Is it possible to do math without Numbers?
What would such an alien math look like?
>>7973967
Vectors aren't numbers, they are just represented by numbers.
Look at geometry, there are no numbers there, just we represent properties of shapes with numbers.
Knot theory also uses no numbers.
In answer to your question, it really depends on your definition of mathematics. Is geometry mathematics? Or is what we use to describe geometry mathematics?
If the answer is the latter, then maths must use numbers, if it's the former then certain branches of mathematics do not necessarily need numbers.
>>7973967
Yes. Just like ZFC but without the infinity axiom.
>>7973986
>knot theory
stop trying to promote your useless field, you fucking loser
>Vectors aren't numbers, they are just represented by numbers.
>>7973986
The definition of a knot is roughly speaking a closed embedding of S^1 into R^3. The real numbers feature so often in that phrase I can't even.
OFC aliens would use base 10=2*5
that image has no imagination
>>7973999
Knot theory is not useless moron. Ever heard of genomics? fucking pleb.
>>7973967
>Is it possible to do math without Numbers?
Yes.
>What would such an alien math look like?
Entirely different from ours. It has been speculated that enumeration (altough in different bases, probably) would actually be the only common thing between our math and theirs, since it's an incredibly basic concept, and an incredibly useful one too.
>>7973967
"Numbers" are merely symbols and those symbols can be anything for anything.
You basically asked, "can you do math without symbols?"
let your minds be blown :^)
Maths are Maths here and far far away. Any rational being would mainly share with us its reason, which is universal. Surle they could have any other kind to represent numbers, but they'd be using them anyways. They'd freaking need numbers to compute.
>>7973967
>>7975556
There is only one complete totally ordered field anyway (bar isomorphism), so it's very likely, if not certain, that an advanced alien species would also do math with real numbers.
>>7977229
but these are still numbers
>>7975360
but anon, this is not a new kind of math
it's a new kind of science
>>7977229
Jesus, it's so beautiful and full of patterns.
>>7973967
Yes sometimes you can work on sets, graphs, logic and more advance mathematical objects without using numbers in any way.
But you can also use Numbers in probably any math, at least for counting.
Real numbers have to be motivated by completion in some set theoretic or analytic way so from an algebraic approach they may seem less natural.
I'm not sure what is the quickest way to get the real numbers from category theory. There's an obvious copy of the additive integers in the path category of the category with one object an identity and two morphisms that undo each other. And then multiplications by integers are the functors from the path category to itself, but I'm not sure how to find the relationship between additions by integers and multiplications by integers without making reference to sizes of sets again. Maybe that association is arbitraryish?
>>7973986
>Look at geometry, there are no numbers there, just we represent properties of shapes with numbers.
but it makes its 100x easier to use maths to describe geometry. Given how most maths (im not going to say all so as to avoid triggering /sci/) is an abstraction of geometry, I reckon an alien species would have relatively similar mathematical principles to us, but they just might represent them differently. Sort of like the difference between arabic numerals and latin numerals- the principles are the same but the presentation is the difference.
>>7974730
Basically this. It's not about the symbols, but the abstraction they represent. Aliens will have the same abstractions, but with different symbols.
>>7973967
Math is not possible without some level of symbolic manipulation. Math is essentially the study of logical arguments and symbolic representations.
>>7973967
>thinks mathematics has anything to do with numbers
look at this pleb and laugh
>>7978312
>mathematics
>has anything to do with numbers
Math is ultra-firm logic. Any logic can take it's place, and despite the claims of liberal arts students science uses many types of logic.
>>7978322
>Any logic can take it's place
>what is Gödel's incompleteness theorems
>>7978325
Do you happen to have a reasonably easy to understand text that explains Gödel's properly? I thought it was about it being impossible to prove something is entirely consistent from within itself, but it seems I'm missing things.
>>7978382
I don't know, I'm not a mathematician and I don't know much about Gödel's works, so I can be wrong.
Gödel's incompleteness theorems is basically about that you can't make finite set of axioms that can be used to prove any problem.
It showed that Principia Mathematica can never archive its goal in describing any mathematical problem in symbolic logic from which all mathematical truths could in principle be proven.
I think I just watched Numberphile video about it or had it on Set Theory lectures or something.
>>7978325
Godel's incompleteness theorem applies to all logic, including math.
>>7978408
>Gödel's incompleteness theorems is basically about that you can't make finite set of axioms that can be used to prove any problem.
No, the incompleteness theorems are about the ability of a logic to prove certain theorems and the completeness and consistency of the logic. Specifically, the theorems apply only to logics which are at least powerful enough to describe arithmetic. There are plenty of weak logics which the incompleteness theorems don't apply to.
A set of axioms is complete if every formal statement s that can be generated by the ambient formal system can be proven or disproven from s, otherwise that set of axioms is said to be incomplete.
The first incompleteness theorem says that if F is a formal system which can describe arithmetic, then F is incomplete, meaning there are F-generable statements which can neither be proven nor disproven by F.
The second theorem is about consistency. A formal system is consistent if it never derives incompatible statements, i.e. it cannot derive that one of its sentences is both true and not true. The second theorem states that if F is a formal system which describes truth-evaluation, deduction, etc. and arithmetic, and if F can deduce its own consistency, then F is inconsistent (i.e can deduce its own inconsistency as well).
There is a slightly subtle finiteness statement packed into the idea of deduction, which may have led to confusion about the general statement.
>alien math
i think you mean most modern math
also
>summoning demon arithmetic guy
>>7973967
Gauss claimed Number Theory is the queen of mathematics. I don't think it is possible with my level of mathematics unless you're studying set theory and logic
>>7973999
> knot theory is useless
>what is fluid dynamics
>what is navier-stokes
>what is differential geometry
>>7974213
I haven't heard of knot theory elsewhere than in memephile
>>7973967
literally algebra fucking mudslimes invented this shit like a thousand years ago
>>7978525
how can one learn that? are there any major advantages or this is just a
meme ?
>>7978863
Not 100% true. The infancy of algebra can be traced back to ancient Greece. Though I do suppose Persian scholars gave it a larger push
>>7978863
>mudslimes invented this shit like a thousand years ago
mudslimes= aliens proved?????
>>7980684
prove it cuck
>>7973967
> what is geometry
>>7973999
You must be a troll
>>7977229
Let's try to stay away from anything that can be represented by an abacus.
>>7978058
Sometimes I wish I was autistic, so many patters to find and to fall in love with.
>>7981873
prove that arabs invented algebra.
>>7982011
>>7981873
>>7980684
...
>not using google
The word "algebra" is derived from the Arabic word Al-Jabr, and this comes from the treatise written in 830 AD/CE by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, entitled, in Arabic Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, which can be translated as The Compendious Book on Calculation by Completion and Balancing.
Also read: https://en.m.wikipedia.org/wiki/History_of_algebra
>>7980668
that picture explains everything you need to learn it, and there's no obvious advantages
in fact, it seems that just writing down numbers in that system becomes an NP problem because you need to find the prime factors of that number
though, on the other hand, you would immediately know the prime factors of a number just by looking at it
>>7975360
what am I seeing here?
>>7973986
Is math a social construct?
>>7977229
>X times 10 is not 10 times X
it appears changing to base 12 causes a single number to lose commutativity
>>7982274
Not actually "social". There is no human interaction.
Yet the roots of math is human thought. Pure human thought, forged with logic, made to describe the universe.
>>7973967
Like this OP
