Maths: Trustworthy Tool or Questionable Map?

[John Richard]

One of the most powerful tools of investigative science is maths. Theories are often debunked simply because its associated mathematics failed in some practical way.

Yet math is full of mysteries:

We cannot state the ratio of a circle. Pi is a name given to a "transcendant irrational" that is really the unresolved question of, what is the ratio of a circles radius to its circumference? I am not questioning the practical value of what we do know, I have used it often when programming ratio relationships and cams on servo control systems. But I have to program in compensation for the accummulated "error" of using Pi. No matter what resolution of Pi, there will ultimately be an error to compensate for. This shows up in cyclic systems probably better than anywhere else.

Math predicts the infinite divisibility of a fixed length. But we know from quanta that this is not true, that there is a limit to smallness. Or at least that seems to be the conclusions from present physics.

Math predicts infinity, yet the concept of an infinite universe is doubted.

Math predicts more dimensions than the four we can whitness around us, and yet, as far as I am aware, no empirical eveidence of further dimensions exists.

My question is simply this, should we place our faith in the predictions of math, or not?

 

[Hurkyl]

We cannot state the ratio of a circle.

False. In fact, you just stated "the ratio of a circle". Of course, I suspect that was shorthand "the ratio of a circle's permiter to its diameter".

But I have to program in compensation for the accummulated "error" of using Pi.

No, you had to program in compensation for the accumulated error of using a finite binary approximation to pi.

No matter what resolution of Pi, there will ultimately be an error to compensate for.

Pi is an exact quantity.

Math predicts the infinite divisibility of a fixed length.

(Second-order) Euclidean geometry predicts the infinite divisibility of a fixed Euclidean line segment.

But we know from quanta that this is not true, that there is a limit to smallness. Or at least that seems to be the conclusions from present physics.

(1) No, that is not the conclusion from present physics.
(2) Even if we did, it would merely imply the universe is not a model of Euclidean geometry.

Math predicts infinity

Certain mathematical structures have infinite elements, or particular elements named "infinity".

yet the concept of an infinite universe is doubted.

Math says nothing about the universe. If the universe is not infinitely large, that simply means physicists should not assume it is a model of a mathematical structure of infinite size.


And the rest of your post just repeats the mistake made in the past two examples.

 

[John Richard]

What is the exact quantity of pi?

I don't want the nubers to 50 or a 100 decimal places, I want the full ratio. I was under the clear impression, (happy as hell to be wrong though), that the ratio was unresolveable.

I know we can measure the length of the circumference and the diameter but then we get into the difficulties of resolution of construction and measurement, which although theoretically absolute, are not practically so.

The binary equivalent as a finite approximation is endless no matter how manny bits in the binary word unless a formula exists that succinctly defines the ratio of the circle.

I am on pins about your comment that Pi is an exact quantity?

 

[John Richard]

I forgot to mention Hurkyl, as a mentor you have the ability to lock a thread or better still to delete it.

Given the sound rebuttal I would be grateful if you could save me any further embarrasement by doing so. Please?

John Richard

 

[Hurkyl]

Er, I suppose there's no problem locking it. One of the philosophy forum mentors can unlock if it turns out I shouldn't have.