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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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I read that as "Twenty two minutes plus two minutes", which is obviously a duration of 24 minutes. Even if I had read it as hours, there's nothing wrong with 24 hours or even 30, 48, or 100. (A thousand hours might be pushing it, though.) Also, I will refer to midnight as 24:00:00. If it was three hours, then I wouldn't answer 1:00 like you're suggesting either. I'd say "01:00 the next day" because time isn't truly modular, it's just mixed base and convention says that we exclude the most-significant parts when possible.
I'm not sure about more esoteric ones, but in spherical and hyperbolic geometries pairs of lines with constant distance simply don't exist. Lines converge or diverge (for spherical/hyperbolic, respectively), and the set of points that are a constant distance from a given line are a curve for both of them: you can either have a line or you can have constant distance.
In fact, proving that lines with constant distance never intersect is utterly trivial if you assume they exist:
intersection is when the distance is zero
the constant distance is nonzero
therefore, they don't intersect.
But your clock would read
01:00.We use this concept in programming all the time. If the week ends in Sunday we don't say that the day after that is Monday the next week, it's Monday (this doesn't change if the week ends in Saturday). In fact, many people consider Friday
23:00+02:00to still be Friday night.Yes, I meant "two straight lines that indefinitely extended in a two-dimensional plane that are both perpendicular to a third line", like in this picture, which are kind of parallel. The point is the standard concept of "parallel" more or less only exists in Euclidean geometries.
That's merely convention, omitting information that can be derived from context for brevity. If you want to make a formal argument, you need to include that information again. Everyone is aware monday is next week, that's why you don't spell it out if it isn't relevant, but if you're e.g. scheduling business on a weekly base, you might have to say "Tomorrow is monday, which is next calendar week".
No. In programming it's literally impossible to include information that wasn't meant to be included. If you have an int to store the weekday, that's all the information stored in that int.
Not having all the information is a huge problem in programming, and historically it has been a big headache to deal with dates and time.
But if a program doesn't need any information other than the weekday, it may use that and nothing more.
If you're omitting the information of which week it is because it's not relevant, you're omitting information, and that means you can't use the result to support your argument, because it's missing information.
Information is always limited. Humans and all rational agents always operate with limited information. There is no omission.
In our case, informations isn't just limited, but artificially limited, i.e. omitted. The information is indeed still available, just by deriving it from context. We both know monday after sunday is next week.
You're making an argument based on information you know is incomplete, and the missing information invalidates it. Don't do that.
Wrong. Information by its very nature is limited. Nobody is "artificially" limiting the information that can fit in one bit, one bit can only fit one bit of information. Period.
This is the foundation of information theory.
There is no context attached to information. One bit is one bit. You can try to do some clever tricks with two bits, or four bits, but at the end of the day the information is the information.
No, we don't. You are assuming where the week starts.
All information is incomplete.
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]
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That's a red herring. We're not talking about bits. We're talking about the information we have about your example, which was given in english.
Liar. The end of the week being sunday was included in your description of the example.
Not all information is incomplete in the sense that reasoning from it leads to false conclusions. Stop defending your fallacious argument.
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