A hundred years old and expecting a hundred more — for a power-law lifetime that is not optimism, it is arithmetic. Three survival laws, run on the same axis, show when age is evidence and when it is a countdown.
Exact, not staged. The purple line is the Pareto mean residual life e(t) = t/(α−1) — exact for t ≥ xm = 1 and α > 1, and α > 1 is a hypothesis, not a footnote (the slider stops at 1.1 on purpose; the cliff is below). The blue line is a memoryless exponential, e(t) = 1/λ at every age; its level is matched by construction to the Pareto's expected remainder at the chosen age — same expected future today, and the only thing that differs is what another year does to it. The gold curve is the human-shaped comparison: the mean residual life of a Normal(80, 10) lifetime, computed numerically from the closed-form Mills ratio — e(70) = 12.88, e(80) = 7.98 (= 10√(2/π)), e(90) = 5.25 — and it decreases at every age, not just past the mode (the Normal's failure rate rises throughout; truncating the “lifetime” at zero would change these values by about 10−15, invisible at any zoom). The dots are 400 survivors at the chosen age, drawn exactly from the conditional law: given survival to t, a Pareto restarts as t × a fresh Pareto(α) — self-similarity is the Lindy property itself, so no rejection sampling was needed and none was faked. Dots beyond the top of the axis are pinned visibly to the edge as triangles and counted in the stats; a mean tick beyond the top is pinned the same way, with its value in the sim-mean stat. Same seed, same dots: add ?seed=N to the URL to pin a run; Re-run bumps it.
What Lindy actually claims, and for what: the effect is a statement about the nonperishable — books, ideas, technologies, anything without an organism's clock. In Antifragile, ch. 20, Taleb draws exactly that boundary: for the perishable, each day of survival shortens the expected remainder; for the nonperishable, each day lengthens it — his running example is a book whose decades in print imply the expectation of decades more. The gold curve is the honest contrast: ask the same question of a human-shaped lifetime and age is a countdown, not a credential. And the fine print is load-bearing. The mean-based claim needs α > 1: at α ≤ 1 the expected remainder is infinite — at α = 1 and t = 100, cutting the integral off at 104 years reads 460.5 years, at 106 it reads 921.0, at 108 it reads 1381.6; it grows like t·ln(U/t) and never settles. The median survives where the mean blows up: median remaining life t(21/α−1) is finite for every α > 0 — exactly t at α = 1 — which is why the median formulation below is the more expressive one. With salt: a rising expectation is a property of the survival law, not a promise about any single thing — Lindy grades distributions, not destinies.
The name is an accident of geography: Lindy's delicatessen in New York, whose late-night show-business regulars — in Albert Goldman's telling — theorised about the careers of television comedians. Goldman's “Lindy's Law” (The New Republic, June 13, 1964) tied a comic's expected run to his exposure — a fixed stock of material depleted by use — in effect the opposite direction of the modern effect, and Goldman himself offered it as “a cautionary fable” rather than prognosis; what survived was the name. The modern form is Mandelbrot's, in The Fractal Geometry of Nature (1982, p. 342, as cited in Ord 2023): the expected future of a body of collected works equal to its past — precisely the α = 2 case, this page's default slider. Antifragile records the division of labour as Taleb remembers it: the perishable/nonperishable split was his suggestion, and Mandelbrot signed off on power-law tails for the nonperishable side. Eliazar's “Lindy's Law” (Physica A 486, 2017, 797–805) formalized the effect as an anti-aging property — remaining expected lifetime increasing with age — tying it to Pareto's and Zipf's laws, with a median-based formulation under which a Pareto of any α > 0 qualifies. And the linear mean-excess of the Pareto that this page runs is textbook extreme-value theory: Ghosh & Resnick (2010).