Math: Did we discover or create it?

[Pyrotex]

Originally Posted by Qfwfq

Like any language, German, Hindi etc... it can be used to represent facts about reality. A mathematician is however not in the least concerned with reality. The sentence "Every cow is an excellent Tango dancer" is a perfectly correct, spotless English sentence, regardless of reality.

I take exception to that. I am a mathematician, and I am totally concerned with reality. "4 + 3 = 8" is a perfectly correct, spotless mathematical expression. It is also contra-reality ((WRONG)) and therefore worthless.

I disagree that mathematics is a "language". We only say things like that, and confuse ourselves in the process, because we have no abstract meta-word ((class)) to include 'mathematics' and 'German' as members. We try to cram 'mathematics' into the class of 'languages' and do ourselves a great disservice. When we speak of math as a 'language' on a par with German, we muddy the conversational waters. And we wind up making deductions about as worthless as "4 + 3 = 8".

[Edge]

Originally Posted by Pyrotex

This question is easy to answer with a thought experiment.
Pretend that there is another inhabited planet in another galaxy, say that big one in the constellation Andromeda. The people on this planet get tired of making stone arrow points and turn their thoughts to more abstract subjects. Like 'lines' and 'triangles' and 'circles'. A million planetary rotations later, they have 'higher mathematics'.

Now, is it the SAME mathematics that WE have? Ignore the irrelevant details, like we use 'X' but they use '@', we use '=' and they use '}'. Is it the SAME math?

The answer has to be YES. Math will work the same for them. The relationships they discover will be the same relationships we have discovered. The applications of math to the physical world will be the same applications that we have used.

Therefore, mathematics is NOT an 'invented' concept. It is universal, and therefore 'discovered'.

Woa, interesting answer. Well, it seems true, there has been many mathematical languages (mayan, egiptian, etc.) and all of them were not good until the discovery of the zero, negatives, etc...

This can get tricky since math can also have another base other than a decimal one...

[Edge]

Originally Posted by virtualmeet

I think you're right when you're saying that mathematics is just a language between others used by humains to describe their feelings... The main difference between The mathematical language and the others comes from the fact that in the first one, there are no flaws inherent in it's basics because they are not made by humans. Other languages can contain flaws (in fact all of them have some well known and very popular ones) as rules !!
Humans like to contradict themselfs, just for fun...we are indeed very complicated creatures (more than nature can ever build by itself).

That's the thing. Does really language have flaws?

I have seen some pages trying to prove math is wrong...

[virtualmeet]

Originally Posted by Edge

That's the thing. Does really language have flaws?

I have seen some pages trying to prove math is wrong...

Oh yes...for example, if you write an SF novell, wich is mainly a lot of unverifiable facts and non logical statements, then your is book is a big flaw. BUT, it can be accepted and even rewarded by humains because the language you used is not supposed to be 100% true, so no one will ask you to prouf every single word in your book. Writing someting with the mathematical language is an another story because you have to respect a lot of rules. You can put your imagination and creativity away and just act like a "machine". Math in fact can never make something wrong because it doesn't create or invente new things...other languages did and this is why they are more accepted by humains .

[virtualmeet]

Originally Posted by Pyrotex

I disagree that mathematics is a "language". We only say things like that, and confuse ourselves in the process, because we have no abstract meta-word ((class)) to include 'mathematics' and 'German' as members. We try to cram 'mathematics' into the class of 'languages' and do ourselves a great disservice. When we speak of math as a 'language' on a par with German, we muddy the conversational waters. And we wind up making deductions about as worthless as "4 + 3 = 8".

Why is it so difficult to accept the fact that Mathematics is just a "language"? this isn't make it less relevant it just put it in it's right place. You say it yourself, the rules in the basics of mathematics are universal and so they are discovred by humains from nature. we create mathemaics (as a language) to represent thoses rules because the existings ones were and still messy ones. If you look at all other science, you will see a lot of formulas represented by only one language : mathematics. It's just a specialised language that we use to represent facts discovred by other experimental sciences.

Originally Posted by Pyrotex

When we speak of math as a 'language' on a par with German, we muddy the conversational waters. And we wind up making deductions about as worthless as "4 + 3 = 8".

This is true if you write theses sentences as a humain language (German or others) but it it can't be worthless in mathematical words because it might be a deduction from rules. So it's just a deduction nothing else...

[snark1100]

there's a pleasant book on this question - Conversations on Mind, Matter, and Mathematics - by a French mathamatician, Connes, and Changeux, a French neurobiologist. Connes argues the Platonic side, mathematics exists independantly of human mind, and Changeux, that it is a human invention.
No one wins the debate, but i have moved closer to thinking of mathematics as a human invention. Without a logical mind of some form existing, it is difficult to see any mathematics.

[Loricybin]

it seems to me that this is one of those "shades of grey in between"

almost a trick question, but a good question.

consider this. . .
if you have two apples and eat one, you have one apple left.
the mathematical structure for this being 2 - 1 = 1.

there were still two apples, and one was subtracted and placed in a whole new equation, but my point is this
without mathematics, wouldn't the outcome have been unchanged?
youd still have an apple in your hand and you still would've eaten one.

so wouldn't it be safe to assume that math itself is just a process of naming things in simpler terms?

because if math is simply names for things that exist, but not physically, then math must have existed all along, just not under the assumed identity of MATH.

so i believe math always existed, and we merely defined it into understandable terms

[Pyrotex]

Originally Posted by Edge

Woa, interesting answer. Well, it seems true, there has been many mathematical languages (mayan, egiptian, etc.) and all of them were not good until the discovery of the zero, negatives, etc... This can get tricky since math can also have another base other than a decimal one...

Not tricky, really. The base of your number system doesn't matter. All the rules of arithmatic work just as well in binary, octal, hex, base 12, whatever, as long as your numeric notation allows for ZERO. Some bases are just more 'convenient' than others.

For example, in our decimal system, thirds are a pain in the butt. But in base 12, EVERY number ending with one or more zeros, like 1000 or 200, are EVENLY divisible by 3! And by 2 and 4 and 6. But NOT by 5!

[Pyrotex]

Originally Posted by Drip Curl Magic

...A lot of scientists have come up with formulas to explain our surroundings... but those formulas were based around the mathematics system that we already know. It's possible that if we were to make a new counting system, that we'd still be able to come up with just as many workable calculations.... but we'd have to re-work every formula that scientists have ever come up with.....

Your conclusion, er, may not be, uh, entirely correct. [Sanctus, help me out here] The Formulas that scientists use actually do not care what base your counting system is in. Really. For example,

Force equals Mass times Acceleration. F=mA.

We can choose any (one) counting system, and there are an infinite number of them. We multiply the value of m times the value of A. We get the product in that same counting system. However, we must pre-define our system of UNITS.

We can have mass in Kilograms, acceleration in Meters per Second squared, and Force in Newtons.

Or mass in Slugs, acceleration in Feet per Second squared, and Force in Pounds.

As long as you are consistent, and have a well defined set of UNITS, the counting system doesn't matter. It's just arithmatic. And F always = mA.

[Qfwfq]

Originally Posted by Pyrotex

I take exception to that. I am a mathematician, and I am totally concerned with reality. "4 + 3 = 8" is a perfectly correct, spotless mathematical expression. It is also contra-reality ((WRONG)) and therefore worthless.

It isn't contra-reality, no.

I'ts in contradiction with Peano's axioms. It's also false in the various Z_n groups. OTOH, 4 + 8 = 3 is false in N but true in Z_9.