Would you say math was discovered or invented?

[Icebreaker]

Would you say it's discovered or invented?

 

[Kerrie]

To say that Mathematics is discovered has the presumption that any form of intelligent life in our universe has the ability to understand Math also. To say that Math is invented is doubting the existence of the reality we are a part of, which can be a disruptive thought to many. I lean towards the idea we invented the language of math once we discovered how it works.

 

[cragwolf]

To say that Mathematics is discovered has the presumption that any form of intelligent life in our universe has the ability to understand Math also.

It presumes no such thing. Perhaps not all forms of intelligent beings are able to comprehend mathematics. Some intelligent beings might find it easy, some might find it hard (I think we fit in this category), and some might find it incomprehensible. Who knows?

To say that Math is invented is doubting the existence of the reality we are a part of, which can be a disruptive thought to many.

Again, I don't see this as being necessarily so. There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws. Again, who knows?

 

[etc]

a similar question may be, "would you say language is discovered or invented?"
so my answer is this: math is a means to describe physical reality much like language is a means to describe our thoughts, while physical reality and our thoughts exist independently of the way they are desribed. therefore, both math and language were invented to describe concepts already discovered.

this post took me way too long. time to hit the sack.

 

[Icebreaker]

Physics is the means to describe reality. You don't really need math in physics to actually describe it -- you can do it in english. It just happens that using math in physics is a lot more practical. Math wasn't invented/discovered with the sole purpose of describing reality.

Saying that math is "discovered", assumes that an answer exists whether we know it or not, and it is only a matter of time before we find it. Saying otherwise means that an answer may not exist... but what it means, I can't really interpret.

 

[Kerrie]

It presumes no such thing. Perhaps not all forms of intelligent beings are able to comprehend mathematics. Some intelligent beings might find it easy, some might find it hard (I think we fit in this category), and some might find it incomprehensible. Who knows?



Again, I don't see this as being necessarily so. There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws. Again, who knows?

So, you have lent your constructive criticism on my answer, now where is yours? Is math invented or discovered, and why do you think so?

 

[Eratosthenes]

Mathematics is an idea.

 

[arildno]

I would say that we may discover consequences from axioms , but that to a quite large extent, we invent those axioms along with those objects we choose to study through math.

 

[etc]

Physics is the means to describe reality. You don't really need math in physics to actually describe it -- you can do it in english. It just happens that using math in physics is a lot more practical. Math wasn't invented/discovered with the sole purpose of describing reality.

Saying that math is "discovered", assumes that an answer exists whether we know it or not, and it is only a matter of time before we find it. Saying otherwise means that an answer may not exist... but what it means, I can't really interpret.

i think math was "invented" because it's more practical than language ...

edit: we know an answer exist by the very definition of a problem. whether you find it's logical or not .. well, that's subjective.
honestly, i don't understand why you equate the discovery of math with a logical universe.

 

[saltydog]

Math is invented

We create Mathematics as a metaphor for our perceptions (discovery). In our absence there is no Mathematics. The Earth revolved around the sun before we got here but the math describing it wasn't.

SD

 

[Icebreaker]

honestly, i don't understand why you equate the discovery of math with a logical universe.

I did? Where?

 

[etc]

Saying that math is "discovered", assumes that an answer exists whether we know it or not, and it is only a matter of time before we find it.

i can only assume that by "answer" you meant something logical ( because math is ruled by logical principals ).
yes, no, maybe?

 

[NeutronStar]

Mathematics. Would you say it's discovered or invented?

I'm currently writing on a book I call, Mathematics as a Concrete Abstraction that addresses this very issue. Which mathematical concepts have been discovered and which have merely been invented.

I am completely convinced that the following conditional statement is true.

IF mathematical formalism is supposed to correctly represent the quantitative nature of our universe, THEN our current modern mathematical formalism is incorrect.

Obviously is isn't incorrect even every detail. Fortunately most of mathematics is on solid ground. In fact the bulk of mathematics from the early Greeks up until about 1850 is salvageable. This even includes the calculus which was introduced around 1700.

However, around 1850 (or shortly thereafter) the mathematical community has made a terrible wrong turn away from the ontological discovery of the relationships and behavior of quantity, and toward an arbitrary subjective invention.

Please note that I'm not saying that arbitrary symbolic logical axiomatic systems are not worthy of study. I simply object to lumping them under the umbrella of mathematics. It only serves to distort the original purpose of mathematics.

Unfortunately I believe that you will find that the vast majority of modern mathematicians are all for continuing on this path. Most of them are not the least bit concerned whether mathematics correctly reflects any quantitative ontological behavior that the universe might exhibit. In fact, most of them will argue that it isn't even the purpose of mathematics to address or be concerned with such issues.

I totally disagree of course. I believe that there is a lot to gain from understanding just which parts of mathematics were discovered from ontological truths, and which parts were arbitrarily invented by whimsical logicians. I have found that it is possible to separate these different types of ideas, and by separating them there is wisdom to be gained.

 

[cragwolf]

So, you have lent your constructive criticism on my answer, now where is yours?

Yes, but don't take it personally.

Is math invented or discovered, and why do you think so?

My answer is: I don't know.

 

[Kerrie]

My answer is: I don't know.

Well, you must know something if you are in a position to critisize! That's a pet peeve of mine-able to tear up one's argument but have none of your own.

It presumes no such thing. Perhaps not all forms of intelligent beings are able to comprehend mathematics.

Perhaps there are other forms of intelligent beings who comprehend math beyond what we do. When I said if math was discovered, we automatically assume that it is "real" and thus other forms of life would be able to discover it too. Being disovered means our mathematical formulas aren't just "made" by humans, but exist for any form of intelligent life to discover as well.

There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws.

Note I did say the reality "we are a part of". If you and I agree that 2 + 2 = 4, then I can safely say that we are of the same reality.

I lean towards the idea we invented the language of math once we discovered how it works.

So crag, what is your criticism of this idea? And why?

 

[Les Sleeth]

There is no proof that reality is constructed along mathematical lines. There is only data perceived and interpreted by humans that suggests reality may follow mathematical laws. Again, who knows?

What are you talking about? No proof? What kind of proof do you need before you accept that major aspects of physical reality, at least, can be mapped by math? That is either an incredibly ignorant statement or you are just being contrary.

 

[Les Sleeth]

Imagine a universe where there is nothing but absolute chaos. Will math work? Even if you say probabilities can be formulated, if the chaos is absolute, probability is shot to hell.

Math is a language that corresponds to the order that exists in our universe. The more order there is in a situation, the better math works; the less order there is, the more one has to fall back on probabilities.

We invented the math, but we could only because we discovered that order is solidly part of our universe.

 

[selfAdjoint]

Math is a language that corresponds to the order that exists in our universe. The more order there is in a situation, the better math works; the less order there is, the more one has to fall back on probabilities.

True in general, but the amount of order required for math to get a grip is constantly being reduced - and probability is no longer the only recourse. Consider complex systems and deterministic chaos, two fields that have grown up in my lifetime, to handle stuff that would have been a mytery to the greatest when I was a kid. Or consider consider the evolution of thermodynamics from Clausius (linear closed systems at equilibrium) to Onsager (linear open systems near equilibrium) to the present (nonlinear open systems far from equilibrium).

 

[Les Sleeth]

True in general . . .

Well, I'm nothing if not a generalist.

. . . the amount of order required for math to get a grip is constantly being reduced

But would you still agree: no order, no math.

 

[cragwolf]

What are you talking about? No proof? What kind of proof do you need before you accept that major aspects of physical reality, at least, can be mapped by math? That is either an incredibly ignorant statement or you are just being contrary.

You do know the difference between proof and supporting evidence?

 

[Les Sleeth]

You do know the difference between proof and supporting evidence?

Absolutely, it is one of my favorite subjects. I think, however, you've chosen the wrong subject to be skeptical about. Order in this universe is likely more confirmed than any other single property.

 

[Microburst]

Would you say it's discovered or invented?

X-RAy was discovered!
mathematics was definitely invented, don't forget the imaginary numbers..
square root of -1 i

 

[vinter]

Is Math a language?

The fact that we write 33 as 33 and not as "-, is due to maths as a language. But the fact that 33 + 33 = 66 is a law of the universe.



Basically, I'm getting confused.

 

[Microburst]

Yeah I guess you can call it grammar of size, shape, and order…

 

[NeutronStar]

X-RAy was discovered!
mathematics was definitely invented, don't forget the imaginary numbers..
square root of -1 i

The whole idea of negative absolute numbers is an invention. In reality (that is to say that ontologically speaking) the universe never displays an absolute negative quantitative property. Negativity is actually a relative property between quantities. So on this point alone modern mathematics is grossly ontologically incorrect.

Number is suppose to be the idea of a cardinal property of a set or collection of things. So how can we imagine a set that contains less than no objects? We can't. The idea of negativity is actually a concept that has to do with relationships between sets. So the idea that there can be an "absolute" number -1 us absurd. All that can exist is the number 1 that has a property of being negatively relative to some other quantity. How the mathematical community as a whole let that one get by is completely beyond me.

Imaginary numbers are actually the same type of thing. They represent ontological ideas of quantity, but the sign of the number is its imaginary attribute (just like the sign of a negative number is its attribute of negativity). It actually refers to a relative situation.

If you give me 3 bucks, it looks negative to you, but it looks positive to me. Yet the actual quantity is always 3. The negativity doesn't belong to the concept of number. It's a relative property between sets, not an absolute property of sets. Yet, mathematical formalism has axioms that permit absolute negative sets to exist. It's clearly ontologically incorrect.

The idea of absolutle negative numbers is definitely an invention of humans. It's not a necessary concept for mathematics to work. Clearly a mathematical formalism can be constructed that treats relative properties between quantities ontologically correctly. There's really no need to be inventing these absolute concepts of quantities that have no counterpart in the real world.

This is one very good illustration why mathematics is not a science!

Yes, current mathematical formalism most certainly is an invention. But it doesn't need to be that way. It could have been constructed as a sound science based solely on the scientific method by simply observing the ontological behavior of the quantitative nature of our universe and describing it correctly.

Unfortunately we didn't take that route so modern mathematics turned out to become a mere whimsical invention that may or may not reflect the true nature of the universe. Most mathematicians don't seem to be very concerned about whether its ontologically correct anyway. They're having too much fun satisfying arbitrary axioms.

 

[Hurkyl]

In reality (that is to say that ontologically speaking) the universe never displays an absolute negative quantitative property.

At least you've not ranting about zero this time. I'd respond in full, but I don't want to hijack the topic. You might want to check out some of the history of the cubic and quartic formulas, though, which forced the mainstream acceptance of negative and complex numbers.

 

[cragwolf]

Absolutely, it is one of my favorite subjects. I think, however, you've chosen the wrong subject to be skeptical about. Order in this universe is likely more confirmed than any other single property.

Order != mathematics.

 

[MathematicalPhysicist]

Is Math a language?

The fact that we write 33 as 33 and not as "-, is due to maths as a language. But the fact that 33 + 33 = 66 is a law of the universe.



Basically, I'm getting confused.

yes maths is a language and the fact that some use it as a tool in other empiricial disciplines doesn't change the fact it's a language.

now those pure mathematicians and metamathematicians are those who actually expand the vocabulary in maths on general and practical maths with physics,biology and so on are those who are using maths to describe nature.

it seems to be a big problem (especially from americans who want everything to be practical) nowadays that people only categorize maths as describing nature solely.

 

[NeutronStar]

At least you've not ranting about zero this time. I'd respond in full, but I don't want to hijack the topic. You might want to check out some of the history of the cubic and quartic formulas, though, which forced the mainstream acceptance of negative and complex numbers.

I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set.

So in this sense modern mathematical formalism simply has it incorrect. They idea that sets (or numbers) can have an absolute property of negatively is simply an axiomatic invention. This concept has not been "discovered" it has been incorrectly "invented" out of thin air.

If I give you 3 apples that represents -3 apples to me, but to you it's +3 apples. Do you see my point? The very same apples are both negative and positive at the same time depending on the point of view. The number 3 is absolute, but the property of negativity is not. So why did the mathematical community decide to invent the idea that -3's can somehow be said to exist as absolute mathematical numbers? It's simply ontologically['i] incorrect with respect to the observed behavior of the quantitative properties of the universe. (i.e. It's wrong!)

The same thing goes for imaginary numbers, but that's a little more complex (if you'll forgive the pun) so I won't bother confusing things by speaking to it.

I fully understand and use negative numbers, imaginary numbers, and even zero. But mathematical formalism has all of these concepts incorrectly defined with respect to the ontology of the universe.

I refer back to my previous conditional statement which I firmly believe,…

IF mathematical formalism is supposed to correctly represent the ontological quantitative nature of our universe, THEN our current modern mathematical formalism is ontologically incorrect.

That doesn't necessarily meant that mathematics is logically flawed within it's own system of axioms (which I happen to also believe is true none-the-less), but it simply means that mathematics does not correctly represent the ontological quantitative nature of our universe.

That also doesn't meant that I can't used negative numbers, or imaginary numbers, or zero. It simply means that I can recognize the real meaning of these concepts (where I'm using real here to simply mean ontologically correct) in spite of their incorrect arbitrarily invented mathematical definitions.

Zero, for example, is not a number or quantity. It's the absence of a number or quantity. There is a difference! And it's actually quite significant. Especially when considering other more advanced concepts such as transfinite numbers, irrational numbers, and even the number of points that can exist in a finite line segment. How you view these higher-level concepts, and therefore what conclusions you draw from them, is dependent on how you view the notion of zero.

Mathematics has zero incorrectly defined. Where I'm using "incorrect" here to mean "ontologically incorrect".

 

[Les Sleeth]

I fully accept the notion of negative numbers and imaginary numbers. I use them all the time. I just recognize that they aren't absolute or distinct ideas of quantity. They are always relative relationships between quantities. Yet the mathematical community has defined them as absolute or "stand-alone' concept. Like it's perfectly acceptable to talk about an absolute negative number. Like as if that concept has merit without any relation to anything else. That is simply incorrect. By that I mean it is ontologically incorrect. No quantity in the universe can have an absolute property of negativity. It just doesn't make any sense. It's a relative property between sets, it's not an absolute property of a set. . . . Zero, for example, is not a number or quantity. . . Mathematics has zero incorrectly defined. Where I'm using "incorrect" here to mean "ontologically incorrect".

Interesting observations, but I would be surprised if those relying on math to do science don't understand your points. I can see how such views might develop if one only works with numbers, and never has to verify predictions.

 

[NeutronStar]

I can see how such views might develop if one only works with numbers, and never has to verify predictions.

I too fully understand where the pure mathematicians are coming from. However, I also firmly believe that pure mathematics could be both, logically abstract, and ontologically correct. So I don't understand why mathematicians don't strive to make it both logically abstract, and ontologically correct.

Well, actually, I do understand why the mathematical community historically went down this path. I just disagree with the direction that they have chosen to take. What I don't understand is why the scientific community isn't in an uproar about it.

Who is at the helm of the mathematical community? Any why have they chosen to completely ignore the original historical foundation of mathematics? (i.e. The observed ontological quantitative properties exhibited by the universe?)

To answer my own question, I believe it was their thirst for some idealized logical purity that is disconnected from physical reality. Personally I think that notion is absurd. The quantitative properties of our universe exist because the physical universe exists. Any attempt to try sweep that under the carpet is nothing short of silliness.

It's just plain silly. It really is!

More importantly, as we continue down this path we will get further and further away from ontological truths. All aliens will recognize numbers like π and e because these quantitative relationships arise from ontological situations.

But will all aliens agree with the axiom of the existence of an empty set? No. Why not? Because that's strictly a human invention that is actually quite ontologically incorrect. Aliens would laugh at such a notion as being a display of our ignorance. The aliens will, however, understand the concept of a set itself, because that is ontological. They will just have to explain to us that we don't fully understand the concept of sets, and then show us why it is ontologically incorrect to claim that an empty set can exist.

I'm not even an alien and I know that much!

In fact, whenever we ask whether we are inventing a concept, or discovering it, I think it is a good test to think in terms of extraterrestrials. Would they come to the same conclusions? If so then it must be a discovery. Or might they think up something else? If so, then we must be inventing an arbitrary concept.

 

[Hurkyl]

My response here.

 

[Icebreaker]

If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than ours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.

 

[selfAdjoint]

If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than hours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.

Not so, just because the medieval Europeans didn't know about the New World didn't mean it wasn't there, nor that the geography they did no was wrong. Just because mathematicians have only discussed certain systems and there are other systems yet unkown to us doesn't invalidate the systems we know. Mathematicians are continually dealing with aliens who discover different systems and new perspectives on old ones. It's called the younger generation.

 

[Icebreaker]

Exactly, it is not invented because one of the two must be "wrong", and therefore there must be a true and universal answer.