The Volume Problem

[R.V.]

If one were to turn up the volume of music and then turn it down again very quickly (say with infinite speed), will the part where he turns it up even exist? Would the change in volume even exist?

So does 2*infinity = 0?

 

I initially posted this on 4chan's science board but never got any good answers or ideas how to solve this problem.

https://boards.4channel.org/sci/thread/14349334#p14349347

Edited March 31, 2022 by R.V.
Correction

[joigus]

I suppose you mean 0*infinity= a finite quantity; "infinity" representing rate of change, and 0 representing elapsed time.

2*infinity=0 certainly doesn't make sense.

If your question is the first one, it does make mathematical sense with the proper auxiliary qualifications (having to do with limits), but it's too idealised to correspond to a real situation.

[studiot]

2 hours ago, R.V. said:

If one were to turn up the volume of music and then turn it down again very quickly (say with infinite speed), will the part where he turns it up even exist? Would the change in volume even exist?

So does 2*infinity = 0?

 

I initially posted this on 4chan's science board but never got any good answers or ideas how to solve this problem.

https://boards.4channel.org/sci/thread/14349334#p14349347

I don't see a problem here.

The mathematics of the Ancient Greeks couldn't handle this question, and they developed many paradoxes involving their inadequate methods of analysis.

Modern maths answers this as follows:

 

Yes the spike exists, but it has zero duration in time.

Incidentally you have a slight error in your maths.

When you turn up the volume, you multiply by a positive number.
But when you turn it down you multiply by a negative one.
So the result is not x2 but x1 then by -1 = 1x(-1) = -1.

OK so you have a spike of zero width.
Or a pulse of zero width with a positive-going edge, followed by a negative-going edge.

The point is that you only have one of these and 1 is a finite number.

The Ancient Greeks' paradoxes all depend upon having an infinite count of these and they couldn't understand that an infinite count of these could add up to a finite total.

We now call the pulse in question a 'Dirac Delta Pulse', which has some interesting and very important properties in modern Physics as well as pure Mathematics.

Another example, that can be observed on an oscilloscope, is the fourier summing of sine waves to make a square waves.
You can see what are known as 'Gibbs phenomenon' on the scope.
As we approach more and more nearly vertical sides to the square wave, the leading and trailing edges extend further and further beyond the horizontal parts, culminating in spikes.

 

The important point is that

[joigus]

On 3/31/2022 at 11:25 AM, studiot said:

The important point is that

Well...?