Why do we believe in math?

[Savy]

I'd say it's probably both invented and discovered.

I think we can all agree that's definitely wrong.

Savy should change his name to Certainty

Probably

[wufwugy]

I think we can all agree that's definitely wrong.

If it's an invention that coherently models reality to a degree, it's emergent from the state of reality and thus discovered. Saying it's one or the other might just be a matter of scope.

In my estimation.

[CoccoBill]

Saying it's one or the other might just be a matter of scope.

Agreed. Nomenclature, syntax etc obv invented. Underlying rules and principles discovered. If anything else, makes no sense to me.

MMM where's a good synopsis of arguments for and against?

[MadMojoMonkey]

Agreed. Nomenclature, syntax etc obv invented. Underlying rules and principles discovered. If anything else, makes no sense to me.

MMM where's a good synopsis of arguments for and against?

I haven't researched this in years. Start with google.

On the one hand, smart people have to think long and hard to figure out new cool stuff in mathematics, so it seems like it's an inventing process, mentally.

On the other hand, it seems like extreme hubris to think an alien species could come to Earth, we show them our math, and they're, "Who would've ever suspected there was order in the universe? Look at this, guys!" If it's just there to be sussed out, more of a discovery process than invention.

Big names in mathematics disagree over how it feels in the moment. Some even posit spiritual guidance or epiphany.

[a500lbgorilla]

I haven't researched this in years. Start with google.

On the one hand, smart people have to think long and hard to figure out new cool stuff in mathematics, so it seems like it's an inventing process, mentally.

On the other hand, it seems like extreme hubris to think an alien species could come to Earth, we show them our math, and they're, "Who would've ever suspected there was order in the universe? Look at this, guys!" If it's just there to be sussed out, more of a discovery process than invention.

Big names in mathematics disagree over how it feels in the moment. Some even posit spiritual guidance or epiphany.

Was the wheel invented or discovered?

[Savy]

Was the wheel invented or discovered?

Invented. If only there was a career in this.

[MadMojoMonkey]

If it's an invention that coherently models reality to a degree, it's emergent from the state of reality and thus discovered. Saying it's one or the other might just be a matter of scope.

In my estimation.

This is another assertion which makes me think myself in circles.

Math is cool and beautiful and fun whether or not it has anything to do with reality. Just like Tetris. or Chess, etc.

Sure, the widespread knowledge of mathematics wouldn't be a thing if not for mathematics being neatly present in nearly all profitable endeavors (or how would you even know if it was profitable? U C wat I did, huh?). However, it would still be a thing. 'Cause it's super fun to try to poke holes in it only to discover it had you on a scavenger hunt all along. It's super fun to find an actual hole to poke in it, only to realize that it's only a hole because of this one assumption, and when that assumption is lost, this whole other world opens up.

Math is inviting, stimulating and rewarding. Even if the profitability was removed, people would still play this game.

[wufwugy]

This is another assertion which makes me think myself in circles.

Math is cool and beautiful and fun whether or not it has anything to do with reality. Just like Tetris. or Chess, etc.

Sure, the widespread knowledge of mathematics wouldn't be a thing if not for mathematics being neatly present in nearly all profitable endeavors (or how would you even know if it was profitable? U C wat I did, huh?). However, it would still be a thing. 'Cause it's super fun to try to poke holes in it only to discover it had you on a scavenger hunt all along. It's super fun to find an actual hole to poke in it, only to realize that it's only a hole because of this one assumption, and when that assumption is lost, this whole other world opens up.

Math is inviting, stimulating and rewarding. Even if the profitability was removed, people would still play this game.

Given this, do you think it is the case that mathematics models reality to a degree and thus it is appropriate to think of mathematics as a real thing -- even if abstract or metaphysical -- regarding reality?

[Poopadoop]

Given this, do you think it is the case that mathematics models reality to a degree and thus it is appropriate to think of mathematics as a real thing -- even if abstract or metaphysical -- regarding reality?

What do you mean by 'models reality'? The maths doesn't model anything. It's the people applying it that are doing the modeling.

(There is a related philosophical question about whether scientific models are meant to approximate the truth or capture it, but don't think that's what you meant.)

[wufwugy]

What do you mean by 'models reality'? The maths doesn't model anything. It's the people applying it that are doing the modeling.

(There is a related philosophical question about whether scientific models are meant to approximate the truth or capture it, but don't think that's what you meant.)

I mean something along these lines: the equation 2 + 2 = 4 is a mathematical framework that models reality, like, say, when we have 2 and 2 apples. Regardless, the terminology I chose might not be appropriate. Perhaps what I mean to say is that mathematics provides a framework with which reality can be coherently described.

[Poopadoop]

I mean something along these lines: the equation 2 + 2 = 4 is a mathematical framework that models reality, like, say, when we have 2 and 2 apples. Regardless, the terminology I chose might not be appropriate.

Ah, gotcha.

But I still wouldn't say it 'models reality' because the word 'model' suggests some kind of abstract representation that doesn't necessarily capture the full truth (to me at least). In that sense math doesn't 'model' reality it just 'is' reality.

Perhaps what I mean to say is that mathematics provides a framework with which reality can be coherently described.

I think it's us who provide the framework and maths is the tool we use to do so, but this may just be a rephrasing of what you said.

[MadMojoMonkey]

Given this, do you think it is the case that mathematics models reality to a degree and thus it is appropriate to think of mathematics as a real thing -- even if abstract or metaphysical -- regarding reality?

Argh. "to a degree..." Sure... to a degree. What have we communicated to each other, here?

Some math is used to describe reality, but much more math is sets of logically consistent statements. Goedel's Incompleteness Theorems suggest there will always be true statements within any robust logical framework which are not supported by any finite set of axioms within the framework. Assuming reality is of finite complexity, then math will always have true statements to make which are beyond any axioms which are related to reality.

I can prevaricate enough to say that, ultimately countability is the fundamental requirement for math (the math I am familiar with, at least). I can accept that reality has to provide something to be counted as a seed of this proof that math exists. It's the root of my (albeit silly) "math between the universes" argument. I like saying math between the universes.

Ultimately, though, I'd say that math's relationship with reality ends there. Furthermore, the actual existence of countable somethings isn't entirely relevant, it's just a comfortable proof. Math already starts with the axiom, suppose stuffs can be ordered into an arrangement, and the ordering is deterministic, then we can name the elements of the ordering and talk about them. Lets call the first ordering position, "1," and the next, "2," ... Whatever. It's all symbols for the abstraction of this concept of multiple identifiable somethings.

A number isn't real, or in any way tied to reality. A number is a symbol for the concept of a position in an ordered arrangement. We happen to find all sorts of ways to describe reality with numbers, but often we do so with moderate to passing ignorance and the numbers we say are the model are later shown to be not the right numbers. *sigh* The model is made by humans. We are playing a game with incomplete information, and we update our models whenever new information is brought to light.

[Poopadoop]

"Discovered" makes more sense to me than "invented." Like, if we hadn't come along and starting counting on our fingers and toes, there would be no maths? Meh. There might not be maths textbooks, but there would still be maths.

An epiphany doesn't imply an invention. By definition, an epiphany means you just realised (discovered) something.

Somewhere out there are a bunch of equations that no-one has discovered yet, but which are invariably true. Even something like 13478342470 + 234890584325 might never have been calculated, but I would hardly say if I solved it, that would make me an "inventor" of maths.

p.s. The exception to the rule would be Ong, who does invent his own maths.

[a500lbgorilla]

"Discovered" makes more sense to me than "invented." Like, if we hadn't come along and starting counting on our fingers and toes, there would be no maths? Meh. There might not be maths textbooks, but there would still be maths.

An epiphany doesn't imply an invention. By definition, an epiphany means you just realised (discovered) something.

Somewhere out there are a bunch of equations that no-one has discovered yet, but which are invariably true. Even something like 13478342470 + 234890584325 might never have been calculated, but I would hardly say if I solved it, that would make me an "inventor" of maths.

p.s. The exception to the rule would be Ong, who does invent his own maths.

It's like you want to discount humans for inventing things and recognize humans for discovering things. People are doing it, why pick at these nits?

[Poopadoop]

It's like you want to discount humans for inventing things and recognize humans for discovering things.

Well no, it's not like that. All I said was if something already exists you can't really invent it, you can only discover it. As far as giving people credit for one versus the other, there's no value judgment implied in what I said; you're reading things into my words that aren't intended.

If I had said something along the lines of "Newton didn't accomplish much because all he did was discover gravity, not invent it." then you would have a point.

People are doing it, why pick at these nits?

The question was raised regarding whether maths are invented or discovered, and I offered an answer. If you prefer to believe people invent maths, then by all means feel free.

[a500lbgorilla]

Well no, it's not like that. All I said was if something already exists you can't really invent it, you can only discover it. As far as giving people credit for one versus the other, there's no value judgment implied in what I said; you're reading things into my words that aren't intended.

If I had said something along the lines of "Newton didn't accomplish much because all he did was discover gravity, not invent it." then you would have a point.




The question was raised regarding whether maths are invented or discovered, and I offered an answer. If you prefer to believe people invent maths, then by all means feel free.

Maths doesn't exist without someone to codify it. And once someone lays down the rules to describe math, they begin to explore where those rules take them.

edit: remember, there are entirely useless maths.

[a500lbgorilla]

I think we can all agree that's definitely wrong.

Hahaha