What is your opinion on pic related? Can you prove him wrong?

Ultrafinitst or not his rational trig is much more computationally efficient compared to classical trig. Pair that with it only needing algebra available to a middleschooler I think it will become the dominant teaching style for early education

He was a Lie theorist before he became an ultrafinitst. Chapter two of his book is literally about lines in finite fields.

lmfao

His most recent videos concern the definition of groups for compatibility and how to extend abstract algebra in an ultrafinite context

>tfw to intel

He was being ironic you sperg.
I hate writing collision code because it always breaks on edge cases

Youre working within the context of formal systems to begin with, which he rejects as a constructionist. On the basis of measurements and constructions that are possible he can still describe phenomena in nature that would be attributed to trig and calculus.

Personally I think if one claims mathematics is only a formal system then they have to also deny that it is a science. For lots of history humans have not had as succinct notation for math, and formal systems were developed in responce to math, not the other way around. Arguments about quantities can be captured with symbols, but the symbols themselves are not the arguments. Axioms being strings to start with, or rules of inference, are different then assumptions you cannot address from a more simple logic. In ultrafinitism as prof Wilderger has shown only relies on a fundamental trichotomy of nothing, something, and an anti something (0, 1, -1). Everything else is demonstrated by definition and application. The professor has shown that he can do arithmetic, geometry, trigonometry, calculus, and linear algebra through the theory of ultrafinitsm in a way that matches the praxis of its application.

Is this man Veeky Forums's Stallman?

Can you give a single instance of a real number manifesting in our reality? Can you demonstrate any infinite process actually dictates the epistemological source of phenomena?

It is well known that associativity breaks down in infinite sums, can you provide a concistent arithmetic for infinite sums? The ordinal theorists have been trying, yet they have failed at that. Can you point to any collection of objects that can have elements removed and maintain its cardinality?

Hi Norman howareye?

shut up, stinkburger lmoa

I think there is a lot to what he is saying. I got through my freshman year as an applied maths major, stopping at differential equations, and intro to logic/proofs. I have had a lot of additional maths training and his ultrafinite perspective makes it so that I can at least take a more consistent approach to analytic existentialism. His rational trig is an amazing invention and the algebra is laughably easy. I will be pushing for educational reform in my lifetime and I do think that his form of trig should displace rational trig in classrooms. Rotations are better served in the complex numbers and triangles do not need transcendental process to describe their properties. Mathematics CAN be developed from a constructionist basis and be internally justified from bottom up.

Im not even close to wildberger I just respect coherent arguments that are grounded in both theory and praxis.

Also I kinda think memes are overatted gg

Pi comes up pretty commonly mate

Norman please go

Yeah? where are the perfect circles?

I like how only memes are sent against the ultrafinitsts. memes or people who dont know enough to make a coherent argument

I dont dispute iterative methods of calculating pi, just any actual manifestation of an infinitely specific quantity of pi.

Why does it invalidate an abstract concept if you can't find an exact physical copy of it?

This shit was dealt with well over 2000 years ago man

[math]a^{(b^c)} \neq {(a^b)}^c[/math]
Exponentiation isn't associative either. Do we throw it to the volcano too?

It's not just about finding physical analogs. It's also about formal verification of proofs. Remember Schininja? That's a big failure of the classical math.

Why are you really that stupid, that is not a counter argument to my claim: addition is associative, associativity breaks down in infinite sums, infinite sums are not consistent.

Dont come at me with that weak shit

Abstract concepts are invalid as being connected to the structure of the physical world if they cannot demonstrate any connection to the physical world. Inductive knowledge like math cannot claim to be science if it incorporates inscrutable objects in its reasoning.

Formal systems are arbitrary, a limiting position, and are seperate from math. The theory of proof can also be founded on the idea of constructions, not just strings. Math is about arguments of quantity.

Arguments that cannot be scrutinized are voodoo. Formal systems can be a poor vessel for the epistomological nature of the universe and yet still be precise enough to work out. Ultrafinitism is advocating for a more precise interpretation and understanding. In this endevor we get rational trig, which can be logically extended from arithmetic, is computationally faster, and algebriacally easier.

Reality has nothing to do with math. Thats for monkeycists.

>reality has nothing to do with math

So it cannot claim to be a science? are quantites not real? can any situation that deals with quantities claim to have a scientific approach?

Transcendentalist gtfo

Mathematics is not a science by any definition
nobody has ever claimed it is

it has applications to the sciences because many scientists like to use numbers

I claim that constructivism is a science, and that all its conclusions about quantity are valid for use in science.

You can't prove him wrong because what he says regards his emotions and not math nor debatable truth. How can you disprove claims like "I'm not fond of the existence of reals", "I'm not convinced by the contents of most of real analysis textbooks" or "FTA seems counterintuitive to me"? Actually, all of these claims are true, but they regard his feelings and don't say anything about maths

Do you yourself understand what you said?

There's no such thing as "infinite sum", there are only limits of sequences of partial, finite sums

Do you yourself even know what Im arguing about? Im a math major in training, a math teacher for competitive math in elementary settings, and a student of modern logic.

A lot of my understanding of formal systems outside my education does come from the book GEB by Douglas Hoffsteader but I think that text suffices

>conveniently ignoring all the actual math he does in his videos

As a constructivist they arent feels so much as fact. Real numbers cannot be demonstrated, are less than optimal models for the contiuum, and the context where they origionally come up, geometry, is better served without them.

Tie a piece of thread to the pencil, pin the other end of string to the table, draw something keeping the string fully tensioned, voila, there's your perfect circle

Can you claim that it is a perfect circle in all levels of precision? if you look at the grains of the paper is it a platnoically smooth plane? if you look at levels of plank lengths is the graphite distributed in a continuously smooth curve with no jumps or irregularities?

There are no perfect circles in every degree of precision, there are no perfect equilateral triangles, there are no real numbers. Yet quantities still happen. Math is still possible

Operation on numbers is not exactly the same as operation on infinite sequences, whew lad that's a surprise

So. What's your point expressed in consistent language?

Sums dont happen between elements of sequences to begin with. Im not talking about sequences, im talking about sums

what is the result of 1 - 1 + 1 - 1 + 1 - ... =?

there is not a single answer because associativity no longer works, and assuming doesnt invalidate other claims about arithmetic on infinite scales makes you a cuck

I'm not saying all of his maths is wrong, I'm saying his arguments like "constructions of reals don't appeal to me" or "how can infinity be real if our eyes aren't real?" are not valid mathematical claims and there's nothing to disprove because all he does is he shares his feelings.

Ok. Look. There are formal systems which are understandable by computer. Computer can help verify or even prove certain results. In case of Shininja, it's not possible, because his "proof" is a heavily classical garbage. The mathematicians are really having some butthurt cos of him. On contrary, intuitionistic logic does bridge math to computers. Coq, for instance, works with inductive constructions

>how can infinity be real if our eyes arent real
>nice straw, keep grasping

If you only look at his meta talk about something then sure you could say its based on feels. However If you also compare his math to formalist approaches then you see how deficient formal rigor is.

>plank lengths
Have you ever seen one? Have you touched it? Can you draw it on the whiteboard? You're making the same thing mathematicians you despise do, assume existence of ridiculous object you haven't proven existence of.

They can experimentally be derived in the cannon of physics. Are you gonna start invalidating their results?

I think you're talking about infinite series, and the number the series converges to is not a result of addition but is limit of the sequences of partial sums, no addition here.

youtube.com/playlist?list=PL5A714C94D40392AB

Learn a thing or two

It doesn't add up to any number because the series diverges

Yet dont some divergent series still have values?

And what's rigorous about wildberger who gives formal definition of naturals as lines on the whiteboard and addition as "just add them together lol"?

>partial sums
>no addition here

If I could do an finitie amount of things in a process that wasnt unconcludable, surely there is some sort of number I would arrive at?

He gives formal definitions of lines in terms of euqations in his book, and addition can be thought of as the combining of two data strucutures. In his first video he is demonstrating such a thing according to his definition.

And the existence of reals can be experimentally derived by straight edge and compass, are you gonna invalidate the results?

Yes, like 1+2+3+...=-1/12

*if I could do an infinite amount of things.

I sit down and add 1 then subtract 1, and repeat forever. at the end of infinite time, what number do I have?

Or even without numbers. I place down a blue square, then next to it I place a red square, at the end of this infinite process, what was the last color I place?

He gives a definition of a strike on a whiteboard?

Reals cannot experimentally derived with a straight edge or compass because our constructions are only so precise, and we are operating in a finitely described universe, so our constructions do not mirror platonic ideals

But you know the experiments deriving Plank length base off conventional maths, use reals, limits of functions, and probably infinite series as well? So if you and wildberger accept results of these experiments you accept the existence of reals, and if you reject maths these experiments were based on you reject their results as well

This is a really weak argument. Experimental results are fundamentally given in ratinal numbers, and the phenomena of processes modelled by calculus, as well as calculus, do not rely on reals to manifest. Algebraic calculus is possible, and Wildberger has done many videos on them.

youtube.com/watch?v=Js2mwsHc4p4&index=11&list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf

Im talking in circles and this point and I have an actual tutoring job to go to. take my arguments or leave them