Someone named David Fenger thought he could “correct my math” in Probability Zero:
“I went through Vox’s math. He dropped two critical terms (size of genome and cell divisions per generation) and got an answer that was out by about 5 orders of magnitude.”
He’s incorrect, and what he did is confuse three different mutation rates. There are three entirely distinct quantities that can all be described as “the mutation rate”:
- Per-base-pair, per-cell-division ≈ 10⁻¹⁰
- Per-base-pair, per-generation (μ) ≈ 1.2–1.5 × 10⁻⁸ (Kong 2012, Jónsson 2017)
- Per-genome, per-generation ≈ 70–100 mutations per individual (Kong 2012, Nature 488: 471–475)
This is how they’re related: (3) = (2) × genome size = (1) × cell divisions per generation × genome size
My calculations don’t start at (1) or (2). They start at level (3) — the empirically measured ~100 de novo mutations per generation per individual, directly observed in trio sequencing. That number is already the product of genome size and cell divisions per generation and the per-base-pair per-division rate. Both terms he claims I “dropped” are terms that are baked into the third. You don’t multiply them in again because that would be double-counting by a factor of roughly 3 × 10¹¹.
The Cross-Taxa Channel Capacity paper uses level (2), μ ≈ 1.3 × 10⁻⁸ per bp per generation. Genome size appears explicitly in that paper as L = 3.2 × 10⁹, and the channel capacity is derived as C = L × r. Cell divisions per generation don’t appear because we’re already at the per-generation level — that’s the whole point of using μ rather than the per-division rate.
So in both formulations Mr. Fenger’s “missing terms” are either explicitly present or were already absorbed into the empirical measurement. Moreover, we already know his “math” is incorrect or he never actually did it.
If I had used the per-bp per-cell-division rate (10⁻¹⁰) and forgot to multiply by both cell divisions (~400) and genome size (~3 × 10⁹), you’d be off by about 12 orders of magnitude, not 5.
If I used μ (10⁻⁸) and forgot to multiply by genome size only, I’d be off by about 9.5 orders of magnitude, not 5.
There is no clean way to drop “size of genome and cell divisions per generation” and end up five orders of magnitude off. It’s nonsense that doesn’t correspond to any actual arithmetic operation the math from Probability Zero.
Ironically, I am off by at least one order of magnitude, but the other way. I didn’t utilize the full range of genetic differences between the chimp and human genomes, because I was not familiar with the Yoo (2025) paper than published them, so the probability of evolution by natural selection is actually less than the zero of Probability Zero.