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felipec  unbelief  1yr ago (felipec.substack.com)   3217 thread views

2+2 = not what you think

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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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

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+02:00 to still be Friday night.

I'm not sure about more esoteric ones, but in spherical and hyperbolic geometries pairs of lines with constant distance simply don't exist.

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.

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

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.

In our case, informations isn't just limited, but artificially limited, i.e. omitted.

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.

The information is indeed still available, just by deriving it from context.

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.

We both know monday after sunday is next week.

No, we don't. You are assuming where the week starts.

You're making an argument based on information you know is incomplete, and the missing information invalidates it.

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]

This can be less than one bit

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.

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.

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.

No, we don't. You are assuming where the week starts.

Liar. The end of the week being sunday was included in your description of the example.

All information is incomplete.

Not all information is incomplete in the sense that reasoning from it leads to false conclusions. Stop defending your fallacious argument.

We're talking about the information we have about your example, which was given in english.

The information in English is limited too. Information is always limited.

"Tomorrow is Monday" has limited information.

Liar. The end of the week being sunday was included in your description of the example.

This was my example:

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)

The case where the week ends in Saturday is included. If today is Sunday we say:

  1. Tomorrow is Monday (if the week ends in Sunday)

  2. Tomorrow is Monday (if the week ends in Saturday)

My example was crystal clear in explaining that the day the week ends does not matter in describing what day comes after Sunday. This information is not available from the phrase "tomorrow is Monday".

You claim the information is available because if the week ends in Sunday "we both know" when the week ends. No, we don't, because I don't. If you want to claim you know when the week ends from the phrase "tomorrow is Monday" go ahead, I do not know.

And it doesn't seem to me you are engaging with my argument.

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