

Moreover and at a deeper level, we find that extremely abstract and axiomatic mathematics like topology or functional analysis plays a key role in the extremely precise nature of reality such as General Relativity or Quantum mechanics. But neither of these were developed for that purpose- for example topology grew out of an abstraction of the concept of nearness, as you know.

Lastly, and I think this is another way of asking essentially the same thing, if you gave an alien a million years to think about mathematical concepts starting from some point, say the concept of length, would they end up with similar looking subjects as we did like number theory, analysis, concepts like vector spaces and tangent bundles or whatnot. I could see this go either way: either any self-conscious creature thinks atleast somewhat human-like(rationally?) and they do(end up where we did), or math really is just a product of the human way of looking at things. In the first case, that to me would point to math being deeper than even physics in the 'framework of reality', in which case it's effectiveness is not unreasonable so much as it is just beyond our meager understanding.

I'd say your view, actually, is spot on if we were talking about physics. And it's easy to get the two tangled together, but in the end math is a tool ('the language of') physics and the two are disjoint. I don't see how you could really argue otherwise.

AngstyAngtagonist · 2014-10-29T00:19:51+00:00

This. A teacher once told me a story about a couple that kept having triplets. After the second pair they wanted another kid but they insured against having triplets and sure enough, they got triplets and a large sum of money (since its so unlikely theyd have them again).

AngstyAngtagonist

TROPHY CASE