sfpotter

I learned to program because I wanted to make video games as a kid. I studied math because I got bored of programming. I worked as a programmer because I needed a job and it was the thing that paid the most among the things I was qualified to do (I actually thought I wanted to be a chef...). I went back to grad school because I thought programming apps was tedious and a dead end and wanted to get a job in research. I got a postdoc because I was pretty decent at it and liked what I was doing. I left academia to go do industrial R&D because academia was a dumpster fire and I needed more money and predictability for my family. I'm now writing niche numerical libraries for a small company because it's what I ended up intensely specializing in and I still like what I'm doing. I'm mixed on LLMs, but they're unavoidable. They've made some parts of my job easier, and they've made some parts harder. I still have to write a lot of code by hand because the LLM's code is often wrong.

*moves back to NYC*

The determinant of a polynomial mapping is a polynomial, which is the subject of the conjecture. To get the Jacobian determinant, all you need to do is compute partial derivatives of polynomials, and add, subtract, and multiply them together. All of these operations map polynomials to polynomials.

The crux of the assumption is that if a polynomial mapping is invertible everywhere (Jacobian nonzero everywhere), its Jacobian must be a constant. Why? Because the only polynomials which are zero nowhere are constants.

No. This is about polynomials. The assumption that the Jacobian is nowhere zero is what is doing so much of the work. This means the Jacobian must in fact be constant. But obviously there are many mappings whose Jacobians are not constant.

"At present, no language can rival, let alone surpass, Fortran when it comes to implementing long-lived, large-scale, massively-parallel scientific and engineering applications; not even C and C++."

Huh??? A tremendous amount of scientific computing happens in C, C++, and many other languages. I have worked with Fortran, worked with Fortran-heavy labs in academia, and this is just a nonsensical thing to say.

So far as we know, consciousness only takes place in biological organism. A computer isn't a biological organism, therefore the burden of proof for claiming that an LLM is extraordinarily high. To me, this makes it reasonable to dismiss the idea. If you want to demonstrate that LLMs are conscious, you better start working on your neuroscience and philosophy PhDs.

There's a reason so many cab companies have fleets of Priuses.

"Serious delirium!"

He didn't pooh-pooh anyone's careers.

"Legibility" here just means something that is visibly important/useful/scrutable/not a waste of time to (i.e. "is legible to") a manager.

This is what the field of numerical analysis exists for. These details definitely have been treated, but this was done mainly early in the field's history; for example, by people like Wilkinson and Kahan...

This is just subdivision of Bernstein polynomials. The unifying way of looking at this is via the blossom of the Bezier curve (Bernstein polynomial). You can derive all manner of shifts, change of basis transformations, and so on using the blossom. Subdivision is just a shift of the domain of definition of the original polynomial.

It could easily be both.

The truck would come by once a week to pick up all of our dirty diapers and drop off a new set of clean diapers. The service provided a bucket with a cloth bag inside of it that had enough capacity for one kid for a week. Packaging up = closing the lid of the bucket and leaving it outside the door of our apartment. They would drop off a new one of these buckets full of clean diapers each week (visiting many other people at the same time). Beyond all the environmental benefits, living in the city this was actually super convenient.