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Fact that pi is irrational may point at something fundamental missing in our knowledge system. It appears that we cannot precisely measure circle length/area i
by zoomablemind 3y ago
Fact that pi is irrational may point at something fundamental missing in our knowledge system.
It appears that we cannot precisely measure circle length/area in units of radius and vice versa. Basically, the unity as such does not exist in our knowledge, nor can we truly comprehend infinity.
Perhaps, unity and infinity are just our abstractions for something else.
- xigoi 3y agoThe fact that π is irrational has absolutely nothing to do with physically measuring circles or with infinity. We know the value of π exactly.
- zoomablemind 3y ago> ...We know the value of π exactly. Perhaps you could share that exact value with the rest of humanity. And I mean the number value, not the nominal value.
- xigoi 3y agoWhat do you mean by “number value”? There are many different ways to calculate π, the most famous (but converging very slowly) being π = 4 atan(1) = 4 (1 - 1/3 + 1/5 - 1/7 + …)
- zoomablemind 3y agoThere are many ways to obtain inexact value of pi. Being irrational number, there are no finite number of digits (e.g. in decimal form or other base) to represent the pi value exactly. Nor can such value be expressed as ratio of integers. Likewise, in your representation the ellipsis hides away the infinity.
- xigoi 3y agoπ has a finite amount of digits in base π. Why arbitrarily limit yourself to integer bases? If you can compute a number to any desired precision, then you know its exact value. And this still has nothing to do with measurement of the physical world. We cannot measure anything exactly.