News from the LHC

[Triple Zero]

As for string theory, as far as I can tell, it seems to have become more an area of maths than physics. Mathematicians love it, it apparently has lots of interesting structures and tie-ins to other obscure topics in abstract maths. The idea of actually testing it against reality seems to have taken a back seat.

DING DING DING

of course it's easier to dismiss it as "religion" when a certain type of research is completely incomprehensible even in it's simplest form.

there's nothing wrong with tests against reality taking a back seat in maths, it's been often enough that new discoveries in math only gained practical application half a century later. and it's still quite more solid than certain aspects of other sciences, because of mathematical proofs generally being somewhat more rigorous than most experimental proofs.

I'm not entirely sure if what they're doing now is strictly string theory, though. My friend's Masters thesis used only 5 or 6 dimensions--or was it 9... I forget, anyway it was incomprehensible, but I don't think it was "string theory" specifically.

[LMNO]

That's fine, as long as they've stopped advocating for it as a GUT.

[Triple Zero]

Only thing I've ever heard claimed was "if we manage to figure this out, it might help us find that GUT". I mean it's just mathematical powerhousing, and everybody in theoretical physics are doing the dimensional reduction these days whether they call it string theory or not

[Mesozoic Mister Nigel]

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

[Nephew Twiddleton]

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

Mathematics is a useful language to describe reality.  But that's all it is, a language. Reality is not mathematics. Mathematics can express things that are, as far as we can tell, impossible. Hell, we have a number called infinity. As far as we can tell, the only thing that is infinite is nothingness. There is a finite amount of matter, and there is a finite amount of time for it to have its heyday. There is an infinite amount of time for two particles to basically chill out 20 light years away from each other.

The future is bleak. I'm glad I'll be way fucking dead before that.

[hirley0]

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

FINE BY ME
being currently opposed to both camp's This:
what they did was make a field, lemme say Magnetic
then they next tell you the Found a Particle.
you can believe them if you like.
i prefur not to.
My reason is this | THEY | &i do me they
hold the S{second) as a non variable
hypotheosizzing that every S is the same
& its pure BS. {Basic Science) & that
it extends into all branches Q r s & T
so issue 1 is the S itself
issue 2 is the $ D'nomination boo2them2

[Triple Zero]

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

That's just arguing semantics.

No actually it's worse.

The only difference between a theoretical physicist and a mathematician is whatever they did the first few years of university. And of course astronomers often end up mathematically bending dimensions as well. Multidisciplinary research is all the thing, most of the math they learned for that kind of stuff is easily picked up given the rigorous background they all (ought to) have.

At the time one is doing that type of research it matters fuck all whether you started out as a physicist, mathematician or astronomer (some of them even get degrees in two, the smartypances). None of them would argue what they're doing is theoretical physics, however. And if you'd say "well it's basically just maths, isn't it?" they might smile and agree like a dentist that gets told he's basically doing a type of masonry, right?

I'm not sure what you're basing your ideas of "the job of physicists" and "the job of mathematicians" on. Nobody actually doing this research is making these kinds of distinctions, it's stupid. The only reason to make a distinction like that is when one field has experience and knowledge the other just doesn't have, like our cooperation with biologists in the Machine Learning projects I was part of: the biologists were really good at doing the grunt work classifying biological things into datasets and the computer scientists were really good at taking those datasets and writing and running computer programs on those numbers. See in that case it was kind of a clear-cut division of tasks, first the one, then the other. Of course it wasn't really like that because some of them were "bio-informaticians" so the lines were rather blurred anyway.

Oh! And my professor leading the whole group, guess what, has his background in physics! I guess he'd LOVE to hear what you think his "job" really is.

Specifically, his field originally was is in Statistical Mechanics (thermodynamics, entropy, etc), a completely different field of theoretical physics. When they do math, the number of dimensions is often equal to the number of particles in the system--that's WAY more than 9--but you never hear anybody complain about that! To give another example how silly it is to restrict people to their specialisations, the connection between Statistical Mechanics and Machine Learning is really kind of odd. On the one hand, they have a lot of overlap in the mathematical tools they use (minimizing energy potential functions in hundreds of dimensions--and unlike the string theory, I can actually explain why that makes sense) but they use it for completely different purposes. Really different. For Physics you get a numerical representation of particles that you can distill certain aggregate quantities from, for Computer Science you get parameters for a computer program that'll answer classification questions for you with a certain amount of accuracy. But we speak the same language and do realize why one is useful to the other. We've been doing that ever since Computer Science became a serious scientific field, in fact, Statistical Mechanics might have even been one of the first fields that profited from CS, when Feynmann started building computers specially fitted for simulations in the 80s.

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

Mathematics is a useful language to describe reality.  But that's all it is, a language.

Are you just repeating this because Roger said it once? Because I disagreed then, and I still do.

You could say exactly the same thing about physics.

Reality is not mathematics. Mathematics can express things that are, as far as we can tell, impossible. Hell, we have a number called infinity.

"Infinity" is a symbol, it's not a number (or as we say in CS, "NaN"). Numbers elements of a set, generated by axioms, such as the Peano axioms for the natural numbers, which if you care to read them, clearly do not generate "Infinity" as a symbol. Just "zero" and "the successor of X" and a few operations and rules on them. You can make arbitrarily high numbers, but not "Infinity". I once had a huge and stupid fight about this with an ex-gf who studied Mathematics, she insisted that "Infinity" was part of N as well. I was right. Though the fight was probably more about that where she came from (Vienna), CS students didn't get as much formal math as I did.

As far as we can tell, the only thing that is infinite is nothingness.

What does that mean? Please define what you mean by having a certain amount of nothingness in a way that makes it make sense to state whether we have an infinite amount of it, or not.

I'm not sure if either a physicist or a mathematician would agree with such a statement, depending on what it even means.

There is a finite amount of matter, and there is a finite amount of time for it to have its heyday. There is an infinite amount of time for two particles to basically chill out 20 light years away from each other.

So?

If you say Mathematics is not real because it's got "Infinity", then may I point you at the mythical physical entity that is called "a closed system" or "a system in a vacuum" .. or hell, even the physical "vacuum" does not exist, anywhere. Also not between the stars. And not because particles randomly pop in and out of existence in a vacuum, no the interstellar medium is in fact quite a lot denser than anything approaching a theoretical vacuum. Still quite a lot emptier than any kind of vacuum we've managed to produce on Earth too

Fortunately, Mathematics actually got one up on these matters. Math has the power to introspect itself and fix what may not actually be Really Real and see if we can build the same kind of things via simpler axioms. I believe it's called Mathematical constructivism, or soemthing like that. That particular field of math doesn't use "Infinity" as a symbol, at all, because it can't be constructed. They also disallow certain types of induction proofs, since those can also be used to prove things that aren't really real. And of course none of that Axiom of Choice thing, as reasonable as it may sound (cause it leads, among other things, to the Banach-Tarski paradox).

Go here, if you dare: http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory <-- That's the current most commonly used foundation of mathematics and if you omit the Axiom of Choice from it, it'll produce things that--as far as I'm aware--are strictly "real". And if they don't, well, let's just say that the field of fundamental math is vigorously attacking such problems (that kind of stuff usually goes right over my head, so I can't say for sure).

Just as much as the scientific field of Physics will jump at anything that seems like a disconnect between their models and Reality, so does Math.

But just like parts of Physics research will happily use Newtonian mechanics if they can get away with it because it's a very convenient short-cut, in the same way many mathematicians happily work with the set of "Real" Numbers, implicitly assume the Axiom of Choice in their proofs, et cetera, because it takes a fuckload of effort to formulate everything in ZF. Just like a physicist wouldn't use Schrodinger's wave equation for everything.

And that's the thing maybe. If you're smart, which you are, the everyday-maths you were taught in school, you can poke at it and figure out a few of the inconsistencies all by yourself. Such as "Infinity" or "the set of all sets that do not contain themselves". That's an advantage over Physics, because it's quite a bit harder to encounter an every day situation that shows how Newtonian physics aren't really accurate. And while you heard about the Quantums they came up with to solve THAT, you might have never heard about ZFC or the Axiom of Choice, maybe you heard about Godel's Incompleteness Theorem, but not about the attempts to "fix" it, because if Math's broken, so is Reality.

[Nephew Twiddleton]

It's not the job of physicists to verify the speculations of mathematicians, but the job of mathematicians to verify the speculations of physicists.

Mathematics is a useful language to describe reality.  But that's all it is, a language.

Are you just repeating this because Roger said it once? Because I disagreed then, and I still do.

Um. No. I wasn't even aware Roger had said it once. I'll read the rest of your post when I get over the suggestion that I'm Roger's pet parrot.

[Mesozoic Mister Nigel]

Trip, the reason I said that is because if you ask a mathematician what the math describes, most of them don't really care. They care whether the math WORKS. I've had this exact conversation with a few mathematicians now, and no, it's not semantics. And the exact words used the last time I had this conversation was "Physicists come to us to say "This works, and I need you to describe why". We just do the math. Mathematicians don't give a fuck".

So that's how, according to some mathematicians I know, they identify themselves as separate from physicists. 

I'm not sure I follow your explanation that mathematics is not a language. How is it not a language?

[Faust]

Oh this is the thread?

Might as well cross post this so:

This argument as a concept doesn't really mean anything. Mathematician and physicist are umbrella terms. For instance someone calling themselves a physicist working exclusively with Fourier modelling could be almost if not exclusively a mathematician. Then there are areas of statistics that are indistinguishable from control engineering etc... actually googling Joseph Fourier has brought up this argument and it seems to be a couple of hundred years old and isn't really resolved.

[Golden Applesauce]

Reality is not mathematics. Mathematics can express things that are, as far as we can tell, impossible. Hell, we have a number called infinity.

"Infinity" is a symbol, it's not a number (or as we say in CS, "NaN"). Numbers elements of a set, generated by axioms, such as the Peano axioms for the natural numbers, which if you care to read them, clearly do not generate "Infinity" as a symbol. Just "zero" and "the successor of X" and a few operations and rules on them. You can make arbitrarily high numbers, but not "Infinity". I once had a huge and stupid fight about this with an ex-gf who studied Mathematics, she insisted that "Infinity" was part of N as well. I was right. Though the fight was probably more about that where she came from (Vienna), CS students didn't get as much formal math as I did.

Infinity is or is not a number, depending purely on your definition of "number".  The natural numbers and infinity is a perfectly good set of things to call "numbers": it has all of the numbers you normally use for counting stuff, plus you can answer questions like "How many numbers are there?" with a number, which is useful. You lose a bit because you can't do a lot of algebra (is infinity equal to itself? is infinity equal to infinity + 2?), but if you just want to count stuff everything works well enough.

This works exactly the same way as answering "If you have three apples, and then lose three apples, how many apples do you have?" with "Zero apples." Zero is used here to mean a numerical quantity indicating how many apples you have, so the person answering it clearly understands zero to be a number. If you go back to a culture that didn't use zero as a number, you'd get a response like "That's a trick question - at that point, you don't have any apples!" because in his system, you don't have a quantity of apples, which is different from having a quantity (which happens to be zero) of apples.

@Trip - NaN is totally a number, it's just terribly named. Pull up your nearest Javascript console and type

Code Select Expand

typeof(NaN) You are correct that the Peano Axioms do not generate anything resembling infinity as an element, and all elements of ℕ are finite - but the more commonly used ZF axiomatically includes ℕ itself as a set. ℕ (more commonly referred to as ω or ℵ₀ in this context) is therefore the least/first "infinite number" in the set of Ordinals and the set of Cardinals (a generalization of ℕ, which might have been what your ex-gf was thinking of), and a perfectly good numeric answer to questions like "What's a number bigger than any integer?" or "How many prime numbers are there?"

[Mesozoic Mister Nigel]

I had a feeling I'd get some good responses if I posted the question on Facebook, since I know some of each, and one of the first things I ever noticed about mathematicians and physicists is that they like to make it clear that they are different from each other even if you don't ask them.

A couple of people said, to paraphrase, that all physicists are mathematicians, but not all mathematicians are physicists. My favorite response was one dashingly handsome fella who said that physicists use math to explain the physical universe, while mathematicians use math to explain other math.

My thought is that you have to use math intensively in quite a few professions, but that doesn't make you a mathematician, any more than someone who uses computers intensively in their profession is a computer engineer.

[Golden Applesauce]

A couple of people said, to paraphrase, that all physicists are mathematicians, but not all mathematicians are physicists. My favorite response was one dashingly handsome fella who said that physicists use math to explain the physical universe, while mathematicians use math to explain other math.

My thought is that you have to use math intensively in quite a few professions, but that doesn't make you a mathematician, any more than someone who uses computers intensively in their profession is a computer engineer.

That sounds about right. Physicists are always making statements that mathematicians would say are false, to which the physicists respond "Yeah, well, I guess you can construct a counter example, but a counter example like that doesn't actually occur in the real world, so we don't care." Here's a quote from a quantum physics textbook introducing Hilbert space:

... moreover, the inner product of f(x) with itself, <f|f> = ∫|f(x)|²dx, is real and non-negative; it's zero only* when f(x) = 0...

*What about a function that is zero everywhere except at a few isolated points? The integral would still vanish, even though the function itself does not. If this bothers you, you should have been a math major. In physics such pathological functions do not occur, but in any case, in Hilbert space two functions that have the same square integral are considered equivalent. Technically, vectors in Hilbert space represent equivalence classes of functions.

There's no actual thing called Hilbert space outside of physics. In mathematics, Hilbert spaces are mathematical spaces with a particular structure; the set of all square-integrable functions, with the additional structure that two points are equivalent if they have the same square integral, is a particular example of a Hilbert space. It so happens to be the only Hilbert space that quantum physicists care about, so they use the phrase "Hilbert space" to refer to that particular one. If this had been a textbook on quantum physics written by a mathematician, the author would have pointed out that the elements of this space are equivalence classes rather than functions first, because that's the kind of detail that mathematicians consider really important (and which physicists think is acceptable to gloss over as more confusion than it's worth.)

[Telarus]

"Infinity" is a symbol, it's not a number (or as we say in CS, "NaN").

I love this. I read it once sober, and once on 90 proof rum, and could still understand it. THAT'S MATH.

[LMNO]

one dashingly handsome fella who said that physicists use math to explain the physical universe, while mathematicians use math to explain other math.