Group Testing: A 3Blue1Brown-Style Explainer
A from-scratch animated explainer on pooled/group testing: expected value and linearity of expectation, the classic pool-size optimization (k* = 1/√p), a concrete numeric payoff, a recursive re-splitting idea that pushes the expected test count toward the sparse-regime information limit, and Robert Dorfman's 1943 origin story.
I built this because I couldn't find an accessible visual explainer of the idea that actually motivated it: a positive pool doesn't have to be tested member-by-member once it's flagged — it can be recursively re-split into smaller sub-pools instead, which pushes the expected number of tests from the classic single-split optimum down toward the information-theoretic limit for sparse infection rates. That specific insight didn't seem to have a clear online treatment, so I made the teaching material myself, in the animated-math tradition popularized by 3Blue1Brown.
The video runs nine chapters: expected value and linearity of expectation, the group-testing setup (with a native 3D pooled-sample demonstration), one positive case versus many, deriving the exact expected-test formula, the Bernoulli probability bound, optimizing the pool size, a concrete numeric payoff at N=100,000, the recursive multi-stage splitting idea and its entropy-bound comparison, and finally Robert Dorfman's 1943 paper — the two-stage method he introduced for syphilis screening of WWII recruits, with a recreation of his original Table I and Figure 1.