Reminder that you cannot count past 10^200

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youtube.com/watch?v=XKy_VTBq0yk
en.wikipedia.org/wiki/Infinite-dimensional_vector_function
web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf
youtube.com/watch?v=SrU9YDoXE88
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Thanks, I'll keep in mind not to try.

Why [math] 10^{200} [/math]?

Number of atoms in the universe I suppose

Wildburger thinks of numbers as a line that you can extend indefinitely but he doesn't like the idea that you can contain all those numbers inside a box

There are only about [math] 10^{80} [/math] atoms in the universe, although that's my back of the envelope calculation, so it could be wrong.

>the idea that you can contain all those numbers inside a box
I love how informal he is about this shit. A box. Fucking math literalism. Yeah, the universe probably isn't continuous at the smallest scale either, but math isn't a literal description of the fucking universe.

He actually says inside a set

youtube.com/watch?v=WabHm1QWVCA

youtube.com/watch?v=XKy_VTBq0yk

And why does that stop us from counting? Assuming I never died and could survive everything that happened from now to the end of the universe, I could potentially count forever.

Will real numbers be one day regarded like how we view luminiferous aether today?

I'm assuming the chances you'll forget the correct order of digits at that point becomes extremely high.

Go to 9m38s

youtube.com/watch?v=WabHm1QWVCA

10^200+1

Get rekt fag.

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>muh computational power

I really don't understand why this is such a problem, it's just a practical limitation.

10^80=10E80
10^81=10E81
(...)
10^201=10E201

Checkmate

>computational power
that's not the issue, retard. The issue is that the number is so large that it can't actually be physically represented in the universe.

Does he have anything to say about digital computers?

>that's not the issue, retard

He repeatedly says that some number "doesn't exist" if you can't compute it, or some variation on that.

Who is this retard?

>needing the number to be physically represented
Why?

Well, I think that if you try to compute all the possible permutations of all the atoms in the universe, you'll probably end with a number of magnitude greater than 200. And still, it's a physically represented number.

>The issue is that the number is so large that it can't actually be physically represented in the universe.
That's just a practical limitation.

>cherrypicking and putting things out of context


He literally said you cannot have a datastructure that contains all of the natural numbers. He is merely questioning the axioms of set theory.

can you exhibit it?
if not, then I don't believe it exists.

>He literally said you cannot have a datastructure that contains all of the natural numbers. He is merely questioning the axioms of set theory.
What does one have to do with the other? Answer: nothing

It's all just baseless rhetoric.

Exhibit the number 1.

Also, no one cares if you believe anything though. Mathematics is not a matter of belief.

He has a phd from Yale. I don't think he is a retard.

>It's all just baseless rhetoric.
Not at all. Can you have a vector [math]v \in \mathbb{R}^\infty[/math]? Then how come you can have limitless amount of members in a set?

Wildberger just doesen't like the consept of infinity.

>Exhibit the number 1
[ | ]

>Also, no one cares if you believe anything though. Mathematics is not a matter of belief.
it is. It's a matter of what axioms you accept as the foundation of your system.

That's not the number 1, that's just a representation of 1. If I ask you to show me a mountain exists do you draw a picture of it?

>it is. It's a matter of what axioms you accept as the foundation of your system.
So axioms are a matter of belief? No you fundamentally don't understand what axioms are, probably because you've been watching too many Wildberger videos.

en.wikipedia.org/wiki/Infinite-dimensional_vector_function

>Wildberger just doesen't like the consept of infinity.
Exactly. Not liking something is not a mathematical argument.

>[ | ]
How is this any different to writing 1, bot are just representations of concepts, and if that counts why not just do something like [eqn] [~~ | \underbrace{\cdots } _{10^{1231}} |~~] [/eqn]

Not that guy but what are axioms?

Why do you people treat a Professor with a PhD from Yale as a dumb ass random guy? Do you think you know more math than Wildberger?

10^200 + 1
Checkmate.

sorry dots don't mean anything.
1 is [ | ]
2 is [ || ]
it's natural.
What is "..."??? It's meaningless.

Numbers are m-sets.

>If I ask you to show me a mountain exists do you draw a picture of it?

1 is something as opposed to 0 which is nothing.

For example, something can be a strike like this on your screen: |
I just showed you 1.

>Not liking something is not a mathematical argument.

It is when you deal with axioms.

>If someone has a Ph.D they're literally infallible

Having a Ph.D implies that someone is likely right, it doesn't Guarantee it. Look at Linus Pauling, Ph.D, Nobel prize winner, literally a genius. Yet towards the end of his life he started believing that mega doses of vitamin C were keeping him alive. Just because he had a Ph.D didn't mean he was right.

>Lines are natural
>dots aren't

You can't make this up. Dots just represent repeated application of something.

I didn't mean he is right because he has a phd, but people here talk about Wildberger like he is some random poster from Veeky Forums

Axioms are the fundamental premises from which all mathematical statements are derived. Saying that you believe or disbelieve an axiom doesn't make sense, as there is no such thing as a true or false axiom. That would imply that axioms themselves are derived in some way or that there is a way to tell that an axiom is "false". There are only interesting axioms and non-interesting axioms. The latter are usually inconsistent or lead to trivial results.

Why? I think I have explained clearly why. He uses irrational, mathematical rhetoric. Instead of defending his rhetoric, you fell back on his credentials. I don't know as much about Lie algebras as Wildberger, but he is not talking about Lie algebras. He is barely even talking about math.

>1 is something as opposed to 0 which is nothing.
Now you are trying to explain 1 to me when I asked you to show me that 1 exists. Clearly 1 does not exist and you are just trying to hide this fact. Mathematicians are so dishonest.

>Dots just represent repeated application of something.
dots can't represent a random number at your convenience.
A certain number of dots can.
But 3 dots can't entail any number you want at your leisure.

damn, you're right.
Therefore real numbers don't exist, case in point.
thanks for making my point for me.

Wildberger rejects axioms: web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf

Wildberger does not argue "I don't like your axioms, my axioms are more interesting." His argument is "my mathematical beliefs are how reality is, everyone else's is false."

Wildberger is a crank youtuber. His PhD doesn't change that and is frankly irrelevant.

And neither do "natural" numbers. But nice attempt to move the goalposts.

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

>And neither do "natural" numbers.
That's what we're trying to tell you.

>I lost the argument so I'll try to use words I don't understand
that's what the argument was about in the first place.

>this is what mathematicians actually believe
youtube.com/watch?v=SrU9YDoXE88

Not the guy your responding to, or the initial guy

Can you give an example of an interesting and non-interesting axiom?

My guess is that a "relatively" non-interesting axiom would be something like 1+1=2, which is based in mathematics were familiar with?

Axioms of non-interesting set theory:
1. There's a set, called the empty set

Axioms of an interesting set theory:
[insert ZFC axioms or whatever here]

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can you exhibit you micropenis?
if not, then I don't believe it exists.

I don't really care if you believe in my penis, its only purpose is to evacuate my ammonia-loaded urine.
But apparently you care if I believe in infinity or in real numbers.

Pretty sure you don't care if I care about you believing in infinity or real numbers either.

then why do you want to force everyone to believe in infinity and real numbers?
Let wildberger develop his theory in peace.

I actually agree with this.

This is why shit like the "a monkey who types an infinite number of characters will eventually type Shakespeare" shit frustrates me because even time in this world as we know it is not infinite.

What if you want to model a universe with more mass than our own. It would be useful to have larger numbers because more particles.

then it's not astrophysics anymore, it's astrology.

At 11:53 he says "the complexity of [a number that big] becomes far from uniform."

What does that mean? I get the argument but how is it "far from uniform" ?


Also, it sounds a bit ridiculous but couldn't we say that mathematics is not a representation of this universe but rather of a "make-believe" universe where the number of particles is much, much larger, and just say that math is a representation of that universe?

You're assuming that, I literally just came in this thread to ask you pics of your dick.

He's right that mathematics does not reflect reality. But I don't think it was ever supposed to nor do I think it would be more useful if it did. What reason does he have that it should represent reality and my position is therefore wrong?

>But I don't think it was ever supposed to
but it was... it was supposed to help us describe what we see. Geometry and arithmetics didn't start as vector spaces with norms and groups/rings.
It started as a way to find patterns in the world.
Somewhere along the way it became about something else.

It's really not though. Rather than watch a 24 minute video of garbage with made up, useless, objects, just take 5 minutes to look up "countably infinite," "uncountably infinite" and "at most countable." That is what mathematicians really believe and it takes like 5 minutes to grasp and makes intuitive sense once you get it. Really simple stuff.

>including zero in the natural numbers

well you can write 10^10^10^10^10^10^10^10+23 easily, it only has a few characters.
But imagine a number that's a bit smaller, but that isn't necessarily expressed in such a small number of characters and procedures. That number would have high complexity. For example a product of prime numbers up until some randomly big point. You can't describe it properly without writing the whole multiplication of the 10^10^10^10^10^10*something first prime numbers. Or by writing every digit it has. There are numbers like that that are smaller than z, but more complex.

>infinity
>InfinitIES
>intuitive sense once you get it
kek, it doesn't make sense.

You seem to have lost track of who's being sarcastic and who's not.

>My guess is that a "relatively" non-interesting axiom would be something like 1+1=2, which is based in mathematics were familiar with?
Well for one, that's not actually an axiom. And no, it's not what I'm talking about. Learn about ZFC and then come back.

Time in this world as we know it is infinite.

>Also, it sounds a bit ridiculous but couldn't we say that mathematics is not a representation of this universe but rather of a "make-believe" universe where the number of particles is much, much larger, and just say that math is a representation of that universe?
Yes, and we DO say that in varying terms, but idiots suffering from math literalism must question everything from the basis of reality and become finitist like wildeburger.

That's kind of the point of axioms, we declare a set of rules to start with and see where they lead. When faced with issues, we have three options: throw out an axiom, modify an axiom, or avoid doing what brings out the issue.

>But imagine a number that's a bit smaller
So 10^10^10^10^10^10^10^10-n where n is a small number

The Kolmogrov complexity of integers is very uniform, unlike what Wildberger says.

10^80 = 1E80

moron

is this guy sick or something?
>thhose black eyse
>that weirdly tanned skin
does he have aids?

that escalated quickly

If we adopted Wildberger's axioms (even though he doesn't admit they are axioms) we would have much more difficulty describing what we see. This seems rather hypocritical. First you complain that standard mathematics isn't real enough, now it seems you want to throw out modern physics that best describes our world because it uses that mathematics. Until Wildberger actually describes reality better, he's just a crank.

Line up all the atoms in the universe so that you have a line of 10^80 atoms. Now raise the rightmost atom 1 meter above all the other atoms, such that it can be represented as a binary digit 0000....0001. The number 2^10^80 can be represented using this system and so on if you create different levels of height for the atoms to go to, such that you can eventually represent numbers such as 10^10^80. Very large numbers can technically be represented in our real world in a situation such as this

he got the reals sucked out of him m8

No it's not. The whole entropy thing kind of ruins that.

How so? I don't think you know what you're talking about.

I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons

put my glasses on just to watch this video. made me feel more smarter while watching

in the context of bijections between sets, it's completely straightforward, Just because the language used seems counter intuitive at first doesn't mean it fails to express a meaningful idea

>If we adopted Wildberger's axioms (even though he doesn't admit they are axioms) we would have much more difficulty describing what we see.
no we wouldn't.
How could it be more difficult since it already doesn't work? Physics is weak in its current form, it needs mathematics based on reality to reach its ultimate form.

>vsauce

get over yourself user
everybody understands the notion of different infinities, it's trivial.
Only smarter people are able to see that the concept doesn't belong in our mathematical constructions.

Nice troll.

>babushkas
That means grandmother. Matroshka is the word he's looking for. Somehow though this makes me rage far less than seeing vsauce's stupid face.

>he fell for Cantor's diagonal argument

Why does it matter if it's vsauce that's saying it, is it false or not?

>Only smarter people are able to see that the concept doesn't belong in our mathematical constructions.
if you're going to appeal to authority, at least have it make sense. Finitism or similar rejections of larger sets are still very much a fringe beliefs, and I doubt the majority of notable mathematicians hold them

>nice troll

>what are singularities
>no theory of everything
>navier stokes unsolvable
>P=NP???
>quantum physics = we can't know nothing
>regularization of the casimir effect, among others

I'm sure you can explain all that with "real"-valued functions.

It would be better to throw out the reals and deal exclusively with points moving on discrete grids. That sounds like reality.

How does finitism solve any of those "problems"? Getting rid of quantum mechanics because infinity makes you sad doesn't do anything. You're like a child throwing a temper tantrum.

Wow, Is this how intellectuals talk? First time I've seen it. Veeky Forums is great.

You can't label every real number with a unique integer. We choose to express this as saying that one infinity is bigger than another. You, like everyone else winning about some obvious flaw in modern math, are arguing semantics over a name chosen to describe an abstract concept.