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Deleting my previous example which is too verbose. Here's a good example: >> what is laguerre geometry? > Laguerre geometry is a branch of geometry developed

Deleting my previous example which is too verbose. Here's a good example: >> what is laguerre geometry? > Laguerre geometry is a branch of geometry developed by the French mathematician Edmond Laguerre in the 19th century. It is a non-Euclidean geometry that deals with the study of conic sections, curves, and surfaces in 3-dimensional space. Unlike Euclidean geometry, Laguerre geometry allows for the existence of lines and planes with complex, imaginary or dual coordinates. The Laguerre distance between two points is defined as the square root of the cross ratio of four points, and the geometry itself is often referred to as the geometry of cross-ratio invariants. The Laguerre geometry has applications in projective geometry, algebraic geometry, and physics. The nontrivial parts of this are just wrong. Laguerre geometry is geometry where oriented lines are the basic objects rather than points, and other objects are constructed as envelopes of lines rather than loci of points. It is a kind of dual to inversive geometry (with "laguerre transformations" analogous to "möbius transformations").

NikolaNovak 4y ago
Thanks - genuinely appreciate the example! If you don't mind, since I don't know the concept myself, where would you scale it on the axis of obscurity and controversy? My own meagre check: In terms of obscurity - there's no Wikipedia entry for it, and a quick google search does not provide a super quick and simple definition to my ignorant and superficial check. There's tons on Laguerre transform but not on "Laguerre geometry". What there is, gives definitions that are not the same as the one you provided and is not consistently worded. I am not capable of reconciling and judging are they comparable or not, and are there more than one way of defining interpreting or explaining, nor exactly how wrong the AI definition is. At the same time, search for lobochevski geometry, which the most obscure one I know in my limited mathematical awareness, is amply and consistently covered - yet, still beyond the threshold of obscurity and consistency that I would use for AI. And search for Euclid geometry, which is what I'd expect AI to define correctly, is of course plentiful (which is why I'd expect AI to succeed, a bit circular there:). So it may be simply that our expectations and need/use of LLM AI are different? To your original point, I'm indeed using it for stuff that's basic and common and it seems to work well there. If that's all it works well for, it's bloody amazing and very useful for many - even if definitely not (yet?)useful for all people, domains, or cases.
- jacobolus 4y ago
  The reason it’s topical for me is that I have been trying to do the research to write better Wikipedia article(s) about the subject. The one currently at https://en.wikipedia.org/wiki/Laguerre_transformations https://en.wikipedia.org/wiki/Laguerre_transformations doesn’t do an adequate job with the basics IMO. I gathered a long list of resources at https://en.wikipedia.org/wiki/Talk:Laguerre_transformations#List_of_references https://en.wikipedia.org/wiki/Talk:Laguerre_transformations#... (As commonly happens, I am currently a bit stuck on making a bunch of diagrams...) This is not controversial, but it is moderately obscure. (But not that obscure.) * * * I don’t have any particular “expectation”. I am just disappointed that the current versions of these tools do not give any indication about their level of certainty. I have asked a wide range of questions that prompted responses which were substantially bullshit. But if I hadn’t followed up might have seemed plausible enough. Stuff like asking for translations of material written in Latin, asking about word etymologies, asking about court cases, asking for summaries of famous old books, ... I have had a few conversations like: “Who discovered thing A” “It was X, who ....” “wasn’t it Y?” “Yes I am sorry. I was incorrect. It was Y, who ...” “Wasn’t it actually Z?” “Yes I am sorry. I was incorrect. It was Z, who ...” If you try you can get it to make up nonsense about a whole string of false discoverers. It would be better if it instead say “I have no idea about the precise answer, but people P and Q were working on similar topics around that time” or whatever.

NikolaNovak 4y ago

Thanks - genuinely appreciate the example! If you don't mind, since I don't know the concept myself, where would you scale it on the axis of obscurity and controversy? My own meagre check: In terms of obscurity - there's no Wikipedia entry for it, and a quick google search does not provide a super quick and simple definition to my ignorant and superficial check. There's tons on Laguerre transform but not on "Laguerre geometry". What there is, gives definitions that are not the same as the one you provided and is not consistently worded. I am not capable of reconciling and judging are they comparable or not, and are there more than one way of defining interpreting or explaining, nor exactly how wrong the AI definition is. At the same time, search for lobochevski geometry, which the most obscure one I know in my limited mathematical awareness, is amply and consistently covered - yet, still beyond the threshold of obscurity and consistency that I would use for AI. And search for Euclid geometry, which is what I'd expect AI to define correctly, is of course plentiful (which is why I'd expect AI to succeed, a bit circular there:). So it may be simply that our expectations and need/use of LLM AI are different? To your original point, I'm indeed using it for stuff that's basic and common and it seems to work well there. If that's all it works well for, it's bloody amazing and very useful for many - even if definitely not (yet?)useful for all people, domains, or cases.

jacobolus 4y ago
The reason it’s topical for me is that I have been trying to do the research to write better Wikipedia article(s) about the subject. The one currently at https://en.wikipedia.org/wiki/Laguerre_transformations https://en.wikipedia.org/wiki/Laguerre_transformations doesn’t do an adequate job with the basics IMO. I gathered a long list of resources at https://en.wikipedia.org/wiki/Talk:Laguerre_transformations#List_of_references https://en.wikipedia.org/wiki/Talk:Laguerre_transformations#... (As commonly happens, I am currently a bit stuck on making a bunch of diagrams...) This is not controversial, but it is moderately obscure. (But not that obscure.) * * * I don’t have any particular “expectation”. I am just disappointed that the current versions of these tools do not give any indication about their level of certainty. I have asked a wide range of questions that prompted responses which were substantially bullshit. But if I hadn’t followed up might have seemed plausible enough. Stuff like asking for translations of material written in Latin, asking about word etymologies, asking about court cases, asking for summaries of famous old books, ... I have had a few conversations like: “Who discovered thing A” “It was X, who ....” “wasn’t it Y?” “Yes I am sorry. I was incorrect. It was Y, who ...” “Wasn’t it actually Z?” “Yes I am sorry. I was incorrect. It was Z, who ...” If you try you can get it to make up nonsense about a whole string of false discoverers. It would be better if it instead say “I have no idea about the precise answer, but people P and Q were working on similar topics around that time” or whatever.