Lindy effect explained

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, the longer its 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] [1]} Nassim Nicholas Taleb has expressed the Lindy effect in terms of "distance from an absorbing barrier".^[4]

The Lindy effect applies to "non-perishable" items, those that do not have an "unavoidable expiration date".^[2] For example, human beings are perishable: the life expectancy at birth in developed countries is about 80 years. So the Lindy effect does not apply to individual human lifespan: all else being equal, it is less likely for a 10-year-old human to die within the next year than for a 100-year-old, while the Lindy effect would predict the opposite.

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." The term Lindy refers to Lindy's delicatessen in New York, where comedians "foregather every night [to] 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:^[5]

Benoit Mandelbrot defined a different concept with the same name in his 1982 book The Fractal Geometry of Nature. 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."

In Nassim Nicholas 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.

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."^[6]

Taleb further defined the term in Skin in the Game, where he linked Lindy with fragility, disorder and time.^[7] To Taleb, "the theory of fragility directly leads to the Lindy effect," as he defines "fragility as sensitivity to disorder," and states that "time is equivalent to disorder, and resistance to the ravages of time, that is, what we gloriously call survival, is the ability to handle disorder."^[7] As time operates through "skin in the game," Taleb believes that "[t]hings that have survived are hinting to us ‘ex post’ that they have some robustness." He concludes therefore that "the only effective judge of things is time," which in his view answers the "age-old meta-questions: Who will judge the expert? Who will guard the guard? [...] Well, survival will."^[7] He further states that the Lindy effect in itself is "Lindy-proof," citing the words of pre-Socratic philosopher Periander ("Use laws that are old but food that is fresh") and Alfonso X of Castile ("Burn old logs. Drink old wine. Read old books. Keep old friends.").^[7]

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

c \leq T < inf ty (with a lower bound c \geq 0 ):^[1]

$$\backslash mathrm\; [T-t|T>t]=p\; \backslash cdot\; t$$

Here the left hand side denotes the conditional expectation of the remaining lifetime

T - t , given that T has exceeded t , and the parameter 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

$$\backslash Phi(t)\; :=\; \backslash text(T>t)\; =\; \backslash left(\backslash frac\backslash right)^\backslash epsilon\; \backslash text\; \backslash epsilon\; =\; 1\; +\; \backslash frac$$

which has the hazard function

$$-\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac\backslash frac$$

This means that the lifetime

T follows a Pareto distribution (a power-law distribution) with exponent \epsilon .^{[8] [9] [1]}

Conversely, however, only Pareto distributions with exponent

1 < \epsilon < inf ty correspond to a lifetime distribution that satisfies Lindy's Law, since the Lindy proportion p is required to be positive and finite (in particular, the lifetime 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 T - t , which corresponds to Pareto distributions for the lifetime T with the full range of possible Pareto exponents 0 < \epsilon < inf ty .^[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]

See also

• Doomsday argument
• Memorylessness
• Longevity escape velocity
• Paul Skallas, popularly known as LindyMan
• Planning fallacy
• Preferential attachment
• Survivorship curve
• Survivorship bias
• Weibull distribution
• Copernican principle

Notes and References

1. Eliazar. Iddo. November 2017. Lindy's Law. Physica A: Statistical Mechanics and Its Applications. 486. 797–805. 2017PhyA..486..797E. 10.1016/j.physa.2017.05.077. 125349686 .
2. Book: Nassim Nicholas Taleb . 2012 . Antifragile: Things That Gain from Disorder . Random House . registration . 514 . 9781400067824.
3. Book: Nassim Nicholas Taleb . 2007 . The Black Swan: The Impact of the Highly Improbable . Random House . 159 . registration . Like many biological variables, life expectancy. . 9781588365835.
4. Web site: Lindy as a Distance from an Absorbing Barrier (Chapter from SILENT RISK). Taleb. Nassim Nicholas.
5. Web site: The simple rule that can help you predict the future . Tom . Chatfield . 24 June 2019 . BBC . 21 May 2020.
6. Book: Antifragile: Things That Gain from Disorder . 9780679645276 . Taleb . Nassim Nicholas . 2012-11-27.
7. Book: Taleb . Nassim Nicholas . . 2019 . Penguin . Great Britain . 9780141982656 . 141-152.
8. Web site: The Lindy effect . Cook. John . December 17, 2012 . John D. Cook . May 29, 2017.
9. Web site: Beethoven, Beatles, and Beyoncé: more on the Lindy effect . Cook. John . December 19, 2012 . John D. Cook . May 29, 2017.