Showerthoughts

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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The most popular seem to be lighthearted, clever little truths, hidden in daily life.

Here are some examples to inspire your own showerthoughts: 1

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A drunk person wandering outside will always find their way back but a drunk bird probably won't. (programming.dev)

submitted 2 years ago by [email protected] to c/[email protected]

27 comments fedilink hide all child comments

Explanation: Random walk in 2D has a unity probability of making it back to the starting point as the number of steps approach infinity but random walk in 3D only has ~0.34.

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[–] [email protected] 4 points 2 years ago (1 children)

That doesn't make sense to me. Sure, the probability in 3D is gonna get really low. Never 0 though since there is a chance the previously taken steps will be done in reverse. And since we talk about infinity here .. the drunk bird should also find home.

[–] [email protected] 8 points 2 years ago* (last edited 2 years ago) (1 children)

I was maybe a bit sloppy when I said it "quickly drops to 0" instead of it "quickly tends to 0". It'll of course always be positive - in fact if N is the sum of the absolute value of the three coordinates of its current position, the probability of returning to the origin is strictly greater than 1/6ᴺ.

But it does tend to 0 in such a way that the probability of its random walk ever returning to the starting position is not 100%. It has a 34% chance of ever getting back at the very start of its journey - but if it gets too far off track that probability is going to tend to 0 fast enough that it's not likely to ever make it back, even with infinitely many steps. Here's a youtube video (that I did not watch myself) that seems to go over the topic.

[–] [email protected] 2 points 2 years ago

Here is an alternative Piped link(s): https://piped.video/watch?v=iH2kATv49rc

Piped is a privacy-respecting open-source alternative frontend to YouTube.

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