6 HN users recommended this explainer6 months2019–2025score 6.5
Years with an HN recommendation, 2007–2026
HN recommends it as an accessible explanation of number categories and why almost all numbers are unknowable.
Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.
“here's a video that explains from the basics what kinds of numbers exist” (HN, 2019)
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]
Covers known numbers and the quest to define normal numbers
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]
Numberphile has a video explaining the relationship between the number categories, and includes a brief discussion of where Chaitin's Constant belongs. [this video]
Explains relationships between number categories including Chaitin's Constant
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]
Lays out classes of numbers; normal numbers vastly dominate
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.
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]
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