He grew up to lead the hunt for the Calydonian boar, a beast the goddess Artemis had sent to ruin his father’s land. When the boar was dead, Meleager gave its skin to Atalanta, the huntress who had drawn first blood. Althaea’s brothers said no woman should keep the prize, and they took the skin from Atalanta. Meleager killed his uncles for it.

Althaea brought out the brand. Ovid has her hold it over the flames four times and pull back four times. Then she turned her face away and threw it in. The wood gave “a strange groan.” Far off, in his hour of victory, Meleager felt “the flame of burning wood scorching with secret fire his forfeit life.” No blade had touched him. He burned from the inside, and as the log burned down, his pain eased. When the last flame went out, so did he.

Meleager’s life ran on one piece of wood, and the wood set all three of its stretches. While the brand lay hidden, he was well. While it burned, he was still alive, and he burned with it. When it went out, he died.

The middle stretch is the gap from part one: the years a person lives but does not live well. The first part of this series drew every country’s life as a birthday cake, with its unhealthy years pulled out. Each year a baby born there can expect to live is one candle, and each year’s worth of poor health takes one out. That piece counted the pulled candles. It never asked what put them out: what lit the log.

A candle can be blown out, and the flame leans away before a thin gray ribbon of smoke climbs off the wick. It can be pinched out with wet fingers, with a short hiss. The cake loses one either way. Up close, you can tell which.

Not every teller agreed that the brand killed him. In the second century, a Greek travel writer named Pausanias found Meleager in a painting of the underworld at Delphi and stopped to sort the causes. Homer blamed a Fury who heard his mother’s curses. Two other poems blamed Apollo. A playwright put the brand on stage, retelling a story everyone already knew. One death, three causes. Pausanias wrote all three down and did not pick one.

Pausanias could leave the question open. The World Health Organization cannot. It gives every lost healthy year a cause, and it counts the years people spend sick, not only the deaths.

In 2019, the same two causes took the most healthy years in 149 of 185 countries. One was aching backs and joints. The other was a troubled mind: depression, anxiety, drink, and drugs. In Australia, those two took nearly half.

Odds are, they are coming for your own candles too. They rarely arrive like a fever. They come as a stiff back on a cold morning, or a month when getting out of bed feels heavy, and each one takes a sliver of a candle.

Where countries differ is what comes after those two. A few put something else ahead of them. In Lesotho, infection alone took a quarter, ahead of both. The troubled mind came second. Across most of Africa, infection comes next, and in a few countries hunger. Across most of Europe, falls and other accidents come next, then diseases of the brain and nerves.

A country losing its candles to infection needs clinics, medicines, safe births, and food. One losing them to bad backs and heavy minds needs physiotherapists and counselors. Sort the countries by how their candles go out, and each can learn from the ones that share its trouble. That kind of sorting is called clustering.

The paper did that sorting and found three piles. I ran that kind of sort, let a different test choose the count, and found two. The count decides which countries share a pile, and so which neighbors each one learns from.

One sort can be luck, a quirk of which countries happened to be in the data. So I put the 185 countries in a hat and drew 185 names, putting each one back before the next draw. Some countries came up twice, and some not at all. Then I sorted again. I did that two hundred times. The trick is called a bootstrap, and it asks the question Pausanias left open: which answer keeps coming back?

Two piles, nearly every time. In one, more candles than elsewhere are blown out, by infection and hard births. In the other, more than elsewhere are pinched out, by the slow wear of chronic disease. The paper’s three almost never did. Any cause you are sure of deserves the same test, down to the one you give for your own bad week.

The piles did not hold still. Between 2000 and 2019, some countries crossed from one pile to the other. Every one of them crossed in the same direction, and none crossed back.

Where the Candles Went

The piles are built from WHO’s counts of healthy years lost to each disease, country by country. The unit is the year lived with disability. A year spent with a condition counts as part of a healthy year lost, and the part grows with how much the condition takes out of a day. A year of mild hearing loss costs a sliver of a candle. A year of severe depression costs more than half of one. This piece uses only the unwell half of WHO’s ledger.

The losses fall into 22 categories, such as cardiovascular disease, mental and substance use disorders, and neonatal conditions. The counts come per 1,000 people of all ages. A country with more old people carries more of the diseases of age, such as arthritis and dementia, even if no age group there is any sicker than anywhere else. The year is 2019, the last before COVID-19 got a category of its own.

Before any sorting, the 22 categories have to share one scale. Aching backs and joints vary a great deal from country to country: the typical distance between a country and the average country is about seven and a half healthy years per 1,000 people. Hard births vary by about a seventh of one. Left raw, the big categories would drown out the small ones. So each category is restated as how far a country lies from the average, in units of that category’s own typical spread, its standard deviation. A score of +2 on maternal conditions and +2 on bad backs now read alike: unusually high, for that disease.

Figure 3 shows what separates one country’s disease profile from another’s.

Figure 3a. Disease burden in 22 categories across 185 countries, 2019, with similar countries and categories grouped together. Each category is scaled on its own, so colors compare countries within a category.

Panel (a) is every country’s profile at once: 22 categories down the side, 185 countries across the top. Warm cells run high for that category, and cool cells run low. The trees along the edges come from hierarchical clustering. The method starts with every country on its own. It keeps joining the two closest groups until one group is left, and the tree records every join. This one uses Ward’s method, which at each step makes the join that adds the least spread inside the groups. Countries with similar profiles end up side by side, and so do categories that rise and fall together.

The first split at the top of the tree sets 46 countries apart from the other 139. Those 46 carry the heaviest chronic burden on the map. The other 139 run from the infection-heavy end of the world to its middle.

Figure 3b. Countries on the first two principal components of their 2019 disease-burden profiles, colored by region. The first component carries 54 percent of the variation.

Twenty-two categories give every country a position in twenty-two dimensions, and no one can see that. Principal component analysis finds the flat view that loses the least. Picture the 185 countries as beads hanging in a dark room, with a lamp throwing their shadows on a wall. As the hanging beads turn together, the shadows widen and narrow. The direction where they spread widest is the first principal component. The widest direction at right angles to it is the second. The first captures 54 percent of the total spread among countries, and the second only 7, so the view is mostly a left-to-right story. Because every category was standardized first, the axes follow which diseases rise and fall together, not which ones are biggest.

The panel plots every country on those two axes, colored by region. Each ellipse is drawn to hold about 95 percent of its region’s countries. The paper drew three regions. I drew all six, since the coloring does not move the axes. Europe lands furthest left, Africa furthest right, and the other four regions overlap in between. The paper’s panel shows that Europe-to-Africa separation too.

Figure 3c. How much each disease category contributes to the first two principal components, 2019. Categories are labeled where either value passes 0.2 (dashed lines).

Panel (c) shows what the left-to-right axis is made of. Each arrow is one category. How far it reaches left or right, its loading, says how hard that category pulls on the axis. Each axis has a fixed budget of pull, shared among the 22 categories: the squared loadings add up to one. If all 22 pulled equally, each would come to about 0.21, and the dashed lines at 0.2 mark roughly that fair share.

Pulling right, toward the infection-heavy end: nutritional deficiencies, congenital anomalies, maternal conditions, infectious and parasitic disease, and respiratory infections. Pulling left, toward the chronic end, musculoskeletal disease pulls hardest, and eight other categories follow close behind.

Skin disease and intentional injuries alone hover near zero. Every other category leans one way or the other by a similar amount, between 0.14 and 0.28. No single disease drives this axis. It measures a whole profile tipping at once, and that is the epidemiologic transition: infections and hard births giving way to chronic disease as a population lives longer. Some of the tipping is age itself.

Two Piles, Not Three

The paper sorted countries into piles with k-means clustering and reported three. K-means works like this. It takes a set number of piles and drops that many markers at random. Every country goes into the pile of its nearest marker. Each marker then moves to the middle of its pile. The countries are reassigned, the markers move again, and the cycle repeats until nothing changes. The final piles depend on where the markers started, so I ran k-means from 25 random starts and kept the tightest result. I sorted on the first six principal components rather than the raw 22 categories. Together they hold 81 percent of the spread, and dropping the rest trims small, scattered variation.

K-means needs to be told how many piles to make. The paper chose three with the elbow method. It plots how tight the piles are against how many there are. More piles always make them tighter, so the method looks for the bend where one more pile stops helping much.

On this data, the bend is hard to read. Going from one pile to two removed about half the spread. A third pile removed about another sixth, and a fourth about a twentieth. After that, the curve runs nearly flat. It bends sharply at two and again, more softly, at three. The paper’s three is a fair reading of that curve.

I let a silhouette test choose instead. For each country, it compares two distances: the average distance to the other countries in its own pile, and the average distance to the countries in the nearest other pile. The score runs from -1 to 1. Near 1, the country sits snugly at home. Near 0, it sits on the border. Below 0, it sits closer to the other pile than its own. Averaged over all 185 countries, two piles scored 0.40 and three scored 0.35. Four piles scored 0.34, and five to eight scored lower still. The test picked two. The elbow and the silhouette are reading the same data, and they disagree. Figure 4 shows the split.

Figure 4a. The two k-means clusters from 2019, on the principal-component axes from Figure 3b.

Panel (a) lays the two clusters over the axes from Figure 3. Cluster 1, with 78 countries, holds the chronic-disease left. Cluster 2, with 107, takes the infection-heavy right. Where they meet, near the middle of the horizontal axis, the points run straight through with no empty band between the two colors.

These are the two ways the candles go out. In cluster 2, on the right, more of them than elsewhere are blown out: by an infection carried on a breath or in water, a plate that stays empty, a birth that goes wrong, a baby who starts life sick or malformed. In cluster 1, on the left, more than elsewhere are pinched out close at hand, by the wear of a long life: joints that ache, a mind that struggles, a heart that tires, a growth that spreads, a fall on the stairs. Every country loses candles both ways. The piles sort by which way runs higher than the world’s average.

Figure 4b. Regional makeup of each cluster.

Panel (b) shows which regions fill each cluster. Cluster 1 is more than four-fifths Europe and the Americas. Cluster 2 is three-fifths Africa and the Eastern Mediterranean. The sort never saw a map, and it still came out close to one.

Figure 4c. Healthspan-lifespan gap in 2021 by cluster.

Panel (c) asks whether a country’s cluster relates to its gap, using part one’s 2021 figure, the latest year WHO publishes. It does. Cluster 1, the chronic-disease cluster, has a median gap of 10.4 years, against 8.7 for cluster 2. A rank-sum test asks whether one group’s values tend to run higher than the other’s, without assuming a bell curve. If the two clusters’ gaps came from the same spread, a difference this large would almost never turn up. The countries that lean toward pinched candles are the ones where years lived and years lived well are furthest apart, the long-lived countries from part one.

Part one predicted each country’s gap from two numbers: its life expectancy and its health spending. The paper’s model had a third, chronic-disease burden, and part one left it for this piece. I added it here. Each ten extra healthy years per 1,000 people lost to chronic disease comes with about a month more gap. The p-value, worked out cup by cup for the lady tasting tea, is 0.021: a difference this size would turn up about one time in fifty. The share of the country-to-country spread the model explains barely moves, from 0.819 to 0.823. The cluster does worse than the chronic-disease burden. Once life expectancy and health spending are in the model, it adds nothing. The difference between the two piles’ gaps is mostly the difference in how long their people live.

Figure 4d. Healthspan-lifespan gap in 2021 by cluster within each region. Africa’s cluster 1 is a single country.

Panel (d) checks whether the chronic-disease cluster’s wider gap holds inside each region, since cluster and region travel together. In four of the six it does: cluster 1 has the wider gap in the Americas, Eastern Mediterranean, Europe, and Western Pacific. Africa cannot answer the question, since only one of its countries, Mauritius, landed in cluster 1. South-East Asia reverses, with cluster 2 slightly higher, in a region of ten countries.

The paper checks its piles with a random forest. A random forest is a crowd of decision trees. Each tree is a short run of yes-or-no questions, such as “is the cancer burden above this line?” Each is grown on a random resample of the countries and is limited to a random handful of categories at each question. Then the crowd votes.

Each tree is tested only on the third of the countries it never saw. Pooled over 500 trees, the forest sorted my two clusters correctly 98.4 percent of the time, missing 3 of 185 countries.

But k-means draws a clean line even through a cloud with no gap in it, and the forest was only asked to find that line again. The 98 percent shows the line is easy to redraw. It cannot show whether the countries fell into two piles before anyone drew it.

The forest leans hardest on musculoskeletal disease, cancer, and oral conditions. Boruta, the paper’s second check, pits each category against a shuffled copy of itself. Twenty of the 22 help tell the two piles apart, one is borderline, and skin disease does no better than its copy.

None of these checks asks how much the two-pile answer depends on which 185 countries were in the data. A bootstrap does. These are the two hundred sorts from the opening. They ask Pausanias’s question: which answer keeps coming back? Each one reruns the whole sort from the standardizing onward and records which count wins. Two won 188 times, or 94 percent. Three, the paper’s count, won twice. Four won six times and five won four. A bootstrap measures stability, not truth. It shows the silhouette would keep choosing two on a slightly different roster of countries.

Whether the piles are real groups is another question, and there the evidence leans the other way. In their textbook on clustering, Kaufman and Rousseeuw, the second of whom invented the silhouette, suggest reading an average from 0.26 to 0.50 as weak structure that could be artificial. An average of 0.40 falls in that band. The tree in Figure 3a made its first cut somewhere else, at 46 against 139. Figure 4a shows no empty band where the two piles meet. The fairest description is a gradient, from infection-heavy to chronic-heavy, with most of the world strung along it, blown at one end and pinched at the other. Two piles is the cleanest way this data offers to cut that gradient. Three is not a better one. For a country looking for others that share its trouble, the ones to learn from are its neighbors on that slope, whichever side of the cut they fall on.

No Country Crossed Back

Everything above sorts one year, 2019. The transition behind Figure 3c happens over decades. So I reran the whole sort on 2000, 2010, 2015, and 2019 separately. Each year got its own standardizing, principal components, and k-means. I held the count at two every year, so the number of piles could not change under a country, only which side of the line it fell on.

A country’s position is therefore always relative to the rest of the world that year. If every country had shifted toward chronic disease at the same pace, none would have changed piles. A move means a country traveled further than the world around it.

Twenty-two of 185 countries changed piles between 2000 and 2019. Every one moved from the infection-heavy pile to the chronic-disease pile, which grew from 56 countries to 78. None went the other way. Eleven moved between 2000 and 2010, three between 2010 and 2015, and eight between 2015 and 2019. Ten of the twenty-two are in the Americas: Colombia, Costa Rica, Ecuador, Grenada, Mexico, Panama, Peru, Saint Lucia, Saint Vincent and the Grenadines, and Trinidad and Tobago. The other twelve are spread across the other five regions, with China, South Korea, Thailand, and Turkey among them.

No country crossed and then crossed back at any of the three steps. If countries were simply wobbling across the line between piles, some would wobble back. If each move were a coin toss, the chance that all 22 would fall one way is about one in two million. Still, WHO’s yearly figures are modeled estimates, and models of this kind smooth their estimates over time. That smoothing may hide some of the back-and-forth a raw count would show. It cannot explain why every move runs in the same direction.

The piles caught a transition in motion, and a slow one: twenty-two countries in nineteen years. In each of them, the way the candles go out tipped from blown toward pinched. Althaea pulled back four times. When the brand finally went in, it stayed, and so far these twenty-two have stayed too.

A Closing Reflection. Pausanias kept all three causes for one death. A bad day can have more than one too.

1. The last time you felt run down, and every cause that could have done it, the weather, a bad night, work, not only the one you said out loud.
2. A cause your household hands out by habit, the cold that “goes around every winter,” the kid who is “just tired,” and the voice you first heard say it.
3. A day that was neither good nor bad, and what your body told you before you were out of bed that morning.

Althaea’s log gave a groan when it went into the fire. Real wood makes its own sounds as it burns: a hiss where the sap boils, a crack where a knot splits, a soft settling when the middle gives way. From across the room, it all sounds like one fire. The next time something small costs you an hour of feeling well, a stiff neck, a short night, a sharp word, listen for what lit that fire before you give it a name.

Where This Came From

The study replicated here is Garmany and Terzic (2025), in Communications Medicine. Its three disease-burden clusters, and the random forest and Boruta checks it runs on them, are the paper’s design. The paper chose its three clusters with the elbow method. The two-cluster result, the silhouette test that chose it, the elbow curve rerun on this data, the bootstrap, the cluster tracking from 2000 to 2019, and the chronic-disease burden added to part one’s model are my own. K-means numbers its piles arbitrarily on each run, so the tracking matches them year to year by whichever pairing shares the most countries. The disease-burden data is WHO’s Global Health Estimates, 2021 round, at the middle of WHO’s five-level cause outline. The sort uses 2019, the last year of the paper’s window, because COVID-19 enters the cause list as its own category in 2020 and would tilt the 2020 and 2021 profiles. The data was downloaded year by year on 28 August 2026 as years lived with disability per 1,000 people, both sexes, all ages. Part one noted that this data lives somewhere else. WHO’s data service stops at regional totals, and the Global Health Estimates program posts the country-level version as one plain spreadsheet per year, with no login. The code and the full results tables are public at github.com/gauranii/GapYears.

Meleager’s story is pieced together from three sources. The Fates’ decree is from Apollodorus’s Library (1.8.2-3), in James George Frazer’s 1921 translation, which hides the brand in a chest and also gives the version where Althaea curses her son and he dies in battle. The quenching with drawn water, the brand hidden in her own room, the four false starts, the groan from the wood, and the “secret fire” are from Ovid’s Metamorphoses (8.451-525), in Brookes More’s 1922 translation. Pausanias’s three causes are from his Description of Greece (10.31.3-4), in W. H. S. Jones and H. A. Ormerod’s 1918 translation, where he is describing Polygnotus’s painting of the underworld at Delphi.

The shift the first principal component traces, from infections and hard births toward heart disease and cancer, is what Omran (1971) named the epidemiologic transition. The reading of an average silhouette from 0.26 to 0.50 as weak structure that could be artificial is from Kaufman and Rousseeuw (1990).

Part three follows the gap from 2000 and projects it to 2100.

Intellectual Honesty Note. Reading the brand’s three stretches as healthy years, unwell years, and death is this piece’s own device, not the myth’s. So are the candles and the two ways they go out. The hiss, crack, and settling of burning wood in the closing are this piece’s own images. Only the groan is Ovid’s. Matching blown-out candles to infection and pinched ones to chronic disease is part of that device, not a medical grouping. The Australia and Lesotho shares, and the 149 of 185 countries whose two largest causes are musculoskeletal disease and mental and substance use disorders, are my own counts from the 2019 WHO data, as shares of years lived with disability. They stand in for the pulled candles, which WHO computes from those years. The regional descriptions in the opening come from those counts: infection is the third-largest cause in 35 of Africa’s 47 countries and nutritional deficiencies in 6, and unintentional injuries and neurological conditions share third place across Europe’s 50. The clinics and counselors are illustrations, not recommendations drawn from the data. The hearing-loss and depression examples of how much a year costs are rounded from the disability weights WHO borrows from the Global Burden of Disease study. The Ward tree split, the medians and rank-sum test for Figure 4c, the chronic-disease burden model, and the one-in-two-million coin-toss figure are my own calculations from the repository’s data. Chronic-disease burden is the sum of WHO’s noncommunicable categories for 2019, set beside part one’s 2021 gap, life expectancy, and health spending. As in part one, the model covers 183 countries, the 185 less the two with no health-spending figure. The reading of the clusters as a gradient cut in two is my interpretation of the silhouette score and the figures, not a formal test.

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