They’re probably the only things that “create” information in the sense that you can always grab another slice. Thank you delicious pi!
It’s irrational, which just appears random (which is why I said pseudorandom).
It is not. If I in July in Europe will say “there is no snow outside”, I give you very little information. If in same conditions I will say “there is snow outside”, I will give a lot of information.
Amount of information is proportional to (logarithm of) improbability of outcome.