They’re probably the only things that “create” information in the sense that you can always grab another slice. Thank you delicious pi!
Is it actually information? I can give you the number two, but it’s not useful information until I also tell you which digit is significant and what the number means. Communicating information is still limited by the speed of light.
Situationally, yes. “I want the next digit of pi” is information in that sense of the word. It’s not a particularly useful piece of information unless you’re building something that requires a circle with a circumferential precision larger than the width of our entire universe.
How many digits of Pi would you have to read for you to be able to reconstruct all of the information in the Universe up to this moment?
None, because the digits of π have absolutely nothing to do with the universe.
I don’t see why not, it’s just numbers, which is all we store most data as.
You could use it as a source of pseudorandom numbers to encrypt an infinite data steam, e.g. we’ll encrypt using e, starting at position 40468.
Randomness is the opposite of information.
It’s irrational, which just appears random (which is why I said pseudorandom).
You don’t want your encryption keys to be predictable.
