felipec.substack.com
Changing someone's mind is very difficult, that's why I like puzzles most people get wrong: to try to open their mind. Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.
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Notes -
One bit fits one bit of data. This can be less than one bit of information (e.g. if I encode each 0 or 1 in an equal-probability channel as 000000 or 111111 I get 1/6 of a bit of information each, or if a non-uniform data source with probability p=1/3 of the next bit being 1 gives me an expected 0 then I get 0.58 bits out of that) or it can be more than one bit (if I see an unexpected 1 instead then that's 1.58 bits of information).
If it's a noisy channel then "000000" might not be very "artificial", that might be the safest way to communicate. If it's not a noisy channel then I've just wasted 5 bits; the limitation to 6 bits might have been natural, but the further limitation to 1 was not. Natural limitations and artificial limitations are not opposites; you can have both at once.
[edit to fix weird formatting; I can't seem to get a tilde to be a tilde, whether I escape it with a backslash or backticks or what, without it either disappearing or turning into a strikethrough formatter]
Yes, but it cannot be more. The point here is that information is not being "omitted", there's always limits to how much information can be transmitted, stored, processed, etc.
And in general programmers try to not use more information than necessary, this is not unique to this field, it's just easier to see because the information can be precisely measured.
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