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RE: What is infinity and does it exist?
Interesting post, thank you.
I disagree with one point though:
If the universe truly is infinite, everything you have ever imagined and haven't imagined must exist . . . somehow!
Not necessarily. What if the universe is not like π but more like an infinitely long sequence of some finite pattern?
I find the image of the fractal you posted to be a perfect and intuitive counter example. It certainly is infinite and yet we encounter the same pattern over and over again.
@fminer05, Thanks for reading and for the excellent question. The entire post was inspired by something Brian Cox says. Starting at 26:38 of JRE#610, "If the universe is infinite, which it may well be, in fact there are many ways the universe can be infinite, then that would happen [monkeys reproducing Shakespeare]. If it's in accord with the laws of physics, then it can happen. And everything that can happen, in an infinite universe, will happen, because the universe is formally infinite. I contend that in an infinite universe, even the most unlikely possibility must happen, in fact, formally, an infinite number of times."
So what I wrote "If the universe truly is infinite, everything you have ever imagined and haven't imagined must exist." Is actually not quite accurate, according to world renowned physicist Brian Cox. Everything you have ever imagined must exist only "If it's in accord with the laws of physics, then it can happen." In my gut I feel like my statement is still correct (Multi-verses with different laws), but my gut can be very wrong sometimes.
Are there any physicists on Steemit who can help? This topic is endlessly fascinating to me ;)
I think if the universe is an infinitely long sequence of some finite pattern, then Pi couldn't exist in that universe, since Pi doesn't ever repeat. But we need to ask a physicist.
The fractal image is of the Mandelbrot set which, like Pi, is infinite and never-repeating. While there are elements of similarity on different scales, the same pattern is not encountered over and over again. Similar patterns appear, but there is novelty on all scales.