Lifespan of a System Depending on Its Type: The Lindy Effect

The lifespan of a system is determined by its type, as well as by internal and external factors:

• Physical systems (equipment, machinery)

  • Depends on the material, operating conditions, and level of maintenance.

  • Example: an incandescent bulb lasts ~1000 hours, an LED — tens of thousands of hours.

• Biological systems (organisms)

  • Lifespan depends on the species, genetics, and environment.

  • Example: bacteria may exist for minutes, while trees — for thousands of years.

• Social systems (states, organizations)

  • Depends on the stability of institutions, resources, and culture.

  • Example: empires may exist for hundreds of years, while startups — for a few months.

• Informational/mathematical systems (algorithms, models)

  • Lifespan is determined by relevance and applicability.

  • Example: Euclid's algorithm for GCD has existed for millennia, while some IT systems become obsolete within 5–10 years.

General Laws and Principles of System Lifespans

• Physical systems (equipment, materials)

  • Governed by the laws of thermodynamics (entropy increases, wear is inevitable).

  • The laws of material strength and fatigue determine service life.

  • Example: an engine's service life depends on heating/cooling cycles and friction.

• Biological systems (organisms)

  • Governed by the laws of biology and evolution.

  • Limited by aging processes, mutations, and environmental influences.

  • Example: cells have a division limit (the Hayflick limit).

• Social systems (states, organizations)

  • Governed by the laws of sociology and economics.

  • Existence depends on the stability of institutions, resources, and cultural norms.

  • Example: empires collapse when the balance of power and resources is disrupted.

• Informational/mathematical systems (algorithms, models)

  • Governed by the laws of logic and relevance.

  • Their existence is limited not by physics but by applicability.

  • Example: Euclid's algorithm is eternal as an idea, but a specific IT system becomes obsolete due to technological progress.

Universal Patterns

1. Law of entropy: any system tends toward destruction or simplification over time.

2. Law of limited resources: a system exists as long as there is energy, information, or support.

3. Law of adaptation: the better a system adapts to changes in its environment, the longer it lives.

4. Law of self-organization: complex systems can extend their existence through internal restructuring.

5. the Lindy law: if something has already existed for X years, then the expected remaining lifetime is also approximately X years (or proportional to X).

6. the Gompertz law - the probability of death grows exponentially with age,

7. Failure rate of a physical system: break-in (defects, early failures), stable operation, rapid wear and aging

The Lindy effect (also known as Lindy's law) — is a theoretical phenomenon whereby the future life expectancy of some non-perishable objects, such as technologies or ideas, is proportional to their current age. Thus, the Lindy effect suggests that the longer something exists or is used in the present, the longer its remaining life expectancy will be. Longevity implies resistance to change, obsolescence, or competition, as well as higher chances of continued existence in the future. Where the Lindy effect applies, mortality decreases over time. Mathematically, the Lindy effect corresponds to a Pareto distribution for lifespan.

The name of the Lindy concept comes from Lindy's, a New York delicatessen restaurant where comedians first voiced this idea. According to it, a show that has run for only two weeks is likely to last about as long again, whereas a show that has already run for two years can expect roughly two more years of existence. This theory was later developed by mathematicians and statisticians. Nassim Nicholas Taleb formulated the Lindy effect in terms of «distance to an absorbing barrier».

The Lindy effect applies to non-perishable items, such as books, that is, to those that have no «inevitable expiration date» . For example, people are perishable — life expectancy in developed countries is about 80 years. Therefore, the Lindy effect does not apply to the lifespan of an individual person — all else being equal, the probability of a 10-year-old dying within the next year is lower than that of a 100-year-old, whereas the Lindy effect would predict the opposite.

If something has already existed for X years, then the expected remaining lifetime is also approximately X years (or proportional to X).

For example:

• A book has been in print for 50 years → it will likely remain in print for another ~50 years

• A programming language has existed for 30 years → there is a high probability it will remain in use for a long time to come

• A technology has been in use for 10 years → it is not “on its way out”, but on the contrary, most likely stable

This does not work for people, but for:

• ideas

• books

• technologies

• companies

• cultural phenomena

For humans, the Lindy law does not apply directly, because a person has a biological limit.

This is the opposite of things with a fixed service life, for example:

• a battery (not applicable),

• a person (not applicable),

• a license (not applicable),

• a subscription (not applicable).

For objects with a limited service life, the Lindy effect does NOT work. Other laws apply to them, for example the Weibull distribution (THE LAW OF WEAR)

(the most universal and realistic)

Used for: equipment, mechanisms, bearings, batteries, auto parts, and even biological systems.

It accounts for three phases of life:

• Infant mortality (defects, early failures)
• Stable operation
• Rapid wear and aging

It is precisely this law that is used by: engineers, the aviation industry, medical equipment manufacturers, and industry.

For living organisms, for example, the Biological limit (Gompertz law) is used - the probability of death grows exponentially with age,

Estimated probability of death for a person at each age (for the USA, 2003). Mortality rates double every nine years after reaching the age of 30.

Analysis of the graph shows that the test period can conventionally be divided into three periods. In the first of them, the function λ(t) has elevated values. This is the run-in period, or the period of early failures due to hidden defects. The second period is called the period of normal operation. This period is characterized by a constant failure rate. The last, third period — is the aging period.

Table: Application of the Lindy Law and the Law of Wear by Industry

Lindy's delicatessen restaurant on the corner of Broadway and 51st Street in New York

The origin of this term can be traced to Albert Goldman and his 1964 article in The New Republic titled «Lindy's Law». The term Lindy refers to Lindy's delicatessen restaurant in New York, where comedians «gather every night to discuss recent events in show business». In this article, Goldman describes a folk belief among observers of the New York media that a comedian's amount of material is constant, and therefore the frequency of appearances predicts how long their show will last:

Benoit Mandelbrot, in his 1982 book The Fractal Geometry of Nature, proposed a different concept under the same name. In his interpretation, comedians do not have a fixed supply of jokes for television appearances. On the contrary, the more appearances they make, the more future appearances are predicted for them. Mandelbrot expressed mathematically that for certain things limited by the lifespan of their creator, such as human promises, the expected future lifespan is proportional to the past. He refers to Lindy's law and the parable of the graveyard of young poets, and then applies this to researchers and their publications: «However many works a person has produced over past years, on average they will continue for just as long again. When they do stop, it happens exactly at the halfway point of what was promised» .

Nassim Nicholas Taleb, in his 2012 book Antifragile: Things That Gain from Disorder, was the first to openly name his idea the Lindy effect. He expanded its application beyond the lifespan of the producer to cover anything without a natural upper bound, and incorporated it into his broader theory of antifragility.

According to Taleb, Mandelbrot agreed with the expanded definition of the Lindy effect: «I [Taleb] proposed the boundaries of perishable/non-perishable and he [Mandelbrot] agreed that non-perishable objects obey a power-law distribution, whereas perishable ones (the original interpretation of the Lindy effect) serve only as a metaphor».

Taleb later defined the term in his book Skin in the Game, where he linked the Lindy effect to fragility, disorder, and time. According to Taleb, «fragility theory leads directly to the Lindy effect», he defines «fragility as sensitivity to disorder», and asserts that «time is the equivalent of disorder, and resistance to the destructive effect of time, that is, what we proudly call survival, — is the ability to cope with disorder» . Since time acts through «skin in the game», Taleb believes that «things that survive hint, after the fact, that they possess a certain robustness». He concludes from this that «the only effective judge of things — is time», which, in his opinion, answers the «eternal meta-questions: Who will judge the expert? Who will guard the guards? [...] Well, survival» . He further argues that the Lindy effect is itself proof of the Lindy effect, citing the words of the pre-Socratic philosopher Periander («Use old laws, but fresh food») and Alfonso X («Burn old logs. Drink old wine. Read old books. Keep old friends»)

Among modern proponents of the Lindy effect are the Twitter user Paul Skallas, known as LindyMan, and Marc Andreessen, co-founder of Andreessen Horowitz. Skallas promotes a lifestyle inspired by the Lindy effect, an eclectic combination of Mediterranean writers such as the Greek philosopher Plutarch and the Catholic theologian Thomas Aquinas, as well as presumed lifestyles of Mediterranean peoples. In her article for The New York Times, Ezra Marcus notes that Skallas's approach to the Lindy effect differs from Taleb's statistical analysis in that it focuses on lifestyle aspects such as diet, dating, and exercise. Skallas urges skepticism toward new products and ideas whose longevity has not yet been proven. Skallas acknowledges that cultural longevity does not imply moral value, noting, for example, that sexual abuse by a wealthy person such as Jeffrey Epstein is also «Lindy».

Mathematically, the relationship postulated by the Lindy effect can be expressed by the following statement about a random variable T corresponding to the lifespan of an object (for example, a comedy show), which is assumed to take values in the range c (with a lower bound )

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 the «Lindy proportion» by Iddo Eliazar) is a positive constant .

This is equivalent to the survival function of T

which has a failure rate

This means that the lifetime follows a Pareto distribution (a power-law distribution) with exponent ε

In contrast, only Pareto distributions with exponent correspond to a lifespan distribution satisfying the Lindy law, since the Lindy proportion p must be positive and finite (in particular, it is assumed that the lifespan T has a finite expected value). Iddo Eliazar proposed an alternative formulation of the Lindy law involving the median instead of the mean (expected value) of the remaining lifespan T−t , which corresponds to Pareto distributions for the lifespan T with the full range of possible Pareto exponents . Eliazar also demonstrated a connection with Zipf's law and socioeconomic inequality, arguing that «the Lindy law, the Pareto law, and Zipf's law are, in essence, synonymous laws».

Often Confused with Other Effects

Here are similar but not identical concepts:

1. Survivorship bias
   We only see those who survived, and ignore those who disappeared.

2. Regression to the mean
   After extreme values, everything returns to normal.

3. System inertia
   Something that has worked for a long time is hard to break.

• Doomsday argument
• Memorylessness
• Rate of increase of life expectancy
• Planning fallacy
• Preferential attachment
• Survivorship curve
• Survivorship bias
• Weibull distribution
• Copernican principle
• Survival analysis