Back in the 2010s lindy was this esoteric-ish word out of Taleb's books with the origin story of some cafe in New York or whatever it was, comedians speculating their job prospects on which shows will last how long type thing. Then on Twitter it gained memetic acceleration describing these exotic Mediterranean aesthetics and soul nourishing visuals, at which point this guy Paul Skallas basically made it his thing to classify memes and trends as lindy or not-lindy. And now in the middle of 2020s the word lindy is heard everywhere, not to mention black swan and other phrases finding their roots to Taleb's books.
Cool to see Taleb making a technical paper out of it which I just read. I think he's following his own thesis and converting practitioner-findings into theories, rather than having theories convert to practices; something he argues against in his books. Though, with time, I now personally believe that both those routes can yield fruitful ideas and practices; and the more level-headed point might be that new ideas and knowledge may come from unpredictable sources. I guess I ought to read Paul Feyerabend to gain clarity on this.
I'm not gonna pretend I understand all the math in the paper, but I want to make note of some terms here that stood out to me in it. Also, there is this loosely synced behavior I notice between Taleb and Wolfram, in which they seem to hover around similar topics using different terminologies and disciplines, where Wolfram seems to have developed an entire language to describe things mathematically and a physics project to go along with it. Personally I find Wolfram much easier to understand and think his stuff is like bitcoin in the early 2010s but at a much larger scale, and probably much more worthy and useful in the longer run. Deep lindy.
Anyway, I asked Grok to give me the concepts in Taleb's paper:
Core Concepts and Framework
Lindy Effect / Lindy Property: The idea that the longer something has survived (e.g., a technology, idea, book, or entity), the longer its expected remaining lifetime. In the paper, this emerges when the conditional survival probability improves with age under certain stochastic conditions. Mathematically tied to declining force of mortality with time (or age).
Absorbing Barrier: A lower boundary (often at 0) in a stochastic process that, once hit, "absorbs" or ends the process (e.g., ruin, death, failure, or extinction). Survival corresponds to the distance or time until first hitting this barrier.
Brownian Motion (Wiener Process): A continuous-time stochastic process with independent, normally distributed increments. Used here as the underlying model for the "health," "value," or "position" of the entity. Zero-drift or negative-drift versions are analyzed.
First-Passage Time (Hitting Time): The random time at which the process first reaches the absorbing barrier. The distribution of this time determines survival probabilities and the Lindy property.
Force of Mortality (Hazard Rate, λ(t) or μ(t)): The instantaneous rate of "failure" (absorption) at time t, conditional on having survived up to t. Defined as λ(t) = f(t) / S(t), where f(t) is the density and S(t) the survival function. Declining hazard rate with t produces Lindy-like behavior.
Survival Function S(t): Probability that the process has not hit the absorbing barrier by time t (i.e., "still alive/surviving").
Drift (μ): The deterministic trend or average direction of the process per unit time.
Zero drift (μ = 0): Leads to power-law tails in survival times and declining force of mortality → Lindy property holds.
Negative drift (μ < 0): Introduces a downward pull (like aging or entropy), eliminating the Lindy property; hazard rate may increase or behave differently.
Power-Law Survival / Power-Law Tails: Survival probability S(t) ~ t^(-α) for large t (heavy-tailed decay). Arises in zero-drift cases; implies no characteristic scale and Lindy behavior.
Demarcation / Classification of Tails (Thin vs. Fat): The paper provides properties distinguishing tail behaviors, often using a parameter λ (lambda).
Thin-tailed cases (e.g., exponential or lighter) typically have increasing force of mortality with time.
Fat-tailed cases (subexponential or heavier) can exhibit declining hazard.
Note: Galley proofs contain noted typos (e.g., lambda values in the demarcation box on page 2; original had λ=1 for certain cases, with corrections discussed).
Key Distributions and Processes Mentioned
Lévy Distributions (Lévy Stable Distributions / Stable Laws): A family of heavy-tailed probability distributions closed under addition (stable). Includes cases with infinite variance. Relevant for modeling processes with fat tails; the first-passage times or increments in the absorbing barrier model can relate to Lévy processes (generalizations of Brownian motion with jumps).
Cauchy Distribution: A specific symmetric stable distribution (Lévy stable with α=1, no mean or variance). Extremely fat-tailed (no moments exist). Often appears in limits or as a contrast in tail behavior discussions; hitting times or ratios in Brownian-related models can yield Cauchy-like properties.
Inverse Gaussian Distribution: Sometimes arises in first-passage times for Brownian motion with drift (Wald distribution). Used in survival modeling.
Bessel Process (e.g., 3-Dimensional Bessel Process): Arises from Brownian motion conditioned to avoid absorption or reflected at the barrier. Mentioned in related Taleb works on censored paths and surviving processes; positive drift in surviving paths after conditioning on non-absorption.
Subexponential Distributions: Class of heavy-tailed distributions where the tail of the sum is dominated by the maximum (one big jump). Linked to fat tails and potential Lindy properties.
Other Technical Phrases and Concepts
Zero-Drift Process: Brownian motion without systematic trend. Yields power-law survival times and declining force of mortality → classic Lindy.
Negative Drift / Aging Pull: Introduces entropy-like degradation; removes the Lindy property as older entities face higher effective risk of absorption.
Conditional Survival / Remaining Lifetime: Expected future life given current age. Increases with age under Lindy conditions.
Ergodicity / Non-Ergodicity: Implicit in survival conditioning (paths that survive are a biased sample); related to Taleb's broader work but tied here to absorbing processes.
Thin-Tailed vs. Fat-Tailed Classes: Demarcated by tail index or moments (e.g., via λ parameter in the paper).
Thin tails: finite moments, often increasing hazard.
Fat tails: power-law or heavier, can have declining hazard under zero drift.
Error Detection via Community / Lindy Proofs: The paper's proofs help detect inconsistencies in models or claims about longevity/survival (community "Lindy testing" via time).
Brief Summary of Structure (from Shared Pages)
The four pages cover:
Introduction to force of mortality in the absorbing barrier context.
The underlying stochastic process (Brownian motion variants).
Derivations for zero-drift case → power-law survival + Lindy.
Effect of adding (negative) drift → loss of Lindy.
Demarcation properties for thin/fat tail classes (with λ parameter; typos noted in galley for λ=0/1 values).
Implications for survival, hazard rates, and real-world applications (ideas, technologies, institutions that "age" differently).
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