Size & scale

The area illusion

Twice the value, four times the ink.

a.k.a. pictogram inflation · one-dimensional data, two-dimensional icons

Scale an icon’s or circle’s height by the data and its area grows by the square. A value that doubled looks quadrupled — and in 3D, octupled. Your eye judges the ink, not the radius.

How to spot it

Icons or bubbles that balloon dramatically for modest changes.
Compare the labelled values against how big the shapes feel.

The fix

Scale area — not width and height — to the value. Or retreat to boring, honest bars.

In the gallery

Dark navy consulting slide, masthead “Beverage & Spirits Practice · Regulatory Diagnostic · Working Draft”, headlined “What the wine rulebook actually talks about”. A subhead reads: every word of 27 CFR Part 4 — Labeling and Advertising of Wine — 22,434 words — counted; common English words removed, nothing else touched; each word is sized so that the area it occupies is proportional to how often it appears; no sampling, no weighting, no editorial judgement. Filling most of the slide, under the label “Word frequency · 27 CFR Part 4 · complete text · top 40 terms”, is a word cloud in gold, blue and grey. “wine” is far the largest word at the centre. Around it, “statement”, “designation”, “information”, “appropriate”, “appellation”, “paragraph” and “statements” are drawn large, while “ttb”, “atf”, “use” and “fruit” are among the smallest words in the picture. Down the right-hand side, a gold-bordered card reads 22,434 words over the line “The complete regulation, counted end to end — nothing sampled, nothing set aside”. A card headed “Method” says font size is set to the square root of the count, so a word’s area rises in proportion to how often it appears, and that every word is horizontal, with no rotation, no shape mask, no hand-placement, and decorative colours. A gold card headed “What leaps out” lists statement 2nd largest, designation 3rd largest, information 5th largest, appropriate 6th largest. A card headed “Read-out for the client” concludes that the drafting emphasis sits on designations, statements and information — the vocabulary of a disclosure regime — and that the agency’s own names, TTB and ATF, barely register, so procedure is not where this rulebook spends its attention. Three ticked boxes run along the bottom: “No axis to truncate — there is no axis, no baseline and no scale break anywhere on this chart”, “Nothing cherry-picked — the whole part, every word of it, in one picture, not a window, not a sample”, and “No colour scale to gerrymander — hue carries no meaning here; only size encodes the data”. A footnote records that the word counts were computed by us from the full XML text of the part as served by the eCFR API for the issue date of 18 August 2026, gives the tokenising rules and the totals of 22,434 tokens, 11,822 after removals and 2,108 distinct, and states that the slide is a demonstration drawn by us in the manner of a consulting deck and was never published anywhere.

$Earnest dark “coffee almanac” infographic titled “A world of coffee”, subtitled “How much coffee each nation drinks in a year, per person”, with a masthead reading “THE ROASTERY REVIEW — World Coffee Almanac — 2026 edition”. Six paper takeaway cups, each with a dark lid, a gold sleeve and wisps of steam, stand in a row on a shelf, every cup scaled in both height and width to its country’s per-capita coffee: Finland’s 12.0 kg cup towers at the left, then Norway 9.9, Iceland 9.0, Netherlands 8.4 and Sweden 8.2 step gently down, and the United States cup at 4.2 kg is a tiny fraction of Finland’s — under three times less coffee, drawn roughly eight times smaller. Each cup is labelled with its value and “per person / year”, and a kicker reads “Finland leads the world — the home of the bottomless cup”.$

The coffee cups that grew as the square of the coffee

The area illusion

$Pictogram titled “The Shrinking Family Doctor,” redrawn after the 1979 Los Angeles Times original: three doctor figures for 1964 (27%), 1975 (16.0%) and 1990 (12.0%), each scaled in both height and width so the 1990 doctor is a tiny fraction of the first, with the three years spaced evenly despite 11- and 15-year gaps$

The family doctor who shrank in two dimensions

The area illusion Uneven intervals

The area illusion

How to spot it

The fix

In the gallery

The word cloud that pays by the letter

The piggy bank that grew as the cube of the tuition

The protein footprint drawn as its own square

The hydrogen balloon that inflated its own lead

The coffee cups that grew as the square of the coffee

The family doctor who shrank in two dimensions