The leading three authors are from Germany, Mexico, and Switzerland resptfully.
The sentence they want should capture the notion of being robust when poked with a stick.
A pencil on it's tip is a fragile system, one burp and it falls to the table, far from the intial state. Marbles in fruit bowls are anti-fragile, given a good shake (up to a threshold) and they remain in the bowl and return to the low centre.
Reading further, they want more; that repeated perturbations should deliver benefit, that systems in an warped egg carton configuration can be annealed to reveal an optimal point by vigorous shaking slowly reduced in degree.
Having now read the whole paper it doesn't seem novel wrt to the state of dynamic system discussions in the mid 1980s other than the insertion of "antifragility" as nomenclature into the mix.
> A pencil on it's tip is a fragile system, one burp and it falls to the table, far from the intial state. Marbles in fruit bowls are anti-fragile, given a good shake (up to a threshold) and they remain in the bowl and return to the low centre.
I believe what you're describing is a stable vs unstable system, not fragile vs antifragile.
You can perturb a bowl with a marble, and the marble will still end up in the middle because it will return to stable equilibrium point (an "attractor"). Yours is an illustration of a stable system. Whereas a marble placed in an upside down bowl (with no ridges, just a half sphere), when perturbed, will fall off. This is an unstable system. These are classic examples used in (Lyapunov) stability theory.
Fragility and antifragility aren't about stability (returning to equilibria), but gains or losses after perturbation, which is related to convexity/concavity.
When you perturb an anti-fragile (or convex) system, it doesn't return to equilibrium but in fact improves. Conversely, when you perturb a fragile system, it degrades. The analysis is usually done with Jensen's inequality rather than Lyapunov.
EDIT: not sure why the downvotes. I'm pointing out a fact. The examples do not demonstrate antifragility, but stability, which is not the same concept.
Thanks for this- lots of people on here are misunderstanding the concept of anti-fragility as the same as robustness, e.g. in a control system. They are not at all the same- anti-fragility is a system progressively improving in a lasting way in response to an appropriate stressor, e.g. like a weight lifter getting stronger from weight training, or getting weaker from skipping training. It is not robustiness but literally a negative fragility: a system whose function is impaired by lack of stress (e.g. fragile to lack of stress), and improved by stressors.
My initial motivation was to point out the authors likely weren't native in English.
I meandered onwards to waffle about the nature of what they were describing, which to my mind at least begins with a notion of stability, in pursuit of a better succint opening line (which I don't have).
You've said:
Fragility and antifragility aren't about stability (returning to equilibria), but gains or losses after perturbation, which is related to convexity/concavity.
I've said:
Reading further, they want more; that repeated perturbations should deliver benefit, that systems in an warped egg carton configuration can be annealed to reveal an optimal point by vigorous shaking slowly reduced in degree.
We likely both agree that an anti-fragile system should not spiral out of control. I assume when you refer to "convexity/concavity" you mean at a scale greater than local, at the scale of the warp in an egg carton as I made reference.
My principal gripe with such discussion, as I said, was I don't see much that is new other than language over what was discussed in the mid 1980s .. but perhaps I've not read enough.
Thanks for engaging. You're right in that the ideas are not new, but I feel the language and the framing somewhat is.
I'm not sure if you've come across N. N. Taleb's work -- he's the guy who coined the term "antifragility" = things things that benefit from perturbation. In it he argues that the antifragility is a property of systems that satisfy Jensen's inequality [1]. If the system's function f is convex, then:
E[f(X)] > f(E[X])
X is a random variable representing perturbations to the system, and f(.) is the system's response. If Jensen's inequality is satisfied (which is only true if f is convex), the inequality tells us that the average response to variable inputs (E[f(X)]) is greater than the response to the average input f(E[X]). This means that the system benefits more from variability in the input than it would from a constant, average input.
Antifragile systems, in that sense, are not conventionally "stable". Taleb describes a spectrum: Fragile -> Robust -> Antifragile
Stable systems often fall into the robust category -- they can withstand stress without breaking, but they don't necessarily improve from it.
It's a really subtle nuance.
An example from life: the young person who takes no risks, has a stable job, does well enough but isn't really interested in moving or taking on new opportunities. They'll never make it big. This is stability.
But the young person who starts a startup and keeps taking risks, iterating and pivoting. If they win, they win big. If they lose, they only lose a few years of their early life. This is antifragility, and it is actually a departure from stability.
It's not just an old scientific idea, but a popular idea discussed at length by the ancient greeks: Talebs whole thing is taking ideas from ancient philosophy, especially stoicism and translating them into rigorous math concepts for modern applications and audience. He's also obsessed with "The Lindy Effect" which implies that older ideas are generally also likely to be more valuable and lastingly useful.
The sentence captures the notion clearly, it just sounds a little awkward, especially for an opening sentence in an abstract, which is usually carefully crafted. I think you're probably correct that this is because the authors aren't native English speakers.
The sentence they want should capture the notion of being robust when poked with a stick.
A pencil on it's tip is a fragile system, one burp and it falls to the table, far from the intial state. Marbles in fruit bowls are anti-fragile, given a good shake (up to a threshold) and they remain in the bowl and return to the low centre.
Reading further, they want more; that repeated perturbations should deliver benefit, that systems in an warped egg carton configuration can be annealed to reveal an optimal point by vigorous shaking slowly reduced in degree.
Having now read the whole paper it doesn't seem novel wrt to the state of dynamic system discussions in the mid 1980s other than the insertion of "antifragility" as nomenclature into the mix.