Top all-time · #4372
Alex Kritchevsky
Personal blog · alexkritchevsky.com · on HN as ajkjkmathsciencephilosophy
Alex Kritchevsky's personal blog at alexkritchevsky.com covers math, science and philosophy. Since 2018, 18 different Hacker News readers have linked it 25 times, most often “The Case Against Geometric Algebra”. It is still writing: the last post was on 2026-08-17, and you can follow it by feed.
Too few sampled comments (7) to say how often HN recommends it.?
Why HN links it
HN readers link Alex Kritchevsky's posts on geometric algebra, including a critique arguing that differential forms are a clearer way to think about it, and on triple products of partial derivatives.
Summarised by Claude from a sample of 7 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most-linked posts?
- The Case Against Geometric Algebra8 people · 8 mentions · first linked 2024-03-02
- Aphantasia (and how not to do math in your head)2 people · 2 mentions · first linked 2022-03-03
- The Zen of React2 people · 2 mentions · first linked 2022-09-20
What Hacker News says?
Agree with a lot of this, but, some quibbles: 1. yes, un/controlled forms are messed up and need work 2. yes, contexts should replace Redux and Redux should go away. but in practice having a few contexts is pretty manageable. Currently we use Redux for all the dynamic state and contexts for everything else and it works pretty well. It is quite easy, also, to write your only little `useSelector()` wrapper around a no…
Comment linking /2022/09/17/react.html
on “React I love you, but you're bringing me down”Submitted The Case Against Geometric Algebra as a story · 25 points
HN discussionHere's a critical take on geometric algebra: https://alexkritchevsky.com/2024/02/28/geometric-algebra.htm... tl;dr: GA's geometric product is a mixed-grade differential form, which is quite weird. Why not just think in terms of differential forms? Maxwell's equations are so sweetly summarized as dF=0 and d*F = J.
Comment linking /2024/02/28/geometric-algebra.html
on “An intuitive guide to Maxwell's equations (2020)”Submitted Everything Is Logarithms as a story · 21 points
HN discussionNeat. Some of us can't see things in our heads at all (aphantasia), so we definitely can't do things this way. Although now that I think about it there is still some element of what's described in this article. There's no visual shape involved in the way I model numbers, but it resonates to think of 7 as "10 with a 3 missing", but also as "5 with a 2 on it". The concepts are built in reference to their closest multi…
Comment linking /2019/09/15/mental-math.html
on “How I See Numbers”Submitted The Case Against Geometric Algebra as a story · 11 points
HN discussion> "What are recent developments in linear algebra?" Have you heard of geometric algebra? It takes a while to wrap your head around, but unifies a lot of mathematics in a very elegant way. For instance, you can view Euclidean geometry as a special case, and concepts like quaternions and rotations can be explained in a very natural way. There are a few good resources below if you're interested. [0]: http://geometry.mr…
Comment linking /2020/10/15/ea-operations.html
on “Graph Theory and Linear Algebra [pdf]”Submitted The Essence of Lagrange Multipliers as a story · 3 points
HN discussionBy the way, I love your blog post https://alexkritchevsky.com/2024/02/28/geometric-algebra.htm... I didn't understand this part: > I strongly believe that if GA would make this distinction they would lose a lot fewer people. It is a completely interesting and useful thing to talk about “a representation of a particular class of operations that makes composition and inversion easy”, and completely offputting when you…
Comment linking /2024/02/28/geometric-algebra.html
on “Poor Foundations in Geometric Algebra”Submitted Aphantasia (and how not to do math in your head) as a story · 3 points
HN discussion> As for pure math—it seems like research mathematics readily talks about and uses Clifford Algebra, but is uninterested in or specificaly avoids the terms and concepts that are specific to Hestenes’ “Geometric Algebra”. I can speculate as to why: even by the 90s/00s, GA had gotten a bad reputation because of its tendency to attract bad mathematicians and full-on crackpots. https://alexkritchevsky.com/2024/02/28/geo…
Comment linking /2024/02/28/geometric-algebra.html
on “Geometric Algebra”Submitted Aphantasia (and how not to do math in your head) (2019) as a story · 3 points
HN discussionAn article that argues against GA: https://alexkritchevsky.com/2024/02/28/geometric-algebra.htm... TLDR: - GA tends to attract a lot of crackpot. In fact most mathematicians avoid the name Geoemtric algebra and call it Clifford algebra to disassociate with them. - Most of the usefulness of GA comes from just exterior algebra and exterior product/wedge product is more important than geometric product. - It shows up i…
Comment linking /2024/02/28/geometric-algebra.html
on “Geometric Algebra”Submitted How to invert a matrix as a story · 3 points
HN discussionI wrote an article which might help? https://alexkritchevsky.com/2022/10/12/react-2.html It's based on a theory that hooks click better for a lot of people if they see an MVP implementation of one and understand the programming problem it is solving.
Comment linking /2022/10/12/react-2.html
on “React 19 Beta”Submitted The case against geometric algebra as a story · 2 points
HN discussionThe baseless log here is just a torsor [0]! Lots of things are torsors: position, currency values, calendar dates etc. the vales themselves are arbitrary, and translating/scaling them by some value doesn't make a functional difference. Torsors let us talk about these things without needing to make such an arbitrary choice a priori. In the case of baseless logs, the underlying set is "information units", i.e. log 2 i…
Comment linking /2024/02/28/geometric-algebra.html
on “Everything Is Logarithms”Submitted Data Science Isn't Science as a story · 2 points
HN discussionThere's a better explanation of it at https://alexkritchevsky.com/2024/12/18/triple-products.html
Comment linking /2024/12/18/triple-products.html
on “Triple Product Rule of Partial Derivatives”Submitted Exterior Algebra #5: EA as Linearized Set Theory? (2019) as a story · 2 points
HN discussionAs it sounds like you're aware, if a 3x3 matrix is considered as three vectors that form a parallelogram, the 2x2 minors form three vectors in the bivector space ∧^2 R^2 that represent the area vectors for the three faces of that parallelogram. Here's a hand-wavy version in a sort of pseudo-notation: if the matrix is M = (a,b,c), then the first step of condensation forms (a∧b, b∧c). Confusingly, you drop the last ro…
Comment linking /2018/10/09/exterior-2.html
on “How Lewis Carroll Computed Determinants”Submitted The Essence of Quantum Mechanics as a story · 2 points
HN discussionSubmitted Existence Is Pain as a story · 2 points
HN discussionSubmitted The Zen of React as a story · 1 points
HN discussionSubmitted The Essence of Complex Analysis as a story · 1 points
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