WhoresonWells
Since this is everyone’s favorite example of telescoping sums, let’s do it another way just for giggles.
Combinatorial proof
The denominator is P(n+1, 2) which is the number of ways for 2 specified horses to finish 1st and second in an n+1 horse race. So imagine you’re racing against horses numbered {1, 2, 3, …}. Either you win, which has probability 0 in the limit, or there is a lowest numbered horse, n, that finishes ahead of you. The probability that you beat horses {1,2, … , n-1} but lose to n is (n-1)! / (n+1)! or P(n+1, 2) or 1/(n2+n), the nth term of the series. Summing these mutually exclusive cases exhausts all outcomes except the infinitesimal possibility that you win. Therefore the infinite sum is exactly 1.
Unless Maine also repeals their use of instant runoff voting for the presidential election, their own votes won’t count toward the national popular vote. The compact makes no provision for counting ranked ballots, and there isn’t really any fair way to do so anyway.
I have a bolo tie whose slide ornament is carved anthracite.
I’ve never shoveled coal.
The Gargoyle by Andrew Davidson
It starts with the nameless narrator experiencing a near-fatal car crash due to his drug and alcohol induced hallucinations. During his lengthy recovery in the burn ward, he meets a psych patient who alleges their story begins 700 years ago in a German monastery. She tells him stories about their past in Germany, including how she obtained and translated a copy of Dante’s Inferno predating all known German translations. She tells other stories too, about a Japanese glass craftswoman, an Icelandic Viking, an Italian blacksmith, maybe some others, most of whom die young and tragically. She’s also a talented sculptor of stone gargoyles, a skill she allegedly learned from the narrator. The narrator suspects her stories are just the delusions of a schizophrenic, but can’t go back to his pre-accident life, so he agrees to go home with her to continue his recovery, and maybe learn a little more about her and why she’s taken an interest in him.
I’m about 3/4 through it and impressed with how it’s written. Unfortunately, I never read the Divine Comedy, so I’m pretty sure I missed some things that a better educated reader would have recognized.
Fish would eat you if they got the chance.
Once, I made an account for something that let me write my own security question and answer. I thought that was much better than the usual options and wrote something that cryptically referenced a difficult problem I once worked on. The answer could possibly be found online, but only to someone who properly understood the question. Later, when I needed to authenticate myself again, I got my security question. The answer isn’t something you typically memorize, but I knew what the prompt meant and how to work it out so I did so.
But I was too slow. Apparently you had to answer within one minute. It took me about ten so it locked me out. Tech support helpfully reset my password after merely verifying my phone number and SSN which are probably known to thousands.
Can we just let gender-neutral toilets be the default so we can all stop worrying this? The fact that the stranger shitting next stall over may or may not have a penis is not a problem. Having to scrape turds off my shoe because someone followed this guy’s advise and shat on the sidewalk makes it my problem.
Not sure about MIchigan in particular, but other states have, in relatively recent history, given ballot access to presidential candidates who were unambiguously constitutionally ineligible for the office. It doesn’t make much sense to me either, but apparently neither the 14th amendment, nor any other federal law restricts who can run for president, merely who can hold the office if elected.
