The short version appears to be that the author has managed to replace standard linear algebra notation with an alternative (but mathematically equivalent) graphical notation, which is harder to do computations and write programs in.
This submission is the latest in a trend of what I would classify as "math-lite" category theory and Haskell articles that reach the HN front page, which purport to explain something interesting but end up just rehashing standard mathematics in opaque ways.
I really wish this would stop. Fortunately (unfortunately?) I've been down this road a few times and know to avoid getting sucked in, but I can easily see a bright, curious person wasting a lot of time before realizing that the content is merely linguistic, not mathematical.
Is (for example) category theory a useful organizational tool in certain abstract branches of mathematics? Sure (those branches being, basically, algebraic topology and algebraic geometry). Is it a grand unified theory of math? No, it's just some useful vocabulary. Most mathematicians go their entire lives without writing a paper mentioning categories. Getting excited about category theory is like getting excited about matrix notation – useful, sure, but not where the meat is.
I also find any claims that category theory is relevant to the average working programmer to be dubious at best.
(And yes, I realize the graphical notation presented in this article is not category theory. I am making a broader point about certain kinds of articles I see, which also applies here.)
This submission is the latest in a trend of what I would classify as "math-lite" category theory and Haskell articles that reach the HN front page, which purport to explain something interesting but end up just rehashing standard mathematics in opaque ways.
I really wish this would stop. Fortunately (unfortunately?) I've been down this road a few times and know to avoid getting sucked in, but I can easily see a bright, curious person wasting a lot of time before realizing that the content is merely linguistic, not mathematical.
Is (for example) category theory a useful organizational tool in certain abstract branches of mathematics? Sure (those branches being, basically, algebraic topology and algebraic geometry). Is it a grand unified theory of math? No, it's just some useful vocabulary. Most mathematicians go their entire lives without writing a paper mentioning categories. Getting excited about category theory is like getting excited about matrix notation – useful, sure, but not where the meat is.
I also find any claims that category theory is relevant to the average working programmer to be dubious at best.
(And yes, I realize the graphical notation presented in this article is not category theory. I am making a broader point about certain kinds of articles I see, which also applies here.)