“Mathematics has no generally accepted definition.”

Interesting. I was surprised not to find the working definition I use listed among the main categories. I view mathematics as abstract magic - the art of those things unseen which can be manipulated and used as real providing only they are named, and thus invoked, precisely enough; their discovery or creation, naming, and manipulation.

#Mathematics: μάθημα (máthema) τικὴ (tikḗ, tékhnē)

#Math is "the art of teaching" and "the art of learning".

It studies the structure of the constructs of the human minds that can be comunicated through language.

That's why we find so much math in #Science, because Science is our attempt to force our perception of reality into such structure.

It's not science until we can describe it with math, moving it from one person mind to the humanity culture.

@Shamar Maybe when we talked about your talk? 🤔 (I took only one coffee today so don't trust me)

@Shamar @feonixrift @aral @natecull @freakazoid @enkiv2 @Azure @alcinnz @ondiz

I'd argue that mathematics of different species would converge.

From my POV, mathematics is about finding interesting patterns, extracting them from the phenomena that exhibit them, finding ways they can be further generalized or extended, and studying the properties of those patterns which are independent of where these patterns appear.

@Shamar @feonixrift @aral @natecull @freakazoid @enkiv2 @Azure @alcinnz @ondiz

But we perceive the pattern because they exist.

If there were no patterns in the world, i.e. if every time you do something it has unpredictable consequences, then no creature could develop any means of increasing its chance for survival.

@Shamar @feonixrift @aral @natecull @freakazoid @enkiv2 @Azure @alcinnz @ondiz

I agree that "interesting" is a subjective word, but it only decides which mathematical concepts we discover. If 2 species find the same pattern interesting, they'll end up discovering the same abstract concept behind them.

Also, it's not like being interested itself is something unique to humans. Many other species also exhibit curiosity.

@Shamar @feonixrift @aral @natecull @freakazoid @enkiv2 @Azure @alcinnz @ondiz

I think that if we found a different civilization whose development level is in the same order of magnitude as ours, they'd also have concepts like "big" and "small", natural numbers, and probably some understanding of "analogy".

@enkiv2 @Shamar @Azure @alcinnz @freakazoid @feonixrift @natecull @ondiz @aral

Well yeah, magnitude is irrelevant in many fields of math. But what about partial order? Logic has the implication, set theory has subset-of.

yet many of the creatures perceive the reality in a similar way to ours, at least at the lowers level: they have sight, smell, hearing.

But even without that, I'm pretty sure that they would have natural numbers anyway.

@Shamar well yeah, language is the foundation of all formal reasoning. Especially written language.

@Shamar I think we're touching on a topic that appeared in "The Cambridge Quintet", where Turing insisted that a Turing Machine can do any kind of reasoning that a human can do, while someone else (Wittgenstein?) argued that without having human-like sensory experience, the machine will never understand the semantics of the language.

IMO we're all just turing machines.

(Given enough paper and ink. Otherwise, we're just finite state automata.)

>Machines do not have them.

IMO there's nothing preventing them from having them.

>why a human might want to describe himself as a machine.

Maybe because I'm humble.

Certainly because I don't think I'm fundamentally any better than the computer I'm using right now.

Because I don't see a reason why a bunch of neurons connected together would fundamentally be any smarter than a bunch of transistors connected together.

@kragen @Shamar @aral @Wolf480pl @ondiz @natecull @alcinnz @Azure @enkiv2 @feonixrift Having a way to write down equations is different from having techniques to transform one equation into another or directly solve the equation other than by brute force.

The space of problems which cannot be solved symbolically is dramatically larger than the space of problems which can, so you need numerical methods no matter what. You don't need symbolic methods AFAICT.

André E. Veltstra@aeveltstra@greenpencil.social@Shamar @I disagree with that. It can be science without using math. It's just that scientific principles are easiest to express in a language designed for it. Karl Popper, who wrote the book on the scientific method, didn't write it in maths. He wrote it in philosophy.