As someone with coding expertise but very little knowledge of math terminology, and without looking up any of the terms mentioned: I can tell there is a joke here. I cannot tell where the joke is, because I don’t have a solid enough understanding of what I can only assume are made up terms or terms related to matrix algebra (and/or whatever related fields are indicated. An annoying part of learning these sorts of things is when you don’t even know enough to be able to identify the precise field being used.)
Did you make up some of those terms to make this a trick question?
After posting this comment to record my confusion I will then allow myself to search for those terms and find out how good or bad my guesses are.
My penalty for being wrong is everyone gets to laugh at me proportional to how far off I am
The claude.ai chat interface only lets claude run javascript code, but “import numpy as np” is python. As a result, the code doesn’t run. This is an extremely common and funny issue for me across claude versions, but it must be caused by something in my prompting style if other people aren’t hitting it
Typically if I don’t stop it claude does eventually recover, the new version was able to catch itself and switch to javascript after only three script submissions! In the end, claude 4 opus produced a confident, well informed, and completely wrong answer, but its a nasty problem that I didn’t expect it to solve- has to do with quantum time reversal. The humor doesn’t really involve the math. ( For reference, if the METR time horizons people want to steal it, this problem took me about 4 hours, but I am an unusually slow mathematician. If you know that the common name for this is an antilinear eigenvalue, not a conjugate eigenvalue, then it can be solved with a simple arxiv search, but one is not always gifted the True Name of a math concept by which its literature may be summoned; and I had not found the true name yet when I prompted claude or made the original post)
What’s the solution? Is it a trick question? I don’t see how you have nontrivial solutions for a complex matrix unless it is very special like, say, a diagonal matrix composed of roots of unity shifted by phase angle.
If you form the block matrix Y = (real(A), -imag(A) ; -imag(A), -real(A)), the real valued eigenvectors and eigenvalues of Y correspond to conjugate eigenvectors and eigenvalues of A; the complex conjugate pairs of eigenvalues of Y don’t correspond to anything. Then, for any angle theta, you can multiply a conjugate eigenvector v of A by exp(i theta) to get a new conjugate eigenvector, and find its associated eigenvalue by elementwise dividing A conj(exp itheta v) by v. The conjugate eigenvalues form up to 10 continuous rings around the origin,
Haha, yet more context I didn’t have much probability of understanding I work in C# almost exclusively and so I’ve never used an LLM with the expectation that it would run the code itself. I usually explicitly specify what language and form of response I need “Generate a C# <class/method/LINQ statement> that does x y and z in this way with parameters a, b, and c”
I’m pretty sure there at no nontrivial solutions to the equation unless A has certain (non-random) properties like being real-valued. Generating random complex matrices will never find a nonzero conjugate eigenvalue.
I see. Maybe. However much I can at this inferential distance It’s funny how things like matrices are critical for some types of coding (AI, Statistics, etc) but completely unnecessary for others. As a software developer who is not in AI or statistics they have never come up once, though perhaps I would’ve been able to spot potential use cases if I had that background. Similar to how I frequently see use cases for SQL where inferior options are being used in the wild[1].
As someone with coding expertise but very little knowledge of math terminology, and without looking up any of the terms mentioned:
I can tell there is a joke here. I cannot tell where the joke is, because I don’t have a solid enough understanding of what I can only assume are made up terms or terms related to matrix algebra (and/or whatever related fields are indicated. An annoying part of learning these sorts of things is when you don’t even know enough to be able to identify the precise field being used.)
Did you make up some of those terms to make this a trick question?
After posting this comment to record my confusion I will then allow myself to search for those terms and find out how good or bad my guesses are.
My penalty for being wrong is everyone gets to laugh at me proportional to how far off I am
The claude.ai chat interface only lets claude run javascript code, but “import numpy as np” is python. As a result, the code doesn’t run. This is an extremely common and funny issue for me across claude versions, but it must be caused by something in my prompting style if other people aren’t hitting it
Typically if I don’t stop it claude does eventually recover, the new version was able to catch itself and switch to javascript after only three script submissions! In the end, claude 4 opus produced a confident, well informed, and completely wrong answer, but its a nasty problem that I didn’t expect it to solve- has to do with quantum time reversal. The humor doesn’t really involve the math. ( For reference, if the METR time horizons people want to steal it, this problem took me about 4 hours, but I am an unusually slow mathematician. If you know that the common name for this is an antilinear eigenvalue, not a conjugate eigenvalue, then it can be solved with a simple arxiv search, but one is not always gifted the True Name of a math concept by which its literature may be summoned; and I had not found the true name yet when I prompted claude or made the original post)
What’s the solution? Is it a trick question? I don’t see how you have nontrivial solutions for a complex matrix unless it is very special like, say, a diagonal matrix composed of roots of unity shifted by phase angle.
If you form the block matrix Y = (real(A), -imag(A) ; -imag(A), -real(A)), the real valued eigenvectors and eigenvalues of Y correspond to conjugate eigenvectors and eigenvalues of A; the complex conjugate pairs of eigenvalues of Y don’t correspond to anything. Then, for any angle theta, you can multiply a conjugate eigenvector v of A by exp(i theta) to get a new conjugate eigenvector, and find its associated eigenvalue by elementwise dividing A conj(exp itheta v) by v. The conjugate eigenvalues form up to 10 continuous rings around the origin,
Haha, yet more context I didn’t have much probability of understanding
I work in C# almost exclusively and so I’ve never used an LLM with the expectation that it would run the code itself. I usually explicitly specify what language and form of response I need “Generate a C# <class/method/LINQ statement> that does x y and z in this way with parameters a, b, and c”
I also didn’t get it but felt embarrassed to ask, appreciate you taking the hit. (Admitting it feels easier after someone else goes first.)
I’m pretty sure there at no nontrivial solutions to the equation unless A has certain (non-random) properties like being real-valued. Generating random complex matrices will never find a nonzero conjugate eigenvalue.
I see.
Maybe.
However much I can at this inferential distance
It’s funny how things like matrices are critical for some types of coding (AI, Statistics, etc) but completely unnecessary for others. As a software developer who is not in AI or statistics they have never come up once, though perhaps I would’ve been able to spot potential use cases if I had that background.
Similar to how I frequently see use cases for SQL where inferior options are being used in the wild[1].
To whom it may concern: Please Stop using Excel like that. It’s a crime against humanity, performance, and good data
There’s a good chance I got math-sniped and completely misinterpreted what Hastings is pointing at.