Purity

[quote]I am a student talking about stuff I am learning in calculus class, so what I say may feel uniformed and thats because I am not that far ahead in the maths and sciences. Please keep that in mind if I am missing large chunks of proves or evidense that disprove my thought process. I am taking calc, and we are going over some things and one thing came up about a right triangle. We all know how to calculate the length of the hypontinuse. If we have a right triangle with sides of lengths equal to 1, the hypotinuse will equal the square root of 2. Whats the issue here? Well, the hypotinuse has a finite length, we know that just by looking at it, but the decimals in root 2 go on forever. How exactly can a number that goes on forever represent a finite length?

This got me thinking, and it turns out there are serveral other issues at the basic level of math that have this same issue. Like how a positive times a negative make a negative, but 2 negatives make a postive. The explanation I was given was that it was made this way because any other way would basically break how math is used in science (directional uses I guess), but this set of rules is not really proven to be true, it is just accepted as such. Or how a positive number 1 and a negative number 1 will equal zero, but not in nature! Things just dont disapear in nature if they hit their 'opposite.' If matter and anti matter meet, they do not just zero out and disapear, a reaction occurs, so maybe they are not opposites, but instead materials that react together different from what we are used to seeing on earth. A positive charged object and a negative charged object meet, but they do not disapear, nor do the fields disapear, because if those 2 items ever seperate, those fields will exist again. But in math, when solving an equation, I can cancel things out nice and easy with this rule.

This is what math is, a version of applied logic, but not how nature works. I am fine with that, except we apply math to understanding nature and that is causing my brain to melt at trying to let go of these kinds of things. Am I just learning rules to a complex game or is there a fundamental truth in math that can be applied appropriately to nature?

I ask this because man kind loves to break things down into simpler parts, they like clean looking numbers and integers and shapes, but nothing in nature ever looks like that. I am liking how fractal geometry can take something as a whole thats seemingly complex, and break it down from the whole rather than by simpler parts (please note my knowledge of fractals comes from a Nova special).

I am basically a math major, so does it get any better for after calculus? Am I going to learn why this is so and why it can be applied to nature? Or am I just learning the rules of a game? Apologies if I rambled on.[/quote]

- cowgill, a member of CollegeConfidential.com

By purity:
sociology -> psychology -> biology -> chemistry -> physics -> mathematics -> philosophy

Note that, if you reverse to 'purity' arrow, you get 'applicability'. For instance, sociology is applied psychology and mathematics is applied philosophy.

The applicability sequence is chronological. Sociology is the youngest science listed; philosophy is arguably the oldest. The sequence is also an order of simplicity: with each next science, a set of axioms and empirical data is added. The first, the purest, is also the simplest.

By applicability:
philosophy -> mathematics -> physics -> chemistry -> biology -> psychology -> sociology