unforum

[Slithy]

You guys ready to move on to our next topic: "String Theory: Fact or Fiction?" yet?

~Slithy

[Olorin]

[thebruce]

[Olorin]

[RI_Barnica]

[yanka]

[neon snake]

[tanner]

[neon snake]

[SilentAvenger]

tanner, two things.

One, about grasping infinity. People can, indeed, grasp infinity, to the extent of grasping anything else: You grasp a thing's effects and rules.

For example, you can prove you grasp the number 472 because you are able to imagine 472 of something else, say, 472 carrots. But, infinity is a concept of a higher abstraction than that of 472, it is of an abstraction level equal to the abstraction of the concept "number". You cannot imagine the concept of a number, yet you can clearly show the private cases of this concept. Equally, it is not possible for a human to imagine the "infinity", but it is quite possible for people to conceptualize it.

About proofs:
Mathematics, on its own, is the area of thought, which specializes in finding the structure and rules within a given set of axioms. The most basic field is number theory, which focuses on the most basic axioms of math. More advanced fields are Geometry, Group theory, Graph theory, Trigonometry, and many more. These fields insert a bunch of new definitions and sometimes extra axioms to the mix.

Science is the area of thought specializing in finding a set of axioms that, using (usually) mathematical methods, can create a set of rules producing similar results to a real-life system. Physics specializes in the sub-atomic level, mostly, Chemistry specializes in atomic and inter-atomic connections. Biology specializes in the inter-molecular connections between Carbon, Hydrogen and Oxygen based molecules. Beyond those three basic sciences, there are even broader sciences, which cover a more specific set of axiom sets, but on a more macro level. Even Psychology uses a set of axioms, but not of a numeric nature. As you leave the micro level, and enter the macro level, the axioms become less and less of a numeric nature, and become more generic, yet they are still axioms.

When you have a scientific "hypotheses" or a "theory" (experiment-"proved" hypotheses), you have a new set of axioms that is being offered as giving a better correspondence to the real-life experimental results. There is another type of scientific discoveries, these are PROOFS, that if a certain theory is correct, then some other rule must be correct. An example of this happened recently, "Quantum Darwinism" was PROVEN. As in, if Quantum physics is correct as it currently stands, Quantum Darwinism is too. (See recent Slashdot article).

The last type of area of thought is Technology, which is the area specializing in taking various scientific and mathematic discoveries and proofs, and creating from a combination of them a "product", which in itself does is not a contribution to the systems of axioms, but rather an implementation of a private case of them. Invention is what fules Technology.

*ends long post. I should stop making posts like this, I just cant help it!*

[Slithy]

Since you guys seem to enjoy arguing about mathematical concepts and proofs, I thought I might throw this your way:

The Clay Mathematics Institute is offering a $1,000,000 USD prize for solutions to each of their "Millenium Problems":

Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier-Stokes Equations
P vs NP
Poincaré Conjecture
Riemann Hypothesis
Yang-Mills Theory

Maybe you guys could start your own group and go after some of the prize money. If any of you are interested, I'd advise you to do this quickly, before the U.S. Dollar depreciates too much further.


~Slithy

[tanner]

hmmmmm - i fully agree avenger -- maybe i didnt express myself well

and im very happy grasping infinity --- i love it

[thebruce]

[neon snake]

In general, mathematics is a little...purer (?) than some other sciences. A lot of maths is fairly black and white - its either right or wrong, equations balance or they don't, period.

A lot of real-world examples, whilst based on robust theories are proved by hypotheses, evidence and confidence levels (I conclude that xxx is true, at a 98% confidence level, and the like), simply because of the difficulty of including all the factors.

The beauty of mathematics lies in the basics, they are true and inarguable.

Sidenote - when at university, a lecturer mentioned three famous volumes of mathematics, written a few hundred years ago. Midway through volume two, they managed to prove conclusively that 1+1=2.

I can't remember much more than that, not even enough for Google to help - anyone got any ideas?

[neon snake]