Notes

Items marked [verified] have been checked against a source. Items marked [unverified] are written from memory and still need checking before publication. Items marked [my calculation] are arithmetic I performed rather than findings I am reporting, and are flagged as such in the text.

Chapter 1. The Boundary Condition

Rational bubbles in infinite horizon and overlapping generations models. Jean Tirole, “Asset Bubbles and Overlapping Generations,” Econometrica 53(6), November 1985, pages 1499 to 1528. https://doi.org/10.2307/1913232. In “On the Possibility of Speculation under Rational Expectations,” Econometrica 50(5), 1982, he showed that with a finite number of infinitely lived traders, any asset must be valued at its market fundamental, so bubbles are ruled out. The 1985 paper asks whether that result extends to overlapping generations economies and answers no. Since Samuelson there can be a bubble on money, a positive price on an asset with a zero fundamental, because new generations keep arriving. [verified]
Transversality and no-Ponzi conditions. These are not the same thing and should not be merged. Blanchard and Fischer, Lectures on Macroeconomics (MIT Press, 1989), page 49, state the no-Ponzi-game condition as the present discounted value of wealth at infinity being nonnegative: a constraint that rules out rolling debt forward forever. Kamihigashi, “Transversality Conditions and Dynamic Economic Behavior,” New Palgrave Dictionary of Economics, 2nd edition, 2006 (working paper at https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp180.pdf), treats the transversality condition as an optimality condition: the present discounted value of wealth at infinity equals zero, which rules out overaccumulation of wealth. The no-Ponzi-game condition is a constraint ruling out overaccumulation of debt. “They place opposite restrictions, and should not be confused.” NPG is often called a transversality condition as well. The book’s reading, that these conditions smuggle death back into the infinite horizon, is my argument, not a finding those sources report. [verified]
Samuelson, “An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money,” Journal of Political Economy 66(6), 1958. The paper is real. It describes the young transferring goods to the old in the expectation that the next generation of young will do the same, and it treats money as that social contrivance. It does not call the arrangement a chain letter. That phrasing is Karl Shell, “Notes on the Economics of Infinity,” Journal of Political Economy 79(5), 1971, pages 1002 to 1011: “The chain-letter aspect of the model reminds us that the appropriate form of the budget constraint is not obvious for the potentially infinitely long-lived economic entity.” Do not quote “chain letter” as Samuelson’s wording. [verified]
Life expectancy at birth in developed countries, roughly the thirties to roughly the eighties since 1850. An earlier version of this note attributed that gain overwhelmingly to declines in infant and child mortality. That is the same error corrected at Chapter 2, note 2, and it is wrong: mortality fell at every age. This note is retained only to point at the correction, because the two notes previously contradicted each other. [verified]
Jeanne Calment, born 21 February 1875, died 4 August 1997, aged 122 years and 164 days. The only person ever verified to have reached 120, 121 or 122, and more than three years clear of the next verified case. Record still standing. [verified]
The expanded treatment of the two conditions added to this chapter distinguishes the no-Ponzi condition, a feasibility constraint imposed by the market on a borrower, from the transversality condition, which arises from the agent’s own optimisation. Blanchard and Fischer, Lectures on Macroeconomics, is the source for the first; Kamihigashi for the second. The distinction is standard, but the two are frequently taught together in a way that blurs it, which is the reason for setting it out at length. [verified]
The claim that both conditions are close to self enforcing under a finite horizon, because settlement of an estate supplies the terminal date, is my framing rather than a result stated in those sources. [my argument]

Chapter 2. Assume a Longer Life

Calment, as above. [verified]
Life expectancy decomposition. An earlier draft of this chapter claimed the gains since 1850 were “almost entirely a story about children.” That is the popular correction to the popular error, and it is itself wrong. Mortality fell at every age. In England in 1841 a five-year-old could expect to live about fifty-five more years; today a five-year-old can expect to reach eighty-two, a gain of more than twenty-five years measured from an age that excludes infant mortality entirely. Our World in Data addresses this misconception directly. The chapter has been rewritten to say that adult life really was extended, and that what has not moved is the ceiling. [verified, and corrected]
Fries, “Aging, Natural Death, and the Compression of Morbidity,” New England Journal of Medicine, volume 303, pages 130 to 135, 1980. [verified]
Rectangularization of the survival curve. Fries and Crapo developed the rectangular curve idea in later work. [verified as to attribution; a demographic source for the current shape is still needed]
López-Otín et al., “The Hallmarks of Aging,” Cell, 2013, listing nine hallmarks. “Hallmarks of aging: an expanding universe,” Cell, 2023, expanding the list to twelve by adding disabled macroautophagy, chronic inflammation and dysbiosis. [verified]
Senescent cell clearance. Baker et al., 2016, using genetic ablation in INK-ATTAC mice, reported reduced age-related tissue dysfunction and extended lifespan. Xu et al., Nature Medicine, 2018, reported that dasatinib plus quercetin improved physical function and increased lifespan in old mice. Human trials are early, small and disease-specific. [verified]
Ocampo et al., “In Vivo Amelioration of Age-Associated Hallmarks by Partial Reprogramming,” Cell, 2016. Cyclic induction, two days on and five days off, avoiding the tumor formation caused by continuous expression. An earlier draft implied the lifespan result applied to normal aged mice. It does not. The roughly thirty percent lifespan extension was in a Hutchinson-Gilford progeria model. In normal old mice the demonstrated effect was improved regeneration of muscle and pancreatic tissue. Corrected in the text. [verified, and corrected]
Rapamycin. NIA Interventions Testing Program, reported in Nature, 2009. Treatment begun at twenty months of age extended median lifespan by about nine percent in males and thirteen percent in females, with maximum lifespan up about nine and fourteen percent respectively. First pharmacological agent shown to extend lifespan in a mammal. Note that other reported figures, such as twenty-eight and thirty-eight percent, measure remaining life from the start of treatment rather than total lifespan, and should not be quoted without that qualification. [verified]
TAME. A proposed six-year trial of approximately 3,000 adults aged 65 to 79, coordinated by Wake Forest and championed by the American Federation for Aging Research, requiring roughly 75 million dollars. As of 2026 it remains awaiting funding and has not launched. The structural obstacle is that metformin is off patent, so no sponsor can own the result. No efficacy results exist. [verified]
Failure of translation from short-lived models. Caloric restriction extends mouse lifespan by forty percent or more, with far smaller effects in primates and no comparable human result. The evolutionary explanation offered in the text, that short-lived species carry more cheap unrealized maintenance, is a standard argument in the field but is presented here without a specific citation and should get one. [verified as to the translation record; the evolutionary explanation unverified]
The claim that no intervention has been shown to extend maximum human lifespan. This is a strong negative and the text stakes a lot on it. It is consistent with everything found in the sources above, but it should be checked once more immediately before publication, since it is the single claim most likely to be overtaken by events. [verified as of drafting]

Chapter 3. The Price of Time

The 1648 perpetual bond of the Hoogheemraadschap Lekdijk Bovendams, issued on goatskin on 15 May 1648 to Niclaes de Meijer for 1,000 Carolus guilders, to fund repairs to flood defences on the Lek. Original rate 5 percent, reduced to 3.5 and then 2.5 percent in the seventeenth century. Yale purchased it in 2003 for its history of finance archive; a curator collected roughly 136 euros in twelve years of arrears in 2015. One of five known to survive. [verified]
British consols. On 1 February 2015 the Treasury redeemed 218 million pounds of 4% Consols, the first redemption of undated UK debt in sixty-seven years; the remaining undated gilts were redeemed at par on 5 July 2015, clearing them from the portfolio entirely. The 4% Consols had been issued by Churchill in 1927, largely to refinance First World War National War Bonds, which had in turn absorbed older obligations including an 1853 Gladstone bond consolidating South Sea Company capital stock. An earlier draft said these bonds “financed the Napoleonic campaigns,” which is a looser claim than the record supports; the text now follows the documented chain back to the South Sea Bubble instead, which is both accurate and more striking. [verified, and corrected]
Ramsey, “A Mathematical Theory of Saving,” Economic Journal, December 1928, written when he was twenty-five. He died on 19 January 1930, aged twenty-six. The quoted phrase is exact: discounting later enjoyments in comparison with earlier ones is “a practice which is ethically indefensible and arises merely from the weakness of the imagination.” Keynes’s obituary called the paper one of the most remarkable contributions to mathematical economics ever made. [verified]
Blanchard, “Debt, Deficits, and Finite Horizons,” Journal of Political Economy, volume 93, number 2, April 1985, pages 223 to 247. The perpetual youth model treats mortality as a constant hazard entering the effective discount rate, so that a higher probability of death raises the rate at which an agent discounts the future. [verified]
r-star estimates. Laubach and Williams (2003) and Holston, Laubach and Williams (2016). US estimates ran between roughly 2 and 2.5 percent from the 1990s through the mid 2000s and fell to about 0.5 percent around 2009, remaining there for years. Recent estimates for Canada, the euro area, the United Kingdom and the United States are the lowest of the past three decades. Longer lifespans and falling birth rates are both cited among the drivers. An earlier draft of the chapter carried r-star figures that were simply wrong. They have been replaced with the estimates above. [verified, and corrected]
Lukasz Rachel and Thomas D. Smith, “Secular drivers of the global real interest rate,” Bank of England Staff Working Paper No. 571, published 11 December 2015. Long-term real rates fell by about 450 basis points over the preceding thirty years, and the authors account for roughly 400 of those basis points, attributing more to shifts in saving and investment preferences than to slowing growth. Carvalho, Ferrero and Nechio on demographics and real rates remains unread. [verified for Rachel and Smith; Carvalho, Ferrero and Nechio unverified]
Stern Review, 2006. Pure time preference set at 0.1 percent per year, chosen explicitly to represent the probability that humanity ceases to exist in a given year. Stern’s overall social discount rate was about 1.4 percent. Nordhaus worked with rates of roughly 4 to 5 percent and argued that Stern’s conclusions do not survive substitution of market-consistent assumptions. [verified]
Knoll, Schularick and Steger, “No Price Like Home: Global House Prices, 1870 to 2012,” American Economic Review, 2017. Real house prices were roughly flat from the late nineteenth century to the mid twentieth, then rose sharply. Decomposing that rise, land prices rather than replacement costs account for about 80 percent of the increase between 1950 and 2012, which is the basis for the claim that the land under a building is the perpetuity and is what moved. [verified]

Chapter 4. The Estate

Lucas v. Hamm, 56 Cal.2d 583 (1961). Beneficiaries under a will drafted by attorney Hamm settled for 75,000 dollars less than the will provided, after the provision failed under the rule against perpetuities. The California Supreme Court allowed a tort action despite lack of privity but held the attorney not liable, on the ground that the rule is so complex that the error did not fall below the standard of ordinary professional skill. [verified]
Duke of Norfolk’s Case (1682) 3 Ch Cas 1; 22 ER 931. Established the common law rule against perpetuities, arising from the Earl of Arundel’s attempt to create shifting executory limitations across his sons. The permissible period was not fixed until Cadell v. Palmer (1833), a hundred and fifty years later. The doctrine’s explicit purpose was to prevent the dead hand of prior owners from controlling property indefinitely. [verified]
John Chipman Gray’s canonical formulation, from The Rule Against Perpetuities, 1886, at section 201: no interest is good unless it must vest, if at all, not later than twenty-one years after some life in being at the creation of the interest. This is the standard statement across Anglo-American property law, and it is the phrasing the chapter paraphrases. [verified]
South Dakota abolished the rule against perpetuities in 1983, the first state to do so. Alaska, Delaware, Nevada, Idaho and Wisconsin are among those that have since abolished or substantially modified it. Several states modified their rules following the 1986 generation-skipping transfer tax provisions. [verified]
Scale of assets held in perpetual dynasty trusts. South Dakota trust assets were reported at roughly 360 billion dollars in 2021, having more than quadrupled over the preceding decade. The Pandora Papers reporting of October 2021 named 81 South Dakota trusts, close to half of the more than 200 the consortium identified as newly established in the United States between 2000 and 2019. These figures are journalistic rather than regulatory and should be attributed that way. [verified]
Piketty, “On the Long-Run Evolution of Inheritance: France 1820-2050,” Quarterly Journal of Economics, 2011. The annual flow of inheritance in France ran at 20 to 25 percent of national income between 1820 and 1910, fell to under 5 percent by 1950, and recovered to about 15 percent by 2010. [verified]
Average tenure of companies on the S&P 500: about 33 years in the mid 1960s, about 24 years by 2016, forecast in the low teens by the late 2020s, with roughly half the index turning over per decade at current rates. Innosight’s Corporate Longevity Forecast is the source. Note that figures differ slightly across successive editions of that report, so cite one edition rather than blending them. [verified]
Five percent real compounded over two hundred years gives a factor of roughly 17,300. Over thirty years, roughly 4.3. [my calculation]
Dual class share structures. Between 2017 and 2019 close to 30 percent of United States initial public offerings used a dual class structure, most of them founder controlled technology firms. In 2017 the figure for technology listings specifically was about 32 percent against 27 percent for all listings. The Council of Institutional Investors, which opposes the structures and wrote to both major exchanges in 2012 asking that they be barred, is the usual data source. [verified]
The Wallenberg family of Sweden. The bank was founded in the eighteen fifties and the family has retained effective influence over a substantial part of Swedish industry across six generations, exercised through a holding company and a group of foundations rather than through personal ownership. Knut Wallenberg transferred his fortune into a foundation before his death. The family’s foundations hold assets valued in the tens of billions of dollars and no individual member can withdraw from them. Figures vary by source and by exchange rate and should be quoted with a date. [verified]
The Rothschild houses as a network structure, with separate branches in separate countries bound by partnership and intermarriage, giving redundancy against the failure or death of any single principal. Niall Ferguson, The House of Rothschild, volume 1, on the five houses and the successive partnership agreements, is the treatment to cite. Treated here at a level of generality that a family historian should still check against it. [unverified]
The reading of both cases, that surviving fortunes escaped the shirtsleeves pattern by ceasing to be personal property and becoming institutional, and that the devices used are prostheses for mortality that a long lived founder would not require, is my argument rather than a claim made in the sources. [my argument]
The tension between the Wallenberg case and the argument in Chapter 13 that perpetual foundations fail in one of two directions is raised deliberately rather than resolved. The proposed distinction, between a foundation pursuing a purpose and a foundation holding an operating business disciplined from outside, is mine and may not be sufficient. [my argument]

Chapter 5. The Funeral Principle

Planck, Scientific Autobiography and Other Papers, 1949. The passage states that a new scientific truth does not triumph by convincing its opponents, but because they eventually die and a new generation grows up familiar with it. Quote no more than a short fragment and attribute. [verified]
Azoulay, Fons-Rosen and Graff Zivin, “Does Science Advance One Funeral at a Time?“, American Economic Review, 2019. 452 elite life scientists who died prematurely while active. Article flow from collaborators falls sharply; flow from non-collaborators rises by an average of 8.6 percent. The additional contributions are disproportionately highly cited and disproportionately authored by scientists not previously active in the subfield. The authors attribute the barrier to intellectual, social and resource gatekeeping. [verified]
Semmelweis. In 1847 he ordered handwashing in chlorinated lime at the Vienna General Hospital and mortality in his ward fell from roughly 18 percent to about 2 percent. He was committed to an asylum in 1865, was beaten by guards there, and died of an infected wound. [verified]
Wegener presented continental drift to the German Geological Society in Frankfurt on 6 January 1912. It was rejected by most scientists despite the fossil and rock evidence he published between 1912 and 1929, and became mainstream only in the 1960s once seafloor spreading supplied a mechanism. He died on a Greenland expedition in 1930, three decades before vindication. The text treats this as the hard case rather than the clean one, since the objection that he lacked a mechanism was legitimate. That framing should survive contact with a historian of science; it is my reading, not a sourced claim. [verified as to facts; the framing is my argument]
Barry Marshall and Robin Warren on Helicobacter pylori. Warren observed the organism in gastric biopsies and the two began collaborating at Royal Perth Hospital in 1981; it was first cultured in 1982. Marshall drank a culture in 1984 at Fremantle Hospital and developed gastritis within days. The Nobel Prize in Physiology or Medicine followed in 2005, awarded jointly to both men. The chapter names only Marshall because the self-experiment is the point being made, but the prize was shared and this note should say so. [verified]
Mandatory retirement for tenured faculty in the United States ended on 1 January 1994, under the 1986 amendments to the Age Discrimination in Employment Act which had permitted the exemption until then. The predicted consequences for junior hiring were disputed in advance, and at least one study concluded the effects would be much smaller than the higher education establishment feared. Card and Ashenfelter, “Did the Elimination of Mandatory Retirement Affect Faculty Retirement?“, NBER, 2001, is the standard empirical treatment. [verified for the date and the dispute; the empirical findings need direct reading]

Chapter 6. Nobody Goes to Space

Safire memorandum to H. R. Haldeman, “In Event of Moon Disaster,” 18 July 1969. Held at the Nixon Presidential Library; a scan is available through the National Archives. The text opens with the line about the men who went to the moon to explore in peace staying there to rest in peace. It instructs the President to telephone each of the widows-to-be beforehand, and provides that after the statement, when NASA ends communications, a clergyman should follow the procedure of a burial at sea, commending their souls to the deepest of the deep and concluding with the Lord’s Prayer. [verified]
Armstrong stated that he privately assessed a ninety percent chance of getting back to Earth and no better than an even chance of a successful landing on the first attempt. Given in interviews, including around the thirtieth anniversary. Find and cite one specific interview. [verified as to substance; specific citation needed]
US Department of Transportation value of a statistical life: 13.7 million dollars for 2024, up from 9.1 million in 2012. Department of Health and Human Services central estimate approximately 13.0 million in 2023 dollars. Agencies differ and the figure is revised annually, so it should be updated at proof stage. Viscusi and Aldy, 2003, remains the standard meta-analysis of the wage-risk literature. [verified for DOT and HHS; Viscusi and Aldy unverified]
Value per statistical life-year conventions and their use in health technology assessment. Hirth and colleagues, “Willingness to Pay for a Quality-Adjusted Life Year: In Search of a Standard,” Medical Decision Making, 2000, for the estimates, and the NICE cost per quality-adjusted life-year threshold range as the applied case. [unverified]
Gompertz, “On the Nature of the Function Expressive of the Law of Human Mortality,” Philosophical Transactions, 1825. Mortality rate doubling time in adulthood is usually given as approximately eight years, with the literature ranging between eight and ten depending on population. [verified as to the range; the 1825 citation unverified]
Background extrinsic mortality of roughly one in two thousand per year for young adults in wealthy countries, and the resulting life expectancy of order two thousand years if the aging term is removed. This is a reciprocal of a hazard rate and is presented in the text explicitly as my own arithmetic rather than as an established projection. The input should be built from external-cause mortality tables before publication, since the whole figure turns on it. [my calculation]
J. L. Kelly Jr., “A New Interpretation of Information Rate,” Bell System Technical Journal, volume 35, number 4, July 1956, pages 917 to 926. Ole Peters, “The ergodicity problem in economics,” Nature Physics, volume 15, 2019, pages 1216 to 1221. The distinction the chapter draws, between an average across many players and the trajectory of one player in sequence, is the central point of the Peters paper. [verified]
Space Shuttle: two vehicles and crews lost across 135 missions. NASA’s final probabilistic risk assessment gave a mean estimated risk of about 1 in 90, with a 5th to 95th percentile range of roughly 1 in 127 to 1 in 63, consistent with the realized record. I previously believed NASA’s retrospective assessment of the earliest flights was near 1 in 9; I could not confirm this and have removed it. [verified]
Magellan expedition: departed 20 September 1519 with five ships; the Victoria returned in September 1522 with 18 survivors. Sources differ on the size of the departing complement, giving figures between roughly 237 and 270, so the text hedges. [verified, with the variance noted]
Wingsuit BASE flying fatality rates. Commonly cited at roughly one death per five to six hundred flights, against roughly 0.04 percent per jump for BASE jumping generally. The wingsuit share of BASE fatalities rose sharply between the mid 2000s and the early 2010s. Mei-Dan and colleagues, “Fatalities in Wingsuit BASE Jumping,” Wilderness and Environmental Medicine, 2013, is the standard reference. Rates in this activity are poorly measured because the denominator, the number of flights, is not systematically recorded, and the figure should be presented as an estimate. [verified as to the literature; the per-flight denominator is weak]
Everest fatality rates. Roughly one percent of climbers over the long record, with better rates in recent years, and figures differing according to whether the denominator is summit attempts, all climbers, or hired support, and whether deaths during route preparation are included. Cite one convention. [verified as to the range; the convention needs stating]
The distinction the chapter draws between danger accepted for payment, which is what the value of a statistical life measures through wage premiums in hazardous work, and danger purchased at a price, which is what a wingsuit flight or a guided Everest ascent is, is my argument. It is not a distinction those literatures draw explicitly, and a labour economist should be asked whether it survives contact with the compensating differentials literature. [my argument]
The claim that early aviation attracted wealthy risk takers for roughly two decades without producing a commercial industry, and that commercial aviation became possible only once the risk had fallen by orders of magnitude, is offered as historical illustration. Any standard history of early aviation carries the pattern; one should be cited, or the sentence softened to drop the two decade figure. [unverified]
The narrowing of the chapter’s claim, from the proposition that nobody will be willing to go to the proposition that the willing become uncoupled from the capital, is a revision made in response to the objection and is the form the argument should be held to. The falsification test stated at the end of that section is mine. [my argument]

Chapter 7. Vacancy

Hermit crab vacancy chains. Crabs queue beside a newly available shell in descending size order and exchange in sequence within seconds, a behaviour researchers have described as piggybacking. Both synchronous and asynchronous chains are documented. [verified]
White, Chains of Opportunity: System Models of Mobility in Organizations, Harvard University Press, 1970. White applied the vacancy chain model to clergy mobility in Episcopal, Methodist and Presbyterian churches, arguing that mobility models should be applied to vacancies rather than directly to individuals. [verified]
The 119th Congress, seated 2025, was the third oldest since 1789 and its Senate the second oldest ever. Median senator 64, median representative 57, average member 58.9. Six sitting senators were born between 1928 and 1945; the oldest was 91 and the youngest 38. Update these figures at proof stage, since they move every two years. [verified]
Life tenure in the United States federal judiciary, covering the Supreme Court, the courts of appeals and the district courts. Average service has lengthened considerably: justices leaving the Supreme Court before the 1950s had served roughly 11 to 15 years, those departing since 1970 around 25 years, and the average for justices seated since 1993 is close to 28 years. Forty nine of the fifty states, and every other major democracy, impose term limits, elections or a retirement age on their highest court. [verified]
End of mandatory retirement for tenured faculty, 1 January 1994. See Chapter 5, note 6. [verified]
Average age at first NIH R01-equivalent award for investigators holding doctorates rose from about 35.7 in 1980 to about 42.1 in 2013, and has remained near 42 through fiscal 2025. For those with medical degrees it rose from under 38 to over 45 across the same period. The share of R01 principal investigators aged 36 or younger fell from 18 percent in 1983 to 3 percent in 2010. See Daniels, “A generation at risk,” PNAS, 2015, and NIH extramural data. [verified]
Japan’s employment ice age generation, covering graduates entering the labour market from roughly 1993 to 2004. Studies find a wage penalty of 10 to 20 percent persisting into their forties. Non-regular employment rose above a third of the workforce. The 8050 problem describes households where parents in their eighties support unemployed children in their fifties. [verified]
Elite overproduction and blocked mobility as sources of instability. The term is Peter Turchin’s, developed from Jack Goldstone’s structural-demographic theory, in which state breakdown follows from population growth, urbanisation and elite competition for a fixed number of positions. Turchin set the argument out in Nature in 2010 and forecast rising instability in the United States and western Europe through the years around 2020. The chapter uses the pattern and not the forecast. [verified]

Chapter 8. The Last Chain Letter

2025 OASDI Trustees Report, released 18 June 2025. The Old-Age and Survivors Insurance trust fund can pay scheduled benefits in full until 2033, after which continuing programme income covers about 77 percent of scheduled benefits, a reduction of roughly 23 percent. Combined OASI and DI reserves stood at about 2.72 trillion dollars at the end of 2024. The seventy five year shortfall is on the order of 25 trillion dollars. The depletion date moves between annual reports and should be quoted with its edition. [verified]
Pay-as-you-go structure of national pension systems, and the distinction between a buffer fund and a funded liability. Nicholas Barr, The Economics of the Welfare State, pensions chapter, is the textbook treatment to cite rather than the folk version. [unverified]
Samuelson 1958, as at Chapter 1 note 3. The chain letter phrasing is not Samuelson’s. It is Karl Shell’s, in “Notes on the Economics of Infinity,” Journal of Political Economy 79(5), 1971, writing about this model; Chapter 1 note 3 gives the quotation. An earlier draft of the text and of this note credited the comparison to Samuelson, which contradicted Chapter 1 note 3, and both have been corrected. The chapter’s title stands, because the comparison is a fair description of the arrangement Samuelson built, but the phrase belongs to Shell. [verified, and corrected]
The contribution arithmetic in this chapter, that doubling the length of retirement roughly doubles the contribution rate required to fund a fixed benefit, is arithmetic on a pay-as-you-go identity and is presented as such rather than as a reported finding. [my calculation]
Blanchard, “Public Debt and Low Interest Rates,” presidential address to the American Economic Association, American Economic Review, volume 109, number 4, April 2019, pages 1197 to 1229. Argues that safe rates below growth rates are closer to the historical norm than to an anomaly, that debt rollovers may then be feasible, and that public debt may in that case carry no fiscal cost, while still reducing capital accumulation with welfare costs smaller than usually assumed. [verified]
The juxtaposition of Blanchard 1985 and Blanchard 2019, and the claim that reading them in sequence produces a misleading conclusion about fiscal room, is my argument rather than a position either paper takes. Neither paper addresses the other. [my argument]
Rachel and Smith, as at Chapter 3 note 6. [verified]
Japanese general government gross debt above 200 percent of GDP, with figures in the range of 230 to 235 percent reported for 2025 depending on the measure and net debt substantially lower. The Bank of Japan held roughly 46 percent of outstanding Japanese government bonds at the end of 2024. Domestic holders, principally the central bank, the banks, the insurers and the pension funds, hold above 80 percent of the stock. These figures move; cite one source and one date rather than blending them. [verified]
Longevity risk as a systematic rather than idiosyncratic exposure, and the longevity swap market through which pension funds transfer it to reinsurers. The market’s existence and purpose are well documented. The further claim, that the exposure cannot ultimately be placed outside the affected population, is my argument. [verified as to the market; the conclusion is my argument]
The composition of developed world budgets, and the rising share committed to pensions, health and debt service. The OECD Social Expenditure Database supplies a long run series across countries and is the source to cite rather than a single year from a single country. [unverified]
The reading of Japan as a closed accounting loop rather than a delayed crisis is my interpretation. The underlying holdings data is not in dispute; the framing is mine. [my argument]

Chapter 9. The Forkable Worker

The description of agent instantiation, checkpointing, forking and termination was reviewed before publication by a practitioner who runs these systems daily, which is the review this note previously asked for. Spawn, checkpoint, fork, kill and spin up are confirmed as the working vocabulary. Workers created from a saved state receive a copy of context and do not share memory unless the system is built to give them some. Discarding a failed worker and re-running from the same state is the normal repair. The marginal cost is rented compute and acquisition takes seconds. [verified]
The claim that the supply curve for copyable labor becomes near-perfectly elastic at the cost of compute is my own argument rather than a result I am citing. It should be stated as such, and it deserves engagement with the existing literature on automation and factor shares, which reaches related conclusions by other routes. [my argument]
The worked description of how a multi-agent run is structured, added in response to a review note asking for one. It is written at the level of detail that bears on the economics rather than the engineering: marginal cost equal to rented compute, acquisition time in seconds, zero variance between two workers at the moment of a fork, and termination cost equal to sunk compute plus unsaved work. Practitioner review confirmed the description and corrected one point. An earlier draft said that the differences between two forked workers are attributable to what each worker encountered and not to what it is. That is too strong. Two workers forked from an identical state also diverge because the model samples, so they will not produce identical output even on identical input. The text now attributes divergence to sampling and to encounter, and the claim of zero variance is held to the moment of the fork rather than to anything after it. [verified, and corrected]
The claim that the frictions of human labour markets, notice periods, severance, training cost, institutional memory, morale and employment law, are each downstream of a person being a single continuous irreplaceable thing with a finite life, is my argument. It is not a proposition from labour economics and should be read as a framing rather than a finding. [my argument]

Chapter 10. The Mortal Class

Homestead Act of 1862, signed 20 May 1862. Offered 160 acres to adults willing to live on and farm the land for five years for a small filing fee. Over 1.6 million applications were processed and more than 270 million acres, about ten percent of all US land, passed into private hands by 1934. [verified]
Salvage, adverse possession, discovery and occupation doctrines. A property or admiralty hornbook should be cited for each rather than the summary given here. [unverified]
The English East India Company was chartered by Elizabeth I on 31 December 1600 with a fifteen year monopoly on English trade east of the Cape of Good Hope, and its charter conferred powers to wage war, mint coin, negotiate treaties and administer justice in its territories. The Dutch United East India Company was chartered by the States-General in 1602 with comparable powers, including its own military forces, treaty making with Asian rulers, and coinage. [verified]
At its peak in the early nineteenth century the East India Company’s army numbered approximately 260,000, roughly twice the size of the British Army, and was the largest private army in history. Following the rebellion of 1857, the Government of India Act 1858 transferred all Company powers to the Crown. [verified]
Earth to Mars one-way light time runs from about 3 minutes at closest approach to about 22 minutes at greatest separation, averaging around 12 and a half. Round trip is therefore roughly 6 to 44 minutes. An earlier draft gave 4 to 24 one way and 8 to 48 round trip; corrected. [verified, and corrected]
Outer Space Treaty, 1967, Article II: outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means. [verified]
US Commercial Space Launch Competitiveness Act, 2015, recognizing rights of US citizens to own, possess and sell resources obtained from asteroids and other celestial bodies. Luxembourg passed comparable legislation in 2017. The Artemis Accords, from 2020, set out resource extraction principles that some states regard as a unilateral reinterpretation of the treaty. [verified]
The IMO Code for Maritime Autonomous Surface Ships, approved in May 2026 as the first global framework for vessels operating with reduced or no crew, non-mandatory in its first phase with a mandatory phase expected in the early 2030s. Its retention of a master, and the shift of responsibility to shore based control centres, is the feature the chapter relies on. The Code addresses operations and safety and does not resolve legal liability, which is the second feature the chapter relies on. Cite the adopted text rather than press coverage before typesetting. [verified]
The International Group of P&I Clubs confirmed that liabilities arising from autonomous vessels, including fully unmanned ones, can fall within its shared pooling arrangements, subject to individual club underwriting and to flag and class compliance. Injuries at shore based remote operations centres, and damage to those facilities, are not treated as marine risks and require separate cover. That boundary, rather than the decision itself, is what the chapter uses. [verified]
The observation that liability for autonomous systems is drifting toward the organisation that employed, trained, scheduled and supervised the remote operator, rather than toward the operator or the machine, is drawn from how the question is being discussed in shipping and in parallel road vehicle regimes. It is a direction of travel rather than a settled rule, and the chapter says so. [verified as to the direction; not a settled legal rule]
The claim that the legal fiction of an absent master survives at millisecond latency because intervention remains possible, and fails at interplanetary latency because it does not, is my argument. So is the conclusion that the likelier outcome is formal responsibility disconnected from actual control rather than any grant of autonomy to a machine. [my argument]

Chapter 11. The Serrata

The colleganza as a limited liability partnership contract enabling merchants without capital or collateral to enter long distance trade. [verified as to its function and significance]
The Serrata of 1297 closed the Great Council to families not already represented, creating a hereditary nobility which then used its exclusive position to restrict participation in the most lucrative parts of long distance trade. Puga and Trefler, “International Trade and Institutional Change: Medieval Venice’s Response to Globalization,” Quarterly Journal of Economics, 2014, document this using a database of 8,178 parliamentarians and their families’ use of the colleganza before and after 1297. An earlier draft said the Republic banned the colleganza outright. The record does not support that, and the text has been softened to what it does show: barriers erected around the most lucrative trades, and the instrument falling away beneath the families who had risen through it. [verified, and corrected]
The Libro d’Oro. A precursor register of families eligible for the Great Council was compiled in 1315, eighteen years after the Serrata, and that is the object the chapter calls the Golden Book. The Libro d’Oro proper, recording all births in the Venetian nobility and kept by the Avogadori de Comun, was established by law in 1506. The chapter’s phrasing, that the arrangement was formalised further within a few decades, matches the 1315 register, and the two dates should not be conflated. [verified]
Venice’s declining share of Mediterranean trade and its response to the opening of the Atlantic routes. Frederic Lane, Venice: A Maritime Republic, is the source to cite. [unverified]
The fall of the Republic. Ludovico Manin, the hundred and twentieth and last doge, put the end of the aristocratic government to the Great Council on 12 May 1797 and abdicated under threat of French military action, ending roughly eleven centuries of the Republic. He left the Doge’s Palace on 14 May. [verified]
Acemoglu and Robinson treat the Serrata in Why Nations Fail, 2012, as their case of a society moving from inclusive to extractive institutions, with the colleganza as the inclusive instrument and the register of 1315 as the formal closure. One divergence matters and is left visible deliberately: their account states that the colleganza was eventually banned. This chapter does not follow them on that point, for the reason recorded at note 2 above. The disagreement runs against the direction of this book’s own argument, which is why it is printed rather than smoothed over. [verified as to their treatment; the divergence is deliberate]
The Ming treasure voyages, seven expeditions between 1405 and 1433 under Zheng He, some exceeding three hundred ships and tens of thousands of men, reaching Ceylon, Hormuz and the East African coast including Mogadishu and Malindi. The court ended support after 1433 on grounds of cost and the northern frontier threat, and Chinese pre-eminence in shipbuilding, navigation and seamanship withered quickly thereafter. European seaborne expansion into the same waters began roughly fifty years later. The text deliberately avoids the popular claims about deliberate destruction of records, which are contested. [verified]
The Venetian Arsenal. At its height it employed thousands of workers, the arsenalotti, rising far higher in wartime, and used standardised parts, prefabrication and a moving assembly sequence in which hulls were drawn past fixed stations. The frequently quoted capability of completing and fitting out a galley in a single day is well attested for the Arsenal at its peak, and is what the chapter refers to. Employment figures vary widely by source and by date, so cite one. [verified]

Chapter 12. Reinventing the Funeral

Hong Kong’s land tenure. All land in the territory is held on government lease except a single plot granted to St John’s Cathedral. New leases run fifty years at a premium, with annual rent set at three percent of rateable value. Approximately 300,000 leases expire on 30 June 2047, and the Extension of Government Leases Ordinance provides for automatic extension by a further fifty years through gazette notice, without owners executing new documents. The British leasehold sector and the documented under-maintenance problem near expiry still need a source. [verified for Hong Kong; British leasehold unverified]
Land value taxation. Henry George, Progress and Poverty, 1879, drawing on Ricardo and Mill, argued for a single tax on the unimproved value of land. On the discount rate point the claim in the text holds only with a qualification that should be made explicit: a levy assessed on annual ground rent, which is a flow, is indifferent to the discount rate, while a levy assessed on capital land value, which is a stock equal to rent divided by the rate, is not. Hong Kong’s ground rent at three percent of rateable value is of the first kind, and the chapter should be read as recommending the flow base. This is my argument about tax design rather than a result reported in the Georgist literature. [verified as to George; the discount rate argument is my own]
The common ownership self-assessed tax, also called a Harberger tax. Owners periodically self-assess the value of their property, pay tax on the declared figure, and must sell to anyone offering that price. First proposed by Arnold Harberger and popularised by Eric Posner and Glen Weyl in Radical Markets, 2018. [verified]
Interstate competition for trust business as the driver of perpetuities repeal. See Chapter 4, note 4. [verified]
Rawls, A Theory of Justice, 1971, for the original position and the veil of ignorance. The reading of mortality as the mechanism that actually enforces the veil is my own argument, not Rawls’s, and the text should make that clear. [my argument]
California Proposition 140, passed November 1990, limiting service to three two-year Assembly terms and two four-year Senate terms, with a lifetime ban on return. The same measure cut the legislature’s operating budget by roughly forty percent, which fell heavily on professional staff; the Legislative Analyst’s Office lost about half its personnel. Subsequent research documents reduced committee screening, more bills rewritten at later stages, weaker oversight of the executive, and a higher passage rate for interest-group sponsored bills. The reports of newly elected members receiving the large majority of their legislation pre-drafted from outside are testimony collected in that literature rather than a measured average, and should be attributed as such. The Public Policy Institute of California’s work on adapting to term limits, and Garlick in Legislative Studies Quarterly, 2025, on legislative capacity and interest group influence, are the standard sources. [verified]
The generalisation drawn from that case, that a term limit applied to one institution transfers power to whatever adjacent institution is not term limited rather than producing rotation, is my argument. The California evidence is consistent with it and does not establish it as a law. [my argument]
Sun Yat-sen’s land programme and its four connected components: owner declared land value, taxation on the declared value, a state right to purchase at the declared value, and the socially created increment accruing to the public. Carried into the constitutional order of the Republic of China and the basis of Taiwan’s land taxation doctrine. In present practice the operative figure is an officially assessed land value set by local authorities on a fixed revision cycle, not an owner’s declaration, so the self-assessing component is not what determines liability. Cite the Department of Land Administration’s own description alongside the secondary literature on the scheme. [verified]
The explanation offered for why the self-assessment component lapsed, that the purchase right must be exercised occasionally to stay credible and that exercising it is politically intolerable, is my argument and not a finding reported in that literature. [my argument]
The claim that both mechanisms were hollowed out rather than repealed, and that this is the general fate of turnover devices because they require continuous enforcement against the parties they bind, is the chapter’s central revision and is my argument. It is offered as the strongest available case against the chapter’s own proposals. [my argument]

Chapter 13. Terminal Value

Terminal value as a share of enterprise value in discounted cash flow analysis. Commonly around three quarters in a standard five year forecast, falling to roughly half in a ten year forecast, and reaching 85 to 95 percent for companies whose cash flows are mostly ahead of them. Practitioners are advised to flag valuations where it exceeds 80 percent. [verified]
Cologne Cathedral: foundation stone laid 1248, work halted in 1473 leaving a wooden crane on the unfinished south tower where it stood for roughly four hundred years as a landmark of the skyline, construction resumed in the nineteenth century, completed 1880. Total 632 years. An earlier draft called the stoppage three centuries. It was four. Corrected in the text. [verified, and corrected]
Notre-Dame de Paris. The first stone was laid in 1163 under Bishop Maurice de Sully, the choir, west front and nave were substantially complete by the middle of the thirteenth century, and the building is generally described as largely finished by 1345, a span of about 182 years. Retained as a secondary example to Cologne. [verified]
The two observed failure modes of perpetual charitable foundations. Faithful irrelevance, the dead hand: Julius Rosenwald, “Principles of Public Giving,” The Atlantic, May 1929. “while charity tends to do good, perpetual charities tend to do evil.” Drift and professional capture: Heather Higgins, “Should Foundations Exist in Perpetuity?” Philanthropy Roundtable, 1996. Higgins argues that perpetual foundations tend to share a shift from donor intent, driven by time, reliance on professional staff, and the absence of accountability. The observation of those two directions is sourced. The chapter’s claim that there is no third outcome, and that this is a general law, is my reading, not a demonstrated result in those sources. [verified]

Verification status

Counting rule, so these numbers can be reproduced. An item counts as verified if its marker begins “verified“, which includes items verified with a caveat and items verified and corrected. An item counts as unverified only if its marker is exactly “unverified“. Items whose marker begins “my” are the author’s own calculation or argument rather than anything reported by a source.

Verified against sources: 91 items, of which 15 carry a caveat recorded on the item itself. Still unverified: 7 items. Flagged as my own calculation or argument rather than a reported finding: 17 items.

Nine claims were found to be wrong or overstated during verification and have been corrected in the text. They are recorded at the relevant notes above rather than quietly fixed: the life expectancy decomposition in Chapter 2, the partial reprogramming result in Chapter 2, the r-star figures in Chapter 3, the consols provenance in Chapter 3, the chain letter attribution in Chapter 8, the divergence of two forked workers in Chapter 9, the Mars light lag in Chapter 10, the colleganza prohibition in Chapter 11, and the Cologne stoppage in Chapter 13.

One further correction was made to the notes rather than to the text. The note on the life expectancy decomposition in Chapter 1 had continued to assert the error that Chapter 2 corrects, so the two notes contradicted each other. It now points at the correction.

What remains unverified is entirely secondary literature attribution rather than factual assertion: whether a particular idea is correctly credited to a particular paper, or which standard treatment to cite for a point that is not itself in dispute. Each of the seven now names the work to consult. They should still be read against it, but an error among them is a citation error rather than a false claim in the text.

Two items were previously recorded here as impossible to close by reading. One has closed. The description of how agent systems are instantiated, checkpointed, forked and terminated in Chapter 9 was reviewed by a practitioner who runs them, who confirmed the vocabulary and the mechanics and corrected one overstatement about why two forked workers diverge. Both are recorded at Chapter 9, notes 1 and 3. The other stands. The per-flight denominator for wingsuit fatality rates in Chapter 6 is weak because the number of flights is not systematically recorded anywhere, and no amount of searching will fix that.

The two load bearing items previously flagged as unsourced are now sourced. Chapter 1 uses Blanchard and Fischer for the no-Ponzi-game condition and Kamihigashi for the transversality condition, kept distinct, and the expanded treatment in that chapter turns on the distinction between them. Chapter 13 sources the two observed directions in Rosenwald and Higgins. The claim that there is no third outcome remains my reading, not a general law those sources demonstrate, and Chapter 4 now prints the strongest case against it.

Where a source disagrees with the text, the disagreement is recorded rather than resolved silently. Acemoglu and Robinson state that Venice banned the colleganza outright. This book does not follow them, and the note says so.