Thread 16759445

He seems like an extremist but I cannot find a single flaw in his arguments. His methods not only work but are buried in logic and this cannot be said about analysis in general. My only objection (and a big one) is that Fourier series don’t make sense in his framework, which are probably the single greatest thing since bread and butter. What gives?

>>16759445 (OP)
>verdict
pussy
only became outspoken after retirement

>>16759460
Wouldn’t he have lost his tenure if he pulled this while active?

>>16759445 (OP)
I saw him in some debate where he said that insanely large numbers like a quadrillion elevated to a quadrillion elevated to a quintillion dont exist because they are just too big

>>16759445 (OP)
He has at least one bad argument that was parroted here for a while. Basically that a random Cauchy sequence can suddenly have massive outliers that make it not converge. No, it can't lol. In that case, it's either not a Cauchy sequence or you don't know if it is or it isn't.

>>16759445 (OP)
Talks like a faggot

>>16759464
Even though it’s a finite number, I understand his concern. The real world has finite resources and there aren’t enough to give this number any meaning.

>>16759460
>only became outspoken after retirement
What the fuck are you talking about? Everyone at UNSW knew his deal and nevertheless respected him. Several professors had Rational Trigonometry on their bookshelves. Also, when he'd teach calculus to first years, he'd mention that he thought the real numbers were bullshit.
>>16759462
It's almost impossible to lose tenure without getting paid out bigly, and as I said, he was well-respected.
>>16759445 (OP)
>Fourier series don’t make sense in his framework
They do; harmonic analysis was one of his areas of interest.

>>16759445 (OP)
Constructive mathematics is valid mathematics.

That said, much of his depiction on the history of real analysis and its apparent problems, even to shit as stupid as him proving the Collatz conjecture or Riemann hypothesis, are garblydoo.

The philosophical arguments against the reals though aren't inherently unreasonable. He just goes a bit far at times, making him crankish.

>>16759462
>think different thoughts
>lose tenure
Are you British?

>>16759470
It’s semantics at this point, but you probably understand his point. Cauchy sequences require a complete space to converge.

>>16759487
no anon i’m just tired

>>16759481
>>16759482
Would you advise a physics student to focus on Wildberger’s approach or is this academic suicide since I’ll have a hard time adapting the problems/solutions from traditional calc to algebraic?

>>16759491
You appear to have that conditional backward.

>>16759504
Semantics…

https://math.stackexchange.com/questions/4144516/confusion-with-cauchy-sequences-in-a-metric-space-being-called-intrinsically-co#:~:text=%E2%80%9CIntrinsically%2520convergent%E2%80%9D%2520wouldn't,%E2%80%9Cnatural%E2%80%9D%2520extension%2520of%2520X.

>>16759531
I’d hate to offend you by guessing your point.

>>16759470
You’re confused. Every convergent sequence is Cauchy, but the converse need not be true. They might be equivalent statements if your playground is only R, yes.

>>16759575
>might be
There was an equally silly offshoot of the bad argument, which I also haven't heard in a while. I define a real decimal so that each digit is either 1 or 0 according as Riemann's hypothesis is or isn't true. It's obviously a real number but you don't know what equivalence class it's in so the real numbers are flawed. QED! Essentially,
>There's a coin in my pocket and it's either a red coin or a blue coin.
>But I can't see whether the coin is red or blue.
>Therefore a blue coin isn't blue.

>>16759445 (OP)
very based—he makes jews and glow niggers seethe

>>16759774
>he makes bergs and wilds seethe
May I introduce you to the early life function, elf, almost as useful as erf.

>>16759804
>almost as useful as erf
not him but i find erf neat
https://en.wikipedia.org/wiki/Error_function

>>16759818
Let's see...
>[math]\mathbb{C}[/math]
>[math]\sqrt\pi[/math]
>[math]\int[/math]
>[math]e[/math]
>[math]dt[/math]
yep, this function is an error alright.

>>16759824
what’s wrong with those quantities or operations?

>>16759824
you know?, i think that im tankful for you being retarded, you deserve it, keep it up

>>16759497
I think some of his series may be fine (for instance algebraic topology, maybe calculus) but just append it with other sources.

Im a bit sympathetic to his kind of POV of finitism and constructivism. Not because I believe those (i like my wacky topologies) but because I think they are valid, misunderstood approaches to math.

But I think learning the base, classical theory is important to build on top of: especially in analysis, where its much simpler to comprehend and applicable to physical theory even if not every function makes physical sense.

>>16759497
You're probably better of learning classical calculus, analysis, differential geometry, and functional analysis. They will be much more helpful to you in physics than Wildeberger's approach.

If, after you understand the way that the vast majority of modern mathematics functions, you still want to learn his approach, then go for it. Why not? Just don't sacrifice your ability to actually understand the important problems relevant to your field because some autistic retired professor preaches a niche and atypical kind of number theory.

can I ask a naiive question here? OP and many follow-ups are about Norman Wildberger. Why is it that it that you guys avoid mentioning both his first name and his second name?

Are you embarrassed about it? Or are you worried the spooks have filters on the words "Norman" / "Wildberger"?

The guy is really not all that controversial. It's not like he's a 9/11 conspiracy theorist or that he's telling you that Oswald didn't act alone. All he says is some pretty academic musings about whether to use integers or real numbers.... and you guys treat it as if he's talking about dancing israelis or NUMEC or something

Why the cold feet in this thread?

Honestly, Wildberger is a legend. He's not right, but he's definitely a good force in the world. We need guys like wildberger.

>>16759445 (OP)
>He seems like an extremist
Then you need to remove your Cauchy limits to see the light of lights.

If your Mathematics professor doesnt cuss out someone every other sentence...your teacher is a woman.

>>16759445 (OP)
>Take set theory
>Get to ordered pairs
>The ordered pair (x,y) is encoded as {{x},{x,y}}
>The ordered pair (x,x) is encoded as {{x},{x,x}}={{x}}
>There's plenty of other little nuances the prof glosses over that don't fit the pattern
>Ask if there's any issues or corrections that need to be made down the line
>Get laughed at
Yeah, wildberger is 100% on to something

>>16759936
[math]dt[/math] is an "infinitesimal" quantity (an ill-defined concept). The others depend on a prior concept of "real numbers", a collective hallucination with no precise definition.

>>16760230
>>There's plenty of other little nuances the prof glosses over that don't fit the pattern
>>Ask if there's any issues or corrections that need to be made down the line
What exactly was your issue? Something wrong with that ordered pair?

>>16760149
Let me guess, you were a Bob Dole campaign advisor?

>>16760354
I campaigned for Ross Perot in 1992 at my elementary school.

Fiery outsider, just like myself.
:^)

>>16759470
he rejects “cauchy but we don’t know where” as fake and gay

>but I cannot find a single flaw in his arguments.
The defeating argument against "Wildbergerist mathematics" is that it's decidedly informal. He doesn't provide formalisations and upon being pressed refused to be more formal about it than he is. Which is to say, he doesn't want to explain his system in formal logical terms as it became a tool after around 1860 in mathematics. One doesn't have to accept first- order logic, a variant of it like second order, or something more exotic that exists. But the guy doesn't provide any formal system encompassing his rules of inference and he knows it. The problem with this is that whatever is allowed or not in his system remains up to him only. He champions a form of constructivism, and rejection of infinities, but it's not like he affirms strict Heyting arithmetic either. He didn't engage with intuitionism proper (which conflicts classical logic also), but he also didn't provide a formalized alternative. He doesn't provide a jumping off point for other people to expand on Wildbergerism.
I like him, he has good videos, good ideas even, he has some breadth. But by his own design, his system can't be taken over, since what mathematical rules he likes - some subset of standard math - is spread over his videos and he has no formal system as we'd know if from the mid 19th century onwards. What remains is inspiring videos where he breaks down criticisms of classical mathematical system which were already fleshed out by Kleene, Heyting and the likes - except those guys worked out fully formal alternatives.

>>16760244
No it isn't. It's a differential, which needn't make any reference to "infinitesimals".
You've just exposed yourself as a mathlet, so kindly leave the conversation.

>>16760404
>>16760145
Does Wildberger’s approach offer any insights into traditional notions seen in math/phys undergraduates?

>>16760392
So does the property itself. You can't just assign the property without proving the property. Either you know it eventually has the property, in which case it doesn't matter what else happens where, or you don't know, in which case you can't say you do.

>>16760404
>it's whimsical and doesn't care about a grand unifying theory
Whatever you think about his reasoning in particular cases, those qualities aren't a "defeating argument" against anything expect maybe a paycheck.

>>16760404
whomst

>>16760371
>Fiery
Can't follow the association. Did you also burn your tongue in elementary school on a lit birthday candle?

>>16759445 (OP)
That's SAINT WILDBURGER to you retards.
Recently I have been talking to GOD who has told me that SAINT WILDBURGER has been sent from the Heavens to right the wrongs of the mathematical world.
One day we of THE ONE TRUE FINITE FAITH will rise up and storm the strongholds of those GOD CURSED INFINITY LOVING SODOMITES and reclaim the HOLY LAND of mathematics for the GLORY OF GOD!
And SAINT WILDBURGER will lead us into battle.
Amen.

>>16760523
Nigger it's been like 5 years already get some new material or get off the stage lol.

>>16760523
a-are you okay?

>>16760515
>Can't follow the association.
Inflammatory, off-the-cuff, uncouth...a wild rebel with a just cause.

"Vote for the Psychosis/Beligerant ticket in 1992, or be sorry."

>>16760542
>Inflammatory, off-the-cuff, uncouth...a wild rebel
No
>with a just cause
Yes
I mean, I persuaded my parents to vote for him, too. But I guess a junior high school brain is somehow less susceptible to weird associations with fire than an elementary school brain?

>>16760546
>No
Be was going to be the TDS of the 90s, and you wouldnt realize that until after he won, like with Trump....then he would have become "Literally Hitler" and every press briefing would be a firestorm. Fire and fury.

>>16760555
That's not at all what anyone was talking about lol.

>>16760556
>anyone
Are you speaking as Legion again? That happens when you fall to Chaos, you speak as a node of the hivemind, (You) no longer exist, youre merely a vessel of {{{the Borg collective}}}.

>>16760408
Sorry but "differentials" are infinitesimal displacements. Your pil-pul wordgames don't work on me.

>>16760565
I'm speaking anecdotally from both 1992 and 2016. No one, not one boomer in 1992, was anything at all like my older boomer lunch mates were in 2015-16, who became TDS zombies overnight. Did you walk into some fire that disfigured your face and makes you equate Perot to fire?

>>16760566
NTA but I'm pretty sure that differentials exclude infinitesimals by definition?

>>16760570
>who became TDS zombies overnight
Because he didnt win, dummy....
A "(less than) stable genius".....

Anon...how would you feel if you hadnt had breakfast this morning?
[hold up notepad to take notes]

>>16760575
Please pretend you can read. He didn't win in 2015

>>16760576
I dont know who youre talking to at this point but youre clearly fishing for validation for your incoherent projections about fire association or dates, youre in a parasocial co-dependent relationship and I dont fraternize with patients.

>He didn't win in 2015
Because the election was in 2016, then why talk about it. How could your "friends" have TDS before Trump was the official canidate? Perot didnt run in 2016...in no way did what you say make sense from any persepctive possible.

Please...STOP LARPing. You have a "breakfast" problem.

>>16760533
Ah yes, but you recognize us. You recognize the DIVINITY of our message. You should join us. Perhaps through the grace of GOD your mathematical sins can be absolved.

>>16760583
>was going to be the TDS of the 90s
No one, literally no one, except maybe Bush, had Perot Derangement Syndrome in 1991. By contrast, TDS in 2015 is one of the realest and most documented phenomena in political history.

>>16760583
>TDS before Trump was the official canidate?
Lol did you live in a cave?

>>16760588
Go to sleep.

>>16760611
You confuse post knowledge with prior ignorance.

You, literally, cannot know what it was like to not have had breakfast this morning....you literally cannot pass a temporal mirror test....you have the mind of a fucking chimp.

>>16760631
Tell me more about your post knowledge.

>>16760635
You failed a temporal mirror test...we're done here.

>>16760648
Are you really done here?

>>16760617
We will not rest until you GOD CURSED INFINITY LOVING SODOMITES are overthrown. Only once your cantankerous souls have been cleansed by HOLY FIRE shall we sleep peacefully.
We have GOD on our side.
We can not lose.
Amen.

>>16760588
>You recognize the DIVINITY of our message.
nah, im fairly certain he recognized the NIGGATRY of your message

>>16760523
more like sinner wildburger

>>16760566
>I want to do everything algebraically
>No, I refuse to learn the basics of algebra
>Instead I just claim that things can't be done.

>>16759482
>Constructive mathematics is valid mathematics.
you know the type of people who invent twists on classic board games like three-players Go and a shitload of chess variants, without having any notable mastery of the original game?

>>16760946
>>16760947
BLASPHEMY YOU SAMEFAG SODOMITE!
You will burn in the discrete flames of finite HELL!
Meanwhile we will look down at you and LAUGH at your torment!
Amen.

>>16760230
I think this a misfortune of taking notation as definitionally this thing.

Like, (x,y) "isn't* seen literally as that set. We have a good idea of what (x,y) means. Rather, {{x},{x,y}} is a possible *formalization* of the concept of (x,y) purely in language of set theory.

Which is to say, set theory should be seen as a kind of model for which you can base all of math on, but whether you *literally* think those concepts are those sets is up to you.

>>16761057
Most think this because they genuinely don't know what constructive math entails. The basic idea is if I say prove the existence of something, I should be able to show the steps to how I get that specific something. Non-constructive math gives you stuff like 'weeell... I know there exists a non-measurable set (with axiom of choice) but I have no clue what it looks like'. It's basically saying 'hold up' to mathematicians pure logic arguments, in particular saying 'well it cant not be true so it is true!' Homotopy Type Theory is an example of constructive foundations, other math like topology can be reformulated intuitionistically via locales and arguably be 'nicer' in some ways (for instance proving Tychnoff theorem without axiom of choice). I don't know all the details but some of it is convincing.

>>16761069
you don't even know the meaning of amen, you larpfag

>>16761093
>proving Tychnoff theorem without axiom of choice
No clue where you're getting this notion from. Tychonoff's theorem is equivalent to axiom of choice.

>>16760466
A core point of the argument is rather that no other person than Wildberger himself can take over his "whimsical" constructivism.

If constructivism is what he want to push, he could have done it better (if he even cared to read 20th century constructivism, which I don't think he has).
I think it's more that he picked up Kronecker and thought through stuff himself, ending up with a non-formal base for rants.

>>16760404
donno

>>16760466
A core point of the argument is rather that no other person than Wildberger himself can take over his "whimsical" constructivism.

If constructivism is what he want to push, he could have done it better (if he even cared to read 20th century constructivism, which I don't think he has).
I think it's more that he picked up Kronecker and thought through stuff himself, ending up with a non-formal base for rants.

>>16760468
donno

>>16760230
(x,x) is {{x}} in this definition, but that's not an issue.
What's important for pairs (x,y) or rather the set XxY of such pairs, is that the fulfill the universal property (e.g. projection of components, all that you need to work with the model as if they are a pair), and this works for the definition {{x},{x,y}}

There's also common complains of non-materialists, such that e.g. 1 is a member of the set (0,7) in this model of the pairs. But that's more of an aestetic unease than a technical argument against it.

>>16761124
I'm not him and don't know HoTT too much either, but the two propositions being ZF equivalent might not necessitate them being so in HoTT.

E.g. I know a "form of" AoC is provable in HoTT.
Like a fairly direct translation. Except of course HoTT doesn't use first-order logic quantifiers but more demanding type formers. So it's a closest translation but in a different context.
To avoid confusion one could say "FOL+\in"-AoC and HoTT-AoC, but that would also get annoying soon.

That might be at play here. I mean after all the theory is "homotopy type theory" with homotopies far closer to being primitives than sets in ZF, so a topology result being different in flavour there may not surprise too much.

>>16761226
You ignorant HEATHEN!
You are scared for you sense the tide is turning against your IDOLATROUS BELIEFS!
You FEAR facing the wrath of GOD!
For surely you will BURN!
Amen.

>>16761226
Is he waving the banner of constructivism in his "rants"? Or are you the one putting that flag in his hand and then complaining about it when he drops it? I have no idea, I'm not a Wildberger expert, I just watched a few of his youtube videos for shits and giggles, one of which contained the preposterous argument about Cauchy sequences, and read the hyper catalan gf paper, which was cool and worth reading if you like combinatorics. In any case, if it's the latter, that's not really a good argument against anything.

All I know about Wildberger is he pointed out that the square root of 2 deeply upset the Greeks. If it upset the Greeks then it means its worth getting upset about.

>>16761378
Sure, I'll pay debnts as soon as you finish calculating that square root

What's wrong with viewing the irrationals as the limits of infinite sequences of rationals? I understand Wildberger doesn't believe in infinite processes because until proven otherwise it's safer to assume a finite universe with finite resources, however I disagree on this point. Referencing Zeno's paradox, in real life Achilles overruns the tortoise all the time. Doesn't this prove that limits of infinite processes are real? How else do you solve Zeno's paradox?

>>16761579
You could just say that the overrun happened faster than you could keep dividing, so trying to divide a lot didn't really help you understand anything.

>>16761616
Makes you wonder if this 2000 year old puzzle was even solved.

>>16761656
It was solved before it was puzzled. Is there any parametrization of the puzzle that doesn't solve itself?

>>16761670
So what's the solution?

>>16761673
What are your parameters? State the puzzle as you see it and give your rules.

>>16761670
It wasn’t solved until last century because this is ultimately a physics problem, not a mathematical one. To measure ever smaller distances or durations, you need higher and higher energies which would eventually create physical singularities aka blackholes. So time and space are not infinitely divisible, but we’ve just learned this recently.

>>16761689
>My ice cream cone was dripping but it's not dripping anymore because we've just recently learned that time and space are not infinitely divisible.
Just state Zeno's paradox as you see it and mark your rules, the rest follows.

>>16761696
I'm not sure what your consternation is, the paradox is well understood and there's not 100 ways to interpret it. The quantities involved are clearly intervals of time and distance, and the question is how can one cover infinitely many intervals of distance in a finite amount of time. Is there another way to interpret this lol? Stop being so mysterious and just answer the questions.

>>16761727
You haven't asked a question yet. Ask one.

>>16761729
>You haven't asked a question yet. Ask one.
>>16761727
>Is there another way to interpret this lol?
I don't even know why I bother at this point

>>16761727
>>16761734
Is it this?
>the question is how can one cover infinitely many intervals of distance in a finite amount of time
I don't see how anyone who's read Landau or du Bois-Reymond or the cliff notes compiled by Hardy or any of their precursors could be confused about whether something finite is commensurate with something infinite. If you mark something as finite and something else as infinite, you've given yourself your own answer.

>>16759445 (OP)
What is the largest integer number?

>>16761751
There isn't one.

>>16761756
So I'll never run out of numbers if I keep adding one to a given number and so they're infinite right?

>>16761807
You described arbitrarily finite but sure, I'll play the antagonist either way. What do you want to say?

>>16759497
Academic suicide. You have to use the language other physicists uses otherwise
You'll be one of those schizos sending gibberish theories of everything to college professors

>>16761579
No, it proves that reality is discrete, not continuous. Therefore mathematics should be based on that if it is to describe reality.

>>16762307
What's the proof that reality is discrete? That's a very hard proof to prove. You can easily shit on that proof by rotating any object in space and seeing how the number of pixels associated to that object is variable.

>>16762307
Aside from that being a retarded idea, it's not even one that would be desirable. Discrete problems are almost always NP hard while you have to try really hard to find a non-polynomial continuous algorithm (and even those are usually because there's some discrete sub-problem it's trying to solve). Aside from it being wrong, recasting the universe as some combinatorics problem does nothing practical for us.

>>16760412
I don't personally think so, but I'm not a number theorist, nor am I someone who is bothered by either the notions of continuity, or the reality that physics based models are almost by definition incorrect. All models are wrong, some are useful. Unless the system itself is logically consistent, who cares if you use approximations and heuristics?

>>16762317
>>16762321
Not him but pretty sure modern physics already proved reality is discrete. In order to probe smaller structures, one needs particles with smaller wavelengths which are associated to higher energies. This goes to say that the further you want to divide reality, one requires higher and higher energies, eventually leading to singularities. This is the basis of Heisenberg's uncertainty principle really. Position and momentum (which is fundamentally related to energy) are conjugates. If you think space is infinitely divisible, then you require infinite energy to do so. I'm not sure why you even debate this point, the case was closed a while ago.

>>16762817
>modern physics already proved reality is discrete
Nothing like that happened. This is a literary argument about physics, where a word reminds you of something so you write a novel in your head around that word.

>>16762817
Heisenberg's uncertainty principle comes from the time-frequency duality in non-stationary Fourier analysis. When you have a non-stationary signal, a short time Fourier transforms can produce a spectral representation of your signal in 2d against frequency and time. To increase your frequency resolution, you have your STFT have a longer observation time. Doing this comes at the cost of decreased time resolution (you make the y-axis more accurate and the x-axis less accurate). The same thing happens the other way. If you do shorter duration observation windows in time, you get less frequency resolution, but a more accurate representation of the temporal character of the time-frequency signal.

That's all it is. A tradeoff in resolution. Nothing to do with discrete vs. continuous physics.

>>16759445 (OP)
He will never expel me from the paradise Cantor created for us. Simple as.

>>16762879
du Bois-Reymond created it. Cantor is just a more evocative name, like you're singing something at full voice instead of hiding it in a woods.

>>16762874
>mumbo jumbo
Wake me up when you've divided space smaller than Plank length.

>>16762905
NTA but the "Planck length" is a limit to what you can see, not to how space works.

>>16762909
You got it wrong since any kind of interaction at Planck length or smaller would create a microscopic black hole, which in turn determines exactly how space works in its vicinity.

>>16762936
Thanks for your novel, we appreciate the art.

ultimately he thinks numbers are described by how many digits you type which means pi ~ 3.14 is different from pi ~ 3.1415 which means the ratio between the circumference of a circle and its diameter is different based on the observer

He is right to point out the bs in modern analysis and specifically the dog shit that is cauchy mathematics but his solution is a not solution and illogical

>>16763097
What's wrong with "cauchy math"? Can you elaborate?

>>16762905
That has literally nothing to do with the uncertainty principle. The whole point of the uncertainty principle is that you can only be sure of what you can observe. It doesn't mean that what you can't observe doesn't exist. It just means you can't be sure of it if you can't observe it.

>>16762905
plank is measure limit, not existence limit

Why does Wildberger assume the universe is finite? It seems to me like this is an open question. I get it, we as human beings cannot do an infinite amount of things, but if the universe is infinite (as well as energy and matter), then IT can. And ultimately we're describing the universe. Does my reasoning make sense?

>>16764583
Yes.

>>16764583
does seem so