The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley I was thinking about this and realized that a clock that shows a fully random time every time you check it gives you the same info as a stopped clock.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley That actually really clears up how I feel when I very occasionally test an LLM. It gives me an answer but I just cannot trust that answer unless I already know.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley It seems like the step of error checking has been missed off and left to the user. It’s as if you sent the time as beeps down a really noisy phone line - you’d need some form of checkbit for each package of information to have any assurance of veracity. We do this with people automatically - if someone tells you something, you’ll place less weight on it being right if that person also says verifiably false things. You might ask more questions to check against known info.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley Strong Sartre energy in this post; you’re conscious of the wrongness then the rightness is negated into nothingness, I like it.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley That is a brilliant point. Thank you
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@riley That actually really clears up how I feel when I very occasionally test an LLM. It gives me an answer but I just cannot trust that answer unless I already know.
@edbo I once pointed out to one that the supposed source reference link it gave was clearly irrelevant, and it apologised, told me how clever I was to notice it, thanked me for noticing it, and gave me another clearly irrelevant link.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley
The supposed misunderstanding is the very point of this notion.So, as a woman, you're basically mansplaining broken clocks?
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@riley I was thinking about this and realized that a clock that shows a fully random time every time you check it gives you the same info as a stopped clock.
@rmvh Indeed. Well, it actually gives you a little bit more enthropy, in that you can use it as dice. A stopped clock is useless in this rôle.
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@riley Precisely the acid test I've given to various LLMs, and precisely how I discovered what I suspected about them is true. They're simply big bull shitters. Ask them something you know, and watch the blatantly false answers come back.
@adam "But how else would humans who suck at bullshitting have access to this crucial skill?"
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@adam "But how else would humans who suck at bullshitting have access to this crucial skill?"
@adam FWIW, there's a standard scientific experiment protocol: give the black box some problems whose solutions you know, and some whose solutions you don't know, but if productive hypotheses were offered, could check them. If the black box gets the first class of problems reasonably right, you'll invest into the necessarily harder problem of verifying whether it got problems of the second class as right, as well.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley umm... That IS the notion of a broken clock being right twice a day. That just because something is sometimes right means it provides any relevant information. That's the whole point of the metaphor.
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@modulux A proof is not information in a strict sense, and largery exactly because of this reason: it's self-contained (or, well, can be, with sufficient formalism available).
In a broad sense, there's some very interesting philosophy that can be done about the notion of information content of Teh Book. But it's mostly the kind of philosophy that requires a larger mug of beer than would be conducive to my upcoming meetings[1], so, as the old Orcish saying goes, nar udautas.
As a general rule, I tend to prefer the interpretation that a proof is a series of "I'd now like to bring your attention to ..." kind of steps: they don't add anything (directly) to your mental map; they suggest where you should look at to find interesting things that are already on the map.
[1] A children's book I once read included a character, one mathematics professor, who argued that it is pointless to ask questions, because there's two possibilities: the answer either is known or is not known. If it's known, what's the point of asking it again? If it's not known, what's the point of asking if there won't be an answer?
And, well, while it's silly in an obvious way, this kind of reasoning actually comes up in the context of proofs-as-information.
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@riley Yes, I heard about it; the most elegant possible proof for a given theorem, roughly?
Rather I was thinking of the notion you stated that proofs aren't information, and I see why you said it. But it doesn't seem intuitive when we compare it to other ways we use the notion.
For example let's say we have a composite number pq. Generally speaking, we would say that getting p and q is additional information. But the proof that some p in particular and some q in particular result in pq would contain no information. It's rather odd to think of.
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This confusion is also what cold reading is based on, btw. Falling for a chatbot is literally the same type of mistake as falling for a psychic telling you that somebody you used to know who had a vowel in their name died.
@baldur 's LLMentalist article is something I have shared repeatedly since it first came out:
The LLMentalist Effect: how chat-based Large Language Models rep…
How to make better software with systems-thinking
Out of the Software Crisis (softwarecrisis.dev)
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S stefano@mastodon.bsd.cafe shared this topic
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@riley Yes, I heard about it; the most elegant possible proof for a given theorem, roughly?
Rather I was thinking of the notion you stated that proofs aren't information, and I see why you said it. But it doesn't seem intuitive when we compare it to other ways we use the notion.
For example let's say we have a composite number pq. Generally speaking, we would say that getting p and q is additional information. But the proof that some p in particular and some q in particular result in pq would contain no information. It's rather odd to think of.
@modulux You know how numeric probabilities can vary depending on how equipotentiality is defined, and it sometimes be left implicit with multiple equally plausible "obvious" definitions?
Modelling the information flow of abstract mathematics as such runs into this same sort of problems. Nobody has axiomatised it; there's a bunch of common intuitive assumptions, but a lot of them are ... well, you can pry them loose and justify it if you want to, and sometimes, get interesting results this way. But a lot of times, you don't get anything, or maybe you will have to nail down your own (quasi)-axioms first. These aren't like the axioms of modern geometry; they're really kind of like what Eukleides wrote in the beginning of The Elements, and then never did anything with because it didn't make any sense.[1]
So you see why I suggested a huge mug of beer for dealing with this stuff.
[1] Caveat: if you go searching, a lot of sources offer modern axiomatic geometry instead of Eukleides' original work — still because his vague notion of foundations didn't make sense, and now we actually have the axioms that could have been used for the conclusions he went on to, pardon the pun, draw. Most of the rigorisation work was done in the 1600s' Italy; the lingering hairy problem of the Parallels' Axioms was eventually solved by Lobachevskiy in early 1800s by demonstrating that it can be reversed without breaking anything else, and Euklidean geometry as understood by moden mathematics generally rests on Hilbert's[2] work from the pinnacle of the 19th century, as in, it was published in 1899. But it can be great fun to read translations of the original Elements, including the crappy parts.
[2] You might have heard of his hotel, which has a countable infinity number of rooms. Ijon Tichy was a repeat customer.
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R relay@relay.publicsquare.global shared this topic
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@baldur 's LLMentalist article is something I have shared repeatedly since it first came out:
The LLMentalist Effect: how chat-based Large Language Models rep…
How to make better software with systems-thinking
Out of the Software Crisis (softwarecrisis.dev)
-
@modulux You know how numeric probabilities can vary depending on how equipotentiality is defined, and it sometimes be left implicit with multiple equally plausible "obvious" definitions?
Modelling the information flow of abstract mathematics as such runs into this same sort of problems. Nobody has axiomatised it; there's a bunch of common intuitive assumptions, but a lot of them are ... well, you can pry them loose and justify it if you want to, and sometimes, get interesting results this way. But a lot of times, you don't get anything, or maybe you will have to nail down your own (quasi)-axioms first. These aren't like the axioms of modern geometry; they're really kind of like what Eukleides wrote in the beginning of The Elements, and then never did anything with because it didn't make any sense.[1]
So you see why I suggested a huge mug of beer for dealing with this stuff.
[1] Caveat: if you go searching, a lot of sources offer modern axiomatic geometry instead of Eukleides' original work — still because his vague notion of foundations didn't make sense, and now we actually have the axioms that could have been used for the conclusions he went on to, pardon the pun, draw. Most of the rigorisation work was done in the 1600s' Italy; the lingering hairy problem of the Parallels' Axioms was eventually solved by Lobachevskiy in early 1800s by demonstrating that it can be reversed without breaking anything else, and Euklidean geometry as understood by moden mathematics generally rests on Hilbert's[2] work from the pinnacle of the 19th century, as in, it was published in 1899. But it can be great fun to read translations of the original Elements, including the crappy parts.
[2] You might have heard of his hotel, which has a countable infinity number of rooms. Ijon Tichy was a repeat customer.
@modulux Oh, btw: Turing's Machines are this way, in part, because they genuinely used to try and go with the notion of information flows in mathematics being like frictionless spherical cows in vacuum. For some things, it's a great simplifications; for others, well, it didn't work out, and we ended up having Complexity Theory.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley Let's say I constructed an elevator with 12 floors. The elevator stops at the next floor every hour on the hour starting from the ground floor at noon and returning to the ground floor at midnight at which point the process repeats. There is a window on the door which shows a broken clock for each floor. Ground floor clock is broken at 12, the next at 1 and so on.
Consider the nature of a fool who gets locked in the elevator and does not know the time. Does the broken clock inform him?
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@riley That’s the point. You got information theory right. You just misunderstood the expression with the clock.
When I say: ‘My AI gave me a correct answer once’, you can reply: ‘Sure, even a broken clock is correct twice a day.’ Thus stressing that coincidental correctness is worthless.
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The notion of a broken clock being sometimes right is based on a gross misunderstanding of what information is.
A clock that always shows the same time is never right, even in the moments of the day when the time happens to be what it shows, because you don't gain any information about what time it is by looking at the clock.
This reasoning also applies to chatbots. If you can't tell whether what you have been given is useful information unless you alreay know the information, then you haven't been given useful information.
@riley Now do "even a blind squirrel occasionally finds a nut"
