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
Replying to
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
Replying to
at infinity all the error terms disappear so you only have to work with the asymptotic behavior. when we do something like model heat diffusion with the heat equation we are *approximating* the behavior of ~avogadro’s # of particles by the solution to a differential equation
14
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
Show replies
Replying to
Or even the fairly small finite. Many times I had to explain to students in queuing theory class that no, they couldn't "simplify" a question by assuming the unlimited queue would never be longer than 100 items because *that's actually much more complicated*.
2
Replying to
Quote Tweet
Calculus lets you deal with things that there are a lot of by rounding "a lot" up to "infinity".
1
5
Replying to
My thesis advisor's husband is a finitist. One day over coffee he explained to me "a limit is a guarantee" and I saw the light.
1
Replying to
hmm maybe i believe this slightly less than i did when i tweeted it actually. apparently there are continuous physical models that are at least very hard to discretize and possibly it's an open question how to do it which is v interesting to me:
3