The tile that is 15% wider and 40% smaller

Dark navy board slide, masthead “Northwood Sourcing Partners · Supply-base review · Board pack, FY27”, headlined “Five anchors carry the world’s log supply — and Canada is one of them”. A subhead reads: where the wood actually comes from, measured the only way it can be measured — every cubic metre of industrial roundwood the FAO recorded in 2024, all 174 reporting countries, one item, one year, one unit; the twelve largest producers named, the other 162 kept on the chart as a single tile; every area exactly proportional to its volume, nothing sampled, nothing weighted, nothing set aside. Filling the left of the slide, under the label “Industrial roundwood production · FAOSTAT forestry production · 2024 · area ∝ cubic metres”, is a treemap of thirteen rectangles. Across the top row, four tall tiles: a gold United States labelled 319.1, then blue tiles for Brazil 199.7, Russia 193.1 and China 192.4, all four the same height and of similar width. A middle row of seven shorter tiles runs left to right: a gold Canada labelled 114.9, noticeably wider than any of the blue tiles above it, then Indonesia 91.8, Sweden 64.9, Finland 54.6, India 49.9, Germany 47.3 and Viet Nam 45.3, each narrower than the last. Along the bottom sits a narrow, tall Chile tile labelled 42.3 and, beside it, a long band running almost the full width of the chart labelled “Rest of world 540.5 — the other 162 reporting countries”. Down the right-hand side, a gold-bordered card carries 72% over the line “Of world industrial roundwood comes from the twelve named countries”. A card headed “Production · 2024 · million m³” lists United States 319.1, Brazil 199.7, Russia 193.1, China 192.4, Canada 114.9, Indonesia 91.8, Sweden 64.9, Finland 54.6, India 49.9, Germany 47.3, Viet Nam 45.3, Chile 42.3 and Rest of world 540.5. A gold card headed “Read-out for the board” argues that the United States anchors the supply, that behind it sit Brazil, Russia and China and then Canada, whose tile is the widest of that second rank and the obvious home for the FY27 sourcing desk, that the Nordic pair sits well behind Canada, and that the four smallest tiles — India, Germany, Viet Nam, Chile — are a tail that can be left to brokers; it recommends a desk in Vancouver and defers the Nordic desk. A card headed “Why a treemap” says thirteen quantities in one picture, each area exactly proportional to its volume, with no axis to truncate, no baseline to move, no second axis, no log scale and nothing pushed off the chart. A final card, “Basis of measurement”, gives 174 reporting countries, 12 named and 162 in the remainder, one item code, one calendar year, one unit. Three ticked boxes run along the bottom: “Areas exactly proportional. Every tile’s area is its share of world output, to the pixel. No axis anywhere on this chart, so no axis is bent”, “Nothing set aside. All 174 reporting countries are on the chart: the twelve largest named, the other 162 kept as one tile rather than dropped”, and “One unit throughout. Every tile is cubic metres of industrial roundwood, one FAO item code, one calendar year, counted once”. A footnote credits FAOSTAT Forestry Production and Trade, item 1865 “Industrial roundwood”, element “Production”, 2024, retrieved 23 August 2026, notes that China is the FAO “China” aggregate and that Rest of world is the FAO World total of 1,955,737,871 m³ less the twelve named countries, records that the tiles were laid out by the squarified algorithm of Bruls, Huizing and van Wijk (2000) largest first, and states that the slide is a demonstration drawn by us in the manner of a board pack and has never been published anywhere. — Showing the misleading chart

The same thirteen numbers on a cream background, kicked “The same thirteen numbers · measured off the drawing · FAO industrial roundwood · 2024” and headlined “The tile that is 15% wider is 40% smaller.” A subhead explains that every area on the treemap really is exactly proportional to its volume and that this is not the problem: a rectangle has two dimensions and the value is their product, so no single measurement on the page is the answer, while the eye measures one dimension at a time — Canada’s tile is drawn 539 px wide against China’s 468 and Canada produces 40% less wood, and the remainder tile holds 1.69 times the United States while being drawn 2.6 times as wide and 0.6 times as tall. Filling the upper left, a panel headed “All thirteen quantities · one zero-based axis · industrial roundwood production, million m³, 2024” draws sorted horizontal bars from 0 to 560: Rest of world 540.5 in gold, annotated “162 countries — larger than any single one of them”; United States 319.1; Brazil 199.7; Russia 193.1; China 192.4, annotated “produces 67% more than Canada; drawn 15% narrower”; Canada 114.9 in gold, annotated “6th by volume · 3rd by tile width”; Indonesia 91.8; Sweden 64.9, annotated “Sweden + Finland = 119.5, which is 4.1% more than Canada”; Finland 54.6; India 49.9; Germany 47.3; Viet Nam 45.3; and Chile 42.3. Below it on the left, a slopegraph headed “Ranked by tile width → ranked by volume” lists the thirteen tiles in each order and joins them with lines; twelve run flat and four are gold and cross, as Canada falls from third by tile width to sixth by volume while Brazil, Russia and China each rise one place. Beside it, a panel headed “The same thirteen numbers, tiled in a different order — identical areas, different shapes” shows three small treemaps with Germany’s tile picked out in gold in each: “Largest first — the layout the slide used”, where Germany’s tile is 222 × 307 px, 1.38:1; “Alphabetical — Brazil, Canada, Chile, China …”, where it is 133 × 513 px, 3.87:1; and “Smallest first”, where it is 204 × 334 px, 1.64:1. A line beneath reads that nothing in the data changed between the three pictures — the same algorithm on the same thirteen numbers, fed in a different order — and that Germany’s tile goes from 1.38 : 1 to 3.87 : 1 and back at a constant area. Six cards run down the right. “Two dimensions, one number” records that the United States produces 2.78 times Canada and its tile is 1.44 times as wide and 1.93 times as tall, that 1.44 × 1.93 = 2.78, that both factors are needed and neither is the answer, and that the reader has to multiply and does not. “Width ranks Canada third” notes that Canada is the fifth-largest of the twelve named producers while its tile is the third-widest on the chart at 539 px against Brazil’s 486, Russia’s 470 and China’s 468, and that height is no help either, since across thirteen tiles it takes three values — 592, 381 and 307 px — and says only which row a tile landed in. “A 0.4% gap, drawn in 1.8 pixels” records that Russia and China differ by 737,123 m³, or 0.4%, that their tiles differ by 1.8 px of width, and that nothing on the chart lets you check it, because a treemap carries no axis. “The remainder is the largest number on the slide” gives 540.5 million m³ across 162 countries, 27.6% of world output and 1.69 times the United States, drawn as a 2,040 × 381 px band along the bottom at 5.4 : 1 where it reads as a footer. “You have to add areas by eye” notes that Sweden plus Finland is 119.5 million m³, 4.1% more than Canada rather than well behind it, and that the four tiles the slide writes off as a tail come to 96% of Russia’s single tile. “What the slide got right” lists areas exactly proportional, one year, one unit, one item code, all 174 reporting countries present, every number printed and a squarified layout that holds most tiles near square — seven things right, and area alone was enough. A gold-ruled callout at the foot reads “A treemap is a good map of a hierarchy and a bad ruler,” and explains that position is judged more accurately than length and length more accurately than area, so the treemap is the one common chart that offers only the least accurate encoding and offers it without an axis; where the question is how something breaks down, roughly, across many categories at several levels, it is the right picture and nothing else fits on the page, and where the question is which is bigger and by how much, it never was. A footnote gives the FAOSTAT source and every value, records that the tile geometry is the squarified layout of Bruls, Huizing and van Wijk (2000) as drawn and quoted in pixels of the published image, credits the accuracy ordering of position, length and area to Cleveland and McGill (1984), and says both drawings are our own. — Showing the misleading chart

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A year of world log production, thirteen quantities, every tile’s area exactly proportional to its volume — and the third-widest tile on the chart belongs to the fifth-largest producer. Canada is drawn 539 pixels wide against China’s 468 while producing 40% less wood, because area is two numbers multiplied and the eye only ever measures one of them.

FAOSTAT Forestry Production and Trade (domain FO) — item 1865 “Industrial roundwood”, element “Production”, 2024, retrieved 23 August 2026, 2024Added August 23, 2026

01The claim

Here is where the world’s logs actually come from, measured the only way it can be measured: every cubic metre of industrial roundwood the FAO recorded in 2024, all 174 reporting countries, one item code, one calendar year, one unit. The twelve largest producers are named and the other 162 are kept on the chart as a single tile rather than dropped — nothing sampled, nothing weighted, nothing set aside — and every tile’s area is its share of world output to the pixel. There is no axis on this chart, which means there is no axis to truncate, no baseline to move, no second axis and no log scale. Read it and the supply base has five anchors. The United States carries it at 319.1 million cubic metres. Behind it sit Brazil, Russia and China — and then Canada, whose tile is the widest of that second rank and therefore the obvious home for the FY27 sourcing desk. The Nordic pair sits well behind Canada. The four smallest tiles — India, Germany, Viet Nam, Chile — are a tail we can leave to brokers. Recommendation: desk in Vancouver, Nordic desk deferred.

02The trick

Every area on that chart is exactly proportional to its volume, and that is not where it goes wrong. It goes wrong because a rectangle has two dimensions and the value is their product, so nothing you can measure on the page is the number. The eye measures one dimension at a time, and on this chart the dimension it reaches for is width. Canada’s tile is drawn 539 pixels wide. China’s is 468. Canada produces 114.9 million cubic metres against China’s 192.4 — 40% less wood in a tile 15% wider — and the same holds against Brazil’s 486 pixels and Russia’s 470. Canada is the fifth-largest of the twelve named producers and has the third-widest tile on the chart. Height cannot rescue the reading either: across thirteen tiles it takes exactly three values — 592, 381 and 307 pixels — because height records which row the packing algorithm dropped a tile into and nothing else. Getting the United States right takes both at once: 2.78 times Canada’s volume, drawn 1.44 times as wide and 1.93 times as tall, and 1.44 × 1.93 is 2.78. Both factors are needed, neither is the answer, and nobody multiplies. Then there is the thing a treemap does not have, which is an axis. Russia and China differ by 737,123 cubic metres, four tenths of one percent; their tiles differ by 1.8 pixels of width, and there is no scale, no baseline and no gridline anywhere on the chart to check that against. Every number a reader takes off a treemap has actually been taken off a label. The shapes are not even a property of the data. Run the same thirteen numbers through the same layout algorithm in a different order and Germany’s tile goes from 222 × 307 pixels to 133 × 513 and back, at a constant area — the picture changes, the data does not. And the read-out’s two supporting claims fail the same way. Sweden and Finland come to 119.5 million cubic metres, which is 4.1% more than Canada rather than well behind it, but seeing that means adding two areas by eye. The four tiles dismissed as a tail come to 96% of Russia’s single tile. Most uncomfortable is how much the slide gets right on the way past: proportional areas, one year, one unit, one item code, all 174 reporting countries present, every number printed, and a squarified layout that keeps most tiles close to square — the well-implemented version of the chart, which is the version this happens to. (The slide is our own demonstration, drawn in the manner of a board pack. The volumes are real, taken from FAOSTAT.)

03The fix

Sort the thirteen values onto one zero-based axis and the ranking is simply there, in the order the bars sit in, and the two questions the board actually asked answer themselves. Canada is sixth, below China rather than beside it. Sweden and Finland together clear it by 4.1%. And the largest quantity on the slide turns out to be the one the treemap laid along the bottom edge like a footer: 540.5 million cubic metres from the 162 countries outside the top twelve, 27.6% of world output and 1.69 times the United States — a remainder bigger than any country in it, which is a finding about a supply base rather than a leftover. The improvement is not decorative and it is not a matter of taste. A bar trades area for length, and length is judged far more accurately than area; a position along a common scale, which is what the sorted bar ends give you, is judged more accurately still. That ordering — position, then length, then angle, then area — comes from Cleveland and McGill’s experiments in 1984, and the treemap is the one chart in common use that offers nothing but the weak end of it, and offers it without an axis. What a bar chart costs is vertical space; what it buys is a ranking anyone can read, room to print the numbers beside the bars, and the ability to draw a group total — the Nordic pair, the tail of four — as its own bar rather than asking a reader to add rectangles in their head. None of which means never draw a treemap. It is genuinely the right picture for the job it was invented for: a hierarchy several levels deep with more categories than a bar chart can hold, read for shape and for share-of-the-whole rather than for rank. A disk-usage map, a budget broken out four levels down, a portfolio by sector and holding — nothing else fits that on one page. The failure here is a single-level ranking of thirteen numbers, which is a bar chart wearing a hierarchy chart’s clothes. When a treemap is the right call, sort the tiles so that position carries something, label every tile with its number, keep the layout near square and say which layout it is, and lift any comparison that actually matters out of the picture and into a small sorted chart beside it. And the check that catches this one in the wild takes about five seconds: cover the labels and try to rank the tiles. If you cannot, the chart never told you the ranking — and if you then read the numbers off the labels, what you have been reading all along is a table.