/sci/ - Science & Math

Is this supposed to be a joke?

>>11402199
The ghost of th Pythagoreans lives only in Wilderberger.

>>11402199

the reals are no less real than the rationals

>>11402238
>I'm so cool because I blindly follow popular dogmas without thinking critically because they're popular

I have a solid, circular shaft of low carbon steel (E=29.5*10^6 psi, approx.) with length L=6 feet, diameter D=6 inches. The shaft is subjected to a torque of T=500 pound-feet at the free end. I want to determine the angle of twist (in degrees of course). Can any smart mathematician help me solve this problem with rational numbers?

>>11402199
I started watching his videos and things made sense and I kinda liked his approach.
But when I was looking for more references on the topic I find nothing more, only him...

>>11402278
>I'm so smart because I blindly deny standard conventions without any reason for doing so
Contrarismism is not the same as skepticism or critical thinking.

>>11402315
because his life's work isn't actually useful to anyone (scientists, engineer, OR mathematicians doing real research), it's just a novelty

>>11402314
prove that a real object has a length. you can't

>>11402436
You see, I took out my tape measure and I measured it to be 6 feet, plus or minus 0.0625 inches or so. I think that counts as length. Do you disagree?

>>11402463
How do you know the tape measure has length?

>>11402546
Checkmate, Atheists

>>11402278
Explain what you believe is wrong about the construction of the real numbers? Which axiom of ZFC do you want to do away with?

>>11402594
How about all of them? And replace them with computation rules instead.

>>11402199
I would not call him great as a mathematician, but his lectures are a bastion of lucidity. He is certainly a great lecturer.

>>11402615
Sorry I didn't realize I was talking to a retard. Have a good day.

>hurr durr length doesn't exist in real life
Is this what Wildbergers really believe?

>>11402662
They believe that when they want to measure their son's height, they have to put up a square next to their son on the wall.

>>11402199
which video is best to get started on his ideas? im watching the 1st but its from 2007 i wager he made a better indtroduction since

>>11402975
i couldnt do more than a minute too boring and didn't even touch the subject

>>11402594
The Axiom of infinity and the Axiom of choice for starters.

>>11402199
>Multiple ways to build the reals from the rationals
>Austounding amount of reasons why completeness and supremum properties are intuitive and make a shit ton of critically useful math work
>Hundreds of years of development and refinement of the ideas underlying analysis by humanities best and brightest
>Retarded youtube dude spews nonsense
>"Heh, you see kid, the reals aren't real, owned xD lelellele"

>>11403020
>Retarded youtube dude
Wilderberger is an immenent professor at the University of New South Wales in Australia, who graduated from Yale and University of Toronto. He's one of the smartest men alive.

>>11403250
>He's one of the smartest men alive.

>>11403250
if he's so smart then why is he going to die of old age?

>>11402594
Powerset is the problem.
Thus, in terms of ZFC, general separation

>>11402199
wait so does he not believe in pi or sqrt(2)? e?

>>11403491
He does, as far as you can actually calculate them

>>11403526
how is he on complex numbers? does he not believe that you can get infinitely close irrational numbers by using series?

>>11403540
He’s a retard. When I say as far as you can calculate them, I mean literally he believes they exists and are equivalent to the further at they’ve been calculated to. So even if you CAN get infinitely close, it doesn’t matter until you do.

Ultimately, his stupidity lies in tying Mathematics to practicality. As if Mathematica was some sort of empirical field. He doesn’t seem to understand it’s just playing around with axioms. You’re either consistent or you’re not, wether there’s a 1 to 1 correlation with reality is irrelevant.

>>11403558
sounds like I'm leaving this pointless thread then so I can study actual math

>>11403558
you ignorant motherfucker

>>11403020
>Multiple ways to build the reals from the rationals
It does not matter if there are 1000 ways to do it if none of them actually work.
>Austounding amount of reasons why completeness and supremum properties are intuitive and make a shit ton of critically useful math work
>Hundreds of years of development and refinement of the ideas underlying analysis by humanities best and brightest
If we used a time machine to go back to the 16-19th centuries and got rid of the mathematicians from that era, humanity would be fucked. For the 20th century ones, I doubt we'd notice much of a change to the timeline.
>Retarded youtube dude spews nonsense
Do you even actually understand his arguments or are you just assuming the status quo position is right by default?

>>11403250
These arguments by prestige is why math got into the mess it currently is in. The machines should be the final arbiters of correctness, not how many humans agree whether a theory is correct.

>>11403558
>As if Mathematica was some sort of empirical field. He doesn’t seem to understand it’s just playing around with axioms. You’re either consistent or you’re not, wether there’s a 1 to 1 correlation with reality is irrelevant.
>Wildberger is an idiot because he does not understand that math is worthless. It is all meaningless rock climbing exercises.

>>11404230
>>Wildberger is an idiot because he does not understand that math is worthless. It is all meaningless rock climbing exercises.

>what I'm not good at is worthless meaningless rock climbing exercises. :((((

Mathematics is still quantitative and still influences engineering and science strongly even if it does not care about applications :))
Ironically it's the type of analysis built on things Wilberger considers not ``real`` that created the most practical and active engineering fields

https://ieeexplore.ieee.org/document/1580791 (this paper is FILLED with asymptotics/limits :))) and it created Compressed sensing)

https://people.eecs.berkeley.edu/~mlustig/CS/CSMRI.pdf
https://scholar.google.com/scholar?as_ylo=2019&q=compressed+sensing&hl=en&as_sdt=0,5&as_vis=1

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=approximation+theory&btnG=&oq=approximation+

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=wavelet&btnG=

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=fourier+analysis+&btnG=&oq=fourier

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=random+matrix+theory+and+wireless+communications&btnG=&oq=random+matrix

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=optimization+mimo&btnG=

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=optimization+control&btnG=&oq=optimization+contr

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_ylo=2019&as_vis=1&q=operation+research&btnG=

etc.too many to list.

Whereas rational trig or algebraic calculus just trade the psychological difficulty with infinite process for the practical AND theoretical difficulties of unable to do useful things such as taking limit. Maybe that's why people dont give a shit about it, just a thought.

>>11404225
>None of them actually work
Your failings to understand them doesn't mean they dont actually work

>non sequitur
Retard, not only are you blatantly wrong but engaging in fallacy.
A shit ton of modern tech depends in post 19th century math, you don't know this because you are an uneducated imbecile

Obligatory post in wildberger thread:
>real numbers are fake and gay
>infinity doesn't exist

>>11404468
> psychological difficulty with infinite process
That psychological difficulty is a signal that what you are studying does not make sense. In particular, reals do not make sense at all from the perspective of modern type theory. Basically, it is impossible that the termination checking considerations (because otherwise you could construct anything) of languages like Coq or Agda can be meshed with current construction schemes for the reals.

Literally every construction you can think of, if you'd programmed it on a computer would diverge and stack overflow in short order. That is the elephant in the room which mathematicians ignore. It might have been something you'd sweep under the rug in the early 20th century, but not so much in the 21st when computers are ubiquitous.

Those links you've posted mean absolutely nothing. ML papers, including deep learning ones all use reals. In fact, I do not think I can think of any paper that actually use rationals. But so what? Would you attribute the success of modern DL to the fact that they use reals? Of course not.

It just happens to be the case the the particular rules you've picked as your proof system have good utility in certain situations, not that they necessarily make absolute sense. And if your rules have a computational interpretation, meaning that can be compiled to actual machine code rather than just compiled in sheep undergraduate brains, then that is a far stronger guarantee of logical correctness.

(cont'd)
> theoretical difficulties of unable to do useful things such as taking limit.
This is such a load of shit. If you watch some of his differential geometry/algebraic calculus lectures, he shows how to do just that using just rationals.

>Maybe that's why people dont give a shit about it, just a thought.
People don't give a shit about math in general, just its practical use. That means algorithms. Algorithms and not proofs are actually the main currency of mathematics as it is practiced in the real world.

It is just idiots like me who actually try studying computer assisted proofs in order to actually understand what proofs are (because that is certainly not something you'd learn in a modern math textbook where they seemingly pull things out of thin air) and then get mad that modern math is more fiction than actual rigor. Everything is a program of some sort. Proofs are programs, and modern mathematicians are the only ones who have convinced themselves that obviously diverging programs have validity as objects. At the scale this delusion is being propagated, this is already on the level of being a fully fledged religion.

It is not a question of whether people give a shit or not, but what is right here. I'd expect actual mathematicians to address the contradictions in their world view and proof methods, not act like braindead religious people who only care about maintaining consensus even if their precepts could only ever make sense to dirt shoveling peasants 2000 years ago.

Fuck them and fuck me for ever considering math as having any sort of intellectual prestige. Even the average code monkey has more intellectual rigor and integrity than a professional mathematician. Why did I even study proofs if in the end I would arrive at these conclusions?

>>11404701
>In particular, reals do not make sense at all from the perspective of modern type theory.
http://math.andrej.com/wp-content/uploads/2016/06/hott-reals-cca2016.pdf
https://arxiv.org/abs/1610.05072

Even in the field of computable analysis, the simplest functions aren’t necessarily computable until we start revising our scheme for decidability or our representation. The simple step function gives us difficulty but we still have a way to talk about it as a computable object

>>11402314
Can nobody respond? Damn, I thought you mathematicians could be of help. This problem is typically very easy, but I would prefer a rational approach.

I have another problem though. I have a sample of material that decays at a rate that is proportional to the mass of material remains. That is, [eqn] m=-k\frac{\Delta m}{\Delta t} [/eqn]
where Δt is a very small increment of time and k is a positive constant of proportionality. Question: is there a way to get mass as an explicit function of time using rationals only? That would be incredible.

>>11404816
In the real world the mass decays in quanta, not continuously. Representing decay as a continuous function of time is nothing more than an abstract idealization.

>>11404826
How do you know this?

>>11404828
When you measure radioactive decay with a geiger counter you get a series of individual clicks, not a continuous stream.

>>11404831
How do you know that's not just the resolution of the counter showing itself?

>>11404835
If a counter is registering 1 click per second with one material and 1000 clicks per second with another, obviously the 1 click per second is not a limitation of the geiger counter.

>>11404843
How does this imply that mass is quantized? Just means that there is a lower limit to the smallest piece of mass the counter can detect.

>>11404814
I am the guy you are responding to. I knew somebody would bring up HoTT. Let me point out one thing first - HoTT is not a computational type theory because univalence is an axiom in it. The HoTT book itself has a construction of reals that is intrinsic to HoTT in a chapter dedicated specifically to it. No doubt, once indexed higher inductive types get implemented at some point somebody will port that to cubical type theory in Agda.

And then I'd be wrong.

Except not. How do I know? Because any such construction would violate the famous sqrt(2) is irrational proof.

>>11405283
>Because any such construction would violate the famous sqrt(2) is irrational proof.
Explain

>>11404895
stupid fucking bug

Hello. mathematicians!
Does anyone have good scan of "Concrete Mathematics: A Foundation for Computer Science"?

>>11404702
>even if their precepts could only ever make sense to dirt shoveling peasants 2000 years ago.
You people are retarded. You don’t see what mathematics really is and have this magical or platonic sense of it so you sperg out when you catch glimpses of how bland, comparatively, it actually is. At some point, you’ll always have some unsupported axiom that you accept because it makes enough sense to be taken as a truth. Godel showed that. To some people the concept of a limit or infinity makes enough sense to them. To others it doesn’t. And that’s fine, that’s why you have zf and zfc. It’s why you have logics with the explosion principle and paraconsistent logics. Work in what makes sense to you and see what results you can derive. What’s not fine is crying that the other side shouldn’t be done. Either show it’s inconsistent or shut the fuck up. You’re crying about a problem that even your side doesn’t solve and never could. It’s just slightly less of a problem and you decided that’s where the line should be drawn. You’re hypocrites at best.
What’s really funny is how how Wilderberger and his ilk want to bring up practicality as if it has any bearing on math, but then point to some vague sense of lack of rigour despite all the practical achievements of concepts they don’t like.

>>11405576
just google + pdf its the first result

>>11405596
>scan
Not this copy without pics. You are not sure about your answer, but you are in a hurry to answer in order to seem very smart.

>>11403250
>he spent all this money and kissed all these asses, so therefore he’s right
This line of reasoning will never be persuasive, ever.

>>11404895
>Just means that there is a lower limit to the smallest piece of mass the counter can detect.
Incorrect.

>>11404826
damn, if resolution is quantized at a subatomic level I guess we should throw out math!

>>11405283
in hott and predicative maths, they use dedekind cuts and they work well

>>11402975
old conan shows, masturbating bear

>>11403294
it's the ultimate proof, to finally not be real

>>11402928
Fucking holy shit almost peed myself

>>11404816

Difference calculus.

>>11406676
If it worked well you could use it to computationally prove sqrt(2)^2=2, which is the main purpose behind the invention of the reals. The new HoTT construction isn't going be able to violate laws of computation, and hence won't be able to do that.

>>11405590
Reality has a computational nature, and accomplishments are made in reality.

Much like modern mathematicians redefined the word **real** to something that is totally not real, they apparently (based on how you are using it) redefined the word **accomplishment** to something that 99.9999% of people would not recognize as such.

> What’s not fine is crying that the other side shouldn’t be done.
Why shouldn't it fine to say what shouldn't be done? We are all intelligent actors in this world, and we have the choice of molding it to our liking. Don't expect me to agree with you here.

You are safe with the confines of your university math department, but outside stricter rules hold.

> Either show it’s inconsistent or shut the fuck up.
Why do we have to play by your rules? Why don't you show your axioms are computational instead?

>You’re hypocrites at best.
That is uncalled for. We have our principles by which we abide.

> vague sense of lack of rigour
It is a very well defined sense of a lack of rigour.

> To some people the concept of a limit or infinity makes enough sense to them. To others it doesn’t.
Some people might not understand limits and infinity, but you should not confuse them with those actively opposing this line of reasoning.

>>11402436

Ask yo mama about my length lololol

>>11405361
Wildberger reinterpreted the proof as not necessarily proving the existence of irrationals, but nonexistence of any such number.

So basically what you have in the HoTT book is just a type definition. You might be able to construct some instances of such a type, but you won't be able to do things like computationally prove sqrt(2)^2=2 which is the whole reason behind the invention of the reals. You simply won't be able to calculate it. HoTT is not some magic that can violate laws of computation.

If I am wrong, then it should be easy to show otherwise.

>>11403250
>immenent
shut up retard

When Matlab suddenly, without any reason, changes strictly rational 1/2 to 0.4999999999, it is a horror. It's terrifying.

>>11406984
You are wasting your time for an imbecile troll, Nikolaj

>>11404816
[math]dt=-k\frac{1}{m}dm[/math]
[math]\implies\int dt=\int -k\frac{1}{m}dm[/math]
[math]\implies t=-kln(\vert m \vert)+c[/math]
[math]\implies \frac{t}{-k}-c=ln(\vert m \vert)[/math]
[math]\implies e^{\frac{t}{-k}-c}=\vert m \vert[/math]
[eqn]\implies \pm e^{-c} e^{\frac{t}{-k}}=m[/eqn]
Set [math]K=\pm e^{-c}[/math]
[eqn]\implies K e^{\frac{t}{-k}}=m[/eqn]

>>11404702
Are you saying only people who study computer assisted proofs `understand what proofs are` and that proof theory contradicts modern real analysis? lol

Maybe to people who worship computers mathematics MUST be equal to the things computers can do, but to the rest of us, mathematics is beyond what computers can do. Mathematics is a creative field that humans do, and it has always been useful, and coincidentally the most diverging programs such as any object of topology (e.g homeomorphisms) or geometry (Calabi Yau manifolds), all of which rely on infinite processes, find applications in all investigations of science into reality (e.g topological field theory). Maybe it's just a coincidence then, nature randomly obeys abstractions beyond reach of the `programs`.

Or maybe you should just study more proof theory to learn what it actually says. It's pretty funny to evaluate the rigour and integrity of mathematicians from the standards of codemonkeys, but I see your point more clearly now `hurr how come it does not look like my compooter programs`.

When will you guys come to terms with the fact that nature speaks in the `non rigorous` language that modern mathematicians cooked up and not your`rigorous` codemonkey friendly language.

>>11405590
Mathematical platonists certainly are not mentally challenged or autistic like people who want to reduce mathematics to formal logic 80 years after Godel. Don't equate mathematics with what sophomores studying mathematical logic can see. What Godel did was just formalizing the bureaucratic restriction boiling down to the axiomatic system's ban on self-referring contradictions. But you may always use a slightly broader system of tools to think and decide what the answer actually is. In fact people who rave about Godel would probably be surprised that we cant construct perpetual motion machines even though we haven't tried all the combinations of cogs and wheels, yet physics is still complex and certainly not bland, lol

>>11407078
Your bullshit is tiring.

>>11406991>>11406942

With the Dedkind cuts in predicative maths, there is a unique square root function, from positive reals to positive reals, and the square of the function is the identity on the positive reals.
That's exactly what is required about square roots

>>11402199
No. Irrational numbers are just as real as any of the rationals, and Wilderberger is a retard or charlatan for saying they aren't real. And all of his supporters are all either trolls or mathematically illiterate.

>>11407141
>Irrational numbers are just as real as any of the rationals,

>literally has to build a new system number where his little imaginary numbers live

>yielding a direct proof of irrationality not relying on the law of excluded middle; see Errett Bishop (1985, p. 18). This proof constructively exhibits a discrepancy between √2 and any rational.


HUHOH

>>11407143
Express sqrt(2) as a ratio of integers. People who accept the existence of irrationals know this is impossible. But I want to know how retards like you answer this.

How do wild burgers do analysis on the rationals without resorting to convergent sequences of rationals (which is essentially what real numbers are)?

>>11407078
Not him, but the intersection of people who study computer proof systems and those who study proof theory is nontrivially large. However, not everyone is as strict a finitist as this guy. Just read any book on computable analysis

Nobody actually important is trying to “codemonkey a proof.” They’re studying the constructibility of proofs to study the constructibility of objects proofs reason with.

>>11407002
Welcome to babby’s first floating point rounding

I have a cylindrical storage tank, 7 feet in diameter and three feet across. How many cubic feet of water can I store in my tank? I need your help, Rational Mathematicians.
>>11407017
Do you mind explaining what the [math] \int [/math] operator does to a rational number?

I have a cylindrical storage tank, 7 feet in diameter and three feet across. How many cubic feet of water can I store? I need your help, Rational Mathematicians.
>>11407017
Do you mind explaining what the [math] \int [/math] operator does to a rational number?

>>11407172
Express 0 as a ratio of two numbers that are not 0.

>>11407525
“ [math] \int [/math] operator”
I’m not a wildburger fan / finitist but hot damn calling it an operator is like peak engineering / physics tier

>>11407531
That operator requires a differential to be complete.

>>11407520
Just saying that it's fucked up.
Floating point arithmetic standard must be reconsidered

>>11407535
If it's not an operator, what is it?
>>11407539
Are differentials rational numbers?

>>11407548
Is a variable a rational number?

>>11407551
Yes. All reported values of [math] m,\Delta m,\Delta t, k [/math] are rational.

>>11407556
Did you just make them up? It doesn't sound very rational to me

>>11407559
No. I measured them.

>>11407560
What's your error of measurement? Can you show irrationals are inconsistent with your measurements?

>>11407548
The differential with respect to a variable is an operator. We call only specific integrals operators, and namely in calculus the big one is the volterra operator when integrating from 0 to t. So it suggests that you’ve come to consider integrals operators through a physics inspired environment more than a math inspired one

>>11407584
>error of measurement
Hot damn your engineering / physics blood is showing
Imagine not knowing what measure is

>>11407616
Then state how you measured them

>>11407532
>Express 0 as a ratio of two numbers that are not 0.
>ratio of two numbers
>numbers
get the fuck off this thread and go back to your high school class

>>11407760
As a ratio of integers, does that clarify it for your autism?

>>11407777
You weren't asked to express sqrt(2) as a ratio of integers that are not sqrt(2). Why did you add an irrelevant factor to the problem?

>>11407777
Also nice quads. Also >>11407789

>>11407789
I'm stating a separate problem just as meaningless as the one you stated. The answer is in your post but you're going to make such a fuss about it because of one person's inability to accept irrational numbers.

>>11407789
Okay, then sqrt(2)/1

>>11407805
sqrt(2) isn't an integer. Jesus Christ, you sound like you're about 8 years old and just learned about irrationals.

God made the integers, all else is the work of man.

>>11407801
>I'm stating a separate problem just as meaningless as the one you stated.
It's not, you failed to form an analogy.

>>11407811
So you are asking to express it as a ratio of integers not equal to sqrt(2),so how is it different from >>11407532 ?

>>11407817
>So you are asking to express it as a ratio of integers not equal to sqrt(2),so how is it different from >>11407532 ?
Because sqrt(2) not being an integer does not imply that a rational is a ratio of integers not equal to itself. You dumb schizo faggot.

>>11407824
So I made an equivalent problem by omitting 0 from the values you can use to express 0. So what's the answer to my question of how to express 0 as a ratio of integers excluding 0?

>>11407838
That's isn't equivalent you nigger.

>>11407844
Then how do you express 0 as a ratio of N_1 being natural numbers or positive integers?

>>11407838
So according to your logic, asking for the name of a bachelor is equivalent to asking for the name of a man, since all bachelors are men. But of course that's false since not all men are bachelors. Equivalence goes both ways.

All bachelors are men

The entire point is you're taking something outside the set and saying you can't make it by what is in the set and sperging out because of it. Irrational numbers aren't the only things you can do that with and you can't make any meaningful statements just because of that.

>>11407859
>sperging out
The only one doing that is you.

>Irrational numbers aren't the only things you can do that with and you can't make any meaningful statements just because of that.
Doesn't follow.

It appears your brain is broken since you don't understand basic logic.

>>11407616
>>11407760
>>11407811
>>11407824
>>11407844
Those are the names calling and diverting from the discussion, post a screen shot showing all the (You)s that go with the sperging

>>11407547
This is actually true. Even excepting the (nan = nan) = false retardation, float exponents really should be in base 10 which humans use.

>>11407871
>They're disagreeing with my schizo posts, they're diverting the discussion! REEEEEEEE
kys schizo

>>11407078
>codemonkey friendly language.
I would not call Coq, Agda or Lean codemonkey friendly by any stretch. Proving even simple things in them is fiendishly difficult and a productivity tank. Exactly why math guys should be prodded to use them. It seems like a fitting punishment how the 20th century went on the math side. They should take some time off from making 'progress' to clean their house.

Codemonkeys don't have a reason to touch them, so the proper audience of those tools actually using them would spur their improvement.

Besides, the issue here is not math being programmer friendly, but actually computable. There is a difference.

>>11407149
Don't trust constructivists. They pretend they like computability and then stab you in the back right away. They'll pull out infinite sets without hesitation in order to 'get things done'.

>>11407939
You sound like a religious fanatic, which you are.

>>11403015
retard

>>11407078
>Maybe it's just a coincidence then, nature randomly obeys abstractions beyond reach of the `programs`.
Does it actually do that?

>>11407871
kys schizo

>>11407871
kys

>>11402331
based

>>11407813
solved

>>11402199
Reals are well-ordered :)
Here is a proof. " fgunkihlfkun678" - let this represent a construction for the well ordering of the reals.
Fields medal please