INTERACTIVE COMPANION · FIELD NOTE · ENVIRONMENTAL ARCHAEOLOGY

The Lead Ledger

A live model accompanying “An Empire's Air Pollution”

← Read the full article · Our calculation

Four links connect a smelter in Roman Spain to a number of IQ points. Emissions dilute into an atmosphere. The atmosphere delivers a concentration. The concentration produces a blood lead level. The blood lead level produces a cognitive deficit. Each link is a single equation, and each equation has a parameter somebody had to choose.

The first model below gives you one slider per link, so you can watch a change at any point propagate all the way to the end. The second reads an ice core: pick a year, get the lead in the ice and the history that goes with it. Everything here is the club's own simplified reconstruction and not the published analysis, and every default setting reproduces a number printed in the article.

Model 1. Drive the chain, link by link

The four equations, in order, with the default values shown in the article:

1 air lead C = E / (v_d A) → 0.514 ng/m³
2 blood rise ΔBLL = exp(a + b · ln C) → 2.391 µg/dL
3 total blood BLL = ΔBLL + baseline → 3.391 µg/dL
4 IQ lost −s · [ln(BLL+1) − ln(baseline+1)] → 2.607 points

Note what is not in link 1. There is no mixing height, because at steady state everything emitted deposits inside the box and the height of the box cancels out exactly. The area \(A\) is fixed here at 1.439 × 10¹³ m², the rectangle from 10°W to 40°E and 30°N to 65°N.

Link 1 · emissions E 3.50 kt Pb/yr The paper's two source scenarios are 3.0 and 4.2. Drag down to 0.05, which is the Iron Age background before Rome existed, and watch the IQ figure fall by barely a third. Seventy times less industry, and the model can hardly tell. Link 1 · removal velocity v_d 1.50 cm/s How fast the atmosphere scrubs lead out, dry deposition and rainout together. This is the number the club had the most freedom to invent. Run it across its whole range and see how little it moves the answer. Link 2 · exponent b 0.140 The published standard error is ±0.054, which is the full width of this slider. Move it one notch at either end. This single parameter is the biggest source of uncertainty in the whole chain, and nothing about the ice cores touches it. Link 3 · Neolithic baseline 1.00 µg/dL What a European child carried before anybody smelted anything, from tooth enamel. Raising it raises total blood lead and lowers the attributable share, because the counterfactual world gets worse too. Link 4 · IQ slope s 3.315 points per log unit From the seven-cohort pooled analysis, with its published standard error of 0.6155. At the low end the empire loses 2.12 points; at the high end, 3.09.

air lead: – blood lead rise: – total blood lead: – IQ lost: –

–

The panel on the right of the stage is the part worth sitting with. It ranks the six adjustable assumptions by how far each one moves the final answer when taken across its own honest range, holding everything else where you have left it. On the defaults, the exponent in link 2 moves the answer by 1.475 IQ points, and the paper's entire published emission range moves it by 0.085. The difficult apparatus contributes the least uncertainty. The borrowed regression contributes the most.

Model 2. Read the core

An ice core is a stack of annual layers, and each layer carries the dust and the dissolved metal that fell out of the sky that year. Click anywhere on the column to open a year. The reader gives you the non-background lead in that layer, the emission rate it implies, what that would have done to a child's blood, and what was happening in the empire at the time.

Read this before you trust the numbers. The shape of the emission curve below comes from the narrative published in the paper and its 2018 predecessor. The absolute calibration to picograms per gram is the club's own, pinned so that the Pax Romana plateau sits at our 3.5 kt/yr midpoint. These are not digitised data and should not be quoted as such. The depth scale is nominal, at a flat 0.19 metres of ice per year.

Year in the core 150 CE Start at 150 CE, on the Antonine plateau, then drag to 80 BCE. That is the trough of the Sullan civil wars, when emissions fell by a factor of six. Watch how little the modelled IQ number changes between them. Emission scenario The ice records how much lead arrived, not where it came from. Switching scenario rescales the whole curve. The IQ answer barely notices, which is the point of the article's seventh section.

Drill the core Sweeps the reader from 600 CE at the top down to 500 BCE at the bottom, one layer at a time. It stops when you leave the tab and it is disabled if your system asks for reduced motion.

layer: – non-background Pb: – emissions: – child blood lead: – IQ lost: –

–

What the two models are for

Model 1 exists to make one uncomfortable fact visible. The stages of this calculation do not carry equal weight, and the weight sits in the opposite place from where the effort went. You can throw the atmospheric parameters around and the answer wobbles by a few per cent. You can nudge a single epidemiological exponent inside its own published error and the answer moves by half.

Model 2 exists to make the other fact visible. The emission record is genuinely excellent. It is dated to the year, it tracks documented history, and it collapses in the 160s CE alongside the Antonine Plague. Whatever happens to the health inference, that record stands, and it is the reason this paper matters.

Put the two together and you get the honest version of the headline. A continent-scale industrial air pollution record, resolved annually, two thousand years old, with a health consequence attached to it that is probably a few IQ points and could be one or five.