What I described isn't really an algorithm, it's just taking the digits of a number, let's say:
foo=3.14159265...
Where after 5 is some continuing sequence of decimals.
The series of functions is literally just:
foo(0) = 3
foo(1) = 3.1
foo(2) = 3.14...
And to be clear, it's not just like, an algorithm that estimates pi, it's literally just a list of return values that is infinitely long that return more and more digits of whatever the number is. That is actually how he defines pi.
https://youtu.be/lcIbCZR0HbU?si=3YxcHfPlCFrlr5h3&t=2080
pi _happens_ to be computable, and there are more efficient functions that will produce those numbers, but you could do the same thing with an incomputable number, you just need a definition for the number which is infinitely long.
To be clear, I don't think any of this is a good idea, just pointing out that if he's going to allow that kind of definition of pi (ie, admit a definition that is just an infinite list of decimal representations), you can just do the same thing with any real number you like. He of course will say that he's _not_ allowing any _infinite list_, only an arbitrary long one.
