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Bill Taylor's avatar

Some great points in this article. Thanks for writing it; I learned a lot.

It’s sometimes a hard task to discuss whether AI has knowledge; or can think. I’d say we humans tend to lionize our own style of knowledge, and too often denigrate AI as ‘less-than’, as opposed to ‘different.’ It becomes a bit tribal unfortunately. I appreciate thoughtful explanations without the defensive baggage.

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David Thomson's avatar

To go to your headline - which is subtly different from your content. I'm confused by your level of description. I think of linear algebra as a formal system, it's a language of symbols. x Longitude y latidude doesn't "know" it's a position on the earth, even if you give it relations to other longitude and latitudes, it's just symbol manipulation. Even if you want to claim that we work on linear algebra and we know stuff therefore linear algebra knows about linear algebra - it's has to be somewhere in the emergent effects of complexity and self reference. At which point... is that still linear algebra you're talking about? Biologists don't talk about bird migration in terms of quantum mechanics.

Going to your definition of "knowing" - do you require interactivity? I assume not, but the word suggests action and situation in time, and so to me implies interactivity. Does interactivity matter? Is it the processing that matters? Does an encyclopedia "know" Pi to x decimal places? Does a calculator that has to generate it? Does an LLM - it has to manipulate statistical patterns and retrieve that information from a search? Does an LLM that uses tools - it will predict that the correct answer is to use a calculator, put in the formula and return the answer - so is it the system that knows or Claude?

Claude I think can tell you to about 20 decimal places without tools, but will fail after that - with tools it can probably go as long as it is happy to calculate. What are the lines between statistical pattern manipulation, and knowledge? Do I know Pi? Off the top of my head to 3 decimal places... Is Claude better at knowing Pi than me? My intuition says that I want to say "no" but that doesn't quite make sense either. Does the question even make sense? Is it just something you can say in English like, "I love the corners on circles."

For myself, I find it interesting that most conversations focus a lot on "knowledge" as in "Cambridge is a city in England" rather than "knowledge" as the relations between things. The word "Cambridge" sits in a host of relationships inside education, class, geography, history and so on rather than atomic facts. The useful part of "knowledge" is, I think, largely in those relationships and structures, not the unitary facts (though they are part of the moorings!). The cool thing about this new technology is that it give us a natural language interface to explore many (all?) of those relationships. Is that "knowledge" yes. Do they "know"... and I feel the language starts warp as if I'm trying to extend a metal measuring tape without it snapping under it's own weight.

It's a slippery word (then again what words aren't!?). Do I think an LLM contains knowledge that it can manipulate? Sure! Do I think they can reason? I'd say not really... because I think the word "reason" includes some sort of intentionality and grounding. But... I'd say yes they reason under the definition of reasoning you gave in your essay! Do I think an LLM has a world model? No, but there is a faded imprint of one from our language use - but that can still be a very useful, very powerful lever to use.

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