So wait did anyone ever fix the whole "to cross a distance I must cross half the distance etc" all distance contain an infinite sum thing? Is the answer just that infinite sums can have finite results?
Conversation
in the mathematical model, yes, infinite sums (over either distance or time) can have finite results. in “the real world” (slightly less idealized model) it’s not at all clear that it’s possible ro infinitely subdivide space or time, or perform infinitely many actions
3
49
a thing that i think mathematicians and physicists don’t do a good job of conveying is that most of our use of large infinite objects like the real numbers is a matter of convenience. the infinite is a convenient approximation of the merely unimaginably large finite
7
2
46
wait
2
11
this is not a universal opinion to be clear but i think it’s quite defensible. doron zeilberger is notably very vocal about this: users.uoa.gr/~apgiannop/zei
2
24
well fuck
1
12
lol sorry was this load-bearing i am happy to talk more
3
2
17
Is that related to this being true?
0.999... = 1
2
3
yeah i think people get hung up on 0.999... = 1 for a good reason, it relies on a specific ontology of what a number is and what an infinite sum is to be meaningful and true and that ontology wasn’t rigorously pinned down until the 19th century (by cauchy iirc)
1
6
then people talk about “1 + 2 + 3 + ... = -1/12” which imo is a pretty mean bait-and-switch, that notation is basically a mathematical pun, it relies on a completely different procedure for evaluating (divergent) infinite sums, the notation doesn’t mean what it looks like at all
Ok yeah hehe thats what I was thinking about next. My understanding of that goes something something Ramanujan something something Euler.
2