Natural numbers

No

Pic seems stupid as fuck. You can switch base to something like base 60, and suddenly you can store much larger numbers, e.g. by inserting the symbol for "59" into every plank cube.

Well yes, what other sorts of numbers exist out there?

theoretical ones

Isn't he just describing a 200 digit number in that picture? Or is he just using 10^200 as a placeholder for "a very large but finite number"?

Give me an example of one.

OR sometimes we just need a number to describe how big of a whole your mom is , but we just can't express that with current mathematical calculations

(10)^10^10^10^10... +23 with (10)^10^10^10^10 tens in the first stack

Sure, it exists, but has no meaningful interpretation. Ya can't even do arithmetic with it

Wildberger is mentally unstable. He's absolutely serious when he says that numbers have a [math]\sup[/math] of [math]10^{10^{200}}[/math].

But he is right and only lately have I understood his stance.

First, to make sense you need a writing system for numbers. Lets say that hindu arabic numbers.

Second, according to wildberger there is a minimum distance in the universe that sort of divides the universe by blocks. There are 10^10^200 of these blocks. This means that the largest integers we could write down and work with in this universe would be integers composed of a digit in each and every 'block' of space.

After you have a number that is made of every possible block of space, how do you get bigger? It is impossible. It does not even make sense to consider a bigger number because it would be impossible to write that number down because it would be longer that then universe.

In this context does it even make sense to consider a bigger number? Why would you do math with a number that for all you care does not even exist?

So in the sense he wants to se math there is a biggest number that depends on how good your system is at encoding information. In his system of msets the biggest number is even smaller than 10^10^200 because he could at most have one 'stroke' per each block of universe so only 10^200 instead of any digit from 0-9 in any possible order in each block of the universe.

Then you could increase your base to work with even bigger numbers but then at some point your base would be too long to be encoded in this univers eand thus there would be a base limit and thus a general biggest number limit.

My main beef with limiting ourselves to such numbers is that the biggest natural number may not be the biggest. Since that number he uses is based on the observable universe, not the entire universe.

Thats like saying we should limit shapes like circles existing, since a perfect circle cant exist physically

A number doesn't have to represent or describe something physically existing in order to exist.

Additionally, the lack of practical use for a number also does not mean that number can't or even doesn't exist.

Yeah but Wildberger says this perspective is foolish of the 'real number cultists'. That we should not pretend we have more numbers than we actually do. Which is why he is creating his own system that will supposedly be as good for doing mathematics as the real numbers but won't have any of the bullshit, as he would call it.

And if you see it from his perspective it makes sense. What does it mean to add 1 to the largest number? Everything kinda breaks down. How is it meaningful to count a number that cannot be counted? It isn't.

Wildberger just does not want to pretend that given any number you can write down, he knows that somewhere out there in space that number can be located. This is, according to him, the single biggest delusion the real number cultists have.

>How is it meaningful to count a number that cannot be counted? It isn't.

you know mathematicians have said the same thing about irrational numbers, 0, negative numbers, imaginary numbers and so on?

But we do have those numbers. He's the one pretending, and he's pretending we don't have them.

Has anyone ever claimed that we can write down every single number?

And Wildberger still says that about irrational numbers.

He is actually okay with imaginary numbers because unlike with irrationals, we do not pretend complex numbers exist. i is an algebraic object that we construct and we give meaning through definition.

It is like how we could create a field of the rational numbers and a 'square root of 2'. A number that does not actually exist but has the defined property that its square is 2.

He has said that this would be perfectly alright for mathematics because here we acknowledge our limits and say 'it would be nice if we could do it anyway. so we will be careful about it and construct a system for it'.

However in modern day mathematics we pretend that irrationals actually exist, with infinite decimals lying somewhere out there.

And hey, in my opinion obviously irrationals are numbers but not under his system.

And by write down, I'm assuming you meant physically write out the digits of a number

He once put it this way

>They say that they can imagine these infinite numbers. I say that they can only imagine that they can imagine those infinite numbers.

And in a sense he is right. We can only imagine that we can imagine infinity, which is fine for me but for him it is not. He wants to be limited by our direct imagination, not by the imagination of our imagination because then in his point of view shit gets too ridiculous.

So he believe that because he can't comprehend infinity, no one else can.

He sounds like a winner to me.

You know he is a PhD right? He understands infinity. He just thinks we have come too far with what we can actually assume. Our axioms are out of line, he would say.

He believes there is an equivalent system to the one we have that does not assume anything too crazy that can still yield meaningful results and he says that if we do not switch soon, someone somewhere will prove a theorem that will be so ridiculous that from that point forward mathematics will be meaningless.

The real numbers are a ticking timebomb.

>You know he is a PhD right?
GASP!

>He believes there is an equivalent system to the one we have that does not assume anything too crazy that can still yield meaningful results and he says that if we do not switch soon, someone somewhere will prove a theorem that will be so ridiculous that from that point forward mathematics will be meaningless.
>The real numbers are a ticking timebomb.
They should revoke his PhD for spreading such nonsensical, unmathematical propaganda.

>An undergrad thinks a PhD should get their degree "revoked" for making youtube videos.
lol, this nigga worse than those reverse-SJW's in /pol/.

What is up with all these stupid threads on Veeky Forums? Do I have too much faith in you people?

If you want to express larger numbers you can just make a different notational choice, like using a larger base. Would the largest expressible number be larger if we used base 60? That is fucking retarded.

Wildberger is a sperging autist who completely misses the point of the natural number system and mathematics as a whole.

Name one advantage of finitism.

Well we won't feel like idiots when somebody finally expresses the largest possible expressible number.

>Name one advantage of finitism.

it stops those inane 1 = 0.99999999... arguments