To claim the sum 1/[2^n] over the natural numbers is 1 is the same as saying “if you flip a coin enough times eventually you will get heads.” Each longer sequence of tails is half as likely as the previous.
-
To claim the sum 1/[2^n] over the natural numbers is 1 is the same as saying “if you flip a coin enough times eventually you will get heads.” Each longer sequence of tails is half as likely as the previous. And they are disjoint events. But, their sum must be 1. One of them must occur, and all of them end with heads. #math
-
Peter Amstutzreplied to myrmepropagandist on last edited by
@futurebird
By definition, a fair coin has to flip heads eventually, the sequence of tails can't be infinite, that isn't a fair coin.How many sequential tail flips do you need to get before you can choose between it being a low-probability event and actually not a fair coin?
-
myrmepropagandistreplied to Peter Amstutz on last edited by
@tetron I think this could be a plot point in testing if one is in a simulation in a sci-fi story. Though I need to think about the implications more.
-
Hrefna (DHC)replied to myrmepropagandist on last edited by
@futurebird This is a fun illustration. It's basically analogous to the geometric distribution (the number of trials until you get a success).
The PMF there is 1/2^k and the CDF as k approaches infinity is (definitionally) one.
-
@futurebird @tetron @gregeganSF has a great plot point related to it where the main character manipulates probabilities. I forget which story it was but I think it's in The Best of Greg Egan or maybe in Sleep and the Soul.
-
That sounds more like the novel “Quarantine”, which is not about being in a simulation, it’s about manipulating wave function collapse.
-
@gregeganSF @futurebird @tetron Yes! That's the one. I kinda binged all the books I could get my hands on in a row so it's been a jumble in my head.
