Post An6PpGZRuWH4VDapeq by futurebird@sauropods.win
(DIR) More posts by futurebird@sauropods.win
(DIR) Post #An6BGayAg622H4jKAC by futurebird@sauropods.win
2024-10-17T13:30:07Z
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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
(DIR) Post #An6BnvM1uOhJ3LmYBU by malin@dice.camp
2024-10-17T13:36:10Z
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@futurebird I don't understand this parallel. The coin is a dynamic process which ends, and the other is an infinite sequence with a limit.
(DIR) Post #An6Brlx8nxnZ3MyY4W by mattmcirvin@mathstodon.xyz
2024-10-17T13:36:50Z
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@futurebird I suppose it involves the strange philosophy of what an event of probability 0 really is. In principle, you could flip forever and never get heads... but the probability is 0; it's one outcome among infinitely many. The boring finitistic interpretation is that you can only ever keep flipping for a finite time, but the longer that time is, the less probable no heads becomes.
(DIR) Post #An6Bxsbyxd4JRUzVD6 by rayhindle@mastodon.social
2024-10-17T13:37:51Z
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@futurebird Isn't there some miniscule chance that the coin would come down on it’s edge?
(DIR) Post #An6CRZsz9BYk3M6Zo8 by futurebird@sauropods.win
2024-10-17T13:43:21Z
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@rayhindle not math coins. but real coins might I suppose. There is also a chance the coin simply never “comes down” having been snatched by a crow attracted to the shiny objects.
(DIR) Post #An6Dy8Dv7FP3loz4Hw by llewelly@sauropods.win
2024-10-17T14:00:27Z
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@futurebird this is the core of a story problem in the first chapter of a calculus textbook.
(DIR) Post #An6PpGZRuWH4VDapeq by futurebird@sauropods.win
2024-10-17T16:13:17Z
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@malin Think of every possible outcome to flipping a coin until you get heads:HTHTTHTTTH…what is the probability of each?ok then what is the sum of that infinite list of probabilities?
(DIR) Post #An6ZJnyx9SngOv9vqy by futurebird@sauropods.win
2024-10-17T17:59:40Z
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@independentpen You are correct the probability for any single fair coin flip is 1/2. But this question is about the probability of multiple events. They are still independent events though.
(DIR) Post #An6ZgVvmQos54oVHO4 by futurebird@sauropods.win
2024-10-17T18:03:46Z
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@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.
(DIR) Post #An6ZwnNJLJQJoO90sq by run_atalanta@pgh.social
2024-10-17T18:06:37Z
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@futurebird @tetron Rosenkrantz and Guildenstern are dead.
(DIR) Post #An6a7tcKTUEaMCSioK by futurebird@sauropods.win
2024-10-17T18:08:42Z
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@independentpen I don’t think it’s that mysterious. We have an experiment : “flip the coin till you get heads” and we have a list of possible outcomes: H, TH, TTH, TTTH .. yes this is a infinite list but it is countable. We also can calculate the probability of every outcome on the list because each individual coin is 1/2 prob. The sum is 1. for any trial one of the outcomes will happen— we can know how likely it was. If we do it over and over we get a distribution.
(DIR) Post #An6aAFzmFBk0LCYVd2 by futurebird@sauropods.win
2024-10-17T18:09:10Z
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@MxVerda @malin yes
(DIR) Post #An6aYXLnMyb97JQqOW by futurebird@sauropods.win
2024-10-17T18:13:28Z
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@alienghic @malin Just take a piece of paper and cut it in half. take one half and cut it in half, take one fourth and cut in half keep going— then say it’s still here no matter how much I keep doing this! ok? (proof by hand waving and scissors)
(DIR) Post #An6abp4pv4FIxn4BHc by michael_w_busch@mastodon.online
2024-10-17T18:11:02Z
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@tetron @futurebird This is where we introduce the students to Bayesian statistics and Poisson distributions.To save them from flipping coins 350,000 times: "Fair coins tend to land on the same side they started: Evidence from 350,757 flips" https://arxiv.org/abs/2310.04153
(DIR) Post #An6ajMHOs4mLxzXJCa by malin@dice.camp
2024-10-17T18:15:27Z
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@futurebird Ah, you're thinking of the coins also as an infinite series, so they also have a limit. Gotcha.
(DIR) Post #An6bDK1hoSDRfMU0h6 by MichaelPorter@ottawa.place
2024-10-17T18:20:52Z
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@futurebird Since we’re talking about flipping coins, and odds, I’d like to share a fun challenge I gave one of my classes many years ago (it’s getting to the point that any teaching story is many years ago 😢).I gave them a grid of, I think, 10 x 10 = 100 squares and told them I wanted them to take the sheet home and do one of two things:Either1. Flip a coin 100 times and record H or T as appropriate, in order, on the grid.or2. Fake it, just fill in the squares with H’s or T’s, but try to make it look like you flipped a coin.I think I told them in advance that when they brought the sheets back, I would be able to tell who faked it and who actually flipped the coins.Okay, memory is fuzzy on actual numbers, but there were something like 25 sheets turned in, around 1/3 faked. I successfully identified the genuine and fake attempts for 23 of the sheets, and misidentified one of each.Not bad, eh? All I did was look for long runs of either H or T, like four or five in a row. If the sheet had one, I judged it genuine, if it didn’t, I judged it a fake. When people think they are simulating a random process, long runs of one result are seen as more improbable than they actually are. I wish I could remember what the actual lesson connection was - I wasn't a math teacher at the time 😄#Probability #ITeach #Math
(DIR) Post #An6cBIfzxfcIqzvgga by MichaelPorter@ottawa.place
2024-10-17T18:31:44Z
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@futurebird @alienghic @malin My favourite kind of proof 😊
(DIR) Post #An6f8L9SbNxzWYzS6a by zillion@freeradical.zone
2024-10-17T19:04:48Z
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@futurebird Having a probaility of one is not the same as certainty, so that doesn't quite work. Probability is a measure, so my claim is analogous to, and true for the same reason as, the fact that there are proper subsets of a unit interval of length one—for example leave out a single point.
(DIR) Post #An6jP88MecmftFjt9E by dmself@mstdn.social
2024-10-17T19:52:38Z
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@futurebird @alienghic @malin From the opposite direction:When I taught pre-cal, students would ask how an infinite series could add to a finite number. I would say "It's proved with limits, which you won't learn until Cal 1, but this will help...", and then I would draw a square, cut it in half, and label "1/2". Then repeat, "1/4", making a spiral shape.Students usually realized that I was never going to get done, but also I was never going to escape the square. So it's always <= 1.
(DIR) Post #An7i9WeLpbUWUmej9U by mauve@mastodon.mauve.moe
2024-10-18T07:13:14Z
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@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.
(DIR) Post #An7qThkx2xOSMmsO4O by gregeganSF@mathstodon.xyz
2024-10-18T07:18:34Z
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@mauve @futurebird @tetron That sounds more like the novel “Quarantine”, which is not about being in a simulation, it’s about manipulating wave function collapse.