Is math

[patches70]

Are mathematics something human beings discovered or are mathematics something human beings invented?

Some really smart people throughout history have argued on the side of one or the other without any real consensus. Where do you stand and why do you have that opinion, whether invented or discovered?

If maths are invented then maybe we can find someone to actually blame for getting horrible dice rolls. If maths is just discovered then I guess it's God's fault we lose a 10to1 fight and stare in incredulous horror as we watch our army dwindle like a sand castle against the incoming tide versus a single unit holding that last territory needed to get that bonus.


What do you think?

[tzor]

First of all mathematics was neither invented or discovered. The laws of mathematics, on the other hand ... were both invented and discovered.

Obviously things like addition were discovered.
The "Fast Fourier Transformation" was invented.
If you want I can explain the dice to you.

show

[Metsfanmax]

First of all mathematics was neither invented or discovered. The laws of mathematics, on the other hand ... were both invented and discovered.

And... as usual, tzor wins the award for most pedantic and least informational post of the month.

[patches70]

I'm just kidding about the dice, it doesn't bother me. RNG's are just like that. It was a serious question though about the maths. Early philosophers argued that math was discovered. Hell, Plato and his contemporaries thought numbers were physical things. The number "1" was known as the "monad" by the Pythagoreans and was the generator of all other numbers and source of all creation. Plato argued that numbers were real things, as real as the universe. Euclid believed nature was the physical manifestation of numbers.

Then there are mathematical concepts that almost certainly don't exist physically since they're truth values are based on rules that humans created. In that light mathematics are a logic exercise and invented by people.

The number zero seems very much an invention. The ancient Greeks who were pretty good at math didn't even consider "0" a number. Most of the time of the Roman Empire they never used zero and never in the entire span of the Roman empire did they even have a symbol for zero. Imagine trying to do maths without using zeros at all now a days. Oh it can be done, but I have to say the number zero is one hell of a jump when it was invented. IMO
The zero as we know it was invented until around the 7th century.

In more modern times it was argued that maths is an invention and do not exist outside man's conscious thought. Math is a language based on patterns the human mind discerns from nature to create a useful but artificial order from chaos. It was said once- "God created the natural numbers, all else was done by man".

Euclidean geometry was said to be proven by some to not be a universal truth by non euclidean geometry. Non euclidean geometry merely showed that euclidean geometry is only one outcome of using one set of particular rules. Thus moving the argument that mathematics is an invention of mankind.

Then there is the cases of mathematics that when developed were nothing more than theories that did not describe any known physical phenomenon but then decades and even centuries later was discovered that those theories ended up describing how the universe was working all along, long before we even had an inkling of such phenomenons a la "the unreasonable effectiveness of mathematics"-
https://en.wikipedia.org/wiki/Unreasona ... athematics
(maybe that should be posted in the "wiki article of the day" thread...).
This pushes the argument back toward the idea that mathematics are discovered rather than invented.


It's quite confusing and I have no idea where I actually stand on the question. I wonder if it really matters either way? A lot of the most influential mathematicians in all of human history have chimed in with their own thoughts on this question.
I am wondering what some of you think about it.
Is mathematics-
an invention or a discovery?
an artificial construct or universal truth?
a human product or natural, possibly divine, creation?

I guess if anyone could actually answer definitively they'd probably get a noble prize for maths at the very least....

[Symmetry]

I think the question is wrong. It's more like a language. A way of communicating ideas that is neither wholely natural nor wholely artificial.

[Metsfanmax]

Can we have another global warming thread maybe? Or evolution? I love seeing people talk about subjects for which their knowledge doesn't extend past grade school.

[Dukasaur]

Can we have another global warming thread maybe? Or evolution? I love seeing people talk about subjects for which their knowledge doesn't extend past grade school.

Somebody stole your favourite slide-rule this morning? I've never seen you quite so deliberately combative about nothing.

In any case, unless the school system has improved dramatically since I was an inmate, they didn't teach the epistemology of mathematics in grade school.

[patches70]

You don't have to be a dick. I never said I had any great knowledge of the subject. Apparently you have knowledge of the subject that extends past grade school.

So-

Are mathematics a human invention or something that humans just discovered?

It's ok for you to say you don't know, mets, I certainly don't know which is why I asked. Hell, even sym just answered the question to the best of his ability. And it seems a fine answer to me and I don't like sym very much, I'm certainly not going to give him shit about his answer or his thoughts.

You on the other hand are just being a dick for no reason. Why?

[Metsfanmax]

I'm not being a dick, I'm serious, I love these threads. Please, give me more.

[Symmetry]

I'm not being a dick, I'm serious, I love these threads. Please, give me more.

And you like to feel superior, and make other people know you're superior, without actually saying why you think they're wrong.

That'd be being a dick, Mets. You're being a dick.

[patches70]

My sarcasm detection software appears to not be functioning correctly. Your post seems sarcastic. It's odd since you gave tzor shit about-

And... as usual, tzor wins the award for most pedantic and least informational post of the month.

when by my estimation your posts thus far in this thread are at the very least equal and most likely greater than tzor's in the least informative department.
Since you appear to be a scientist or at least like playing the part of one on the interwebz, what are your thoughts on the question, if you would so indulge?

Full disclosure: This isn't a trap thread or any such nonsense.

[Symmetry]

I'd actually like to hear Mets' real take on this too. I think a few posters and at least one mod have noticed that his posts in this thread have been a bit out of character.

Patches- think it might be a bit of a bigger question than you realise though. Mathematics and Philosophy have an uneasy relationship. It might be that Mets finds the question uncomfortable. Logic is a basic part of both, and there's some bleed between the disciplines.

[patches70]

And you like to feel superior, and make other people know you're superior, without actually saying why you think they're wrong.
.

I'm not sure why I'd be wrong about anything because I clearly stated I don't know. Surely I can't be wrong about not knowing can I?

I can see the merit in your answer sym likening it to language. As far as I'm aware we have no real idea how language came about either.

[patches70]

Patches- think it might be a bit of a bigger question than you realise though. Mathematics and Philosophy have an uneasy relationship. It might be that Mets finds the question uncomfortable. Logic is a basic part of both, and there's some bleed between the disciplines.

Oh I know it's a big question. Hell, smarter people than anyone who uses this forum have argued this very question for thousands of years.

It always seemed to me that mathematics was an invention but now a days I'm not so sure. Like Duk was saying, as math is presented to us as we learn it seems like it was all invented with new mathematicians building on the prior work of those before them. But in honesty I just don't know at all. It's just interesting to me is all and I just felt like asking.

[Metsfanmax]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

[Metsfanmax]

My sarcasm detection software appears to not be functioning correctly. Your post seems sarcastic. It's odd since you gave tzor shit about-

And... as usual, tzor wins the award for most pedantic and least informational post of the month.

when by my estimation your posts thus far in this thread are at the very least equal and most likely greater than tzor's in the least informative department.

tzor's different, he has an engineering degree and should know better, which is why I never fail to criticize him when he says something silly.

[Symmetry]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

I agree on the false dichotomy. Language was my best analogue. I initially thought that maybe it's best to think of it as a tool, but language seems a better fit. It is both a describing thing and the thing that it describes.

How do you think about it, or do you prefer to avoid the more philosophical side? No meant as an insult if you do.

[Dukasaur]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

"Deep" or not is a value judgement, and it's not worth wading into that morass. The question is, however, "interesting" which is a term burdened with much less baggage.

There are certainly mathematical concepts that may have no real meaning. Infinity, for instance. It is well and good for us to postulate a universe of infinite size, or an infinite number of universes, but in fact there may be real constraints to either, and it may be that there is nothing whatsoever that is infinite, and that infinity is a truly imaginary thing that simply does not exist anywhere.

[Metsfanmax]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

I agree on the false dichotomy. Language was my best analogue. I initially thought that maybe it's best to think of it as a tool, but language seems a better fit. It is both a describing thing and the thing that it describes.

Yeah but that's not really a perfect analogy to the question at hand because the confusion about mathematics is whether it is inherent to the way the universe works, whereas language is a human-created construct used primarily to describe the universe. There is an analogue in the Platonic/ancient Greek view that language actually does describe things intrinsically and that there are 'correct' words for certain objects. In this view language is discovered, not invented. But I'm pretty sure this view should be rejected because the existence of multiple languages severely casts into doubt the idea that there are 'natural' names for things waiting to be discovered by humans. To the extent that humans naturally gravitate toward certain ways of describing things, it's a product of human behavior and evolution, not a property of the universe itself.

How do you think about it, or do you prefer to avoid the more philosophical side? No meant as an insult if you do.

I'm not smart enough to try and answer these philosophical questions. I'm of the "shut up and calculate" school. Much more fun to do math than to philosophize about it.

[Symmetry]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

"Deep" or not is a value judgement, and it's not worth wading into that morass. The question is, however, "interesting" which is a term burdened with much less baggage.

There are certainly mathematical concepts that may have no real meaning. Infinity, for instance. It is well and good for us to postulate a universe of infinite size, or an infinite number of universes, but in fact there may be real constraints to either, and it may be that there is nothing whatsoever that is infinite, and that infinity is a truly imaginary thing that simply does not exist anywhere.

Do you think that there are a finite number of numbers? Think of the biggest number you can. Now add 1. There are an infinite number of numbers.

Don't bother posting your number. You should have figured out that you're wrong by this point.

[Dukasaur]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

"Deep" or not is a value judgement, and it's not worth wading into that morass. The question is, however, "interesting" which is a term burdened with much less baggage.

There are certainly mathematical concepts that may have no real meaning. Infinity, for instance. It is well and good for us to postulate a universe of infinite size, or an infinite number of universes, but in fact there may be real constraints to either, and it may be that there is nothing whatsoever that is infinite, and that infinity is a truly imaginary thing that simply does not exist anywhere.

Do you think that there are a finite number of numbers? Think of the biggest number you can. Now add 1. There are an infinite number of numbers.

Don't bother posting your number. You should have figured out that you're wrong by this point.

Really? A number is a concept, and you have to somehow either store or express that concept. We can hypothetically say there is an infintely large number, but if you can't write it down, or type it into a computer, or speak it out loud, or store it in your own memory, then does it really exist?

Yes, we can hypothesize an infinitely large number, but if we can neither demonstrate it nor store it nor express it, is it real?

[Symmetry]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

I agree on the false dichotomy. Language was my best analogue. I initially thought that maybe it's best to think of it as a tool, but language seems a better fit. It is both a describing thing and the thing that it describes.

Yeah but that's not really a perfect analogy to the question at hand because the confusion about mathematics is whether it is inherent to the way the universe works, whereas language is a human-created construct used primarily to describe the universe. There is an analogue in the Platonic/ancient Greek view that language actually does describe things intrinsically and that there are 'correct' words for certain objects. In this view language is discovered, not invented. But I'm pretty sure this view should be rejected because the existence of multiple languages severely casts into doubt the idea that there are 'natural' names for things waiting to be discovered by humans. To the extent that humans naturally gravitate toward certain ways of describing things, it's a product of human behavior and evolution, not a property of the universe itself.

How do you think about it, or do you prefer to avoid the more philosophical side? No meant as an insult if you do.

I'm not smart enough to try and answer these philosophical questions. I'm of the "shut up and calculate" school. Much more fun to do math than to philosophize about it.

No analogy is perfect- I thought it was a better way of thinking about it though. Animals have language, so it's not as if we can quite say, as we did in the past, that only humans communicate with each other and show conscious intelligence.

If other species naturally have languages, is language really totally a human-created construct?

[Symmetry]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

"Deep" or not is a value judgement, and it's not worth wading into that morass. The question is, however, "interesting" which is a term burdened with much less baggage.

There are certainly mathematical concepts that may have no real meaning. Infinity, for instance. It is well and good for us to postulate a universe of infinite size, or an infinite number of universes, but in fact there may be real constraints to either, and it may be that there is nothing whatsoever that is infinite, and that infinity is a truly imaginary thing that simply does not exist anywhere.

Do you think that there are a finite number of numbers? Think of the biggest number you can. Now add 1. There are an infinite number of numbers.

Don't bother posting your number. You should have figured out that you're wrong by this point.

Really? A number is a concept, and you have to somehow either store or express that concept. We can hypothetically say there is an infintely large number, but if you can't write it down, or type it into a computer, or speak it out loud, or store it in your own memory, then does it really exist?

Yes, we can hypothesize an infinitely large number, but if we can neither demonstrate it nor store it nor express it, is it real?

No, you can't hypothesise an infinitely large number. Whatever that number would be, there would be an infinitely large number of numbers larger.

You're not really getting this as a concept, are you?

Shall we try something a bit less theoretical?

Pi is a pretty key constant- practical too. It's a small number. Do you think that Pi is finitely repeatable in its decimal places?

Hopefully you've realised that you're wrong by this point, at least.

Infinite doesn't mean "big", mate. It means something more akin to "limitless".

[Dukasaur]

I'd actually like to hear Mets' real take on this too.

My real take on this question is that the question is meaningless, that it is a false dichotomy: mathematics need not be considered to have been either invented or discovered in the way patches is presenting. It's a question that sounds deep but really isn't.

"Deep" or not is a value judgement, and it's not worth wading into that morass. The question is, however, "interesting" which is a term burdened with much less baggage.

There are certainly mathematical concepts that may have no real meaning. Infinity, for instance. It is well and good for us to postulate a universe of infinite size, or an infinite number of universes, but in fact there may be real constraints to either, and it may be that there is nothing whatsoever that is infinite, and that infinity is a truly imaginary thing that simply does not exist anywhere.

Do you think that there are a finite number of numbers? Think of the biggest number you can. Now add 1. There are an infinite number of numbers.

Don't bother posting your number. You should have figured out that you're wrong by this point.

Really? A number is a concept, and you have to somehow either store or express that concept. We can hypothetically say there is an infintely large number, but if you can't write it down, or type it into a computer, or speak it out loud, or store it in your own memory, then does it really exist?

Yes, we can hypothesize an infinitely large number, but if we can neither demonstrate it nor store it nor express it, is it real?

No, you can't hypothesise an infinitely large number. Whatever that number would be, there would be an infinitely large number of numbers larger.

You're not really getting this as a concept, are you?

Shall we try something a bit less theoretical?

Pi is a pretty key constant- practical too. It's a small number. Do you think that Pi is finitely repeatable in its decimal places?

Hopefully you've realised that you're wrong by this point, at least.

Infinite doesn't mean "big", mate. It means something more akin to "limitless".

Yeah, I think I know what it mean. I was accustomed to getting 98s in Calculus, back in the day.

My point is that there may be limits to everything. Just because you can say "limitless" doesn't mean that any actual thing is limitless.

We used to think that you could keep subdividing things smaller and smaller until they were infinitely small. Then along came quantum physics and proved that there are finite limits to how small something can be, that "infinitely small" is a purely imaginary idea. I'm suggesting that there may be finite limits to how large something can be, that "infinitely large" is also an imaginary idea.

[tzor]

First of all mathematics was neither invented or discovered. The laws of mathematics, on the other hand ... were both invented and discovered.

And... as usual, tzor wins the award for most pedantic and least informational post of the month.

Thank you. Few people realize the amount of hours I spend in order to get this award. It's not easy to be pedantic. It requires a lot of hard work and study. In fact few people probably know what pendant means. No one ever uses it in a sentence. How sad.