Viewing profile — sleepyams

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…

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 pas…

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…

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 everyon…

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…

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

I recommend the Mario 64 "Half A-Press" video if you haven't seen it: https://www.youtube.com/watch?v=kpk2tdsPh0A

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.

Good points, a large chunk of math is different formalizations of the notion of size, for example (in order of increasing absurdity): https://en.wikipedia.org/wiki/Cardinality http…

This is cool! There is also Orca: https://100r.co/site/orca.html

Yep! More specifically I'm basically talking about geodesics on Riemannian manifolds.

I always wondered why that is for a long time (in basic physics that at least). It wasn't until grad school that I understood that position and velocity are enough to uniquely dete…

I think the field of chaos theory has branched into several other fields, so I would not necessarily agree that it is dead in the water. I personally have worked on projects within…

One interesting result which you may find interesting: https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem I also highly recommend this survey paper by John Baez and Mike S…

I think this is good advice but also not the only possible path towards completing a PhD in math. I get a lot of fruitful research done while binge-watching television, for instanc…

Do you have any recommendations for a good youtube video to watch?

I actually find Pocket to be very useful as a cross-platform bookmarking app

There is a nice characterization of decimal expansions in terms of paths on a graph: Let C be the countable product of the set with ten elements, i.e. {0, 1, 2, ..., 9}. The space …

That makes sense, for example Reddit has a very simple concept with the upvote/downvote, but also more advanced features if you need them. But I would also argue that UIs also impl…

Will we ever solve UI? UI is the meeting place of tech and user, and in a sense it is THE problem for humanity right now. UI informs how we tend to use the internet, and for exampl…

Roughly speculative realism?

I think the insight is that there isn't really a built-in mechanism in particles for making choices, it's more that through experimentation we are _imposing_ a structure that force…

In addition to the other replies, check out Clifford algebras which generalize these types of numbers: https://en.wikipedia.org/wiki/Clifford_algebra