Is math natural or synthetic?

The "infinite amount of prime numbers" thing got me thinking about this one.

Is math natural or is is man made? Think about a few things. The universe is finite. Everything is made of atoms which are made of quarks and probably something smaller yet. But there is a finite amount of it all. It is one big number of atoms, but it is finite. That matter cannot be created nor destroyed should prove this.

Numbers, OTOH, are infinite. We have not named most of them, but we have named a googolplex of them. Maybe more names, I don't know where after googolplex-one, etc, would logically stop. But no matter how you slice it, math can count *more* than anything in nature. Therefore, can it be natural?

While some parts of math, geometry especially, are clearly present in nature, does nature "care" about prime numbers?

If I had brought this up in school as a kid, would it have gotten me kicked out of class?

Quote: AZDuffman

The universe is finite.

Not known yet.

Whether the Universe is finite or infinite is an important question, and either outcome is possible. So far, astronomers have no idea what the answer is, but they're working towards it and maybe someday they'll be able to tell us.

I think it's infinite, no beginning
and no end.

according to that TED talk on the math of sex, math is pattern recognition, which is a natural humanstate, hunters depend upon it so too do gamblers.

Quote: AZDuffman

Is math natural or is is man made?

That's a good question, and one I'm sure PhD mathematicians could talk about for hours over drinks.

On the one hand, primes are primes and will be the same on any planet. I really like that scene, by the way, in Contact, regarding primes.

Then again, I'm often taking the position that math is more like philosophy sometimes, especially in dealing with mathematical paradoxes. For example, I claim that infinity is just a concept to help make certain points in math, but doesn't really exist. I have been asking for years for anyone to prove anything in the natural world that is infinite in nature. So, I would say the concept of infinity is man made.

Yet, I think if there is a god, and he likes me, which he probably won't, he will explain to me the secrets to prime numbers, and I'll kick myself and say, "I should have figured that out."

Quote: Wizard

Yet, I think if there is a god, and he likes me, which he probably won't,

Why would he, he doesn't like anybody
else. Look what he lets his own self
appointed leaders get away with.
That's one hateful, self loathing god..

Quote: Evenbob

Look what he lets his own self
appointed leaders get away with.

Hopefully I'll be judged against them, as a basis of comparison. I don't think I've ever harmed anybody else, other than things like parking at the Hard Rock for free for a few days.

Quote: Wizard

Hopefully I'll be judged against them, as a basis of comparison. I don't think I've ever harmed anybody else,

Is that what they say about you
on Gamblers Glen?

Euclid's Postulates
1. A straight line segment can be drawn joining any two points.

2. Any straight line segment can be extended indefinitely in a straight line.

3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.

4. All right angles are congruent.

Euclid himself used only the first four postulates ("absolute geometry") for the first 28 propositions of is book, "The Elements".

Quote: Wizard

I have been asking for years for anyone to prove anything in the natural world that is infinite in nature. So, I would say the concept of infinity is man made.

Euclid was forced to invoke the parallel postulate on the 29th propositions.

5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

This postulate is equivalent to what is known as the "parallel postulate".

5. Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter how far they are extended.

Unlike the first four postulates, the 5th one included the somewhat non-intuitive concept of infinity. Over the centuries many people attempted unsuccessfully to prove the fifth postulate as a theorem.

In 1823, Janos Bolyai and Nicolai Lobachevsky independently realized that entirely self-consistent "non-Euclidean geometries" could be created in which the parallel postulate did not hold.

Spherical geometry is an easily understood concept where there are no parallel lines and any two lines meet. In spherical geometry, the postulate "Any straight line segment can be extended indefinitely in a straight line" means to connect two points with a "great circle".

Quote: AZDuffman

The "infinite amount of prime numbers" thing got me thinking about this one.

Is math natural or is is man made? Think about a few things. The universe is finite. Everything is made of atoms which are made of quarks and probably something smaller yet. But there is a finite amount of it all. It is one big number of atoms, but it is finite. That matter cannot be created nor destroyed should prove this.

Numbers, OTOH, are infinite. We have not named most of them, but we have named a googolplex of them. Maybe more names, I don't know where after googolplex-one, etc, would logically stop. But no matter how you slice it, math can count *more* than anything in nature. Therefore, can it be natural?

While some parts of math, geometry especially, are clearly present in nature, does nature "care" about prime numbers?

If I had brought this up in school as a kid, would it have gotten me kicked out of class?

I think math is man made. It is our way of making sense of the world. There is a point where math becomes metaphysical, as we attempt to describe situations that do not exist in nature. Consider: Is the order of things in the universe evidence of design? Or are we seeing order where there is actually chaos?

Quote: Wizard

That's a good question, and one I'm sure PhD mathematicians could talk about for hours over drinks.

No wonder they get all the women!

Quote:

On the one hand, primes are primes and will be the same on any planet.

They are, but are they if the other planet uses a different base system? I remember a HS teacher saying something about having worked with a "Base 8" system for some reason somewhere. I believe the huge reason we are on Base 10 is because of having 10 fingers. If that smart kid on "The Simpsons" the name of whom I cannot remember invented math, we would probably be on a Base 8 and count 1-2-3-4-5-6-7-0-11-12-13-14-15-16-17-20.........

So poor prime 19 would not exist! Life would go on for most everything else.

Quote:

Then again, I'm often taking the position that math is more like philosophy sometimes, especially in dealing with mathematical paradoxes. For example, I claim that infinity is just a concept to help make certain points in math, but doesn't really exist. I have been asking for years for anyone to prove anything in the natural world that is infinite in nature. So, I would say the concept of infinity is man made.

Yet, I think if there is a god, and he likes me, which he probably won't, he will explain to me the secrets to prime numbers, and I'll kick myself and say, "I should have figured that out."

This is what I was wondering. No idea how it comes down in the math world. Of course it then asks if math is a science or not. Math is almost always lumped with science in education, for good reason, but in that way it is not. Also why I asked about finite vs infinite. Sounds like you are in the "finite universe" camp that I am in.

Maybe he will tell you there are no secrets to primes?