Antifragility in complex dynamical systems

I am quite curious about your approach, Do you have an example code somewhere?

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.

The whole conversation is very scope dependent. A species can be antifragile specifically because the constituent organisms are fragile. The species evolves not in spite of death and mutation (variation) of the organisms but because of it.

At the same time organisms themselves can be antifragile at a different scope. My body gets stronger when I stress the muscles, and gets weaker when I do not.

Edit to add… it is also very dose dependent. Zero muscle stress and I get weaker. Some and I get strong. Too much and I get rhabdomyolysis — an absorbing barrier.

Same goes for the species. No death means no evolution. Some means evolution. Extinction level deaths are an absorbing barrier.

> 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.

I'd start here: https://arxiv.org/abs/2406.12552

I will say that less is more and "The Bitter Lesson" applies here. Chasing biologically-inspired rabbits, such as STDP and LIF (see paper above/wikipedia), does seem to be a waste of time, especially when we have this thing entirely outside of biology that can arbitrarily replicate, serialize, mutate and simulate billions of instances of the same parent candidate in minutes-hours.

Leaky charge carriers and inability to persist learned weights between candidate instantiations are limitations, not features to emulate. Imagine if you could be reincarnated with all of the exact knowledge you have today. Then clone that 1000 times and apply subtle mutations to it. Then, put these clones in an FFA arena and see who wins based upon a very well crafted fitness function. Then, do all of that over and over thousands of times per hour.