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
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"
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@MissConstrue Are you a chatbot sycophanting me up?
These days, one can never be too cautious.
Are you very concerned that a chatbot sycophanting you up?
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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 think this overstates the problem a bit; it either implies that knowledge transfer is impossible (replace "humans" with "chatbots" in the last sentences) or it assumes humans querying chatbots can't have a method to verify the information but not generate the information to verify (unless that assumption wasn't implied, in which case nevermind!).
There is a name for the logical state you describe about clocks, but I can't remember it right now. I've heard it referred to as the 'stone cow problem': you see a field. You see a cow in the field. You declare there's a cow in the field. What you saw was actually a convincing cow statue, so you're wrong... But there is a cow sleeping behind the statue that you cannot see, so you're right. Big ol' chunks of software engineering puzzles end up being of this kind (any time two systems are manipulating the same memory, there's a risk that system 2 is manipulating state system 1 should be touching, but it is giving the answer system 1 would give, even if the semantic meaning of the answer is entirely different and it's just dumb luck that the bit patterns representing the answers are the same. So your debugging shows no problems and then problems pop up when the behavior of system 2 changes but you think system 1 changed, because you thought system 1 was controlling the data, etc.
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Are you very concerned that a chatbot sycophanting you up?
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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 @riley This is also an illustration of why LLMs have a (very limited) utility in generating computer code.
Computer code has a specific purpose. The generated code can be tested against the task. This can be useful.
But computer code will also have other effects and costs that only a human can validate well.
At most an LLM should be used to generate rough drafts of well defined functions that will be reviewed and tuned by a qualified human.
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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.
FWIW? There is a branch of philosophy focused on the problem you describe – one so old we use an ancient Greek name for it:
> https://en.wikipedia.org/wiki/Epistemology
This is because determining if information is true and actionable has *always* been fraught. AI merely adds a brand new way to get wrong information.
The underlying problem arises when people uncritically believe *anything* from *any source*; human or machine. This is why science has protocols for publishing and re-creating results.
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@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?
@Smohc_Stahc If we made a hammer out of dynamite, would it be a hammer or dynamite?
