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A shower thought turned into a Collatz visualization

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Re: A shower thought turned into a Collatz visualization

#21

Post by coolcase »

90s_dev wrote: post #5

> I've been telling people for years if businesses want employees to have better ideas, they should have more showers in their offices. So far everyone seems to think I'm joking. I'm not. I have definitely noticed that some of my best ideas or breakthroughs come to me when showering, or sleeping, or eating, or driving, or doing the dishes, or basically any mundane autopilot task where my mind is free to wander. But y…

Most places I work have a shower - albeit not just off the main office. Usually part of the building infra. It's great if you cycle to work for example or play sport at lunchtime. It's a good thing if well placed.

Re: A shower thought turned into a Collatz visualization

#22

Post by dotancohen »

coolcase wrote: post #21
90s_dev wrote: post #5

> I've been telling people for years if businesses want employees to have better ideas, they should have more showers in their offices. So far everyone seems to think I'm joking. I'm not. I have definitely noticed that some of my best ideas or breakthroughs come to me when showering, or sleeping, or eating, or driving, or doing the dishes, or basically any mundane autopilot task where my mind is free to wander. But y…

Most places I work have a shower - albeit not just off the main office. Usually part of the building infra. It's great if you cycle to work for example or play sport at lunchtime. It's a good thing if well placed.

What's the trick to finding it?

Re: A shower thought turned into a Collatz visualization

#23

Post by philjohn »

xigency wrote: post #9
gpm wrote: post #6

Earlier quoted context omitted.

I've worked in an office with a very nice (clean, private, towels and soap dispensers provided) shower. Actually two (in separate rooms). And taken showers in them. It definitely was not gross, nor do I think anyone thought it weird, nor was I the only person who used them. After a bicycle commute to work though, not randomly during the day.

Taking a wild guess, was this at Fog Creek / Stack Overflow?

That last 3 companies I've worked for have had this. 2 FAANGs and 1 mid size, household name, tech company.

Re: A shower thought turned into a Collatz visualization

#24

Post by coolcase »

dotancohen wrote: post #22
coolcase wrote: post #21

Earlier quoted context omitted.

Most places I work have a shower - albeit not just off the main office. Usually part of the building infra. It's great if you cycle to work for example or play sport at lunchtime. It's a good thing if well placed.

What's the trick to finding it?

Finding a job with an office with a shower? Guess it is luck lol

Re: A shower thought turned into a Collatz visualization

#25

Post by gpm »

mkl wrote: post #19
gpm wrote: post #4

> The points look quite uniformly distributed to me. If I squint, then maybe I can see some structure, but it's hard to describe and I could be imagining it. It doesn't, these points look like what happens if you ask someone who doesn't know what a uniform distribution looks like to generate a uniformly distributed set of points though. Here's what an actual uniform distribution looks like... much less "uniform": htt…

"Uniformly distributed" doesn't just mean sampled from a uniform distribution. It also means evenly spaced, as is the case here. It reminds me of Poisson disk sampling. Here's an article about Poisson disk sampling that uses "uniform" in the sense the author is, and also compares to the uniform probability distribution: https://medium.com/@hemalatha.psna/implementation-of-poisson...

Really the germane point isn't that it isn't specifically a uniform distribution, but that there is clearly structure to the distribution of those points. The locations are visibly not a set of IID random variables, because IID random variables don't space out that... uniformly.

That said, while I agree "uniform" not followed by an inflection of "distribution" has many other meanings, I do not agree that it the context of math, in a context where there is a standard uniform distribution, and without other relevant context, "uniformly distributed" can properly be understood to mean anything other than distributed via the standard uniform distribution.

Re: A shower thought turned into a Collatz visualization

#26

Post by gpm »

ginko wrote: post #18

Talking about shower thoughts on Collatz visualizations.. A while ago I though of a way of structuring the collatz orbits by arranging integers in a 2d grid with odd numbers being arranged along the X axis and multiples of the power of two along the Y axis. https://gist.githubusercontent.com/ginkgo/13121db56b65b1237e... So essentially any odd number n and all numbers n * 2^m belong to the same group of numbers that e…

Just wanted to chime in and say that's a really interesting visualization of the conjecture, I haven't seen it before (and I have wasted more than a few hours on this problem).

Re: A shower thought turned into a Collatz visualization

#27

Post by snarf21 »

90s_dev wrote: post #5

> I've been telling people for years if businesses want employees to have better ideas, they should have more showers in their offices. So far everyone seems to think I'm joking. I'm not. I have definitely noticed that some of my best ideas or breakthroughs come to me when showering, or sleeping, or eating, or driving, or doing the dishes, or basically any mundane autopilot task where my mind is free to wander. But y…

I think that the shower just slows your brain down just enough to get into flow. I've found that walking and driving do the same for me as well.

Re: A shower thought turned into a Collatz visualization

#28

Post by [deleted] »

manwe150 wrote: post #2

As for the randomness, I have wondered if Collatz sequences are somehow related to the properties of a common prng with multiplier 3/2, infinite length state vector, and mod 2 on the output with this formula: https://en.m.wikipedia.org/wiki/Linear_congruential_generato... . I assume this could be part of what makes the conjecture both interesting and difficult and beautiful. Very cool to see there is some patterns hi…

[deleted]

Re: A shower thought turned into a Collatz visualization

#29

Post by pepinator »

gpm wrote: post #25
mkl wrote: post #19

Earlier quoted context omitted.

"Uniformly distributed" doesn't just mean sampled from a uniform distribution. It also means evenly spaced, as is the case here. It reminds me of Poisson disk sampling. Here's an article about Poisson disk sampling that uses "uniform" in the sense the author is, and also compares to the uniform probability distribution: https://medium.com/@hemalatha.psna/implementation-of-poisson...

Really the germane point isn't that it isn't specifically a uniform distribution, but that there is clearly structure to the distribution of those points. The locations are visibly not a set of IID random variables, because IID random variables don't space out that... uniformly. That said, while I agree "uniform" not followed by an inflection of "distribution" has many other meanings, I do not agree that it the conte…

The notion of being uniformly distributed has a very specific meaning in mathematics [1]. If you don't believe me, maybe you believe Tao [2].

[1] https://en.m.wikipedia.org/wiki/Equidistribution_theorem

[2] https://terrytao.wordpress.com/2020/01/25/equidistribution-o...

Re: A shower thought turned into a Collatz visualization

#30

Post by [deleted] »

pepinator wrote: post #29
gpm wrote: post #25

Earlier quoted context omitted.

Really the germane point isn't that it isn't specifically a uniform distribution, but that there is clearly structure to the distribution of those points. The locations are visibly not a set of IID random variables, because IID random variables don't space out that... uniformly. That said, while I agree "uniform" not followed by an inflection of "distribution" has many other meanings, I do not agree that it the conte…

The notion of being uniformly distributed has a very specific meaning in mathematics [1]. If you don't believe me, maybe you believe Tao [2]. [1] https://en.m.wikipedia.org/wiki/Equidistribution_theorem [2] https://terrytao.wordpress.com/2020/01/25/equidistribution-o...

[deleted]
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