this post was submitted on 05 Aug 2023
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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:

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A drunk person wandering outside will always find their way back but a drunk bird probably won't. (self.showerthoughts)
submitted 2 years ago by gogosempai to c/[email protected]
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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] 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

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