sleepyams

Yes, I think these are related-ish, also to traces on symmetric monoidal categories. If you have any algebraic/categorical formalization of wiring diagrams, this is essentially taking a block with inputs A and C and outputs B and C and connecting the C output to the C input with a self-loop.

Nice, I've also been playing around with creating a programming language based on some concepts in category theory, but I've been focusing more on the concept of polynomial functors. I know there is somewhat of a stigma against category theory on Hacker News for some reason, but it's cool to see people inspired to create new languages inspired by category theoretic ideas.

It was cool to read about "co-choice", although I looked up that term and couldn't really find it used anywhere, do you have a source? (Also I think there is a typo in the type signature in the code block in this section. The codomain of `cochoiceHask` should be `b` right?) The idea of building a loop from a function `Either a c -> Either b c` is very interesting. It reminds me of some of the ideas in the book "Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory" by Joseph E. Stoy, which you should check out if you haven't.

I think that math can still be a creative endeavor, ultimately. In many cases it is not so creative, and really is an exercise in searching the potential solution space (which it is now clear the AI excels at). However, math can also be about the creation (discovery?) of new language itself, which in turn enables us to ask questions that we couldn't previously ask in the first place.

As a mathematician, I don't disagree with you, I do think the recent events have exposed a certain brand of elitism/gatekeeping etc within the mathematical community. While that may be true, it's not always about "finding the solution", oftentimes we first have to learn how to even frame the problem to begin with.

I think that whether we think of consciousness in terms of dualism, or if we think of it as emergent from natural behavior, it really doesn't matter functionally. Either way we are positioning it as something inaccessible from our realm or control.

I believe that we can at least posit some kind of mechanism through which emergence can happen. In my opinion we should look at language and how language evolved. However, i also believe we should expand our study of natural language to things like network protocols, and observe the "protocol hourglass" structure that has emerged from the internet protocol stack.

In my mind, the concepts of control and autonomy are what need to be revisited. We conflate the two: we are autonomous IF we are able to exert control on the environment. However, I think the reality might be that autonomous systems are more similar to an API in the sense that we can interact along the boundary but through the API we cannot exert control over the internal structure of the system (through knowledge or physical control).

I wonder if a solution for higher education is to enforce access to technology both inside and outside of the classroom? I've been teaching math at various institutions for the past 8 years after getting my PhD, and the conversation among my friends and peers has become increasingly bleak over the years. At first LLMs were not great at math, but at this point they can reliably solve the majority of problems one might see in an undergraduate math course. Recently I interviewed for a position at a university and spoke to the Dean of Arts and Sciences who admitted to me candidly that the university didn't really know how to handle AI.

Teachers increasingly must assume that students will not learn on their own outside of the time spent in class. This is difficult because we only see students for a handful of contact hours every week, and there is not enough time to both lecture AND ensure that a student has attained thorough understanding of the material. Teachers have adapted to this in various ways, but another stressor is that students are coming into college much less prepared. When I teach precalc I essentially have to assume that I will need to teach students how fractions work. The current system is not built to support this kind of learning. In order to make sure students are really learning, I now have to cut out major portions of the curriculum to make sure I have time to do active learning during class. It's obvious through students' performance that their understanding of things we work on in class is much more internalized and sophisticated than things I lecture about but assume they will learn on homework problems.

A novel I really love is Anathem by Neal Stephenson. While Anathem is an admittedly goofy work of fiction, I do think Stephenson's vision of the future is compelling: the purity of mathematics education and research must be protected from the hyper-technological outside world. In reality I'm not anti-technology of course, I feel like access to a non-internet-connected computer is fine. But, I wonder if such a model would work for an educational institution?

I think Terrence Tao makes at least 600k at UCLA. Not too bad if you ask me.

This is really awesome! I've been really interested in creating an interactive introduction to basic algebra where parts of the equation can be manipulated using drag-and-drop, but I couldn't really figure out the best way to do it. Maybe using Katex is the way to go?

What does "higher-order" mean?

This is a pretty amazing setup! I think in 2025 I would definitely prefer something like this. However, I think back in "the day" part of what made LAN parties fun was that everyone's PC was so individualized. I remember all of my high school friends and I coming of age and building our PCs. I helped a lot of my friends build their PCs and we all chose different things (such as the amount of RGB LEDs, which I thought were tacky...). I remember a friend of a friend had a water cooling system and I was so excited about checking it out. Also, things like the desktop wallpaper you chose, etc, contributed to this. There was something very magical about it all. Lugging our PCs to each others houses was a real labor of love.

Cool, thanks! I'm currently building a eurorack module where I need to estimate the frequency and phase of a sequence of input gate signals, and an issue I've run into is the delay inherent in the STFT algorithm. This seems like it might work better!

Can this process estimate the phase of the input signal in a given frequency bucket similar to the DFT?

The utility behind complex numbers (for physicists at least) is really that they are a model for certain algebraic and geometric properties that are together very useful.