Nobody Died at Forty

In 1841 the life expectancy of a man born in England and Wales was 40.2 years. That number is real, it is on a real table, and it describes almost nobody who was alive at the time. The commonest adult age of death that year was 75.

Every so often somebody says people used to die at forty, and somebody else says no, that was only the babies, adults lived about as long as we do. The first is wrong. The second is also wrong. The table that settles it has been public for years: the Office for National Statistics publishes the annual probability of dying at every single year of age, for men and for women, for every year from 1841 to 2016. That is 44,352 numbers. This page is that table, opened, with every claim below recomputed in your browser from it.

Start by holding a year in your hand.

One year at a time

Drag it to 1841 and the picture is two mountains with a valley between them. One mountain sits against the left wall: in that year 16.4% of all deaths happened before a first birthday, and 27.3% before a fifth. The other mountain is out at the far end, and it is the taller of the two if you count from age five: the single commonest age at which a man died in 1841 was 75. Press from age 5 above and the chart restates the same year as a cohort beginning at five, which is the only way to see that second mountain at all: at full scale the infants flatten everything to the right of them.

That is not my reading of a table nobody else has looked at. The ONS states both figures itself, in its own article on average lifespan: period life expectancy at birth increased from 40.2 years to 78.6 years for males, and from 42.3 years to 82.6 years for females, and the most common (modal) age at death, for those aged 10 years and over, in 1841 was 75.6 years for both males and females. Recomputing their own table from their own numbers lands on 40.2, 42.3, and a modal single year of age of 75 for both sexes. The arithmetic below is therefore checkable against something outside itself, which is the only reason to trust the parts of it that are not.

Now find forty. It is in the valley. The band from 35 to 44, five years either side of the famous number, took 6.6% of that year's deaths. Life expectancy at birth is an average, and this is an average with almost nothing under it: a number produced by a huge pile of infants and a distant pile of the old, meeting in the middle at a value that was nobody's ordinary fate.

The usual correction, and why it also fails

The correction you will have heard is that the low figure is entirely an artefact of infant mortality, and that an adult who got past childhood lived to roughly the age we do now. It is the better half of the argument and it still does not survive the table.

Take the men who reached their fifth birthday in 1841. On that year's rates they could expect to reach 54.8. Do the same in 2016 and the answer is 79.8. Surviving childhood was worth a great deal, and it did not buy a modern lifespan. It bought 25.1 fewer years than one.

Adult life really was more dangerous, not slightly. Of the men who reached twenty in 1841, 18.3% were dead before forty; in 2016 the same figure is 1.5%. Of those who reached twenty, 46.5% went on to see sixty-five, against 87.7% now. For women the young-adult gap is wider still: the annual risk of death at twenty fell by a factor of 43.4 between those two years, against 18.8 for men, which is what childbirth looks like when you take it out of the numbers.

So whose gain was it?

The question can be asked exactly rather than argued. Take 1841's table and hand it one thing only: the death rates of 2016 below some age, leaving every rate above that age exactly as the Victorians had it. Then read the life expectancy back out. The slider below is that operation.

At age five the answer is 54.5 years, which is 37% of the 39.3 years the figure gained in total. Run the experiment the other way, giving 1841 the modern rates from five upward and keeping its own child mortality, and life expectancy goes to 58.4, worth 46%. The two do not add to a hundred, and the reason is worth holding on to: a child saved in 1841 then had to walk out into 1841's adult mortality, so the two improvements multiply rather than stack. Child mortality is the largest single piece of the gain and it is a long way from being the whole of it.

The straight line under all of it

Turn the same table on its side. Instead of counting deaths, ask what your chance of dying is in the coming year, at each age, and plot it on a logarithmic scale. From roughly thirty-five to roughly eighty-five, in every one of the 176 years, that plot is a straight line. This is Gompertz's observation of 1825: past youth, the risk of death multiplies by a fixed factor for every year you age. A straight line on a log scale is a constant doubling time, and for humans it runs at somewhere around seven or eight years.

The line is there in every year. What changed is its slope. In 1841 a man's risk of death doubled every 10.64 years. In 2016 it doubled every 7.59. The mortality curve did not simply slide to the right, the way a picture of postponed ageing would look. It pivoted. We are enormously safer than the Victorians at every age, and the size of that advantage shrinks steadily as we get older, which is exactly what makes the line steeper.

The largest improvement anywhere in the male table is a factor of 264 at age 2. By ninety it is 2.3, and by ninety-five, 1.9. Almost everything medicine and plumbing and food and peace have won was won in the first half of life. At the top of the table the Victorians and we are nearly in the same position.

The window is a choice, so make it a control

Where you fit the line changes the number, and a page that quoted one window and hid the rest would be quietly choosing its own answer. So the window is a slider above, and here is the whole sweep. Across eight different windows and both sexes, the doubling time is shorter in 2016 than in 1841 in 16 of 16 cases. The magnitude moves a lot. The direction does not move at all.

Two honest wrinkles the sweep exposes. First, the fall is not a smooth march: the male doubling time was longest not in 1841 but in 1876, at 11.76 years, and the late Victorian decades were a genuinely bad time to be an adult man even as infant deaths began to fall. Second, the shortening stopped and turned around: the male minimum is 6.63 years in 1985, and it has been getting slowly longer since. The last thirty years of the table are the only stretch in which old-age mortality improved faster than middle-age mortality.

Without fitting anything at all

There is a standing objection to every claim ever made about a Gompertz slope, and it applies squarely to the paragraph above. The two fitted parameters, the level and the slope, are strongly and negatively correlated by construction, so a report of a rising slope beside a falling level is precisely the pattern that a fitting artefact would also produce. Burger and Missov showed the correlation is an inherent statistical property of the Gompertz distribution rather than a fact about biology; Tarkhov, Menshikov and Fedichev showed that the least-squares fit is an ill-posed problem whose repeated solutions trace out exactly that correlation. Neither of those is a small objection and neither can be answered by fitting harder.

So ask the question without fitting anything. Take one cell of the table and divide it by another: the annual risk at eighty, over the annual risk at forty, inside a single year. If the curve steepened, that number grew. There is no model, no window, no regression, and nothing to be degenerate about.

At forty and eighty, a Victorian man's risk multiplied by 12.2 over those forty years of age. For a man in 2016 the same two ages are 38.9 apart. Across six age-pairs and both sexes, the later year is the steeper one in 12 of 12 cases. The steepening is in the raw quotients, not in anybody's regression.

The fit-free measure also reproduces the turn: the male ratio at forty and eighty peaked at 70.5 in 1987 and has fallen back since, which is the same story the doubling time tells and a good sign that neither is an artefact of the other.

Where this sits in a live argument

Whether the human rate of ageing has changed is genuinely unsettled, and it would be dishonest to present half a page of arithmetic as settling it. The shape of the disagreement is worth knowing, because it is mostly a disagreement about the window.

• Roughly constant. Vaupel argues for shifting mortality: the rate of deterioration looks constant, and death is being delayed because people reach old age in better health. Bongaarts, fitting a logistic model over a very wide adult age range, found the slope nearly constant over time. Colchero and colleagues make the strongest cross-species version, an invariant rate of ageing across the primates.
• Rising. Beltran-Sanchez, Crimmins and Finch, over 630 cohorts, concluded the gains were entirely from falling adult mortality level because the acceleration at older ages got faster. Tai and Noymer, fitting 7,704 life tables, report the slope parameter has increased. Gavrilov and Gavrilova, over 3,662 populations at ages 60 to 85, find rates stable through most of the twentieth century and rising after 2000 in 74% of them.
• The reconciliation, and it is the same lesson as the slider above. Thatcher and colleagues traced the disagreement to the fitting range, reporting that over ages 30 to 109 the slope looks almost constant while over 70 to 90 it rises markedly. Vaupel himself writes that the pace at which death rates increase with age accelerated somewhat over much of the twentieth century and has been roughly constant in recent decades.

What this page claims is therefore narrow and, I think, safe: in this one national table, over these 176 years, the curve is steeper at the end than at the start, in every window tried and in every fit-free ratio tried. What it does not claim is that human ageing itself has accelerated. The rate at which a population's death rate climbs with age is not the same thing as the rate at which a body deteriorates, and the gap between those two sentences is where most of the argument above actually lives.

The same risk, in another century

The pivot has a consequence you can feel. Because the curve rotated rather than slid, a modern age maps onto a much younger Victorian one, and the mapping gets less flattering the older you get.

A man of sixty in 2016 carried the annual risk of death that an 18-year-old carried in 1841. At seventy he matches a Victorian of 50.5; at eighty, one of 67.1; at ninety, one of 81.8. The gap closes as you climb.

And the bluntest form of it: the safest year of a Victorian male life was age 12, the bottom of the curve between infancy and the climb. A boy of twelve in 1841 still faced a higher chance of dying that year than a man of 54 does today. There was no year of a Victorian life as safe as most of a modern one.

The last thing the shape implies

If almost all of the winnable ground was at the young end, and if what is left is a curve that climbs steeply through the eighties, then the return on defeating any single disease at the far end must be small. That is not a guess, it is a routine actuarial calculation, and the United States National Center for Health Statistics publishes it. Eliminating every death from cancer would add 3.20 years to American life expectancy at birth; eliminating every death from heart disease, 3.71; from all major cardiovascular disease together, 5.48. For the individuals who would otherwise have died of those causes the gain is large, 14.6 years for cancer and 11.8 for heart disease, and for everyone else it is nothing at all, and the population average is what you get when you mix those two.

Those five figures are from a different country and a different dataset (Arias, Heron and Tejada-Vera 2013, US data for 1999 to 2001) and are quoted, not recomputed here. The report's own caveat travels with them: eliminating a cause of death is not the same as curing the disease, and its accuracy falls as the estimated gain rises, so the cancer and heart figures are the least precise in the table.

What this table is, and what it is not

Four things about the numbers above that a reader is owed before believing any of them.

One. Nobody lived any of these years

These are period tables. A period life expectancy takes one calendar year's death rates at every age and marches an imaginary person through all of them, so the 1841 figure belongs to somebody who was newborn and eighty in the same twelve months. The people actually born in 1841 met the falling rates of the decades that followed and did better than their period table says. Cohort tables, which follow real birth years, exist and are a different instrument answering a different question.

Two. The top of the table is arithmetic, not measurement

In this file qx is exactly 100,000 per 100,000, meaning certain death, for every year from age 111 upward. That is where the table is closed off, not a finding about people. The life tables here close at 110 for the same reason, the charts stop at 100, the Gompertz windows stop at 95, and the two fitted lines for 1841 and 2016 would only meet at about age 119, which is far outside anything the table measures and is therefore a fact about two straight lines rather than about anybody's body.

Three. Before 1911 the single-year detail is not single-year evidence

This one the table admits if you ask it the right question. Two different calendar years should never carry byte-identical death rates: these are quotients of large counts, printed to the last digit a double will hold. Ask how often it happens anyway and the answer splits the file in half.

The runs are the tell. Every long one begins at an age ending in 2 or 7 and ends at an age ending in 2 or 7: 17 to 22, 27 to 32, 37 to 42, 77 to 82. Those are the midpoints of five-year age bands, and a whole stretch between two of them repeating exactly is what you get when the single-year figures were built outward from five-year groups. So the pre-1911 half of this file carries five-year structure dressed as single years. It is entirely good enough for everything on this page, all of which is about broad shape across half a century, and it would not support a claim about one age in one Victorian year. After 1911 the effect vanishes: zero matches in 5,565 male pairs.

Example: males, 1841 and 1843, ages 37 to 42 inclusive, identical to the last bit. Also 1851 and 1852, and 1858 and 1859, at the same six ages.

Four. Victorian old age was probably even worse than this

Nineteenth-century ages at death and at census were self-reported, and old age was systematically overstated. That error, where it exists, makes the Victorian old look more numerous and longer-lived than they were, which biases the oldest end of the 1841 curve downward in risk. Every comparison on this page therefore understates the improvement at the top rather than overstating it, and the one place I have been careful not to lean is precisely there: the small factors at ages 90 and 95 are the least trustworthy numbers here, and they are the ones the argument does not need.

Sources

1. Office for National Statistics. Mortality rates (qx), England and Wales 1841 to 2016. Ad hoc release 008538, 6 June 2018. Crown copyright, Open Government Licence v3.0. ons.gov.uk. The single source of every number on this page.
2. Gompertz, Benjamin. “On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London 115 (1825): 513–583. The observation that adult mortality rises geometrically with age.
3. Office for National Statistics. Mortality in England and Wales: past and projected trends in average lifespan. 5 July 2022. ons.gov.uk. The source of the two quoted sentences, and the outside check on this page's life-table code.
4. Burger, Oskar, and Trifon I. Missov. “Evolutionary Theory of Ageing and the Problem of Correlated Gompertz Parameters.” Journal of Theoretical Biology 408 (2016): 34–41. The finding that the correlation between the Gompertz parameters is a property of the distribution itself, and should not be used to diagnose a biological process. The reason the fit-free measure above exists.
5. Tarkhov, Andrei E., Leonid I. Menshikov, and Peter O. Fedichev. “Strehler-Mildvan Correlation Is a Degenerate Manifold of Gompertz Fit.” Journal of Theoretical Biology 416 (2017): 180–189. The same objection from the direction of the optimisation problem.
6. Thatcher, A. Roger, Siu Lan Karen Cheung, Shiro Horiuchi, and Jean-Marie Robine. “The Compression of Deaths above the Mode.” Demographic Research 22 (2010): 505–538. Where the disagreement about the slope is traced to the age range fitted, and where SD(M+) is measured for England and Wales among others.
7. Vaupel, James W. “Biodemography of Human Ageing.” Nature 464, no. 7288 (2010): 536–542. The shifting-mortality case, including its author's own qualification that the pace accelerated somewhat over much of the twentieth century.
8. Tai, Tzu Han, and Andrew Noymer. “Models for Estimating Empirical Gompertz Mortality: With an Application to Evolution of the Gompertzian Slope.” Population Ecology 60 (2018): 171–184. 7,704 life tables, and the finding that the slope parameter has risen, with the authors' own artefact caveat attached.
9. Gavrilov, Leonid A., and Natalia S. Gavrilova. “Trends in Human Species-Specific Lifespan and Actuarial Aging Rate.” Biochemistry (Moscow) 87, no. 12 (2022): 1622–1633. 3,662 populations in the Human Mortality Database, fitted at ages 60 to 85: rates stable through most of the twentieth century, and rising after 2000 in 74 per cent of them. Their own reading of the cause is the one this page reaches from a single country, that mortality fell faster at younger ages than at older ones.
10. Arias, Elizabeth, Melonie Heron, and Betzaida Tejada-Vera. United States Life Tables Eliminating Certain Causes of Death, 1999–2001. National Vital Statistics Reports 61, no. 9. National Center for Health Statistics, 31 May 2013. cdc.gov. The five cause-elimination figures quoted in the coda, and the caveats quoted with them.
11. Open Government Licence v3.0. nationalarchives.gov.uk. Reuse permitted with attribution, which is what the first entry is.

Everything in the first entry is recomputed here. Everything in the entries after it is quoted, with its source named on the line, and was not re-derived: those are other people's measurements on other people's data, and saying so is the difference between a citation and a claim.

Contains public sector information licensed under the Open Government Licence v3.0.