@Steve because once I have a mathematical model anyone can use it to make predictions and everyone will agree what those predictions are. There is no room for ambiguity.

A theory is composed of the formalism $F$ (a set of primitive formulas as postulates), rules of correspondance $R$ to relate observable phenomenons with the non-logical terms from $F$, and eventually, an explanatory model $M$ of the theory

Whereas we can (for example) argue about interpretations of quantum mechanics for the rest of our lives without any danger of coming to a firm conclusion.

@JohnRennie, but what I'm asserting is that you can't use it without a physical philosophy, which explains what symbols mean and how they are applied and interpreted (and how observations are related back). You must agree with that surely?

@Steve cf what I said :p

@Blue I conclude that physics is a mental illness.

But nobody ever disbelieved the maths of QM, as far as I'm aware.

ehhhhh

nobody ever is a very strong constraint

And the full interpretation of QM still rages, precisely because it's predictions don't agree with all observations (the rest of the observations being explained by relativity).

@Steve No.

That is not why the issues rage on.

Some references on the topic of theories and models

I mean, yes, people do want to understand how quantum gravity works

Oh god, one of them is named Sneed

@Steve it depends exactly on what you mean by "believes", "maths", and "QM"

All other participants who are addressing me, please bear in mind that I can't talk to you all at the same time.

I could go to @Semiclassical's QM class and say everything is wrong, and I would be correct in a sense

nothing against Semic ofc

@Semiclassical are you TAing again this semester

@0celo7, it may well depend on what I mean by that - what I mean is that nobody ever rejected a working QM mathematical model. They disagree merely as to what physical reality it is describing.

But the question, for instance, of Bell's inequality in experiments is at this point not one of "is bell's inequality satisfied" but "are violations of bell's inequality consistent with relativity"

Plenty of people have rejected QM mathematical models

Early QM models were wrong

because as a practical matter we can do bell-type experiments and we do observe 'nonlocal' correlations

@Slereah is the American office any good?

@0celo7 yeah

@Slereah, but then it follows that they have been rejected because they were falsified - not despite conforming to observation.

@0celo7 It's alright

senior-level electromagnetism

I prefer it to the UK office

But that's because I hate what's his name

Ricky Gervais

@Semiclassical that might be just as bad if you don't properly justify your approximations :P

pffffft

@Slereah y u hate him

@Steve Well it would be odd to reject something that works

@0celo7 he is not funny

I'm a TA, I'm already lying to students just by pretending that I know what I'm doing.

I tried my best but I can't sit through something with Ricky Gervais

@JohnRennie, have you come to any conclusion on what I said, that mathematical models in physics cannot be applied without some sort of interpretational "philosophy" that relates the models to the physical world?

@Semiclassical I taught functional analysis yesterday and thought it would be a disaster, but when you're trying to prove to people that you do know your shit, you can summon the knowledge from deep within

Is @Steve not reading what I'm saying

I'm pretty sure I covered this

@Slereah, as I say, I may have missed something. I can't read and reply to everyone.

@Semiclassical I've always felt that physics would be really hard to TA for because even for an experienced person, there can be really hard "elementary" problems

I suspect what this conversation points to is whether or not theoretical physics invokes metaphysics. (in the sense of concepts, not the supernatural sense0

@0celo7 yeah, I buy that

I think mechanics is definitely like that

@Steve no, because I don't understand what you are asking. This conversation is exactly why abandoning mathematics for philosophical babble is a frustrating exercise.

electromagnetism less so

I was thinking the reverse but I hate/suck at EM

@Semiclassical, yes I'd agree that we're talking about metaphysics in that sense, which is an integral part of physics. Anyone who doesn't discuss the concepts, simply has their own private version of them.

or, to put it in a more slogan-y way: "Is there such a thing as physics without metaphysics?"

I tend to hew to Kant's line: "Concepts without percepts are empty; percepts without concepts are blind."

kant's tack being that one can't do physics without metaphysics, so one had better be as critical/careful with the latter as one is with the former.

@JohnRennie, but I'm not asking you to abandon mathematics. You seem to recognise the domain of knowledge that I'm referring to - you called it your "intuition". What I'm asking is whether you really think that you can apply the mathematics usefully (or communicate about them meaningfully), if you disposed of the intuitio and therefore knew nothing (intuitively or otherwise) about how they would be applied?

@JohnRennie, ...you would end up simply describing a set of abstract rules and mathematical mechanisms, without anybody understanding what things they related to in the real world.

Hello. I am currently getting prepared for ipho and I would like to strengthen my foundation on mechanics, electromagnetism, optics and modern physics. I would also like some resources for problem solving. Can anyone recommend any books or anything else?

iphone?

International Physics Olympiad?

yes sir

are you Indian?

@Steve if the conversation has stalled out, you might check out this paper: michel.bitbol.pagesperso-orange.fr/KantMetaphysicsQuantum.pdf

@Semiclassical no equations, ew

is it topology?

lol

nah. philosophy

@0celo7 nope

@Semiclassical set theory

which from your perspective is probably w

(double ew)

@Semiclassical, it's odd that such strong views are held yet the conversation can stall. I never understand why it is considered a verboten subject.

@boides I can't answer with any authority, but typically working through past papers is the best way to prepare something like that.

@Blue go ahead

@Blue specify stage

@Steve It's not verboten, it's boring. If you enjoy discussing the subject you are perfectly welcome to discuss it with other like minded adults.

10th grade but I know calculus and linear algebra. I just studied with our teacher havent read any books

thats why I am asking for them

Bourbaki

@JohnRennie, indeed - but you realise, all the famous physicists of the 20th century were interested in, and wrote a great deal about, physical philosophy? And that it is a legitimate part of physics? Also, if you employ physical philosophy but aren't interested in discussing or evaluating it, doesn't it make you worried about whether it makes sense?...

uh

@boides how about this web site

yes and no

Famous physicists before WW2, yes.

nice

Famous physicists after, not so much.

thanks alot

...I'm not especially interested in mathematics (although probably still moreso than the average person), but I therefore avoid making claims about it, and simply accept mathematicians views about maths.

@Blue that cramped info is it's greatest feature :p

The shift of the center of gravity vis a vis physics research from Europe to America brought with it a lot less interest in philosophy of physics

There's been revivals, of course, with the big one being the debates about interpretations of QM

but there's a big difference between how philosophy mattered to Bohr and Einstein vs. someone like Feynman

@Semiclassical, I'm just still reading that paper you linked to. It's very interesting how it characterises metaphysics as something that is forever being reworked!

I thought you might dig it.

I wouldn't consider that an authoritative reference, mind---I genuinely don't have enough expertise to validate it

but it's interesting reading if you're into that kind of thing

@Semiclassical where in the US do most of these philosophical debates occur?

@Semiclassical, indeed, I'm not sure yet whether it will go over my head - and I rarely adopt anything myself as an authoritative reference - but it's certainly worth a read. I'm just waiting to see whether there is anything in it I don't agree with!

@skullpatrol no clue.

i like to talk to a certain prof about it, but he's got a joint appt in physics and history

so he's not exactly the typical physicist

right, right... the historical perspective matters

oh no the walls are making strange noises...

it's ghosts

it sounds really bad

doesn't sound like water in the pipes

wtf

you know that Poe story

about how they found dead bodies inside walls

maybe @0celo7 loganpaulvlog'd someone

and the locked spirits are haunting him, as they do in every supernatural horror story ever

I have a belief that philosophers who can't do physics telling physicist that they don't know what their own work means is one of the causes of physicists developing an aversion to philosophy.

@BalarkaSen it might be an issue with the pipes

First of all it is insulting and secondly it gives a great model of philosophers offering up a lot of words that achieve nothing. At the end of the conversation the physical theories are still useful and the philosophers still haven't concluded anything.

@dmckee same with with philosophers --> mathers?

philosophy is interesting

And I ought to be sad about that but I'm not. I just confine my philosophizing to bars and cafes.

@BalarkaSen Philosophy should be interesting. But philosophers seems to work very hard at preventing it from being so. Seemingly in the name of a kind of pseudo-rigor that still doesn't help them solve any problems.

@dmckee I agree that the medium of communication of philosophical material is rather dodgy

It's not really a scientific language

@BalarkaSen I suspect that it has more internal consistency than I recognize. But you have to read tens of thousands of pages to know the field well enough to see and use it.

True

like hyperbolic PDE

The trouble imo is that physicists like to claim that they don't have philosophical commitments when they actually do. That doesn't make the commitments bad or indefensible, but it makes it hard to have sensible conversations.

That and there's a pretty solid cultural barrier.

^ That.

Which, the first or second?

Yes

die

Cultural barrier. Big one.

ah, okay

@Semiclassical wtf

@Semiclassical Not Nice

it's german for 'the' :P

"fuck" is Swahili for "rooster"

Depending on grammatical gender and case, anyway.

loooooool

I think he made it up

that's racist Balarka

oh my GOD COME ON

@dmckee, the problem as I say is that physicists do employ philosophy (often understood by another name, and evidently little-discussed).

Physicists employ philosophy but they don't want to get involved with Philosophy (tm). Because of philosophers.

“The light dove, in free flight cutting through the air the resistance of which it feels, could get the idea that it could do even better in airless space."

@dmckee, but they involve themselves by employing it. I'm not defending necessarily anyone who goes by the name of a philosopher - I'm simply making the point that it is relevant to physics.

That's what I think of when I hear people say that physicists don't use philosophy.

@Semiclassical, haha!

Philosophy is pretty much the earliest known example of thought and reasoning. It should come off as no surprise that any major branch of science should use it

Philosophy departments, on the other hand...

It's invoked in basic principles of reasoning and deduction all the time

So renormalization in qed seems to be taking the three divergent second order terms (e.g. electron self-energy term) and doing a bunch of tricks to these integrals, calling things you get things like 'bare charge' and saying some infinities you get are just part of the constants and then magic...

@BalarkaSen mathematics does not need it

(mathematics is the only science that isn't a mental illness)

it does in fact

(mathematics is not even science by that mode of thought)

it's not a natural science. it's still science by whatever broad enough definition of science

@dmckee, as well, I will admit I don't understand many of the more advanced mathematical elements of physics - partly because my independent interest in maths is lesser, and partly because I'm not willing to accept them purely in their own terms without an explanation of what they mean. But you shouldn't assume that means "philosophers" don't understand "physics", or that those with an interest in philosophy won't notice when physicists make irrational philosophical claims.

@bolbteppa, pure mathematics is not itself a science. It is a tool of science.

@BalarkaSen I think my talk can be salvaged

@bolbteppa You just remove the "divergent part"

there's minimal BS now

Or redefine the constants so that they are, up to some energy

I should at this point also say that the above quotation also comes to mind when people suggest that physics can be done without mathematics. :)

Ask a math student with a B.A. not a B.Sc. if math is an art or a science :p

@Steve Wrong on all accounts.

Mathematics is not fundamentally a tool of science.

^

How insulting to mathematicians to claim otherwise!

then what is it?

Sometimes science is more art than science

Beauty

@skullpatrol It's math.

It might be used by other branches of science as such, but then again we similarly use other branches of science as a tool of our motivation of study

@Semiclassical, that is true. But nobody is arguing for mathematics to be dispensed with in science - it is only the other way around, that many scientists want philosophy dispensed with.

Mathematics can be used to describe music, is music a science

A great many mathematicians work on stuff that has no (current known) uses. They just follow the internal logic.

@dmckee math is what mathematicians do

Or logic

Sometimes (surprisingly often in many peoples view) some of that stuff turns out to have an application latter on.

Math can describe physics where the constants have different values, i.e. not the real world, is that science

@dmckee the unreasonable applicability of mathematics to the real world :P

Math used biological observations to study certain systems changing with time satisfying certain growth equations. That originated various forms of dynamics. We also stole physicist's notion of gauge theory to use for our own purposes.

@Semiclassical hello wigner

It would also be wrong to say math is independent of the other branches of science and is merely something based on some meaningless axioms and following the logic of the axioms

The axioms only give rise to an interesting theory because they are consistent with our perception of the world

@BalarkaSen, I wasn't trying to say mathematics is a mere tool of science, like an adjunct. I'm saying that it is separate from science and not scientific - and the place it occupies within science, is as a tool.

Studying a binary operation on the twin primes is not an interesting endeavor, eg. It'd give you a place in vixra at best

It's not a natural thing to do.

math is a language

@Steve Again, depends on your very subjective use of "science" I am afraid!

@BalarkaSen, you can't apply mathematics other than as a tool of science. It is "meaningless" in its purest form - although I put that in quotations because I'm not intending that to carry negative connotations.

is science also meaningless?

@Steve This seems like a circular conversation to me. What is your definition of "science"?

different sciences use different dialects of math

Without that definition none of your statements carry any meaning whatsoever

And with an ad-hoc definition they are a subjective opinion at best

@0celo7 All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense.

@BalarkaSen, I'm just using the word "science" in the sense of the study of the real/material world. Pure maths is not concerned with studying things that are real, but in the formulation of abstract rules and systems of rules.

@Slereah -><-

@Steve Again, wrong on all accounts. I am afraid you have no real experience with "pure maths" that you are so fond of making unfounded opinions on.

@0celo7, no science is not meaningless, but neither is the maths when employed in science.

The "abstract rules" of mathematics are completely based on the principles of the real world.

ehhhhh

nice gate keeping @BalarkaSen

reddit.com/r/gatekeeping

This discussion is really narrow. There is a distinct difference between the other scientific disciplines and mathematics but it's not as simple as what you say it is

@BalarkaSen, I'm not sure that is true. Historically, mathematics has tended to be used to generalise the principles derived from science. But I'm led to believe (please correct me...) that some mathematics research has been done in a free-standing way, and has found its application later.

@Blue Most mathematicians I have spoken with in real life agree with it.

As I said, studying a binary operation on the set of twin primes is a plausible endeavor, just a meaningless one

Mathematicians like to study structures, yes, but the structures are interesting to us because they carry a very meaningful... meaning

Completely irrelevant, totally abstract structures produce bad mathematics

I think you can plausibly talk about mathematical concepts as 'real' without committing to them being empirical.

@skullpatrol, good reference to @dmckee. The point is that "internal logic" is not meaningful (or has no significance) on its own. It is when mathematics is applied that it acquires meaning.

what is "meaning"?

@skullpatrol why do you always delete things?

@Steve Well, no, they do not "generalize" it. They write down a skeleton of the principles that is suitable to study under the language of mathematics.

Every branch of science has it's own language

Math has it's own too

The guys I know who work on stuff without known application are usually doing generalizations of some existing field of study. Sometime that leads somewhere and sometimes it doesn't.

@0celo7, perhaps you should offer your definition of meaning.

This is the kind of 'philosophizing' I do get tired of tbh

^

@Steve I am not participating positively in this conversation, I just find your position incorrect.

@Blue "Meaning" does not make sense without connection to the "real material world"

The question of what philosophies people in fact have is more interesting to me than debating what philosophy they 'should' have

I can give concrete examples if anyone is up for it

@BalarkaSen this is some mushroom shit

So far this discussion is just pointless abstract bullshit talk

That creates a kind of foundation in human meaning, because math is 'interesting' when they have some connection to human meaning and it is 'interesting' things that people bother to generalize.

@0celo7, it's unfortunate how freely people adopt positions that they are not willing to discuss.

@Blue cryptography

Kifflom.

Was Fermat's last theorem meaningful prior to the discovery of elliptic curve cryptography?

@Steve You mistake me, for I don't have a position on this issue. I do mathematics because it's fun, and no other reason. I don't care one bit about the philosophy or science behind it.

@0celo7 is misinterpreting my point

@0celo7, you do have a position, because you have asserted that maths (removed from its application to anything real) has meaning.

@BalarkaSen I haven't addressed your point.

@Blue Okay, I can do that. The first thing to realize is that Fermat's last theorem was not immediately interesting until Kummer tried to prove it.

Now, Kummer saw a very interesting thing

@Steve It has meaning to me.

@Semiclassical it was meaningful to Fermat :P

or... was it?

who knows?

or cares?

The first approach to understand the solutions of $x^n + y^n = z^n$ is to write the left hand side as a product. The obvious way to do it makes you want to factorize it as $(x + y)(x + \zeta y) \cdots (x + \zeta^{n-1} y)$ where $\zeta$ is the $n$-th root of unity

it's proved NOW!

:-D

Those objects are not integers, but "numbers in the ring $\Bbb Z[\zeta]$" as far as modern terminology goes, but let's ignore that

The point is you have a product of things on the left hand side, and a product of things (z x z x ... x z) on the right hand side

@Slereah Ok here's how the talk is going to go. Careful statement of the Riemannian PMT -> history and timeline of the major papers -> Einstein equations -> DEC and domain of dependence -> ADM equations -> Noether's theorem for mechanics -> Noether's theorem for fields -> Nother's theorem in GR -> ADM energy momentum

@Slereah now the goal is to make this 5 hour talk into a 1 hour talk

@BalarkaSen this chatroom is not big enough for your proof

Remove all the rigor and you should go much faster!

The objection I foresee to this story is whether you just transfer the problem from "Why is Fermat's last theorem meaningful" to "why was Kummer's problem meaningful"

@0celo7, and to be clear, my position was not to slate maths. I simply said it's not itself science, but is a tool of science.

@Semiclassical I have not finished.

That's not where the story is going

@Steve Calling math a tool of science is insulting to some of us

Don't draw conclusions before you have listened to everything

Balarka is spicy

fair enough

this is a standard physicist mentality that I abhor

@0celo7 then flag it!

@skullpatrol I'm not a ********************

@BalarkaSen kek

@0celo7, I don't see why it's an insult - it's more or less a historical fact that it's use and development has been alongside science.

@Steve Because the majority of mathematicians work completely independently of the natural sciences

"math flowered largely in collaboration with applications to natural sciences" != "math is a tool of science"

You seem to be saying their work is merely a "tool of science" when 99.9% of scientists do not have remotely enough training to understand any of the math

@Steve "alongside" not as a science with experiments

In any case, Kummer's observation was that if you treat everything as an integer, the rest of the problem would reduce to just invoking the "unique factorization property" - which, eg, says 6 can be written in exactly 2 ways as a product of two integers: 2*3 = 3*2 = 6

@Semiclassical I am not disputing the former, but he is literally saying the latter.

Sure. I'm agreeing with you.

@0celo7, in much the same way as I could say science is a tool of engineering. It's not a critique. As for maths being independent of science, that's what I said, that when it's completely independent of the real world it becomes meaningless, like a Rubik's cube one's own imagination. It can be manipulated, it follows rules, but without application it bears on nothing.

The entirety of Kummer theory is based upon trying to generalize that fact for this mystical "$\Bbb Z[\zeta]$" and that's indeed how he made a partial progress on the Fermat's last theorem.

" science is a tool of engineering"

those are fighting words

Applied Science

But this is the point. The key reason Fermat's last theorem is an interesting conjecture was (as realized after Kummer's discovery) you wanted to have the right notion of unique factorization property - a completely physical property of numbers, dare I say!

It's true that the historical development of mathematics as a subject was substantially driven by its applications to science. But that doesn't encapsulate it as a subject.

It was no longer an obscure exercise in number theory

But a very natural question to ask

...sigh

@0celo7, they may be fighting words, but not amongst historians. Science only gets the money it does, because of its practical use.

I give up

@Semiclassical what are you sighing for

Are numbers physical?

^

@Semiclassical Duh.

Can they have physical properties?

Of course they are.

honestly I want to leave this conversation but I can't

isn't there a leave button for that

just give me a 30 min ban fam

I'm tempted to ask for the same.

Call me a yew with a J I'll do ya for a flag ;)

sshhh...1 minute time out

@CooperCape Jew is an interesting word because it's both the correct term and a slur...

@0celo7, I don't see why these claims are so contentious. Is it really so bad for an intellectual to acknowledge that their work (and the work of their predecessors) has use, and isn't simply a flight of personal fancy in the imagination?

So far I see all of you made some funny philosophical points instead of a concrete example, which I gave. Now it's up to you to decide whether to take that example or not.

It is kinda odd.

Why is it a slur tho

I think it perfectly illustrate which ideas in mathematics are natural and which aren't

if I call you a Jew while sneering it's a slur

Like no one's going around like "You're such a Christian"

sshhh

Basic properties of numbers is a completely fundamental idea in human perception

Christianity is pure & good and cannot be made bad

"God created the integers, all the rest is the work of Man." -Kronecker

@Semiclassical more like the natural numbers

@Semiclassical Doesn't he have a delta or something...

negative numbers are some Grothendieck completion bullshit

hey, I'm not kronecker

@Semiclassical stop telling God what he created :P

@skullpatrol tell Kronecker that, it's his problem :P

I'm not agreeing/disagreeing with that, mind.

^ General semantics was suppose to have the answer to that.

Anyone know what became of general semantics?

@Blue I don't know what's more fundamental that integers in the real world.

To rephrase my objection from earlier, you've passed the problem from "why is fermat's last theorem related to the physical world" to "why are the natural numbers related to the physical world"

hydrogen

@BalarkaSen Baby smiles.

Sets.

Baby smiles are the most fundamental thing of all.

@dmckee you're growing soft in your old age

@dmckee true dat

@skullpatrol shh old lady

@0celo7 Yup.

@Semiclassical "why are the natural numbers related to the physical world" That's what keeps you metaphysicists up at night?

Seriously?

They were very literally discovered for the purpose of counting.

Distinguishing an object from 2 objects was the first example of thinking in human beings

"keeps me up at night" would mean I think about the question much. I don't: I do not consider integers to be physical

they are concepts, not percepts

@0celo7 one day you'll soften up pal

By that logic you'd have to say most of physics is not physical :P

Correct.