# One rational interval function and one irrational, will they ever collide?

This question may be a little mathy or hardware-y, so I may have to ask elsewhere.

I've recently learned that if a is a positive rational number and b is a positive irrational number, there exists no common multiple between the two.

A common design consideration in threaded or embedded systems is concurrency control, when two functions or threads share resources.

So if function A runs every sqrt(2) seconds, and function B runs every 1 second, they will never run at the same time.

Is it somehow possible to use very accurate measured numbers, to make this possible? Or is it possible using exact/symbolic programs/tools? Or is it not possible at all in machine/computer computational formats?!

• Functions don't run instantaneously, so even if you could measure irrational time, it wouldn't solve the problem. – Yuval Filmus Feb 1 '17 at 15:52

Could you make a theoretical device that could measure an irrational number of seconds? Maybe, but that would be impossibly hard. In the real world the computers clock, which runs the scheduler, is made out of a vibrating piece of quartz creating the ticks. This is vibrating at a few billion times per second. You will never get resolution of time between the vibrations so it provides us with an implicit limit on how accurately we can measure time.

• Well, what if the device will measure in multiples of irrational number? Suppose you will have new measure sec which equal sqrt(2) seconds and it will tell you how many sec passed, 1-2-3-... Same as for length, only if you can measure integer length let's say, you do a regular triangle which will have one side irrational – Eugene Feb 1 '17 at 17:38
• Irrational numbers are great in theory but they really aren't grounded in the physical world. I can define a right angle triangle with the two main sides to be length 1. The hypotenuse would then be length sqrt(2). In the physical reality I can't actually make this perfect triangle because eventually the decimal expansion of the length would require precision smaller the planc length constant and you cant have that. We can define irrational numbers and use them, and they are really useful, but we cant physically make something with irrational lengths – lPlant Feb 1 '17 at 18:28
• Moreover, best to my knowledge is hard to tell about the exact length of an object with precision higher than Plank constant, because things start fluctuating there. So you can't use one etalone object to measure another. What is dsistance or time then?.. – Eugene Feb 1 '17 at 18:39