Somehow the classification of finite simple groups makes me feel uneasy as a mathematician, but I suppose this helps quell that feeling. https://en.wikipedia.org/wiki/Monster_group
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…
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…
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…
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…
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…
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…
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 determine a trajectory on a manifold.
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 the last few years studying chaotic…
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 Stay:…
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 instance. The key is that you have to find…
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 C naturally has the topology of a…
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 implicitly convey a preference for how data…
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 example we are currently involved with UIs…
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 forces a choice in an attempt to extract…
Somehow the classification of finite simple groups makes me feel uneasy as a mathematician, but I suppose this helps quell that feeling. https://en.wikipedia.org/wiki/Monster_group
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…
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…
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…
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…
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…
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…
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 determine a trajectory on a manifold.
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 the last few years studying chaotic…
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 Stay:…
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 instance. The key is that you have to find…
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 C naturally has the topology of a…
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 implicitly convey a preference for how data…
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 example we are currently involved with UIs…
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 forces a choice in an attempt to extract…