I wonder if the number of people who could recite works from memory has substantially changed: while surely the prevalence of such people decreased, world population ballooned! Today we have people that can recite many digits of pi, for example.
370 karma · joined April 21, 2016
Hopefully I'll live the couple of decades to find out if PG's prediction is correct, I would bet against it.
There is no contradiction until n is large enough that F(pi) + F(0) is bounded below 1, hence the statement at the start: we'll pick a large enough value of n later.
Yes, strong policies which impose significant good will always face significant resistance because finite resources cause many to see the world as a zero-sum game. This is the progressive vs reactionary battle.
I later remembered fractions a/b = ac/bc work this way too!
and I suppose the model of localization discussed in the article above counts as well.
Thus the replication crisis of mathematics is revealed. In the words of John Conway: a map is canonical if you and your office neighbor write down the same map.
In fact, I recently learned there is one cardinality for each possible way to order an infinite set. This is slightly confusing because there are many ordinals of each cardinality, but there are just that many cardinals I've decided.
In math, this is called a representation of a Lie group, and there are representations in all dimensions.
Further edit: I guess he's at Arizona right now, but he was at IAS at some point....