All the Numbers - Numberphile

It's fascinating how little we know about everyday numbers like pi and e, it's widely assumed that they are normal but there is no proof for this (and it's extremely difficult to do so). In fact we believe the fast majority of numbers are transcendental and normal but we only actually know of a single normal number, and it is a manufactured number. Numberphile has an excellent video on the numbers we know about and the quest to find / define normal numbers: ▶ this video

You might appreciate this video where Matt Parker lays out the various classes of numbers and concludes by describing the normal numbers as being the overwhelmingly vast proportion of numbers and laments "we mathematicians think we know what's what, but so far we have found none of the numbers." ▶ this video

This video parallels the article, going further. I love the tag line, "We know none of the numbers." ▶ this video

I found Matt Parker's video to be a good way to visualize the fact that we 'know' essentailly 0% of numbers: ▶ this video

Numberphile has a video explaining the relationship between the number categories, and includes a brief discussion of where Chaitin's Constant belongs. ▶ this video

That's actually most numbers, but we don't know any yet. ▶ this video numberphile (math YouTube series) describing some related concepts here.

It feels like every time there's a mathematics post on the front page I post a video by Matt Parker. This time, here's a video that explains from the basics what kinds of numbers exist: ▶ this video

I wonder if this was the inspiration for this numberphile video? ▶ this video The video does go further than the article.

corollary: Numberphile (with Matt Parker of Stand Up Maths) - "All the Numbers". Most are incomputable, of course :) [0] ▶ this video

Such numbers are called "normal numbers". Pi likely is one based on all the digits we've computed for it, but we don't have any way to prove a given number like pi is normal or not. Relevant Numberphile video: ▶ this video

See also this Numberphile video on numbers, including algebraic, computable, transcendental, and talking about numbers beyond those. ▶ this video

It's worse than you make it sound, though: ▶ this video In short, it isn't just that we have more computables than non-computables; there are categories of numbers like "normal" that nominally contain "all the numbers" but we can barely even name a handful.