Why is Math so Powerful?

Post Reply New Topic

Maybe the Pythagorians and the Platonists were right. Maybe math is the underlying reality and everything that we experience through our senses is just appearance.

ruveyn

The first post is catches the essence of this famous article (saw a link to Wigner but non to this specifically):

http://en.wikipedia.org/wiki/The_Unreas ... l_Sciences

With respect to physics, it is an articulation of the relation between physical properties with respect to various coordinate systems.

Physics can be taught without math, however only in a qualitative sense. In fact, to be a good physicist it's important to be able to understand it in a qualitative sense.

Yes, but "pure math" has, well after its inception, been found to have specific and unexpected application. (like tensors)

Robert A. Heinlein said:

* Anyone who cannot cope with mathematics is not fully human. At
best he is a tolerable sub-human who has learned to wear shoes, bathe,
and not make messes in the house.
o Robert Heinlein


ruveyn

I disagree with him.

Math might be powerful but it still falls drastically short on understanding the inner workings of the world. Mainly because too many variables will make a problem very difficult to near impossible to solve. Yet, in reality, things are very complex and include dozens of variables.

But math is a lot better than the other tools we have developed through human history for figuring things out (superstition and such).

[quote="techn0teen"]Math might be powerful but it still falls drastically short on understanding the inner workings of the world. Mainly because too many variables will make a problem very difficult to near impossible to solve. Yet, in reality, things are very complex and include dozens of variables./quote]
Maths are not scared off by complexity, men are.

Math is not purely deductive, it requires an observer. i.e. math is merely a copy of structures in nature. All mathematics is just merely recombinations of information drawn from nature.

Think of a series of 1's and 0's, they are just bits of information, all information necessarily derives itself from nature because it has to be 1) stored somewhere 2) read (detected).

The idea that math is not an empirical discipline is clearly unfounded, some aspects of math are rbitrary but they are empirical in the sense that one is able to define systems of tautologies through recombination.

Physicist Max Tegmark takes this one step further:

"I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our
physical world is an abstract mathematical structure."

"In this essay, I will push this idea to its extreme and argue that our universe is mathematics in a well-defined sense."

http://arxiv.org/PS_cache/arxiv/pdf/070 ... 0646v2.pdf

although I am my no means a mathematical eqaitions satisfying. I spent the wohole of yesterday completing a review exersize. I like the because they are logical and are not un-rgonized. A well set out maths exersize looks like a piece of art.

Why is math so powerful? Because it is both useful and beautiful at the same time. When used skillfully, mathematics is a universal tool for solving problems. I would posit there is no problem ever solved by a human being or team of human beings that couldn't be described by a mathematical equation. And why is this powerful? Because when faced with a complex or seemingly intractable problem of almost any nature, we can always turn to math to either solve the problem or at least help guide the way. Mathematics can be used to test an almost infinite number of hypotheses. As if that isn't enough, math is a beautiful, logical, and symmetrical language. It has been used to produce musical instruments that create the sweetest sounds, and to produce some of the most stunning works of visual art. Useful and beautiful.

Plato said that God ever geometrizes.

ruveyn

Look at the Mathematical Universe Hypothesis , to see how powerful mathematics is.

Edited

A hypothesis, not a fact which leaves the effectiveness of mathematics somewhat of a mystery.

Don't look a gift horse in the mouth. Just accept the Wonder of it.

ruveyn