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Finding Waldo in π

kundor.github.io

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Re: Finding Waldo in π

#31

Post by politician »

kundor wrote: post #8
bscphil wrote: post #5

> The trick is that we can reassign the colors using a palette. And in fact you always need to do this; you have to somehow decide which color each byte should represent. Hmm. I don't know that I agree. There are certainly more objective choices here than just picking any old palette, and in fact there are choices where it's not obvious the result should be considered a "palette" at all. For example, the obvious choi…

That's still a choice of palette; you'll find it listed on Wikipedia [1] under "Regular RGB palettes". There's no doubt it's a much more objective choice than the one I used! I did say I was cheating. Going to 4-bit color won't make it feasible. Even with 1-bit black/white pixels on about the minimum possible 18x24 Waldo face, you have 432 bits to look for, and you're not going to find them without cheating somehow.…

Would not the best choice of palette be the one immediately preceding Waldo in π?

Re: Finding Waldo in π

#34

Post by mcpherrinm »

mcbuilder wrote: post #32

Dumb question, but is any arbitrary string of digits with length N, somewhere in pi?

Not exactly the same thing, but related: I think everyone believes Pi is a Normal Number, but it isn’t proven. https://en.m.wikipedia.org/wiki/Normal_number

I think if we could prove Pi is normal, we could probably also prove your statement to be true (but I’m not sure about that)

Re: Finding Waldo in π

#39

Post by slopbop »

mcpherrinm wrote: post #34
mcbuilder wrote: post #32

Dumb question, but is any arbitrary string of digits with length N, somewhere in pi?

Not exactly the same thing, but related: I think everyone believes Pi is a Normal Number, but it isn’t proven. https://en.m.wikipedia.org/wiki/Normal_number I think if we could prove Pi is normal, we could probably also prove your statement to be true (but I’m not sure about that)

Normal is actually a stronger claim than "contains any finite string as a substring". That normal numbers contain any finite string as a substring is a straightforward consequence of the infinite monkey theorem: https://en.wikipedia.org/wiki/Infinite_monkey_theorem

To see that the converse does not always hold, you could take something like the Champernowne constant https://en.m.wikipedia.org/wiki/Champernowne_constant and pad it with 9s between each integer, ie

.192939495969798999109911991299...

so that you still contain every finite substring, but you have a >50% chance of a randomly selected digit being 9.

Re: Finding Waldo in π

#40

Post by mjburgess »

bkyiuuMbF wrote: post #19

With acknowledgement to the palette hack discussed in the other comments, I still think there's a ton of value in this. So often, people observe patterns in nature that appear to be so unlikely as to be by design. I have family members that are superstitious: if a light flickers at the same time that they mention a recently deceased loved one, it must be "a sign". Similarly, they will point to some overwhelmingly unl…

There are an infinite number of coincidences happening in every moment: a raindrop falling, a light turning off, a wind blowing on mars, a star rotating, and so on.

If one cared to find "something apparently significant" in any moment, one would therefore find an infinity of them.

By comparison, events which are directly causally connected are diminishingly few, and mostly indistinguishable from those coincidences. Hence, most things are actually unknowable, and what few beyond the ordinary, require extremely expensive and technologically advanced science to uncover.

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