A young man named Hippomenes came to watch, meaning to scold the suitors for risking their lives. Then he saw her run, and he entered. Venus, the goddess of love, gave him three golden apples and told him how to use them.

The trumpet sounded, and the crowd shouted his name. Atalanta passed him, slowed to look at his face, and passed him again. With the goal still far off and his breath running dry, he threw the first apple. She turned out of her course to pick up “the rolling gold,” and he took the lead. She caught him. He threw the second, and she caught him again. Near the end, he threw the last one wide, off to the side. She hesitated, then went after it. Venus made the gold heavy in her hands, and she lost.

She was the huntress Meleager gave the boar’s skin to in the story of his burning log, and until that day she had never lost. A line drawn through her record would have said the next suitor would die too. The record was right about every race it had seen. None of those races had apples in them.

Race records still tempt people to draw lines. In 2004, a team of researchers published a short paper in Nature with a startling forecast. They drew a straight line through every Olympic 100-meter winning time for women since 1928, and another through the men’s since 1900. The women’s line was falling faster. Extended forward, the two lines crossed in 2156, when a woman would win in 8.079 seconds and the men’s winner would finish in 8.098.

A reader wrote back to the journal. The authors, the reply pointed out, “omit to mention, however, that (according to their analysis) a far more interesting race should occur in about 2636, when times of less than zero seconds will be recorded.”

Picture that race. The starting gun fires, and the winner is through the tape, catching their breath before the smoke clears.

You keep a record like hers, whether you mean to or not. Years without a serious illness. A back that has never gone out. A blood pressure the nurse calls fine every visit. Drawn forward, that line says the next ten years will look like the last ten. It is right about every year it has seen. What it promises is the years it has not seen, and how many of them you will spend well. One way to learn how far to trust it is to draw a second line through the same years and see whether the two agree.

The gap between years lived and years lived well has a line of its own. In part one, every country got a birthday cake with a candle for each year of life, and the gap was the candles pulled for years spent unwell. A cake counted once is a snapshot. Count it every year from 2000 to 2021 and the pile of pulled candles moves. In Africa it grows fastest, by about one candle every twenty years. The region that pulls the fewest candles today is adding them the fastest.

The paper extends that movement to 2100 and says the gap will widen twenty-two percent. Its line does not run through time. For each country, it drew a line from life expectancy to the gap, then let the United Nations’ forecast of life expectancy carry that line to 2100. I drew three simpler lines, through time alone. They land anywhere from thirty-seven percent down to nine. Left to run, one of them has the Americas pulling out fewer than zero candles by the end of the century, a race won before the gun.

The Pile Moves

For every country, I drew a straight line through its gap from 2000 to 2021 and kept the slope: how many years of gap it adds each year. Figure 5a arranges those slopes by region.

Figure 5a. Per-country trend in the gap, 2000 to 2021, by region, ordered from the flattest median slope to the steepest. Each dot is one country’s slope.

The line inside each box marks the typical country, and the box holds the middle half of the region’s countries. Above the dashed line at zero, the gap is widening.

Africa’s median slope is the steepest, about 0.05 years of gap per year, the one candle every twenty years from the opening. South-East Asia sits just behind it, then Eastern Mediterranean and Europe. The Americas and Western Pacific are the flattest. The paper found the same two regions at the top, Africa and then South-East Asia, with steeper rates of 0.07 and 0.06 over its shorter window. Africa comes out on top here too, though only by a hair over South-East Asia.

What Fills the Pile

Part two sorted the world’s countries by how their candles go out, using WHO’s counts of healthy years lost to 22 kinds of disease. That sort answers which diseases separate one country from another. There is a second question the paper does not ask: which diseases track the size of the gap itself. The paper’s regression uses one number for all noncommunicable disease together. With the 22 categories in hand, they can compete in one model instead.

An ordinary regression with 22 predictors and 185 countries hands every category some weight, noise included. Categories that rise and fall together can also trade weight back and forth almost at random. A LASSO regression adds a penalty. Every unit of weight a category carries costs something, so a category keeps its weight only if it improves the fit by more than the weight costs. The weak ones are pushed to exactly zero and drop out.

How steep the penalty should be is set by cross-validation. The countries are split into ten batches. The model is fit on nine and predicts the tenth, rotating through all ten and scoring the misses. That is repeated across a range of penalties. I report the steepest penalty whose misses stay within ordinary noise of the best one’s, the simplest model that does about as well. Twelve categories stayed at that setting. At the lighter setting with the smallest error, nineteen stayed.

To compare them, each effect goes on a common scale. It asks how much the gap moves when a country carries one standard deviation more of a disease than the average country, with the other categories held where they are. A standard deviation here is one typical step of country-to-country spread. The raw scale would mislead. On it, “other neoplasms” has by far the largest coefficient, about -1.26. These are the growths WHO does not count as cancer. The coefficient says each extra healthy year lost to them per 1,000 people goes with about 1.26 fewer years of gap. But countries barely differ on it. Its standard deviation is about a twentieth of a healthy year. So one standard deviation of it moves the gap by less than a tenth of a year.

On the common scale, mental and substance use disorders lead, at about 0.7 years of gap, nearly three-quarters of a candle. Musculoskeletal disease comes next, at about 0.3. At the lighter setting the two tie, at about two-thirds of a year each. The safe reading is that the troubled mind and the aching body lead together, the same two that take the most healthy years in 149 of 185 countries.

Infectious and parasitic disease points the other way, at about a quarter of a year less gap. That sign holds the other 21 categories fixed. One likely reading: among countries with the same chronic burden, the one with more infection tends to be the shorter-lived one. Shorter lives leave fewer years to spend unwell. That fits part two, where the infection-heavy cluster lost fewer candles.

Cancer was shrunk to zero at both settings. That does not mean cancer costs no healthy years. Across countries, cancer burden rises and falls almost in step with heart disease, neurological conditions, and bad backs, with correlations of 0.84 to 0.88, where 1 would mean they move together perfectly. Once those are in the model, cancer has little left to say. A set that moves this closely can trade weight back and forth, so I also ran an elastic net, a cousin built to share weight across such a set. It dropped cancer too. Six of the ten categories that best told apart part two’s two clusters, the infection-heavy and the chronic, survived the LASSO, though that sort was answering a different question.

The gap is itself built from these disability counts. WHO computes healthy life expectancy by taking the years a population lives at each age and subtracting the share spent with disability, counted age by age. So this regression partly takes the gap apart into its own ingredients. An ordinary regression on all 22 categories, with no penalty, explains about 83 percent of the gap’s variation across countries. “Predict” here means “accounts for,” not “causes.” The useful part is which ingredients differ most from one country to the next. The forecasts ahead carry the gap to 2100 as a single number, and this is what that number is made of.

Before the Gun

The paper’s route to 2100 runs through life expectancy. For each of its 183 countries, it fit the gap against life expectancy over the last two decades. Then it fed in the United Nations’ forecast of life expectancy for every year to 2100 and read off the gap. Its 22 percent is how much the median country’s gap grows along that route.

I rebuilt that route with the UN’s 2024 forecast, the edition the paper used. Fit on 2000 to 2019, each of 185 countries got its own line, and all but one slope upward, at about 0.16 years of gap for every added year of life. Carried to 2100, the median country’s gap grows 20.2 percent, from 9.5 years to 11.4. The paper’s 22 percent came back within two points, without its code. Its range across countries in 2100, 7.3 to 18.8 years, came back as 7.4 to 17.6. Figure 5b follows each region along that route.

Figure 5b. Regional gap projected to 2100 through UN life-expectancy forecasts, my rebuild of the paper’s route. Lines are regional means; bands are 95 percent confidence intervals for each mean. They reflect how much a region’s countries differ, not how uncertain the forecast is.

Every region widens. Africa starts narrowest and stays narrowest, at about 9.8 years in 2100, while the Americas, Eastern Mediterranean, and Europe reach 12.2 to 12.6.

That route leans on the UN’s forecast of how long people will live. A second way to ask about 2100 leaves life expectancy out and follows the gap through time alone. The plainest version is a straight line through each region’s average gap, extended to 2100. Figure 5c draws it.

Figure 5c. Straight-line extrapolation of each region’s average gap to 2100. The dotted line marks 2021, the last year of data.

Africa’s straight line tells a different story. It starts 2021 at the bottom and climbs steeply enough to pass three of the other five regions by 2100. So Africa, widening fastest, ends the century narrowest on the paper’s route and near the top on a straight line. A straight line cannot see a trend bend or level off, and it knows nothing about how long people will live. It is the line through Atalanta’s record, sure of the next race because it has never seen an apple.

A straight line is one choice among several. I fit two more on the twenty-two years of regional data, an ARIMA model and an exponential-smoothing model, two standard ways to forecast a series from its own past. Figure 5d runs all three to 2100 side by side.

Figure 5d. Three projection methods compared by region: straight line, ARIMA, and exponential smoothing. The black line is the observed gap; each panel has its own vertical scale.

They do not agree. Averaged across the six regions, the straight line says the gap grows 37.4 percent by 2100. Exponential smoothing says 11.3, and ARIMA says 9.0. ARIMA’s 9.0 carries a forecast for the Americas that falls below zero, to minus 0.78 years by 2100: fewer than zero candles pulled, the race won before the gun. No gap can be negative. The number is what any of these lines does when dragged seventy-nine years past twenty-two years of data. Leave ARIMA out, and the lines that stay above zero run from 11.3 to 37.4. These are averages of six regional averages, not the median country, so they sit on a slightly different ruler from the paper’s 22 and my 20. The spread is the finding: twenty-two years of candles, followed through time alone, support anything in that range. Followed through life expectancy, the paper’s way, the answer is 20.

The spread is not the same everywhere. In Africa, Europe, and Eastern Mediterranean, the three lines end about four years apart. In South-East Asia and Western Pacific, they end within half a year of each other. The Americas split furthest, because of that ARIMA line.

What Came Back

Across three parts, most of the paper came back. Africa has the narrowest gap. Africa supplies the largest share of the countries losing more candles than predicted, and Europe the largest share of those losing fewer. Africa’s gap is growing fastest, narrowly. Rebuilt the paper’s way, the 2100 median gap grows 20 percent against its 22. Those findings came back from a pipeline built without the authors’ code, which is some evidence they do not depend on one team’s modeling choices. Two things came back different. My disease-burden sort found two clusters where the paper found three. And a line through time alone lands anywhere from 11 to 37 percent, so the paper’s 22 depends on the route it took through life expectancy. Two steps were not rebuilt as the paper ran them. One is its regression, which used GDP and noncommunicable disease burden where mine used health spending. The other is its map of which countries count as neighbors. Part one’s spatial model used such a map to let nearby countries land above or below their predictions together. The paper never describes its map.

I keep a working list of twelve questions that outlast any single project. One asks what it means when a body’s biological age runs ahead of its calendar age, and whether pulling it back would buy more healthy years or only move the same decline later. This series asked a version of that question about whole countries.

A Closing Reflection. Atalanta’s record held for every race until the one with apples in it. A straight line will run as far as you let it. It ran the women’s sprint past the men’s in 2156, then past the starting gun in 2636, and it would have kept going. The line was never the mistake. Forgetting where the data stopped was. Past that edge, the next race might have apples in it.

1. A forecast you make about yourself out loud, “at this rate I will never finish,” “I always get sick in March,” and how many years of evidence it stands on.
2. A trend you are sure of from the last few months, a bill creeping up, a friend texting less, a child outgrowing shoes, and the moment you catch yourself running it out ten years.
3. A number someone handed you with no method attached, a percentage in a headline, a doctor’s rough odds, a coworker’s “it always takes twice as long,” and what would change if you asked how they got it.

The cake got counted once, then sorted by how its candles went out, then watched as the pile of pulled candles grew. One line through that pile said the gap grows thirty-seven percent by 2100. Another said nine. Somewhere this week you will run a line through your own days past the edge of what you know. Listen for the starting gun. If your line already has you through the tape, catching your breath in less than zero seconds, look back at the smoke. It has not cleared yet.

Where This Came From

The study replicated across this series is Garmany and Terzic (2025), in Communications Medicine. The 22 percent widening by 2100, measured on the median country, and Africa’s fastest expansion are the paper’s findings. The per-country trend slopes, the LASSO and elastic net on the 22 disease categories, the straight-line extension, and the three-method comparison are my own additions. The LASSO penalty reported is lambda.1se, the steepest within one standard error of the smallest cross-validated error; the lighter setting is lambda.min. The disease categories are WHO’s Global Health Estimates for 2019, the same data part two sorts. WHO’s healthy life expectancy follows Sullivan’s (1971) method, which is why the gap and the disability counts share their ingredients. The paper’s 22 percent comes from per-country regressions of the gap on life expectancy, carried to 2100 on the United Nations’ World Population Prospects forecast of life expectancy. I rebuilt that method with the World Population Prospects 2024 medium-variant forecast, the edition the paper cites, fitting each country on 2000 to 2019. The 20.2 percent is the change in the median gap from the observed 2019 value. The straight line is an ordinary least-squares fit per region. The ARIMA and exponential-smoothing fits use the forecast package for R (Hyndman & Khandakar, 2008), with each model’s form chosen automatically per region. The code and the full projection tables are public at github.com/gauranii/GapYears.

Atalanta’s race is from Ovid’s Metamorphoses (10.560-707), in Brookes More’s 1922 translation, where Venus tells the story to Adonis as a warning. He ignores her and is killed by a boar. Ovid is Roman, but he is retelling a Greek myth. Apollodorus’s Library (3.9.2), in James George Frazer’s 1921 translation, tells the same race with the suitor named Melanion, and it places the same Atalanta at the Calydonian boar hunt from part two.

The Olympic forecast is Tatem, Guerra, Atkinson, and Hay (2004), a one-page communication in Nature. The reply quoted in the opening is Kenneth Rice’s letter in the same journal later that year, one of several the forecast drew.

Intellectual Honesty Note. A line drawn through Atalanta’s record is this piece’s reading, not anything in Ovid. Some ancient writers kept the huntress and the runner apart as two women with different fathers. This piece follows Apollodorus in treating them as one. The race won before the gun is the reply’s joke, extended into a scene for this piece. The pile of pulled candles is the series’ own device. The negative Americas gap under ARIMA is a real output of the fit, reported as it came out, not a number with any meaning for 2100. The per-standard-deviation LASSO effects, the correlations with cancer, and the 83 percent least-squares fit are my own calculations from the repository’s data.

References

Apollodorus. (1921). The Library (J. G. Frazer, Trans.). William Heinemann.

Garmany, A., & Terzic, A. (2025). Healthspan-lifespan gap differs in magnitude and disease contribution across world regions. Communications Medicine, 5, 381.

Gauran, I. I. (2026). GapYears (Version 1.0.0) [Computer software]. GitHub. https://github.com/gauranii/GapYears

Hyndman, R. J., & Khandakar, Y. (2008). Automatic Time Series Forecasting: The forecast Package for R. Journal of Statistical Software, 27(3), 1-22.

Ovid. (1922). Metamorphoses (B. More, Trans.). Cornhill Publishing.

Rice, K. (2004). Sprint research runs into a credibility gap. Nature, 432, 147.

Sullivan, D. F. (1971). A Single Index of Mortality and Morbidity. HSMHA Health Reports, 86(4), 347-354.

Tatem, A. J., Guerra, C. A., Atkinson, P. M., & Hay, S. I. (2004). Momentous sprint at the 2156 Olympics? Nature, 431, 525.

Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267-288.

United Nations, Department of Economic and Social Affairs, Population Division. (2024). World Population Prospects 2024 [Data set]. Retrieved September 25, 2026, from https://population.un.org/wpp/

Zou, H., & Hastie, T. (2005). Regularization and Variable Selection via the Elastic Net. Journal of the Royal Statistical Society: Series B, 67(2), 301-320.

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.

References

Apollodorus. (1921). The Library (J. G. Frazer, Trans.). William Heinemann.

Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5-32.

Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1-26.

Garmany, A., & Terzic, A. (2025). Healthspan-lifespan gap differs in magnitude and disease contribution across world regions. Communications Medicine, 5, 381.

Gauran, I. I. (2026). GapYears (Version 1.0.0) [Computer software]. GitHub. https://github.com/gauranii/GapYears

Kaufman, L., & Rousseeuw, P. J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley.

Kursa, M. B., & Rudnicki, W. R. (2010). Feature Selection with the Boruta Package. Journal of Statistical Software, 36(11), 1-13.

MacQueen, J. (1967). Some Methods for Classification and Analysis of Multivariate Observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 281-297). University of California Press.

Omran, A. R. (1971). The Epidemiologic Transition: A Theory of the Epidemiology of Population Change. The Milbank Memorial Fund Quarterly, 49(4), 509-538.

Ovid. (1922). Metamorphoses (B. More, Trans.). Cornhill Publishing.

Pausanias. (1918). Description of Greece (W. H. S. Jones & H. A. Ormerod, Trans.). William Heinemann.

Pearson, K. (1901). On Lines and Planes of Closest Fit to Systems of Points in Space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.

Rousseeuw, P. J. (1987). Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. Journal of Computational and Applied Mathematics, 20, 53-65.

Salomon, J. A., Haagsma, J. A., Davis, A., de Noordhout, C. M., Polinder, S., Havelaar, A. H., Cassini, A., Devleesschauwer, B., Kretzschmar, M., Speybroeck, N., Murray, C. J. L., & Vos, T. (2015). Disability Weights for the Global Burden of Disease 2013 Study. The Lancet Global Health, 3(11), e712-e723.

Ward, J. H. (1963). Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 58(301), 236-244.

Wilcoxon, F. (1945). Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1(6), 80-83.

World Health Organization. (2024). Global Health Estimates 2021: Disease burden by cause, age, sex, by country and by region, 2000-2021 [Data set]. Retrieved August 28, 2026, from https://www.who.int/data/gho/data/themes/mortality-and-global-health-estimates

So Tithonus goes on living, and he goes on aging. The first gray hairs ripple from his head and his chin, and she keeps away from his bed. She still feeds him ambrosia and dresses him in rich clothing. His limbs, once supple, stiffen until he can no longer move or lift them. Then she lays him in a room and closes the shining doors. “There he babbles endlessly, and no more has strength at all.” Every morning the dawn goes out into the world, and behind those doors the voice keeps going.

Aphrodite tells this story on the slopes of Mount Ida, to a mortal lover of her own, the herdsman Anchises. Then she refuses him the very gift the dawn once asked for. The goddess of love would not ask for forever without youth.

Picture Tithonus’s birthday cake after a few hundred years. Every candle on it still burns. Take out one for every year he could not get out of bed, and almost nothing is left.

No country is Tithonus, but every country has a cake. It carries one candle for every year a baby born there in 2021 can expect to live. One candle comes out for every year’s worth of poor health. The years of the bad knee, when the stairs get taken one at a time. The years of the pill organizer, seven plastic lids snapped open every morning.

The cake in Australia carries eighty-three candles. Lit all at once, they throw enough heat that everyone at the table leans back. Twelve and a half come out. The cake in Lesotho carries fifty-one, and almost seven come out. The longer life loses more candles.

Researchers call the pulled candles the healthspan-lifespan gap: life expectancy minus healthy life expectancy. In 2025, a paper in Communications Medicine counted them for 183 countries from 2000 to 2019, using World Health Organization and United Nations data. The global median gap was 9.1 years. Then it asked why the gap is wider in some regions than others.

As lives get longer, the gap grows with them: roughly one pulled candle for every six or seven added. That holds even when a country is compared only with its own past. A headline about living longer rarely mentions that cost. Every year added to a country’s average cake comes with nearly two months of the bad knee and the pill organizer. The paper projects the gap to widen 22 percent by 2100, and a baby from the 2021 cakes would be seventy-nine by then.

Counts of healthy years do not stay in journals. In 2017, a review of Britain’s pension age gave a full section to how long people stay well, not only how long they live. Insurers that sell long-term care price each policy on how likely a buyer is to need help bathing, dressing, or eating, and for how many years.

A bet on how long one person will live can go badly wrong. In 1965, a notary in Arles named André-François Raffray, forty-seven years old, bought the apartment of a ninety-year-old woman named Jeanne Calment as a viager, a French sale for life. He would pay her 2,500 francs a month until she died, and then the apartment would be his. He paid for thirty years and died first, in December 1995. His widow kept paying. Calment lived to 122, the longest documented life on record. She spent her last twelve years in a nursing home and her last seven in a wheelchair after breaking her femur at 114. By the end she was nearly blind and deaf. Raffray priced how long she would live. Nobody at that table priced how many of those years she would need help to get out of bed. Of the deal, she said only, “In life, one sometimes makes bad deals.”

Your own plans get built on bets like his: when to retire, how long to save, who will care for whom. Most of them count only the lit candles. A plan to travel at seventy assumes the knee still works at seventy. A promise to look after a parent at home assumes a number of years that nobody wrote down. If the count of healthy years behind a plan is wrong, the time to find out is before the plan comes due.

Anyone at the table can count the candles on a cake, and anyone who doubts the count can count them again. The paper’s cakes cannot be counted twice. Every number in it comes from public data. The code that did the counting was never released, so nobody outside the team can check which of its numbers stand up.

So I counted the candles again myself, rebuilding the study from its methods section and its figures alone. Most of it held. I also added one number the paper did not use: how much each country spends on health. Its link to the pulled candles showed up clearly on only some of the cakes. Parts two and three follow the paper further: which diseases pull the candles, and how many more will come out by 2100.

Counting the Candles

I gave myself one rule going in. Rebuild what the public data and the methods section allow, and say so wherever they stop. When a replication has to guess at every missing step, it stops being a replication. It becomes a different study.

The rule was tested almost at once. The gap itself takes two numbers per country, life expectancy and healthy life expectancy, and WHO hands both out through a public data service. The paper’s second half needs something harder: how many healthy years each country loses to each disease. That data lives somewhere else, and the count of which diseases pull the candles picks it up.

To compare countries, the paper used only the most recent year in its data, 2019, not the full run of years. I did the same, but WHO now publishes both numbers through 2021, so I used the 2021 instead. Matching 2019 to the decimal was never possible anyway. WHO revises its past estimates as new data comes in, so the 2019 figures the authors downloaded are not the ones WHO serves today.

The paper found two things. Africa had the narrowest gap of the six WHO regions. Life expectancy, GDP, and noncommunicable disease burden were the most consistent predictors of gap size. For 2021 alone, 185 countries in all, here is what I found:

• Africa’s median gap, 8.22 years, is the narrowest of the six regions.
• The six regions differ by far more than chance would allow. If the regions did not really differ, a spread this wide would turn up less than once in ten trillion tries (a Kruskal-Wallis test).
• Life expectancy alone explains about four-fifths of the country-to-country spread in the gap. The longer a country’s people live, the more candles come out.
• The paper’s other two predictors went untested here. Its economic number was GDP; I used health spending as a share of GDP instead. Together the two explain 82 percent of the spread, against 81 for life expectancy alone. Its third, noncommunicable disease burden, needs the disease data that part two brings in.

Some numbers moved. The paper counted 183 countries in 2019, and I counted 185 in 2021. Its global median gap was 9.1 years, and mine is 9.3. It puts Lesotho’s gap at 6.5 years, and my count gives 6.84. The finding stays the same: Africa has the narrowest gap, and life expectancy predicts it best.

Two countries have no health-spending figure. Figure 1 uses all 185, and every model after it uses the 183 with a spending figure. That matches the paper’s count, but only by coincidence.

Figure 1 shows the same finding three ways.

Figure 1a. Healthspan and lifespan distributions by region, 2021. Teal is lifespan; red is healthspan.

Panel (a) draws each region’s two numbers as two hills. The teal hill is how long people live. The red hill is how long they live in good health. Where a hill is taller, more countries sit at that number of years. In every region the red hill sits to the left of the teal one, and the space between them is the pile of pulled candles. Panel (c) ranks the regions by that space. In Europe and South-East Asia each hill has two humps, most likely because each of those regions holds two different kinds of country under one name.

Figure 1b. Healthspan-lifespan gap by country, 2021. Darker countries have a wider gap.

Panel (b) maps the gap country by country. The darkest countries are Australia, the United States, New Zealand, Switzerland, and France. Four of them have some of the longest lives on earth. The United States is the exception. Its people live six to seven years less than the other four, and it still loses almost as many candles as Australia.

Figure 1c. Healthspan-lifespan gap by region, 2021, ordered from the narrowest median gap to the widest. Each dot is one country.

Panel (c) lines the regions up, from Africa’s 8.22-year median on the left to Eastern Mediterranean’s 10.22 on the right. The line inside each box marks the typical country, and the box holds the middle half of the region’s countries. AFR, AMR, EMR, EUR, SEA, and WP stand for Africa, Americas, Eastern Mediterranean, Europe, South-East Asia, and Western Pacific.

More Candles Than Expected

The two numbers from the last section give every country a predicted cake: how many candles it should lose, given how long its people live and how much it spends on health. Figure 2 sets each real cake beside its prediction.

Figure 2a. The 94 countries whose gap is larger than their life expectancy and health spending predict, 2021.

Figure 2b. The 89 countries whose gap is smaller than their life expectancy and health spending predict, 2021.

Figure 2c. Regional makeup of the larger-than-predicted and smaller-than-predicted groups, 2021.

Panel (a) colors in red every country that loses more candles than its prediction. Panel (b) colors in blue every country that loses fewer. Panel (c) turns each group into a ring and slices it by region, so the bigger a slice, the more of that group comes from that region.

Ninety-four countries lose more candles than predicted, and eighty-nine lose fewer. The paper and I found the same region at the top of each group. Africa makes up the biggest share of the countries that lose more: 33 percent in my count, 41 percent in the paper’s. Europe makes up the biggest share of the countries that lose fewer: 36 percent in mine, 45 percent in the paper’s.

Some of the countries that lose more are the wide-gap countries from the map: the United States, Canada, Australia, the United Kingdom, France, Germany, Italy, and Spain. Their gap is wide, and it is also wider than their own life expectancy and spending predict. China, Japan, and Russia lose fewer than predicted.

The shares do not match exactly, and the two models differ in two ways. The paper’s model had a third number, noncommunicable disease burden, and mine does not. Adding it could move some countries from one group to the other. The paper also sorted only some of its countries. Its two groups held 61 and 58, which left 64 of its 183 in neither. I placed every country in one group or the other. So Figure 2 shows what two numbers say, not what the paper’s three said.

Where the Spending Link Lives

So far every comparison has used one year of cakes. Most countries have all twenty-two, 2000 through 2021. The paper does not use them this way, so this section is my own.

Comparing the United States with Somalia shows that countries with longer lives lose more candles. It cannot show whether a country loses more candles in the years its own life expectancy rises. For that, the United States has to be set beside its own cake from five years ago. A fixed-effects panel model makes that comparison. It sets aside everything about a country that stays put, its geography, its history, the baseline quality of its hospitals, and looks only at change within each country.

Life expectancy passes this test almost unchanged. Each added year of life comes with about 0.15 years of added gap, whether countries are compared with each other or each country only with itself. That is where the one pulled candle for every six or seven comes from.

Health spending does not pass as cleanly. It is measured as a share of a country’s economy. Across countries, each extra percentage point of GDP spent on health comes with about nineteen more days of gap, about a twentieth of a candle. Compare each cake only with its own past cakes, and that falls to about eight days. The effect shrinks by more than half. Eight days is small, but the data leave no real doubt that it is more than zero. Countries that spend more also differ in other lasting ways, and part of what looked like a spending effect came from those differences. A standard test asks whether those lasting differences are tangled up with life expectancy and spending. It says they are, so the within-country number is the one to trust.

Back to 2021 alone. The regression behind Figure 2 draws one line through all the countries. That line describes the average country. It cannot say whether the countries losing fewer candles than predicted follow the same rule as the countries losing more. Quantile regression checks. Line the cakes up, from the ones that lose the fewest candles for their life expectancy and spending to the ones that lose the most. Quantile regression fits the same two-number model at five points along that line-up: the 10th, 25th, 50th, 75th, and 90th percentiles of the gap.

Life expectancy holds steady at all five, at about 0.16 years of gap for each added year of life. Health spending does not. From the 10th percentile up through the middle, its effect is small, five to nine days, and too uncertain to tell apart from zero. At the 75th and 90th percentiles it turns clear, about twenty days of gap per percentage point. The extra candles that come with spending show up clearly only on the cakes that lose the most for their life expectancy. Those cakes are the top quarter or so, the far end of Figure 2’s red group. With 183 countries, the data cannot say for certain that the rest follow a different rule, only that they do not show this one.

What the Neighbors Share

Figure 2 judges every cake on its own, but no cake stands on the table alone. Neighbors often share a climate, diseases, and trade. If that sharing shows up in the gap, some of Figure 2’s groups could be partly geography. The paper allows for this with a spatial error model, which adjusts the regression for where each country sits. Before building one, I checked whether it was needed.

Every cake misses its predicted count by some amount. A plain regression treats each country’s miss as its own, unrelated to the miss of the country next door. If neighbors tend to miss in the same direction, that assumption is wrong.

Moran’s I measures how much neighbors’ misses resemble each other. To judge it, I shuffled the countries’ misses across the map 999 times and recomputed it after each shuffle. Only about one shuffle in a hundred came out as extreme as the real map. Neighbors do share their misses.

The paper does not say how it decided which countries count as neighbors, so its spatial model cannot be rebuilt, only one like it. In mine, the closer two countries’ center points are, the more their misses are allowed to move together. The pull turned out to be real. Take it out, and the model matches the real cakes far worse, by more than chance could explain. The pull fades with distance, down to about a third of its strength by roughly 1,200 to 1,900 km apart. Life expectancy and spending both still matter after the adjustment, with spending at about fourteen days of gap per percentage point.

Figure 2d puts panels (a) and (b) on one map. A switch on the map flips between the plain view and the view adjusted for neighbors. The red of panel (a) turns orange here: orange countries lose more candles than predicted, and blue countries lose fewer. The ringed countries are the ones that change groups between the two views.

Figure 2d. Gap against prediction, 2021, from the plain regression and from the model adjusted for neighboring countries (spatial error model). Orange is larger than predicted; blue is smaller.

Eight of the 183 countries change groups. Five are in Europe: Austria, Cyprus, Czechia, Denmark, and the Netherlands. All five move from fewer candles than predicted to more. The other three, Zimbabwe, Saint Lucia, and Somalia, move the opposite way. None of the eight moved far. Before the adjustment, each one sat within about a month of its prediction, a twelfth of a candle, right on the line between the groups. A spatial model pulls neighbors’ misses toward each other by design. A few borderline European countries tipping over together is the kind of change it is built to make.

What holds is the regional pattern. After the adjustment, Africa still makes up the biggest share of the countries that lose more candles, at 31 percent. Europe still makes up the biggest share of the countries that lose fewer, also at 31 percent. The paper reports the same pattern holding under its own adjustment.

A Closing Reflection. Every candle on Tithonus’s cake still burns. Counting the lit ones was never the hard part. The hard part is the ones that come out, and a single average will not say which ones those are, or whose.

1. An older person you know well, and the first year you remember them taking the stairs one at a time. Not the birthday with the big number on it. The year the railing started doing some of the work.
2. Something in your own mornings that runs a little slower than it used to, a stiff first step out of bed, reading glasses pushed up and then hunted for, and whether you have ever counted it as time at all.
3. A number you repeat about your family or your hometown, how long people live there, how old your grandmother got, and how it would sound with the healthy years said out loud beside it.

The goddess of the dawn asked for forever and got it, every candle lit. What she forgot to ask for was the part the flames do not show. The next time someone tells you how long a person lived, notice the small pause before anyone asks how long they were well. Nobody at Raffray’s table ever paused there. That pause is where the pulled candles hide. A real birthday cake never takes one out. They show instead in who at the table can still lean in and blow.

Where This Came From

The study replicated here is Garmany and Terzic (2025), in Communications Medicine. It covers 183 WHO member states from 2000 to 2019. The 9.1-year global median, the findings on regions and predictors, and the 22 percent projection to 2100 are the paper’s own. So are the paper’s figures set beside mine in the body: its 183 countries in 2019, Lesotho’s 6.5 years, the 41 and 45 percent shares, and its groups of 61 and 58. Every other number in this piece comes from my own pipeline, run on WHO Global Health Observatory data pulled on 28 August 2026: life expectancy at birth, healthy life expectancy at birth, and current health expenditure as a share of GDP, for 2000 through 2021. WHO revises its historical estimates, so the paper’s figures and mine will not agree to the decimal even where they overlap.

The paper’s data is public and its code is not, so the whole replication is rebuilt from the methods section and the published figures. The regional comparison, the two-variable regression, and the residual maps follow the paper’s design as closely as the methods text allows. The panel model, the quantile regression, and the Moran’s I check are my own additions, not things the paper does. The spatial model is built like the paper’s but uses a correlation structure I chose, because the paper does not describe its own. Distance in my model is measured in degrees of latitude and longitude, so its reach runs shorter east to west than north to south. The standard R packages for spatial error models would not build on my setup, so I fit mine with generalized least squares: the same idea, with different tools. The code, the data pulls, the R packages behind each step, and the list of what worked and what did not are public at github.com/gauranii/GapYears.

The quoted lines and the details of Tithonus’s aging (the gray hairs, the ambrosia and rich clothing, the shining doors) come from the Homeric Hymn to Aphrodite, the oldest surviving version of the story, in Hugh G. Evelyn-White’s 1914 translation, lines 218 to 238. The goddess is Eos in that telling. The frame around it comes from the same hymn: Aphrodite on Ida with Anchises, a cattle herder, and her refusal right after the Tithonus story to give him the gift the dawn asked for.

The pension review is John Cridland’s Independent Review of the State Pension Age (2017), whose recommendation to raise the age from 67 to 68 starting in 2037 the government accepted that July. That rise has not been legislated. In 2023 the decision was put off to a further review, and a third review began in July 2025. Its section on healthy life expectancy begins on page 34. The insurance pricing comes from the actuarial standard for long-term care in the United States, ASOP No. 18, which asks actuaries to set how often claims begin and how long they last, with benefits triggered by trouble with daily activities such as bathing and dressing, or by cognitive impairment.

The Calment details come from her New York Times obituary (1997): the 1965 viager with Raffray, the 2,500 francs a month, his death in December 1995, and her line about bad deals. Her years in the nursing home, the broken femur at 114, and her near blindness and deafness at the end come from the validation study of her age by Robine and colleagues (2019). Raffray’s age in 1965 comes from French accounts of the sale.

The third predictor missing from Figure 2’s model is the disease-burden data. It gets its own treatment in part two of this series, a count of which diseases take each country’s healthy years, along with the clustering the paper builds on top of it. The 22 percent projection to 2100 is taken up in part three, the paper’s forecast set against three simpler ones.

Intellectual Honesty Note. The birthday cake is this piece’s own device, not the paper’s. The candle counts are the 2021 life expectancy and gap figures, rounded into candles. The dawn going out each morning while his voice keeps going is this piece’s own image. The Hymn says only that he babbles endlessly behind the doors. The line that the goddess of love would not ask for forever without youth is this piece’s reading of her refusal, not her words. Calment’s age was challenged in 2018 by researchers who argued her daughter had taken her identity. The French team that validated her age answered in 2019, and most researchers still accept 122. The bad knee and the pill organizer are illustrations, not anyone’s case history. No figure here reproduces one of the paper’s figures directly. Each is redrawn from my own numbers, and where my method differs from the paper’s, the text says so.

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