/sci/ - Science & Math

>>14771227
Mathematics, in its quest to leave behind the real world, is edging closer to metaphysics and religion. They want to have a hermetic cult where mathematicians only need to learn by the rules of mathematics, not prove truths about the observable world.

Wildberger is based but kind of fell out of favor here with his Goldbach "proof."

>>14771227
>If the majority of modern mathematics isn't what we think it is, e.g., "real"
Meaningless statement. It's not what you think it is because you have a misconception.

>How can symbol manipulation hold any sort of coherent truth?
If Bob is unmarried then Bob is a bachelor. Is this true or false? Why is it true?

>What's the value in playing around with abstract reason completely divorced from content?
Your premise is false. Math is often not completely divorced from "content." It's very useful and even what was once considered completely abstract turned out to have applications. Before you can map out a real place you need to have the abstract skill of drawing. That skill can be used to draw real things or unreal things. The better your skill, the more value your drawings have regardless of the content. Math is similar.

>>14771227
If it has no relation to reality how does it produce results that are applicable in reality? Sure, you can claim that all real-life applications use finite precision, but we definitely use stuff like calculus, which relies heavily on the logic behind reals for its theorems. Where's Wildburger's calculus replacement?

>>14771227
Rationals are "suppose we have arbitrary precision".
Reals are "suppose we have infinite precision".
Both are not a realistic model of the universe, but that's fine. The mathematician uses rational and real numbers to prove theorems in an infinitely precise way, it's then the job of the scientist to use these results with limited precision to help with his experiments.

>>14771227
I say
PRAISE THE HOLY WILD BURGER!
For HE shall lead the faithful away from the SIN of INFINITY!
Amen.

>>14771756
>If Bob is unmarried then Bob is a bachelor. Is this true or false? Why is it true?
Bad example. You have to have knowledge of "no-marriage" and the concept of a "bachelor" before you can make analytic statements like that.

>Before you can map out a real place you need to have the abstract skill of drawing. That skill can be used to draw real things or unreal things. The better your skill, the more value your drawings have regardless of the content. Math is similar.
A good start. But not precise enough. What kind of drawings is math engaging in? Beautiful sketches? Or throwing paint at a canvas?

>>14771756
I just don't understand what I've been doing since calculus if real numbers aren't real. I wish somebody could give me a brief rundown.
>t. liberal arts brainlet who took multivariable, linear algebra, and probability then quit

>>14771781
well said. This is why I created the MMP number model, to help a mathematician navigate the asinine linguistics blurring the lines between the physical and metaphysical

>>14771768
He has a series on algebraic calculus.

>>14771768
only the sufficiently autistic can fathom the chasm between precision at arbitrary iteration and [math]\text{exactness}[/math]

but anyone, if given the means, can hear the difference
https://www.youtube.com/watch?v=6NlI4No3s0M&ab_channel=Trippin%27onCookies

what can I say, I do not believe taking a third from ten to be equivalent to four from twelve.

Babylonians seemed to appreciate exactness to a greater degree than we do today, labouring on video related to find all the perfectly rational triangles

https://www.youtube.com/watch?v=L24GzTaOll0&ab_channel=InsightsintoMathematics

> How can symbol manipulation hold any sort of coherent truth?
In fact we need to ban all spoken language, which is just symbolic manipulation using sounds, and carries no truth.

>>14772655
Language has references to the real world. Words for things like "rock", "water", features that belong to a language's locality, etc., don't really change much. But for social and abstract concepts? They can change often.

>>14771866
>>14772217
help
>>14772610
I actually like this idea. Could you give more examples of what fields go where?

>>14771768
>If it has no relation to reality how does it produce results that are applicable in reality?
Because the bulk of it doesn't rely on real numbers, which means it can work on reality

>Sure, you can claim that all real-life applications use finite precision
That is always the case

>but we definitely use stuff like calculus, which relies heavily on the logic behind reals for its theorems.
This only means calculus can be explained with reals. I'm sure there are other explanations that don't rely on reals and infinity since it works in reality

>Where's Wildburger's calculus replacement?
Rational Calculus

>>14772217
>I just don't understand what I've been doing since calculus if real numbers aren't real
You have applied the idea that locally a tangent to a point resembles the curve of that point

If infinitesimals aren't real then how does nonstandard analysis produce results that are applicable in reality?

>>14773239
by mimicking the results of standard analysis in a different language

>>14773208
You are unable to explain why something that supposedly has no relation to reality naturally gives rise to calculus.

>>14772763
>>14773160

>>14772610
>lemma 4 + lemma 1
>infinite amount of displacement on the number line given a unit change in length
wtf does that mean

>>14773257
>why something that supposedly has no relation to reality naturally gives rise to calculus.
What the fuck do you even mean by "calculus"?

>>14771768
Wait till you find out how imaginary numbers are used in real applications.

>>14774002
To be fair imaginary numbers in engineering applications are just a shortcut for 2 element vectors and a special transformation. You can completely replace i with a certain 2x2 matrix and complex numbers with vectors of size 2 and it will work exactly the same. It will just be more cumbersome.

>>14774002
I don't know what your snarky reddit post is about. Complex number math clearly captures useful relationships that occur in reality as well.

>>14773988
Show me Wildburger's rigorous treatment of antiderivatives. :^)

>>14771788
Amen, Brother.

>>14771227
>>14771781
>>14771866
>>14772610
>>14772655
>>14772763
OP here. Anybody have a good response? I have no idea what to think about this stuff. Completely lost on what's "real", what's "fake", and what's "provisional yet useful."

>>14772763
>Language has references to the real world
What is the 'real world'?

>>14774959
The problem is going to end up being one of defining 'real'. If you are a physicalist, then 'real' means something that is physical or can be related to something in the physical world. This raises the question:

if these abstract objects are not in the real world, yet they can be conceived of in minds, then what does that say of the substance of minds? Are minds then not 'real' or part of the real world? If abstract objects are not in the 'real world' but they ARE in minds, and if minds are located in brains (they are not actually), then there must be something non-physical in brains, namely abstract ideas. But then aren't brains part of the 'real' physical world'? This whataburger guy is likely a physicalist. It's an incoherent world view that ends up with the physicalist trying to deny his own consciousness like dennett does. The physical world and abstract objects, logic, numbers, etc, are both grounded in cinsciousness/minds.

>>14774959
So here
>>14775369
That is to say, if abstract ideas are supposedly things thought of by brains, then they are supposedly 'in' brains, and brains ARE in the 'real' world, then abstract ideas are in fact, from the physicalist point of view, part of and 'in' the real world.

>>14771227
Read Oswald Spengler.
Numbers are only a part of some object or phenomenon's quality / form.
Mathematics is inherently limited and also wrong when theories are built on other theories losing contact with reality.

>What's the value in playing around with abstract reason completely divorced from content?
There would be no value. Which is why mathematicians usually give their made up symbols the same properties as the ones real world objects have.

>>14775369
That's a great point. I subscribe to nondualist metaphysical theories, where the material and ideal are intertwined in some way, so I'm interested in seeing where content-less abstraction goes wrong.
>>14775399
I've been reading critiques of Plato and Aristotle on their conceptions of number and have largely come to the same premise. Base number systems are a form of language that lock us into certain correspondences in the world.

bump