Feels over Reals (Literally)

do fucking white american males count as "diversity" in Australia? If so then I need to move there

Well, maybe the immigration into australia is pretty low as they are literally an island. Thus, the local women need someone to dominate and sexually colonize them given that their males are too cucked. And we know that beggers ain't choosers so I suppose they take in anything that is foreign.

Apart from maybe integrals, what's the problem with using rationals? Epsilon-delta definition of limits/continuity/differentiation still work for rationals

Intermediate value theorem is false for continuous functions Q -> Q.

But there is a way to work constructively with the real field, and that's how I know Wildburguer is a hack and a fraud.

I can sympathise with wanting to try and build rational mathematics, because it's (in some ways) simpler and neater than the reals and no-one else is really doing it.
I have no idea what the fuck Wildburger's deal with limits is. Yes, historically they were pretty damn fuzzy, but I'm under the impression that the modern construction is watertight.

The modern definition is rigorous but unintuitive, and constructionists like Wildberfer disagree with it on principle

It's funny that there is a totally algebraic treatment of calculus with infinitesimals but you have to fuck around with ultrafilters which would drive Wildberger up the wall.

10 buckaroonies says wildberger will invent the hyperreals, but will define [math]\epsilon[/math] as a very specific rational number. Probably [math]\frac{1}{10^{200}}[/math] since that's his favorite.

Kek'd at pic

Does Wildberger really try and argue mathematics from physical analogies like that? Because I'm not even a math student, and that's still obviously pathetic.

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the only problem for him is that he bases is new maths on QM which is done by classical math

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Bahaha

The solution for differential calculus already exists but is 100x more complicated than typical analysis.

Deformation Theory over finite bases should work mostly within his parameters.

Yep
youtube.com/watch?v=z_IAB5T0Qoo&index=1&list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
He talks about it a bit around 37 minutes in

>The natural numbers are finite, because you would run out of space to write big numbers.
This is the most retarded idea I have ever heard in mathematics. I don't even know what to say.

as crazy as he is, he didn't just pull these out of his ass. he actually goes pretty in-depth with his explanations and reasoning.

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Don't worry he's going to rederive QM one of these days as a part of his math foundations series

It's happening! Rational calculus is almost here! The madman actually did it!

>holds up right triangle with height and length 1

uhm, try again sweetie

He should write a book about "Conceptual Math".

You mean quadrances 1, 1 and 2 right?

uh Veeky Forums btfo?

Rejecting a question because you don't like the answer isn't terribly impressive.

For someone who champions realist view of mathematics it's especially strange to assert that it's nonsensical to talk about the length of a line.

the best mathematician in the world atm is australia

turns out this dude is actually a talented mathemtician. i dont agree with his reasoning but its pretty creative and maybe something useful will come out of it one day

>the best mathematician in the world atm is australia
He fucked off from Australia though.

What's the quadrature of a circle with a radius of quadrature one?

Even in mainstream mathematics there are one-dimensional sets who can't be assigned a length. For example
en.wikipedia.org/wiki/Vitali_set

Like he said, idiots. This isn't just for people who agree with his skepticism regarding infinite processes. For one, I'm very excited to take the course because it should be easily applicable in numerical analysis and the approach seems interesting in of itself.

I just don't fucking get it. He looks reasonable enough, why not divert his abilities into something more useful? Why the fuck would you want to do math without reals? What's the problem with irrational numbers? Next he won't do complex analysis because he doesn't like imaginary numbers.

No worries, Wildburger sidesteps these problems by defining quadrance for line segments only.

yeah well no shit he's not retarded

It's useful because computers can't do math with reals.

Well, good thing math doesn't care about whether computers like it or not and computers can always round up to a good margin of error.

>Captcha: MontREAL 3410

Maths.

Criticized with ad hominem attack.

You are like the ignorant who mocked Charles Darwin. Fool

When I see such comments I become interested in the subject matter, for clearly this Wilderberger guy has rustled your jimmies, and whatever upsets fools like you is frequently worth investigation.

Yeah thats why you are so famous.

Its a little bit over your head isnt it dear? Now why dont you have a nice glass of warm milk and go to bed?

yes, yes, its all just too much isnt it? Now grab your teddy and go to bed son.

Wildberger...

Yes, just ignore it all, really, dont let it bother you. Now, do you need some help or can big boy tuck himself into bed all by himself?

No. Just someone who isnt as thick as (you) these fuckwits.

I hope (you) these fuckwits are just high school dicks, not University level students, becasue then I could just blame it on under development of cognitive reasoning.

t. undergrad in math

>This is the most retarded idea I have ever heard in mathematics.
Why?
It is as reasonable as to assume that they are infinite.

>is he for real?
are you retarded of course he isnt for """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""real""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
possibly he "is for rational".

>It is as reasonable as to assume that they are infinite.
It's not an assumption at all!
The infiniteness of the (set of) natural numbers follows immediately from their definition. Claims about what you could or couldn't fit into the physical universe are completely irrelevant. The universe could be so small that the largest quantum that fits is "eight", and still nothing in mathematics would change - because mathematics isn't a description of the universe.

Suppose someone DID sit down and determine "Wildberger's Number" (W), the largest value that can be represented in any way in this universe. As any child who's played "who can think of the largest number" knows, W+1 is also a perfectly valid number, and it only takes thee characters to write.

Every time our universe grows a tiny bit, a new number come into existance. Isn't that beautiful?

You dont understand mathematics at all.
I really have nothing else to say, you are discrediting a theory based on your personal beliefs and your misunderstandings about the topic.

Of course in the standard definition of the natural number the set is infinite, but that doesnt invalidate any other theory where it is not.

Well, Wildberger says that W exists, but W+1 doesn't exist. Ultrafinitists don't just reject actual infinities, they reject potential infinities and give a hard limit to how big a number can be. Of course, they never manage to give a satisfactory answer to what that hard limit should be.

>Define addition to be adding n amount of extra lines for addition of n. BTFO

>You dont understand mathematics at all.
Thanks

>Of course in the standard definition of the natural number the set is infinite, but that doesnt invalidate any other theory where it is not.
Right, but were not talking about those other theories. Wildberrger is using (AFAIK) traditional natural numbers, and their "existence" isn't tied to what can be written somewhere in the universe.

>Wildberger says that W exists, but W+1 doesn't exist.
Sure, but I don't see how that's a supportable view. The expression W+1 obviously exists, and so long as W is a natural number then W+1 is necessarily both larger and also a natural number. The question of "would it fit, if you wrote it out some other way" seems irrelevant.

Wildberger doesn't believe in the existence of infinite sets.
For him there are only finite many numbers and thus there's a largest number W such that W+1 isn't defined anymore.

>that doesnt invalidate any other theory where it is not.
But no one is able to establish an acceptable alternative, they never went beyond "real big numbers can't fit inside my computer".
On the other hand, constructive mathematics provides you with tons of different alternatives, so you can't blame mathematicians for not wanting to study your theory, it's just that you never had any to begin with.

Literally in denial of something solved 3000 years ago

>Wildberger doesn't believe in the existence of infinite sets.
Okay, then that's just silly. I'm not even sure it's WRONG in any formal sense, it just seems needless and contrarian.

What? Just because something has not found any practical uses doesnt mean that it is useless, mathematicians can study whatever they want, but not considering alternatives creates an inferior mathematics.

I am not even an (ultra-) finitsits, but still such Ideas are completly valid within mathematics and it is quite possible that they will find their uses.

>For him there are only finite many numbers and thus there's a largest number W such that W+1 isn't defined anymore.
As soon as I see a formal axiomatization of such a system, I will consider taking it seriously.

He understands them perfectly, but you wouldn't know, as you're not a mathematician.

Wouldn't Wildberger's point of view screw up algebra? For example, + would no longer be an operation on Z, so Z loses it's ring structure.

The hard limit in my view should be any number with a finite number of digits. The set of real numbers obviously includes numbers with infinite digits, and in those numbers it is impossible to do many algebraic operations on them computationally. All math should be algorithmically possible in finite time.

You realize there is no limit to the integers and all integers have finite digits right? I'm not sure you understand what is meant by the limit in this case. Also, if you ignore numbers with infinite digits then you ignore all infinitely repeating rationals. But this is competent arbitrarily as it depends on what bare you're in.

*But this is completely arbitrary as it depends on what base you're in.

>I don't know what a semiring is.

Seriously though, Wildberger's insanity goes beyond just identifying all numbers bigger than W.

A semiring is a ring without an additive inverse, but that's not the problem in Wildberger's theory. The problem is that a+b is not always defined in Z.

How does Wildberger define the concept of cardinality?

FFpFpbFpbp

It would be interesting to see the differential equations in QM to be done without the use of infinities. I wonder how this would affect many of the inconsistencies and infinities arising in QM's interactions with relativity and the theories of quantum gravity in general.

It's one of the problems. Wildberger says to say all numbers bigger than W are "too big". So just make a new number (equivalence class) for those and do arithmetic like you do with infinity in elementary calculus. I know it's annoying, but sometimes reading the intro to a Wikipedia page when someone mentions something is not enough to contribute productively to the conversation.

Wildberger doesn't believe in axioms either

>>is he for real?
>yes

wait hes AGAINST reals

I want to code my own raster painter application that paints in a 3D space.
how hard would be to code a basic paint application like mypaint or paint but that paint 3D pixels rather than 2D pixels?
Also how hard would be to also implement in said application basic vertex modeling, like a basic blender?
Also, in the same application being able to draw vector lines, like SAI?
And have basic 3D toon rendering capabilities of the previous shit.

I would appreciate a list of what topics, both math and CS do I need to learn before trying to make this.

Many thanks.

Since there's no good solution to make good 2D using 3D software and I need a solution for my own games, and since I'm starting to learn opengl and 3D computer graphics, I've made a document where I explain all the requeriments I need as a 3D artists and 2D artist to mix both worlds in a 3D solution.
I suppose people here would be interested into my ideas.
I think many of them could be possible to implement in blender, but I don't see them in any 3D software, since they came from my 2D experience with diferent 2D software.
Pls rate.
docs.google.com/document/d/1t2J63EI_WfcPbff3X3hEi--7GB1WN9W6pTOVthX-OH4/edit?usp=sharing

Many of the end ideas for NPR shit are there, like having more than one specular you can edit (basically projecting a circle shape that indicates the light), having a texture for shadows and lights you can paint (like normal modifiers), having diferent render passes for every specular and shadow layer, and treating the shadow as if it were a projected polygon skin onto the mesh you can paint over.

I have so many ideas for NPR rendering, that I feel there's not curent software that make them possible, so that's why I want to make my own software.

Because it's an ambiguitiy

when you talk about doing math with reals you talk about math that can't even exist. Math that you can't even compute.

That leads us to stupid results like banach-tarski.

As for infinite sets: that's just a dumb way of thinking about things. Why not say "n is of the type integer" instead of "n is contained in a set that can't exist"?

i'm unironically watching his lectures and they're pretty clear

I don't think anyone is arguing that he's a bad professor. Just that some of his ideas are very out there.
He does a good job in distinguishing when he's gonna shill his ideas in lectures, so he's not bad. He's just a bit delusional
"Ok so for this next section, we're gonna use the hip and trendy new idea that's taking over the internet 'Rational Trigonometry', it's alot better than what they taught you in school and I predict it'll take over the world soon"

That's just his retarded political rhetoric.

Not easy

>mathematical existence is about computability
hurrrrrrrrrrrrrrrrr

>the result is unintuive therefore the method is wrong
durrrrrrrrrrrrrrrr

At the vert least math as applied to the real world should be computable, let the pure mathematicians live in their made up fantasy lands.

Irrationals are applied all over. Infinities are applied all over. Computability has nothing to do with general application, it has to do with application by computers. Why should computers be the arbitrator of math?

Show me physical proof of an irrational number that is countable in finite time.

How can he be a professor if he don't understand high school maths?
Why the uni didn't fire him for making these dumb videos?

Yes, and there are functions discontinuous at infinitely many points and yet it doesn't mean there are no continuous functions

But W+1 is a valid definition of a number

Proof of a number? That makes no sense. A number is not a theorem. Try again.

I'm talking about physical proof of these numbers being present in reality. We can clearly see natural numbers everywhere. No measurement is infinitely accurate so numbers which require infinite accuracy are unscientific to apply to reality.

>I'm talking about physical proof of these numbers being present in reality.
Numbers are not present in reality, they are used to represent things present in reality.

>We can clearly see natural numbers everywhere.
No, you can clearly see how natural numbers can be applied to reality. You can also clearly see how irrational numbers can be applied to reality.

>No measurement is infinitely accurate so numbers which require infinite accuracy are unscientific to apply to reality.
All numbers require infinite accuracy. You are so confused. 2±0.1 is not a number.

>Numbers are not present in reality, they are used to represent things present in reality.
That's overly pedantic, but to clarify I mean countable representations of human defined grouped objects with their boundaries defined in time and/or space.
>You can also clearly see how irrational numbers can be applied to reality.
They cannot be applied without resorting to techniques of approximation, there is no physical boundary which can exist that fully represents them. This is because as far as we know everything measurable is quantized.
>All numbers require infinite accuracy
For use in physical measurement they just need to be believably accurate. So the fundamental units should be defined at whatever scale of measurement we can be confident will never change no matter how many times the same measurement is done.
>2±0.1 is not a number.
It can be used as one.