Plus, I Got Religion

[Triple Zero]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

It's both.

That's the thing about math, a language that tries to describe this construct as accurately as possible, and the construct is again restricted by what is possible to accurately describe given the language.

[LMNO]

Man, this one is incredibly useful:

[The Good Reverend Roger]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

It's both.

That's the thing about math, a language that tries to describe this construct as accurately as possible, and the construct is again restricted by what is possible to accurately describe given the language.

Bullshit.  If it exists, it can be described by math.

Is a language.

[LMNO]

Almost.  Don't forget about Gödel.

[The Good Reverend Roger]

Almost.  Don't forget about Gödel.

I haven't forgotten a thing, LMNO.  If it can exist in the universe, math can describe it.

[Bebek Sincap Ratatosk]

Almost.  Don't forget about Gödel.

I haven't forgotten a thing, LMNO.  If it can exist in the universe, math can describe it.

Or at least, if it can exist in the universe, math can be used to model some aspects of it.

[The Good Reverend Roger]

Almost.  Don't forget about Gödel.

I haven't forgotten a thing, LMNO.  If it can exist in the universe, math can describe it.

Or at least, if it can exist in the universe, math can be used to model some aspects of it.

Math can describe it in it's entirety. 

[LMNO]

Almost.  Don't forget about Gödel.

I haven't forgotten a thing, LMNO.  If it can exist in the universe, math can describe it.

Ok, I think I know what you're getting at.  No objections here.

[Cramulus]

well I'm missing it. How would math describe, hmmmm, Payne's testicles.



would it be a statement like "<2"?

[LMNO]

Douglas Adams had the right idea.


"Are you sure you know what the question is?"
-Deep Thought.

Also,

would it be a statement like "<2"?

[Bebek Sincap Ratatosk]

Almost.  Don't forget about Gödel.

I haven't forgotten a thing, LMNO.  If it can exist in the universe, math can describe it.

Or at least, if it can exist in the universe, math can be used to model some aspects of it.

Math can describe it in it's entirety. 

Math can describe your Mom in her entirety.

But I defy you to show me the mathematical formula that describes TGRR's Hate. 

[LMNO]

∞+1

[Bebek Sincap Ratatosk]

∞+1

I stand corrected.

[Triple Zero]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

It's both.

That's the thing about math, a language that tries to describe this construct as accurately as possible, and the construct is again restricted by what is possible to accurately describe given the language.

Bullshit.  If it exists, it can be described by math.

Is a language.

But never entirely accurately. When math tries to describe things that exist, it always fails at a certain point. Sometimes this point is far away enough that it doesn't matter for a particular (but not every) practical purpose. This is why math is generally considered "useful".

However, in addition to things that exist, math is also able to describe things that do not exist. Very consistently, even.

Therefore, the language of math describes not reality, but something that is in certain places nearly homologous to reality, and in other places something entirely different. So yes, I consider math to be a construct.

It starts with the axioms. In logic, they define True and False as axioms, define operators on it, and work from there. That's useful in a lot of cases, but when you get down to the nitty-gritty details, it doesn't work in reality and it leaves you only to conclude that, since the reasoning is solid, the axioms must not really exist in reality, at least not in the hard True/False dichotomy as describes by mathematical logic.

In the math of natural numbers, they start with defining zero and the successor function, yielding all the natural numbers. From there you can derive fractions, rational numbers, irrational numbers, complex numbers and a whole lot of things. It doesnt take very long before you start running into trouble that simply doesn't correspond to reality anymore.

One of these troubles is called the Axiom of Choice. It's real simple, it states that you can always take an element from a non-empty set. Somehow this property doesnt follow from the other axioms, which is why they have to assume it. But if you do, you run into paradoxes. However, if you don't you run into paradoxes as well.

Basically I would like to sum it up with a quote from Einstein:

"where mathematics is exact, it does not describe reality.
and where mathematics describes reality, it is not exact."

the first line refers to theoretical mathematics (a language to describe a construct), and the second refers to physics (a language to describe reailty).

[Bebek Sincap Ratatosk]

That's actually one of the things I really like about math... mathematicians acknowledge it as a construct that attempts to remain consistent within its logical framework. Adherents of most other constructs refuse to acknowledge themselves as such. Philosophers, for example.

Math isn't a construct, it's a language.

It's both.

That's the thing about math, a language that tries to describe this construct as accurately as possible, and the construct is again restricted by what is possible to accurately describe given the language.

Bullshit.  If it exists, it can be described by math.

Is a language.

But never entirely accurately. When math tries to describe things that exist, it always fails at a certain point. Sometimes this point is far away enough that it doesn't matter for a particular (but not every) practical purpose. This is why math is generally considered "useful".

However, in addition to things that exist, math is also able to describe things that do not exist. Very consistently, even.

Therefore, the language of math describes not reality, but something that is in certain places nearly homologous to reality, and in other places something entirely different. So yes, I consider math to be a construct.

It starts with the axioms. In logic, they define True and False as axioms, define operators on it, and work from there. That's useful in a lot of cases, but when you get down to the nitty-gritty details, it doesn't work in reality and it leaves you only to conclude that, since the reasoning is solid, the axioms must not really exist in reality, at least not in the hard True/False dichotomy as describes by mathematical logic.

In the math of natural numbers, they start with defining zero and the successor function, yielding all the natural numbers. From there you can derive fractions, rational numbers, irrational numbers, complex numbers and a whole lot of things. It doesnt take very long before you start running into trouble that simply doesn't correspond to reality anymore.

One of these troubles is called the Axiom of Choice. It's real simple, it states that you can always take an element from a non-empty set. Somehow this property doesnt follow from the other axioms, which is why they have to assume it. But if you do, you run into paradoxes. However, if you don't you run into paradoxes as well.

Basically I would like to sum it up with a quote from Einstein:

"where mathematics is exact, it does not describe reality.
and where mathematics describes reality, it is not exact."

the first line refers to theoretical mathematics (a language to describe a construct), and the second refers to physics (a language to describe reailty).