Is math invented or discovered?
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20-10-2016, 10:54 AM
Is math invented or discovered?
Hello, people.

I believe fairly strongly that math is discovered, while our understanding and methods of what we do discover are of our own invention. One simple, classic example is the Fibonacci sequence appearing in nature. I go a step further and say that the universe is basically mathematical. Others might say it has order, structure, but isn't mathematical because it has physical properties, or that calling it mathematical would mistake the map for the territory, but I think the "essence" of mathematics is something pure that defines the essence of reality. Furthermore, I think the "physical reality" is something of an illusion, so there is no distinction between map and territory.

What do you think? Is math invented or discovered? What is math anyways? Does it exist? Is it physical or abstract? What is the distinction between physical and mathematical? I'd like to hear whatever thoughts you have.
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20-10-2016, 11:02 AM (This post was last modified: 20-10-2016 11:19 AM by Gloucester.)
RE: Is math invented or discovered?
(20-10-2016 10:54 AM)unknowndevil666 Wrote:  Hello, people.

I believe fairly strongly that math is discovered, while our understanding and methods of what we do discover are of our own invention. One simple, classic example is the Fibonacci sequence appearing in nature. I go a step further and say that the universe is basically mathematical. Others might say it has order, structure, but isn't mathematical because it has physical properties, or that calling it mathematical would mistake the map for the territory, but I think the "essence" of mathematics is something pure that defines the essence of reality. Furthermore, I think the "physical reality" is something of an illusion, so there is no distinction between map and territory.

What do you think? Is math invented or discovered? What is math anyways? Does it exist? Is it physical or abstract? What is the distinction between physical and mathematical? I'd like to hear whatever thoughts you have.
Commercial necessity for keeping track of trading in the ancient Middle East.

Then it just developed over a few millennia, became abstract, then applied even more and so on...


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20-10-2016, 11:06 AM
RE: Is math invented or discovered?
If a tree falls in the woods dose it make a sound?

Sound waves, vibrate the air. It takes the ear and brain to interpret it as sound. Creatures that don't have ear drums only feel vibrations, not sounds.

I think the same could be said about math. It can't be weighted, measured or touched. It's a tool/method to interpret the world around us. If humans weren't here. Would it mater?

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20-10-2016, 11:23 AM
RE: Is math invented or discovered?
The chicken....

no wait...

the egg......

or...

Maybe it was the chicken.....
...

.......................................

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20-10-2016, 12:02 PM
RE: Is math invented or discovered?
(20-10-2016 10:54 AM)unknowndevil666 Wrote:  Hello, people.

I believe fairly strongly that math is discovered, while our understanding and methods of what we do discover are of our own invention. One simple, classic example is the Fibonacci sequence appearing in nature. I go a step further and say that the universe is basically mathematical. Others might say it has order, structure, but isn't mathematical because it has physical properties, or that calling it mathematical would mistake the map for the territory, but I think the "essence" of mathematics is something pure that defines the essence of reality. Furthermore, I think the "physical reality" is something of an illusion, so there is no distinction between map and territory.

What do you think? Is math invented or discovered? What is math anyways? Does it exist? Is it physical or abstract? What is the distinction between physical and mathematical? I'd like to hear whatever thoughts you have.

I rather think of it as a language. Whatever you consider language to be, so should math.

We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning ~ Werner Heisenberg
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20-10-2016, 12:18 PM
RE: Is math invented or discovered?
(20-10-2016 12:02 PM)tomilay Wrote:  
(20-10-2016 10:54 AM)unknowndevil666 Wrote:  Hello, people.

I believe fairly strongly that math is discovered, while our understanding and methods of what we do discover are of our own invention. One simple, classic example is the Fibonacci sequence appearing in nature. I go a step further and say that the universe is basically mathematical. Others might say it has order, structure, but isn't mathematical because it has physical properties, or that calling it mathematical would mistake the map for the territory, but I think the "essence" of mathematics is something pure that defines the essence of reality. Furthermore, I think the "physical reality" is something of an illusion, so there is no distinction between map and territory.

What do you think? Is math invented or discovered? What is math anyways? Does it exist? Is it physical or abstract? What is the distinction between physical and mathematical? I'd like to hear whatever thoughts you have.

I rather think of it as a language. Whatever you consider language to be, so should math.

I had the same thought, but I think languages are a bit more arbitrary. The English word "tree" and the equivalent words in Chinese and Swahili have no resemblance to each other, and we could agree to use some other (arbitrary) word to refer to a tree, and as long as everyone agreed on it, it would work just as well as the existing ones. There is no intrinsic affinity between the object and the word we use. Even grammar can be quite different in different languages.

But things and processes in nature that have a mathematical structure have a distinct mathematical structure. We can't just agree to use an inverse cube law instead of an inverse square law (unless we redefine cubes and squares). There are cases where different mathematical structures can be used to describe the same thing, though (i.e., the wave/particle duality in quantum mechanics), which makes the whole thing kind of fuzzy for me.

I think that, given the laws of logic (which don't seem to be arbitrary), mathematical systems are constrained to follow certain rules -- they are not arbitrary. But I'm skeptical that they are an exact match with physical reality. I think they are useful in describing physical reality, but I'm reluctant to push it any farther than that.

In short, I think math is both discovered and invented. And I don't think it's identical to physical reality.
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20-10-2016, 01:05 PM
RE: Is math invented or discovered?
(20-10-2016 12:18 PM)Grasshopper Wrote:  
(20-10-2016 12:02 PM)tomilay Wrote:  I rather think of it as a language. Whatever you consider language to be, so should math.

I had the same thought, but I think languages are a bit more arbitrary. The English word "tree" and the equivalent words in Chinese and Swahili have no resemblance to each other, and we could agree to use some other (arbitrary) word to refer to a tree, and as long as everyone agreed on it, it would work just as well as the existing ones. There is no intrinsic affinity between the object and the word we use. Even grammar can be quite different in different languages.

But things and processes in nature that have a mathematical structure have a distinct mathematical structure. We can't just agree to use an inverse cube law instead of an inverse square law (unless we redefine cubes and squares). There are cases where different mathematical structures can be used to describe the same thing, though (i.e., the wave/particle duality in quantum mechanics), which makes the whole thing kind of fuzzy for me.

I think that, given the laws of logic (which don't seem to be arbitrary), mathematical systems are constrained to follow certain rules -- they are not arbitrary. But I'm skeptical that they are an exact match with physical reality. I think they are useful in describing physical reality, but I'm reluctant to push it any farther than that.

In short, I think math is both discovered and invented. And I don't think it's identical to physical reality.

Maybe less ambiguous than other languages? More concise? I see it that way because you can(or should be able to) translate every mathematical concept into another language say for instance English.

We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning ~ Werner Heisenberg
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20-10-2016, 01:26 PM
RE: Is math invented or discovered?
(20-10-2016 12:18 PM)Grasshopper Wrote:  
(20-10-2016 12:02 PM)tomilay Wrote:  I rather think of it as a language. Whatever you consider language to be, so should math.

I had the same thought, but I think languages are a bit more arbitrary. The English word "tree" and the equivalent words in Chinese and Swahili have no resemblance to each other, and we could agree to use some other (arbitrary) word to refer to a tree, and as long as everyone agreed on it, it would work just as well as the existing ones. There is no intrinsic affinity between the object and the word we use. Even grammar can be quite different in different languages.

I would say the nomenclature is arbitrary. The concepts are not. That would hint at some separation or independence from the subject matter. I think math is also that way.

(20-10-2016 12:18 PM)Grasshopper Wrote:  But things and processes in nature that have a mathematical structure have a distinct mathematical structure. We can't just agree to use an inverse cube law instead of an inverse square law (unless we redefine cubes and squares). There are cases where different mathematical structures can be used to describe the same thing, though (i.e., the wave/particle duality in quantum mechanics), which makes the whole thing kind of fuzzy for me.

One could say they have that structure, because math developed as a language to describe them.

(20-10-2016 12:18 PM)Grasshopper Wrote:  I think that, given the laws of logic (which don't seem to be arbitrary), mathematical systems are constrained to follow certain rules -- they are not arbitrary. But I'm skeptical that they are an exact match with physical reality. I think they are useful in describing physical reality, but I'm reluctant to push it any farther than that.

Math exhibits some language behaviors. It can be refined to respond to new challenges. Think Leibniz/Newton and calculus.

(20-10-2016 12:18 PM)Grasshopper Wrote:  And I don't think it's identical to physical reality.

Agreed. It is a great tool to describe the physical world.

We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning ~ Werner Heisenberg
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20-10-2016, 03:35 PM (This post was last modified: 20-10-2016 03:38 PM by Chas.)
RE: Is math invented or discovered?
To believe that mathematics exists independently of minds is no different than believing in spirits or the post-mortem preservation of identity.

It makes one some sort of neo-Platonist.
If you believe mathematics exists independent of minds, show us the Platonic Realm.

Since it does not exist independently, it cannot be discovered; it is therefore invented.
What is discovered is applications of mathematics - discovering how things can be described using this tool.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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20-10-2016, 04:10 PM
RE: Is math invented or discovered?
It's built into the fabric of reality -- the Fibonacci Series, pi, and so on -- but it's also invented insofar as the techniques used to derive some values are the product of human insight.

Nature/nurture, etc etc.
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