[mindslight]

Uncompressability doesn't imply information content, for example the output of a stream cipher. I believe the digits of pi can be calculated algorithmically, no? That program is a bound on the information content of pi.

You can make a similar argument about digitizing film via sampling, rather than digitally recording the state of every atom - you're throwing away a huge amount of information. Not infinite of course, but dwarfing what it takes to accurately represent the movie. That's a philosophical curiosity, but not really relevant to the qualitative situation.

My point with 3.14 was that everybody recognizes it as a reference to pi, and it works well enough to calculate the circumference of a circle in an engineering context.

(FWIW I personally hate "Pi Day" as March 14th, as it reeks of numerology. It should probably be the day/time when the Earth has traveled around the sun its distance from the sun)

[JadeNB]

> I believe the digits of pi can be calculated algorithmically, no? That program is a bound on the information content of pi.

Yes, good point. I was using the term informally, and probably incorrectly, to mean that π (conjecturally) contains any finite string of digits (in any base)—what is formally called 'normality' (https://en.wikipedia.org/wiki/Normal_number). Apropos of your correct belief, there's a lovely so called 'spigot algorithm' due to Bailey–Borwein–Plouffe that can generate any hexadecimal digit of π that you please without having to generate intermediate digits: https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula .

[JadeNB]

> FWIW I personally hate "Pi Day" as March 14th, as it reeks of numerology. It should probably be the day/time when the Earth has traveled around the sun its distance from the sun

Incidentally, wouldn't that be the less compelling "1 radian day"? Also, to celebrate such a day, we'd have to decide: travelled since when?, and then we're right back to arbitrariness (why choose January 1, or whatever other date/time is chosen)?

For me, while it's hardly an accurate picture of what math is or why it matters, I'm happy enough to have anything that gives people a positive impression of mathematics.