The discussion centers on the concept of infinity, particularly in relation to the mathematical constant pi. Participants argue that while pi is proven to be infinite and irrational, its representation in the physical world is limited by our understanding and measurement capabilities. The conversation touches on philosophical implications of infinity, suggesting that mathematical constructs like pi exist in a Platonic realm, separate from physical reality. Ultimately, the forum highlights the distinction between ideal mathematical entities and their practical applications in describing the universe.
PREREQUISITESMathematicians, philosophers, physicists, and anyone interested in the intersection of mathematics and the nature of infinity.
bassplayer142 said: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 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?bassplayer142 said: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.
CompuChip said: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?
The way to think about it, is this:bassplayer142 said: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.
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.bassplayer142 said: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.
bassplayer142 said: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.