November 3, 2025
Weighted sums, heavier shade-throwing
An Illustrated Introduction to Linear Algebra, Chapter 2: The Dot Product
Cute dot-product lesson ignites YouTube-vs-textbook smackdown
TLDR: A friendly explainer shows the dot product as a weighted score for simple choices. Commenters pounced, calling it too shallow and steering readers to 3Blue1Brown, Math Academy, and classic textbooks, igniting a debate over slick visuals versus deep theory in how people learn math today.
An approachable post breaks down the “dot product” — basically a weighted score, like choosing a city by weather vs cost — and the comments turned it into a math cage match. The strongest reaction? Gatekeepers came out swinging, calling it “weaksauce” and demanding real visuals and deeper topics. One top reply points everyone straight to 3Blue1Brown’s YouTube series, while another swears by Math Academy as “the best resource.” Old-school purists flexed bookish cred, dropping Birkhoff & Mac Lane like a mic: “200 pages of proper linear algebra.”
The biggest beef: calling it “illustrated” when the drawings are simple tables. Commenters wanted graphs, geometry, and that swoopy 3D magic, not “hand-drawn boxes” — cue the meme: “dot product of disappointment.” Others pushed to go beyond picking cities and dive into the heavy stuff: matrices, eigenvalues (fancy math features), and “real” proofs. Meanwhile, a quieter crowd seemed to appreciate the friendly vibe and story-first approach, but the snark brigade drowned them out with vectors of shade.
In short, a gentle math explainer got weighted with expectations — and the community did the dot product on the author’s feelings, multiplying critiques by 1.1 and summing them loudly
Key Points
- •The article introduces the dot product via a city selection example using criteria like weather and affordability.
- •Weights are applied to criteria to reflect preferences (e.g., weather weighted by 1.1, affordability by 1).
- •The dot product is presented as a weighted sum: multiply each score by its weight and add the results.
- •Vector notation is used: scores and weights are written as vectors (e.g., [5 1] and [1.1 1]).
- •A concrete calculation shows the effect of weighting: 1.1*5 + 1*1 = 6.5 for San Francisco.