Thread: What good is math?

Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

Math is essential to clarifying an idea and to prove that new ones are consistent with what is known before. Without it, we are severely handicapped, IMHO

Math is the language by which we understand and examine relationships between measurable features of our universe. This leads up to be able to predict results from events, or to deduce the inner structure and atomic makeup of a star, &c. However, math itself is not the limit of our universe and it should not be inferred that if no measurable features of something exist (like a specific image in a dream, for instance, or the soul, &c.), then that thing does not exist. This is a problem which occurs in science and limits its scope of understanding.

Originally Posted by tom

Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

This may all be opinion, but just hear me out.

All things can be represented with math: anything can be given a value and therefore represented by that value. Some ideas are straight-forward and two-dimensional: the growth of a line given y=mx+b, the exponential decay of a radioactive isotope, the exponetial growth of a population infected with a dangerous flu virus. However, math cannot solve all problems, as math is nothing more than a two-dimensional representation of a three-dimensional problem.

As an example: you have a tortise and a heir racing. The tortise, given its slow moving speed, has been granted a 100 foot head start. Now the rabbit easily catches up to the tortise, and will eventually reach the 100 foot point, where the rabbit would obviously pass it. But wait, the tortise has also moved during the time that rabbit has, a good 10 feet at least. So the rabbit must move another 10 feet to be where the tortise is again, but then the tortise has still moved farther ahead. On paper, this is a race the rabbit will lose.

Physics is the same thing as math: there's just a theme to the problems. As I said before, math is nothing more than a two-dimensional representation of a three-dimensional problem... say, a rocket blasting off from a launch pad. The rocket obviously isn't flat, but for all intents and purposes of it blasting off into the air, calculating its trejectories and re-entry pathways, it may as well be. You will find little to no use of a z-axis to give the rocket any form of three-dimensional meaning.

I don't understand what you mean when you say that math is a two-dimensional representation of a three dimensional problem. I have come to understand math as a language. It is a language we use to talk about things. It describes things we can see and things we cannot see. We use it to describe the course of a rocket from the earth to the moon and we also use it to describe the multiple dimensions of string theory. In fact, we cannot talk about a lot of things without using the language of math. You make my point with your second paragraph where you introduce Zeno's paradox. Zeno's paradox is kind of a trick because our language makes many assumptions that math does not. You can define the movement of the rabbit and the tortoise in math utilizing summable infinities. A summable infinity is a series of numbers that are infinite that add up to a finite number---in this case the finite number is the length of the race. If you think for just a moment, as the distance traveled gets smaller and smaller so does the time to cross that distance. This infinite series again adds up to a finite number or amount of time. The rabbit will traverse the distance faster then the turtle and will therefore win the race.

Physics and math are different things. Physics is a science and as a science it creates presuppositions and in turn premises which draw conclusions. Physics uses math to prove the relationship between these premises and the conclusions. Physics is a science and Math is a language...............

Originally Posted by jsleep

I don't understand what you mean when you say that math is a two-dimensional representation of a three dimensional problem. ...............

Ah, here is a nice editing window!
Apparently somebody spake of the type Geometry and/or Trigonometry Math courses that are taught in American High Schools.
Doing String Theories with 11 dimensional integral equations - much more fun ;-)

Originally Posted by jsleep

Physics and math are different things. Physics is a science and as a science it creates presuppositions and in turn premises which draw conclusions. Physics uses math to prove the relationship between these premises and the conclusions. Physics is a science and Math is a language.

Yes, that is exactly correct fellow human being jsleep.

What I find the most useful branch of math(ematics) is Set Theory. I didn't even study any of it until College back in 1967. Now Sets is taught Kindergarden on. There is a notable exception, in the USA some 3/4 of all Junior High (7-9th grades ) and Middle High (6-8th grades) math terachers are not qualified to teach first year Algrbra nor Plane (two dimensional) Geometry.

Strangely, I like to discuss comparative religions. Set theory (and it's twin: Logic) really would be better for the USA Citizens taught as a third year math in High School (instead of Algebra 2, Trigonometry, or Introduction to Calculus). These branches of Mathemeatics are much better for general usage in all fields of Science and all other endeavors of humanity: Sets and Logic.

Yes, and almost always.
Some physics issues do not require math, like Newton's First Law.

I wonder how he came to understand the laws. Do you think the first law of motion is intuitive? If so, how?

Originally Posted by jsleep

I don't understand what you mean when you say that math is a two-dimensional representation of a three dimensional problem. I have come to understand math as a language. It is a language we use to talk about things. It describes things we can see and things we cannot see. We use it to describe the course of a rocket from the earth to the moon and we also use it to describe the multiple dimensions of string theory. In fact, we cannot talk about a lot of things without using the language of math. You make my point with your second paragraph where you introduce Zeno's paradox. Zeno's paradox is kind of a trick because our language makes many assumptions that math does not. You can define the movement of the rabbit and the tortoise in math utilizing summable infinities. A summable infinity is a series of numbers that are infinite that add up to a finite number---in this case the finite number is the length of the race. If you think for just a moment, as the distance traveled gets smaller and smaller so does the time to cross that distance. This infinite series again adds up to a finite number or amount of time. The rabbit will traverse the distance faster then the turtle and will therefore win the race.

Excellent reply Jsleep!

Math is neither good nor bad. Its ethical value is solely dependant on its application.

Math is an idea. It is usfull for clarification of objective reality or more often the obscuration of objective reality. E.g. String Theory.

Math is only one of many ways to understand physics, although many confuse math with physics and objective reality. E.g. String Theory. Math can describe many things that do not have corollaries in objectve reality. And, for those things that do have corollaries it provides at best, always, only approximations. When used as the language of science, like any other language, it provides ideals that may approch and describe objective reality, but must never be confused with reality. Like any language when it becomes indistinguishible from reality, it assumes the aires of religion.