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.