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

by _yb2s 2y ago

Animats 2y ago
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=theater https://archive.org/details/jstor-112510/mode/2up?view=theat... [2] https://www.youtube.com/watch?v=A7wHSr6GRnc https://www.youtube.com/watch?v=A7wHSr6GRnc
- dwattttt 2y ago
  I thought so too, and I thought "this is just robust control with different words", but after reading the abstract I don't think robust control actually describes deriving an improvement from perturbing an input. On the other hand, "persistence of excitation" (a phrase I've heard of but never applied) suggests this too is well trodden ground (Wikipedia suggests end of 70s & 80s)
  - Animats 2y ago
    > I don't think robust control actually describes deriving an improvement from perturbing an input. Not really. But using a step input to get info to tune a control system is well known. Eurotherm's auto-tuning system for temperature control was one of the first commercial products to self-tune PID loops that way. It started by setting the control value to 0 and listening to the sensors for a while to get data on sensor noise. Then it set the control value to some large value and watched the sensed value ramp up, being careful not to overshoot the goal. This provided enough data to tune the controller. Simple, but practical. The paper is much more general, but doesn't cover how to do much. One of the references, the one on traffic control, is more interesting.[1] It's about traffic signal control in the presence of disruption. They only did some simulated experiments on one road setup, though. It's hard to tell if that actually works, but it's a reasonable idea with some data behind it. [1] https://arxiv.org/pdf/2210.10460 https://arxiv.org/pdf/2210.10460
- _yb2s 2y ago
  I am not an expert on control theory, but I don't see how what you quoted is really the same concept as antifragility. A control system can compensate for disturbances, and may even perform better with some types of disturbances but that is just 'robustness' and isn't antifragility - where the system is progressively improved in a lasting way by stressors over time, like a person getting better at a sport by repeatedly training for it.
BOOSTERHIDROGEN 2y ago
Interesting connection can you elaborate more about ideal stoic which part of the philosophy that translate to which math concept.
- _yb2s 2y ago
  Here is a quote from Marcus Aurelius which captures the same key concept as antifragility: “The impediment to action advances action, what stands in the way becomes the way.” What he is getting at here is that adapting to and overcoming challenges improves your skills, and opens up new ideas and possibilities. The stoics believe that if life goes smoothly and easily, it is actively harmful, and that hardship is required for personal growth. The core idea of antifragility (which Taleb rigorously defines as a math/engineering principle in his papers) is also that a certain type of system that responds to a stressor in a specific way, can be progressively improved in a lasting way by experiencing that stressor, and conversely, harmed by not experiencing it. For example, an astronaut that spends time in zero gravity loses muscle mass and can lose the ability to walk, whereas a person doing heavy strength training on earth could train themselves strong enough to stand and walk while holding many times their bodyweight. A more subtle aspect of this for the stoics would be where someone creatively turns a hardship into a unique opportunity. Think someone that loses their job because of a neurodevelopmental disorder, but then ends up studying ways to manage the disorder, and becomes a bestselling author sharing what they learned.

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

by _yb2s 2y ago

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=theater https://archive.org/details/jstor-112510/mode/2up?view=theat... [2] https://www.youtube.com/watch?v=A7wHSr6GRnc https://www.youtube.com/watch?v=A7wHSr6GRnc

dwattttt 2y ago
I thought so too, and I thought "this is just robust control with different words", but after reading the abstract I don't think robust control actually describes deriving an improvement from perturbing an input. On the other hand, "persistence of excitation" (a phrase I've heard of but never applied) suggests this too is well trodden ground (Wikipedia suggests end of 70s & 80s)
- Animats 2y ago
  > I don't think robust control actually describes deriving an improvement from perturbing an input. Not really. But using a step input to get info to tune a control system is well known. Eurotherm's auto-tuning system for temperature control was one of the first commercial products to self-tune PID loops that way. It started by setting the control value to 0 and listening to the sensors for a while to get data on sensor noise. Then it set the control value to some large value and watched the sensed value ramp up, being careful not to overshoot the goal. This provided enough data to tune the controller. Simple, but practical. The paper is much more general, but doesn't cover how to do much. One of the references, the one on traffic control, is more interesting.[1] It's about traffic signal control in the presence of disruption. They only did some simulated experiments on one road setup, though. It's hard to tell if that actually works, but it's a reasonable idea with some data behind it. [1] https://arxiv.org/pdf/2210.10460 https://arxiv.org/pdf/2210.10460
_yb2s 2y ago
I am not an expert on control theory, but I don't see how what you quoted is really the same concept as antifragility. A control system can compensate for disturbances, and may even perform better with some types of disturbances but that is just 'robustness' and isn't antifragility - where the system is progressively improved in a lasting way by stressors over time, like a person getting better at a sport by repeatedly training for it.

BOOSTERHIDROGEN 2y ago

Interesting connection can you elaborate more about ideal stoic which part of the philosophy that translate to which math concept.

_yb2s 2y ago
Here is a quote from Marcus Aurelius which captures the same key concept as antifragility: “The impediment to action advances action, what stands in the way becomes the way.” What he is getting at here is that adapting to and overcoming challenges improves your skills, and opens up new ideas and possibilities. The stoics believe that if life goes smoothly and easily, it is actively harmful, and that hardship is required for personal growth. The core idea of antifragility (which Taleb rigorously defines as a math/engineering principle in his papers) is also that a certain type of system that responds to a stressor in a specific way, can be progressively improved in a lasting way by experiencing that stressor, and conversely, harmed by not experiencing it. For example, an astronaut that spends time in zero gravity loses muscle mass and can lose the ability to walk, whereas a person doing heavy strength training on earth could train themselves strong enough to stand and walk while holding many times their bodyweight. A more subtle aspect of this for the stoics would be where someone creatively turns a hardship into a unique opportunity. Think someone that loses their job because of a neurodevelopmental disorder, but then ends up studying ways to manage the disorder, and becomes a bestselling author sharing what they learned.