# Pi and infinity

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. It just doesn't make sense to me. Almost as far as saying that the everything is made out of something else on to infinity.

I have also thought a lot about infinity in our universe and have tried to wrap my head around a, let's say naturally occurring infinity and I feel like infinity is really just a boundary that we have created. Of course, you can create a mathematical infinity, but math is simply a tool created by humans and therefore has our inherent boundaries built into it. I guess what I'm trying to say is that I don't think thing in nature are infinite, but that they are just beyond our comprehension.

CompuChip
Homework Helper
I think this is more a philosophy thread.
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.

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.

I guess that makes sense. Some believe if you go in a straight line far enough you will be in the same spot again. What if the smaller and smaller you go you actual come around full circle to large things also. Just a weird thought.

Thanks

Do not be confused with space shape/curvature. Some believe that if you go in Physical world on a staight line and if space is positively curved then it would be like following a closed line on a shpere. But if space has zero curvature (flat), then line will never end - infinity.

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

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. It just doesn't make sense to me. Almost as far as saying that the everything is made out of something else on to infinity.
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..

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

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.
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?

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

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

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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?
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.

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.

EnumaElish
Homework Helper
Sure; just like any other irrational. For example $\sqrt 2$.

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 way to think about it, is this:
The system that we have constructed is responsible for this nonterminating decimal problem that you are thinking of. We use symbols to describe general ideas that we see in the physical world or make up based on what we see in the physical world. Alternatively to 3.14159... we have $$\pi$$ as a symbol for perfectly and exactly what it is.

Draw a right triangle having legs each of length 1". How long is the hypotenuse? It would be sqrt(2)-- an irrational number that goes on infinitely, but can be represented finitely by the hypotenuse that you drew on the paper.

What I really was trying to say is this. Imagine you had a circle. You cut a string that is exact diameter of the circle (c=2*pi*r)and then you start at a point on the circle. You go around it 3 times getting 3. Zoom closer and you get 3.1, 3.14, 3.141 etc. Basically you are all saying that this is an approximation of pi because when you get down to the quantum theory nothing can get smaller. If so, then the real pi which is used in our world would be a rational number because It would stop there. If things kept getting smaller forever then pi would be irrational.

Hurkyl
Staff Emeritus
Gold Member
What I really was trying to say is this. Imagine you had a circle. You cut a string that is exact diameter of the circle (c=2*pi*r)and then you start at a point on the circle. You go around it 3 times getting 3. Zoom closer and you get 3.1, 3.14, 3.141 etc. Basically you are all saying that this is an approximation of pi because when you get down to the quantum theory nothing can get smaller. If so, then the real pi which is used in our world would be a rational number because It would stop there. If things kept getting smaller forever then pi would be irrational.
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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What I really was trying to say is this. Imagine you had a circle. You cut a string that is exact diameter of the circle (c=2*pi*r)and then you start at a point on the circle. You go around it 3 times getting 3. Zoom closer and you get 3.1, 3.14, 3.141 etc. Basically you are all saying that this is an approximation of pi because when you get down to the quantum theory nothing can get smaller. If so, then the real pi which is used in our world would be a rational number because It would stop there. If things kept getting smaller forever then pi would be irrational.
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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I totally understand everything that is being said. Please don't think I'm trying to discredit math because I'm definately not. I love math. My mind is just wandering, thats all. Thanks.

Good. Please, understand me correctly, that was not directed to you... That was just an example of where misunderstanding could lead us..
Have fun :)

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