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Antifragility in complex dynamical systems

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Re: Antifragility in complex dynamical systems

#21

Post by defrost »

wenc wrote: post #18
defrost wrote: post #14

Earlier quoted context omitted.

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…

> 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 midd…

You appear to have replied the first draft of my comment as I was expanding it. Thank you for the response.

Re: Antifragility in complex dynamical systems

#22

Post by wenc »

defrost wrote: post #21
wenc wrote: post #18

Earlier quoted context omitted.

> 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 midd…

You appear to have replied the first draft of my comment as I was expanding it. Thank you for the response.

No, I replied to your full post. Just wanted to point out that your examples showed stability, not antifragility.

Re: Antifragility in complex dynamical systems

#23

Post by inciampati »

bob1029 wrote: post #17
_yb2s wrote: post #13

Earlier quoted context omitted.

Very cool, but I'm surprised you're sharing this on here and not in a job interview with a deep learning startup and/or an arXiv paper.

> a job interview with a deep learning startup I am not aware of any DL startups that are interested in techniques which are incompatible with GPUs and back propagation. I think this is a solo journey through the dark forest for now.

Eloquent, realistic, and sad. I'm living my own version of this (in biotech). The journey is the wonder.

Re: Antifragility in complex dynamical systems

#24

Post by krick »

There are now so many bullshit-terms derived from Taleb's bullshit books. Like how people still keep mentioning "black swans" as if it actually means something other (or something more) than "unexpected event". And for some unfathomable reason it keeps traction. Similarly how Mandelbrot "redefined" (i.e. distorted) the meaning of "Lindy effect", and it stuck (however, I didn't notice if it became popular to call a millenia-old banality by than name after Mandelbrot, or Taleb again). It probably should serve as an another example of that if you are arrogant enough, people will follow you just because of that.

However, I guess "antifragility" isn't the worst of these.

Re: Antifragility in complex dynamical systems

#25

Post by defrost »

wenc wrote: post #22
defrost wrote: post #21

Earlier quoted context omitted.

You appear to have replied the first draft of my comment as I was expanding it. Thank you for the response.

No, I replied to your full post. Just wanted to point out that your examples showed stability, not antifragility.

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.

The downvoting of your comment is poor form.

Re: Antifragility in complex dynamical systems

#27

Post by agumonkey »

mo_42 wrote: post #26

I'd like to point out that Norbert Wiener was the first to discover the concept of antifragility (under a different term though). It's also worth checking out more of his works as he initiated the field of cybernetics.

Where did he described this? (Honest question)

Re: Antifragility in complex dynamical systems

#28

Post by Animats »

_yb2s wrote: post #10

I love how Taleb managed to translate an ideal from stoic philosophy into a precisely defined mathematical concept

Some of this reads like rediscovering control theory, which is all about stability and robustness within defined limits. It's more popularization than innovation.

The person who first translated this idea into math was James Clerk Maxwell, in his paper, "On Governors", in 1868.[1] Maxwell was the first to get a mathematical handle on stability of feedback systems. He wrote: "If, by altering the adjustments of the machine, its governing power is continually increased, there is generally a lin1it at which the disturbance, instead of subsiding more rapidly, becomes an oscillating and jerking motion, increasing in violence till it reaches the limit of action of the governor. This takes place when the possible part of one of the impossible roots becomes positive. ... I have pointed out that, under certain conditions, the sudden disturbances of the machine do not act through the differential system on the governor, or vice versa. When these conditions are fulfilled, the equations of motion are not only simple, but the motion itself is not liable to disturbances depending on the mutual action of the machine and the governor." That, right there, is the beginning of the mathematics of antifragility. Today, we call this turning up the P term of a PID controller too high and getting outside the stable region. Maxwell was the first to formalize the role of delay and damping (he calls it "viscosity") in this.

There's "robust control", a useful theory of "antifragility" in industrial use for decades. Here's an excellent video on how this is done.[2] That's worth a watch. Note the emphasis on how the combination of delay and noise can cause instability in a system resistant to both delay and noise separately. This can be dealt with by moving the areas of instability around in the frequency domain.

(Modern control theory has become insanely complicated over the last few years. Until recent years, control theory was mostly linear control theory plus some self tuning. Now, control theorists are trying to figure out how to get the benefits of machine learning while still having predictable error bounds. This means getting into the innards of what neural nets are really doing. I still get IEEE Trans. on Control Systems Technology, but don't understand it any more. So I'm not sure how that's coming along.)

[1] https://archive.org/details/jstor-112510/mode/2up?view=theat...

[2] https://www.youtube.com/watch?v=A7wHSr6GRnc

Re: Antifragility in complex dynamical systems

#29

Post by wenc »

defrost wrote: post #25
wenc wrote: post #22

Earlier quoted context omitted.

No, I replied to your full post. Just wanted to point out that your examples showed stability, not antifragility.

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,…

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.

[1] https://en.wikipedia.org/wiki/Jensen%27s_inequality

Re: Antifragility in complex dynamical systems

#30

Post by aaron695 »

krick wrote: post #24

There are now so many bullshit-terms derived from Taleb's bullshit books. Like how people still keep mentioning "black swans" as if it actually means something other (or something more) than "unexpected event". And for some unfathomable reason it keeps traction. Similarly how Mandelbrot "redefined" (i.e. distorted) the meaning of "Lindy effect", and it stuck (however, I didn't notice if it became popular to call a mi…

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