Weird GPT-4 behavior for the specific string “ davidjl”
This is completely tangential, but I want to share my latest GPT4 story somewhere.I've tried before to gaslight GPT4 into saying things which are mathematically untrue, I lie to it, I tell it it's malfunctioning, I tell it to just do it, it wouldn't do it.I was recently studying linear algebra which can be a very tricky subject. In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). If you ask GPT4 if "C(A) = C(AA^T)" is true, it will understand what you're asking, it knows it's about linear algebra, but it will get it wrong (at the time of this writing, I've tried several times).I couldn't get GPT4 to agree it was a true statement until I told it the steps of the proof. Once it saw the proof it agreed it was a true statement. However, if you try to apply the same proof to C(A) = C((A^T)A), GPT4 cannot be tricked, and indeed, the proof is not applicable to this latter case.So GPT4 was incorrect yet able to be persuaded with a correct proof, but a very similar proof with a subtle mistake cannot trick it.