Math: Did we discover or create it?

[Don Blazys]

To: Chiantiglace.

Notice that I said "one might argue". I was being "hypothetical".

I did not say that it is my "position" or "conviction" that the imagination requires things that are physical. If I did, then I would be contradicting my earlier posts along with my actual conviction that the "imagination" transcends all physicality.

My rather shoddy "evidence" for this "conviction" is that "originality" can not come from anything that is already established but requires an initial non-existence of the thing that is then "created".

To me, this is "one hell of a paradox" as you put it, and personally, I sometimes think that if that paradox were ever to be resolved, then existence itself would come to an end.

In other words, the unresolvability of all such fundamental paradoxes is the fabric of existence.

That's it for me too!

Don.

[interval]

Math is created. To create a math you must setup its main rules (axioms). In theory of number 1+1=2 Setting up different rules you create another math, then in theory of sets, A + A = A

[jimbojones]

It is my opinion that we discovered math. This is because regardless of whether man had ever written down the first equation or pondered a relation, they would still work the same, they just wouldn't have been written down.

[maddog]

Originally Posted by pgrmdave

I think that math is not a science. I also think that it is inherent in nature, and exists whether or not there is somebody to count, as such, it would be 'discovered' rather than 'invented'.

I agree with the going consensus here -- just like the Greeks thought, that Mathematics is discovered. This implies that Mathematics lives independent "out there".

I disagree with pgrmdave in thinking Mathematics is not a science. If Science is subscribing to the notions of Francis Bacon or "following" the Scientific Method as such, this means forming a hypothesis and working towards finding a conclusion. I would challange anyone to understand how Mathematics does Not do this. Of course it Does!

Read any theorem from Mathematics. Hypothesis, chug-chug-chug-to Conclusion. Now I agree I do feel uneasy everytime I see a Proof by Contradiction. If this is what prgmdave finds Unscientific then I am sympathetic.

Originally Posted by pgrmdave

Science, at least good science, follows the scientific meathod, while mathematics does not.

Mathematics definitely does follow scientific method per se in that it does follow logic. Otherwise very little math would be done as no one could prove anything.

See above.



maddog

[maddog]

Hmmm ...

An Update...

I see this thread has been going on for a few years. I finally got to read the whole thing. I still don't feel swayed, though I now remember that the Greeks had this same debate a few thousand years ago. So I guess it is still not answered.

So discovered or created (invented by some), eh ?

Let's for the moment use a little logic. I like the someone awhile ago reminded me of the notion of the 0 (ie the Mayan's didn't use the concept, nor did the Romans).

If the notion of the 0 was invented then what about before it was "invented" ? To whom ? If it was invented by one culture and not another that came before did it exist ?

Whereas if the notion of a 0 was discovered by a culture then it would exist beforehand.

I think I can create a paradox using invention/creation of concepts in math whereas I get around this with respect to discovery.

Say Culture A lived before Culture B. A knew of the 0 and B did not. For Culture B does the 0 exist. No. It has not been invented ? Both Culture are
living on the planet at the same time though A is older than B. Does Invention/Creation force this concept into existence before which it did not exist ?

Switch this. Now Culture A does not know of the 0, yet B being a newer Culture does, it invented it. Now it teaches it to Culture A. So A learns to 0. A didn't invent it so does the 0 exist for Culture A ?

Maybe it is just too foreign for me to comprehend.

If I discover a concept, say Newtons Law. Would it be true for this to be considered the opposite as well. Would Newton to have invented and this Law actually didn't exist beforehand ???

Now if I discover Physical Laws, then why would Mathematics be required to be invented.

Conversely, if Mathematics is an invention then so wouldn't be Physics ?

I respect what Pyrotex was trying to show how universal Mathematics is. More what I attempting is by creating a principle of equivalency classes between Physics and Mathematics. To me such a world where everything is "invented" would be a very "magical" world indeed.

I don't even think that I in any way solved this long standing debate by the above logic (or lack thereof).

Now I do contrast this with Computer Languages (or for that manner any spoken or written language). These are definitely created/invented. There is a distinction though here.

The word "bread" in a culture is agreed upon to mean what one does when they bake some foodstuff in some heating utensil to arrive at some edible commodity.

Contrast this in Mathematics where definitions are not by conventional agreement. Even if so notions or processes or theorems thereafter are DEFINITELY NOT by agreement. Otherwise there is no logic. This I feel make Mathematics Not fit the Language model that Cultures dictate in their communication with each other.

Just an update...



maddog

[Doctordick]

In my humble opinion people spend little time concerning themselves with the question of the meanings of words. Somehow everyone seems to believe that words themselves have meaning; that the meanings they personally attribute to these words are identical to the meanings others attribute to these self same words. If that were the case, languages would be static and unchanging. When one gets as old as I am the change in meanings of many words becomes quite obvious. In many cases, the younger generation has utterly no idea of the meanings of words held by their elders and vice versa.

It may seem that this harangue has little to do with the discussion postulated by this thread but it actually has a lot to do with the issue. Before one can even begin to discuss the question, “Did we discover or create it?”, one needs to first define mathematics. Now I have no idea as to what the posters intend to mean by the word because they have made no effort to tell me. I only know what I mean by the word. Long long ago, I defined mathematics (in my mind) to be the invention and study of internally self consistent systems. Self consistent systems are epistemological constructs which lack any contradiction.

Do self consistent systems exist before we invent or discover them? Well of course they do; we don't invent self consistent systems; what we invent are the representations as, without a way of representing them, we certainly cannot study them. So the answer to the question becomes quite clear, we discover or create representations of self consistent systems so that we can study them.

This brings up another issue often brought up by professional scientists. Why does the universe seem to be bound by so many “mathematical” relationships? The answer should be clear to any thinking person. If mathematics is the invention and study of internally self consistent systems then any usable explanation of anything is indeed a mathematical expression (if the mental model underlying that explanation is not internally self consistent, it fails as an explanation: i.e., it yields inconsistent answers).

What is commonly referred to as “mathematics” are those constructs sufficiently complex to be held as “not obvious” and yet strongly established as “internally self consistent”. A number of years ago I posted a thread pointing out the difference between two very important mechanisms of thought which I called “logical thought” and “squirrel thought” which seemed to fall on deaf ears.

Logical thought has the advantage that the conclusions are absolutely as valid as the axioms (being logical, it is internally consistent); however, it has the problem that, sans mathematics, it is inherently limited to but a few steps.

Squirrel thought (and you need to understand my definition of “squirrel thought”) has the advantage that it is a holistic approach bringing to bear a lifetime of experience thus providing us with quick solutions to problems far to complex to even begin to analyze analytically; however, it has it's own flaw: it cannot be checked and thus must always be taken with a grain of salt as all squirrel decisions can be erroneous.

If you are interested in thinking, you might peruse the thread.

Originally Posted by Doctordick

This is, in fact, the single biggest problem in trying to understand the universe. Most everyone believes the ideas they have arrived at via their personal squirrel decisions are the only possible conclusions which can be reached. The reader should understand that "belief" of anything is a squirrel decision. The ability to communicate (language itself) was acquired through squirrel thought. Accept your squirrel decisions as your best bet when it comes to any serious question, but don't ever think that those squirrel decisions are infallible. You don't have to believe they are infallible before you can follow them; when it comes to life, "you pays your money and you takes your chances".

On the other hand, if you want to do science, you should remember that even your most cherished squirrel decisions could be wrong. Even you guys who are not "crackpots" should remember that. A lot of science is done in the total absence of logical thought and that has to be so; but scientists should not forget that fact. If they do, science folds over to religion. It may work great, but that does not mean it is valid. Think about that next time you see a "poor squirrel decision".

Have fun -- Dick

[enorbet2]

I frankly cannot understand how anyone can propose that Math existed or exists separate from us for us to discover any more than any other human language. The relationships they describe existed but language, whether verbal or mathematical, is a construct, symbology of those relationships. This is a simple as to note that distance existed before even any life evolved but it took humans to invent rulers or measuring devices to quantify them. It might be argued that despite their rare occurrence in Nature, the relationship between the sides of a right triangle and it's hypotenuse existed before Pythagoras came along to notice and QED the results. Math is perfect literally by definition exactly because it is a construct, a set of unbreakable rules regardless of branch (although I understand certain cephalopods prefer Octal, and that's just weird since even cockroaches know hex rulz)

We fall into Platonic Hell when we mistake symbols for the things themselves, even in Math where definitions of terms are precise. We daren't even think about the English Language!