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CompuChip

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I'm not a philosopher, but maybe you will also find "Is infinity impossible?" interesting.

Let me not elaborate on how infinity is a limiting process, not a reachable quantity -- even in mathematics; nor on whether mathematics is a tool created by humans, or we just discovered it as the (most convenient) way to describe the universe.

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Pi is an ideal mathematical entity not from 'our world' in some sence. Some philosophers said that there are Physical World, Mental World and Platonic World. Platonics entities are ideals like infinities, right triangles, real numbers and they proved useful in explaining of objects in a Physical world. So Pi exists as ideal Platonic entity and could be 'projected' to Physical world to describe circle properties, but if you will zoom entity in Physical world you will reach some limit (Planck scale), but in ideal Platonic world you will zoom forever. By using our mind we can probe Platonic world of ideals and calculate Pi with any precision we want.

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Thanks

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According to study of Microwave Background Radiation we can conclude that space is actually flat.

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every theorem is only an approximation of nature. when you make experiments you only expect the numbers to approach your theory, not to fit them exactly.

you cant measure an object to infinite accuracy, therefor an approximation of pi should be good enough.

its just the same as getting any irrational number in any physical equation..

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CompuChip

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Hmm, I said I would get into this discussion but now I am...

I don't think I get what you're saying even here. Probably my scientific mind which won't understand anything other than a definition or a theorem, but: that piece of text isn't really clear. How does zooming in on a circle get you more digits of pi? And by "proven its infinite" do you mean: it has been proven that pi is irrational?Say you take pi and keep zooming on on a circle. You keep getting more digits but you never actually hit the end of pi. It has been proven to be infinite.

Well, like that, for example. Fractals are a cool example. Or all the points on a circle.But how exactly is something infinite constructed in our universe. It just doesn't make sense to me.

And now this is Chinese to me (which, obviously, I don't speak).Almost as far as saying that the everything is made out of something else on to infinity.

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Think about Pi in little bit other way. Pi is basically division. I think you familiar with real numbers which is infinite field. So when you divide a circle's circumference to its diameter then you will divide it infinitely, producing new and new digits to the final Pi number. So precision is simply where you want to stop.I don't think I get what you're saying even here. Probably my scientific mind which won't understand anything other than a definition or a theorem, but: that piece of text isn't really clear. How does zooming in on a circle get you more digits of pi? And by "proven its infinite" do you mean: it has been proven that pi is irrational?

Interesting, that math can describe whole Pi number without representation of a exact value (which is infinite, so that would be effectively impossible). It is irrational number and it was proven in 1761 by Johann Heinrich Lambert and it exists as exact!!! value in mathematics.

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EnumaElish

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Sure; just like any other irrational. For example [itex]\sqrt 2[/itex].

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The way to think about it, is this:Say you take pi and keep zooming on on a circle. You keep getting more digits but you never actually hit the end of pi. It has been proven to be infinite. But how exactly is something infinite constructed in our universe.

The system that

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Hurkyl

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Why would you think this experiment has any bearing on the value of pi? It's certainly not the definition of pi, nor is it any theorem I know.

P.S. you misunderstand quantum theory too.

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Basically, your argument is understandable. Some pseudoscientists use this kind of a argument to descredit math (for instance, they said that there are no right triangles in the real world). I had a hot discussions in the past and I might say that it was very difficult to proof that math is what mathematics understand.. they just do not get it!! with all the proofs and examples. Nevertheless, I just want to say that you should not be confused with it.

Once again, Pi is pure mathematical object, it has very precise exact definition in math. When you will start you measurement you just described, you will find that, if you zoom better, your value will approach Pi, but it is not Pi itself!! You will just find it useful to use pure math object to model a property of real circle... and model it with infinite precision. The same as we use to model a circle with a^2 + b^2 = 1 equation.

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Have fun :)

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I misunderstood that you misunderstood me. Am I understanding this right? Or am I misunderstood? :)

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