Someone explain in words cause i don't get it. Wtf is rational trigonometry and why is it different than regular trig?

Yes, actually that describes it perfectly. The reals are properly defined to any sane mathematician. What Wildberger disagrees with is axiomatic, yet he couches this in political terms and claims he is above axioms, which makes him a crank.

>You have been brainwashed into thinking the form of mathematics is more significant than its function
quite the opposite the function of math is to solve problems, the form required to do so is rational numbers and some additional rules depending on application. No function of math that produces results requires anything beyond rationals. Physics which produces results requires nothing but rationals. Name one thing in physics which requires the concept of a real number to solve, and if it exists what do you use to apply the result? Because the real world is rational how can you even use a real number in any way.

and to clarify, I think real numbers are useful. But they are still just an abstraction. The end result which can be implemented can contain only rationals.

>quite the opposite the function of math is to solve problems, the form required to do so is rational numbers
Why?

>No function of math that produces results requires anything beyond rationals.
That's just plain wrong. Physics is full of irrational constants. So instead of using those constants, you are going to use an arbitrary approximation of the constant. Why when you could just have the ideal constant?

>Name one thing in physics which requires the concept of a real number to solve, and if it exists what do you use to apply the result?
en.wikipedia.org/wiki/Real_number#In_physics

>Because the real world is rational
Then why are reals so useful for modeling it?

>and to clarify, I think real numbers are useful. But they are still just an abstraction.
All numbers, all mathematics, are abstractions. All models are abstractions. The delusion that rationals are more "real" is silly and proves my point that this is unmathematical quackery.

what makes him crank-tier is not what he's doing but how he's going about it

lots of mathematicians have problems with the construction of the reals. only wildberger has made hundreds of hours of video about his complaints

have you ever solved a problem before? What happens when you express your answer as a bunch of irrational constants? You have to evaluate it to do anything with it, and that means approximate it all as rational. Rationals are the only thing used for modeling physics, there is no other way to do modeling and simulation.

Irrationals like sqrt(2) for example are useful in theory until you have to evaluate your answer to position an end effector or set a voltage somewhere. Its just a placeholder for an infinite series evaluated up to the point that it is good enough. You don't need the placeholder, its just useful. The final result is rational.

making hundreds of hours of videos about math is called doing math. You can't discard it because you don't like it. If its useful it will stick if not it will go away sooner or later.

>Wild((((berg))))er
come on now

>You have to evaluate it to do anything with it, and that means approximate it all as rational.
Why would I have to approximate it? What is your obsession with the decimal form? It's really quite cultish. If I have the exact answer then why would I want to approximate it? Again, computation is simply a form and not the answer. If I need to translate my English to Spanish to communicate with my friend, that does not make Spanish inherently superior to English, especially if something gets lost in translation.

>Rationals are the only thing used for modeling physics
That's just dead wrong, as I've already shown you. Irrationals are integral to physics, because they describe physical certain physical constants with infinite precision. You are presuming computation is integral, which is silly. It's the information which is integral.

>Irrationals like sqrt(2) for example are useful in theory
Then what are you arguing about? If it's useful, use it!

>until you have to evaluate your answer to position an end effector or set a voltage somewhere.
Does using sqrt(2) in our theory harm us? No! Would not using it at all harm us? Yes!

>Its just a placeholder for an infinite series evaluated up to the point that it is good enough.
Yes, which makes it massively useful.

>You don't need the placeholder, its just useful.
You don't NEED to use numbers, they're just placeholders. We could just use lines on a board, right Wildberger? So should we stop using numbers?

>I learned linear algebra watching his videos.
What's a zero-characteristic field?

i learn that from the first chapter of hoffman and kunze, but I'm never going to need it for anything.

Wilderberger actually concerns himself with being useful.

Except when he throws out all of physics he can't rationalize.

Rationals give you the entire world of engineering and useful math and physics, the use of reals gives you an imaginary land which humans invented in their heads. Maybe both rationals and reals were just invented. But the interface between the human imagination and the real world is the rational quantity. A line in space subdivided into a discreet number of points is the only way to interact with the world around us.

Am i denying that god exists because it lives only in the mind of humans? No. If human imagine and shape their behavior by the concept of god then he exists. If reals shape the thought which produces algorithms that are translated to rationals then sure reals 'exist' in the way that god exists.

>real world
i mean the observable world here

>Rationals give you the entire world of engineering
But they don't. Irrationals are useful in every field, get over it.

>the use of reals gives you an imaginary land which humans invented in their heads
All mathematics is imaginary. Get over it.

>But the interface between the human imagination and the real world is the rational quantity. A line in space subdivided into a discreet number of points is the only way to interact with the world around us.
You keep repeating this when I already proved it false. It's like a mantra for you. If rationals were really special vis a vis reality, then all our physical constants should be rationals. Yet they aren't. Numbers like sqrt(2) and pi are massively useful for modelling reality, because they describe a model's idealization. Why approximate an approximation? You are not getting more real, more accurate, or more simple. You are being arbitrary.

>Am i denying that god exists because it lives only in the mind of humans?
God is not a useful model. The continuum is objectively useful.

>Am i denying that god exists because it lives only in the mind of humans? No. If human imagine and shape their behavior by the concept of god then he exists. If reals shape the thought which produces algorithms that are translated to rationals then sure reals 'exist' in the way that god exists.
I don't claim numbers exist empirically or non-conceptually, only you do. Try to keep up.

>All mathematics is imaginary. Get over it.
i agree

> then all our physical constants should be rationals
they could be if wilderbergers math catches on

>God is not a useful model.
This is absurd, obviously its a useful model which offers predictive results concerning large groups of people.

>The continuum is objectively useful.
Real numbers are also objectively useful, I agree.

>You keep repeating this when I already proved it false
it's not possible to prove either argument false because both offer complete descriptions of any physical model. I see reals as being overcomplicated, still objectively useful but less useful than rationals if mathematicians get over their infinity and infinitesimals and start looking for ways to simplify things.

>I don't claim numbers exist empirically
theres your problem

>they could be if wilderbergers math catches on
LOL, in your dreams. Physicists have never cared about constructivist mathematics so they certainly won't give two farts about Wildberger's nonsense.

>This is absurd, obviously its a useful model which offers predictive results concerning large groups of people.
You seem to be confusing the concept of God with religion or religious belief. But regardless this fails to analogize to mathematics. No one "believes" in mathematics except for people who drastically misunderstand it.

>it's not possible to prove either argument false because both offer complete descriptions of any physical model.
You're not referring to what I said. I said I proved that your claim "the interface between the human imagination and the real world is the rational quantity" is false, since physics uses irrationals. If rationals were fundamental to our understanding and so simple, why would we even have irrationals in our models?

How is it a problem?

>why would we even have irrationals in our models
you don't need them
because rational numbers do exist empirically real numbers don't
ie. you can measure rational quantities only

>But regardless this fails to analogize to mathematics.
I think this is an interesting comparison to elaborate on.

You can't measure reals. You can measure rationals.
You can't measure God. You can measure observable reality.

So reals are to rationals as God is to observable reality.

>you don't need them
>You don't need numbers! We could do everything with words! Numbers are hoaxes! HURR DURR
Yes, you do need them IF you want to describe certain physical models with infinite precision.

>because rational numbers do exist empirically real numbers don't
OK, show me an empirical number. Go ahead.

>ie. you can measure rational quantities only
Measurement is just an approximation of reality, a model like any other.

>You can't measure reals. You can measure rationals.
>You can't measure God. You can measure observable reality.
You don't measure a number like you measure reality, that makes no sense. Is there a number two somewhere in reality for you to measure? No, just two apples. The number two is a concept in your model describing apples, not what your model describes. So your analogy fails, since you are just conflating two different meanings of the word measure because they sound similar.

Wildberger has no problem with sqrt(2) if it is constructed algebraically, i.e. as the element X + (X^2-2) of Q[X]/(X^2-2). He has done so in his group theory lectures. His real issue is with transcendental numbers, though he doesn't put it that way.

It's a mental illness as old as the Pythagorean cult.
Remember, rational believers killed Hippasus

CS is very much entwined with infinity and uncountability, though.
If Burger can't accept the reals then I doubt he'd accept uncountable languages and some proofs with Turing machines or similar constructions.
t. been to one CS course.

I see his point, but his version of mathematics without infinity ends up being just dull, boring and soulless.

>Rationals for example can represent the roots of a function arbitrarily accurately
because [math]\mathbb{Q}[/math] is dense in [math]\mathbb{R}[/math] :^)
CSlets go back to

Why are mathematicians so dogmatic? Why can't you consider his point of view? It's not like he is proposing some deeprak chopra bullshit. Dude is just saying "hey maybe this thing is wrong"

>Why are mathematicians so dogmatic?
Why is Wildberger so dogmatic? Why can't he just accept that there are no "true" or "real" axioms?

>Why can't you consider his point of view?
I have. Have you?

>Dude is just saying "hey maybe this thing is wrong"
No, he's saying this is wrong, but has no mathematical argument.

His argument is literally "this is wrong", and he gives absolutely no justification for it other than he is personally offended by the notion of limits.

The fact that every atom in the universe can represent 1 unit but not able to be abstracted to 2 units is absurd.

At some point everything is absurd

My point is that numbers are already abstract and their construction should be based on usefulness to us, instead of by physical constraints, like he argues.

kek

>and he gives absolutely no justification for it other than he is personally offended by the notion of limits.
made me kek