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# Lindy effect

The Lindy effect (also known as Lindy's Law[1]) is a theorized phenomenon by which the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current age. Thus, the Lindy effect proposes the longer a period something has survived to exist or be used in the present, it is also likely to have a longer remaining life expectancy. Longevity implies a resistance to change, obsolescence or competition and greater odds of continued existence into the future.[2] Where the Lindy effect applies, mortality rate decreases with time. Mathematically, the Lindy effect corresponds to lifetimes following a Pareto probability distribution.

The concept is named after Lindy's delicatessen in New York City, where the concept was informally theorized by comedians. The Lindy effect has subsequently been theorized by mathematicians and statisticians.[3][4][1] Nassim Nicholas Taleb has expressed the Lindy effect in terms of "distance from an Absorbing barrier."[5]

The Lindy effect applies to "non-perishable" items, those that do not have an "unavoidable expiration date".[2] For example, human beings are perishable: most humans live for about 80 years. So the Lindy effect does not apply to individual human lifespan: it is unlikely for a 5-year-old human to die within the next 5 years, but it is very likely for a 70-year-old human to die within the next 70 years, while the Lindy effect would predict these to have equal probability.

## History

The origin of the term can be traced to Albert Goldman and a 1964 article he had written in The New Republic titled "Lindy's Law".[6] The term Lindy refers to Lindy's delicatessen in New York, where comedians "foregather every night at Lindy's, where ... they conduct post-mortems on recent show business 'action'". In this article, Goldman describes a folkloric belief among New York City media observers that the amount of material comedians have is constant, and therefore, the frequency of output predicts how long their series will last:[7]

... the life expectancy of a television comedian is [inversely] proportional to the total amount of his exposure on the medium. If, pathetically deluded by hubris, he undertakes a regular weekly or even monthly program, his chances of survival beyond the first season are slight; but if he adopts the conservation of resources policy favored by these senescent philosophers of "the Business", and confines himself to "specials" and "guest shots", he may last to the age of Ed Wynn [d. age 79 in 1966 while still acting in movies]

Benoit Mandelbrot defined a different concept with the same name in his 1982 book The Fractal Geometry of Nature.[3] In Mandelbrot's version, comedians do not have a fixed amount of comedic material to spread over TV appearances, but rather, the more appearances they make, the more future appearances they are predicted to make: Mandelbrot expressed mathematically that for certain things bounded by the life of the producer, like human promise, future life expectancy is proportional to the past. He references Lindy's Law and a parable of the young poets' cemetery and then applies to researchers and their publications: "However long a person's past collected works, it will on the average continue for an equal additional amount. When it eventually stops, it breaks off at precisely half of its promise."[This quote needs a citation]

Nassim Taleb presented a version of Mandelbrot's idea in The Black Swan: The Impact of the Highly Improbable by extending it to a certain class of non-perishables where life expectancy can be expressed as power laws.[citation needed]

With human projects and ventures we have another story. These are often scalable, as I said in Chapter 3. With scalable variables ... you will witness the exact opposite effect. Let's say a project is expected to terminate in 79 days, the same expectation in days as the newborn female has in years. On the 79th day, if the project is not finished, it will be expected to take another 25 days to complete. But on the 90th day, if the project is still not completed, it should have about 58 days to go. On the 100th, it should have 89 days to go. On the 119th, it should have an extra 149 days. On day 600, if the project is not done, you will be expected to need an extra 1,590 days. As you see, the longer you wait, the longer you will be expected to wait.[4]

In Taleb's 2012 book Antifragile: Things That Gain from Disorder he for the first time explicitly referred to his idea as the Lindy Effect, removed the bounds of the life of the producer to include anything which doesn't have a natural upper bound, and incorporated it into his broader theory of the Antifragile.

If a book has been in print for forty years, I can expect it to be in print for another forty years. But, and that is the main difference, if it survives another decade, then it will be expected to be in print another fifty years. This, simply, as a rule, tells you why things that have been around for a long time are not "aging" like persons, but "aging" in reverse. Every year that passes without extinction doubles the additional life expectancy. This is an indicator of some robustness. The robustness of an item is proportional to its life! [8]

According to Taleb, Mandelbrot agreed with the expanded definition of the Lindy Effect: "I [Taleb] suggested the boundary perishable/nonperishable and he [Mandelbrot] agreed that the nonperishable would be power-law distributed while the perishable (the initial Lindy story) worked as a mere metaphor."[9]

## Mathematical formulation

Mathematically, the relation postulated by the Lindy effect can be expressed as the following statement about a random variable T corresponding to the lifetime of the object (e.g. a comedy show), which is assumed to take values in the range ${\displaystyle c\leq T<\infty }$ (with a lower bound ${\displaystyle c\geq 0}$):[1]

${\displaystyle \mathrm {E} [T-t|T>t]=p\cdot t}$

Here the left hand side denotes the conditional expectation of the remaining lifetime ${\displaystyle T-t}$, given that ${\displaystyle T}$ has exceeded ${\displaystyle t}$, and the parameter ${\displaystyle p}$ on the right hand side (called "Lindy proportion" by Iddo Eliazar) is a positive constant.[1]

This is equivalent to the survival function of T being

${\displaystyle \Phi (t):={\text{Pr}}(T>t)=\left({\frac {c}{t}}\right)^{\epsilon }{\text{ , where }}\epsilon =1+{\frac {1}{p}}}$

which has the hazard function

${\displaystyle -{\frac {\Phi '(t)}{\Phi (t)}}={\frac {\epsilon }{t}}={\frac {1+p}{p}}{\frac {1}{t}}}$

This means that the lifetime ${\displaystyle T}$ follows a Pareto distribution (a power-law distribution) with exponent ${\displaystyle \epsilon }$.[10][11][1]

Conversely, however, only Pareto distributions with exponent ${\displaystyle 1<\epsilon <\infty }$ correspond to a lifetime distribution that satisfies Lindy's Law, since the Lindy proportion ${\displaystyle p}$ is required to be positive and finite (in particular, the lifetime ${\displaystyle T}$ is assumed to have a finite expectation value).[1] Iddo Eliazar has proposed an alternative formulation of Lindy's Law involving the median instead of the mean (expected value) of the remaining lifetime ${\displaystyle T-t}$, which corresponds to Pareto distributions for the lifetime ${\displaystyle T}$ with the full range of possible Pareto exponents ${\displaystyle 0<\epsilon <\infty }$.[1] Eliazar also demonstrated a relation to Zipf’s Law, and to socioeconomic inequality, arguing that "Lindy’s Law, Pareto’s Law and Zipf’s Law are in effect synonymous laws."[1]

## References

1. Eliazar, Iddo (November 2017). "Lindy's Law". Physica A: Statistical Mechanics and Its Applications. 486: 797–805. Bibcode:2017PhyA..486..797E. doi:10.1016/j.physa.2017.05.077.
2. ^ a b Nassim Nicholas Taleb (2012). Antifragile: Things That Gain from Disorder. Random House. p. 514. ISBN 9781400067824.
3. ^ a b Mandelbrot, B.B (1984). The fractal geometry of Nature. Freeman. p. 342. ISBN 9780716711865.
4. ^ a b Nassim Nicholas Taleb (2007). The Black Swan: The Impact of the Highly Improbable. Random House. p. 159. ISBN 9781588365835. Like many biological variables, life expectancy.
5. ^ Taleb, Nassim Nicholas. "Lindy as a Distance from an Absorbing Barrier (Chapter from SILENT RISK)". Cite journal requires |journal= (help)
6. ^ Goldman, Albert (13 June 1964). "Lindy's Law". The New Republic. pp. 34–35.
7. ^ "The simple rule that can help you predict the future". Retrieved 21 May 2020.
8. ^ Nassim Nicholas Taleb (2012). Antifragile: Things That Gain from Disorder. Random House. p. 318. ISBN 9780679645276. another forty years.
9. ^ Taleb, Nassim Nicholas (2012-11-27). Antifragile: Things That Gain from Disorder. ISBN 9780679645276.
10. ^ Cook, John (December 17, 2012). "The Lindy effect". John D. Cook. Retrieved May 29, 2017.[self-published source?]
11. ^ Cook, John (December 19, 2012). "Beethoven, Beatles, and Beyoncé: more on the Lindy effect". John D. Cook. Retrieved May 29, 2017.[self-published source?]