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August 6th, 2017

This is the fourth and final book in Nassim Taleb's Incerto series, which makes a case for antifragility as a key component of design, taking the art of design one step beyond robustness. An antifragile system is one where variation, chaos, stress, and errors improve the results. For example, within limits, stressing muscles and bones makes them stronger. In contrast, stressing a device made of (say) aluminum will eventually cause it to fail. Taleb gives a lengthy list of examples in Table 1 starting on page 23, some of which seem more plausible than others. An example implausible entry lists rule-based systems as fragile, principles-based systems as robust, and virtue-based systems as antifragile. Although I can imagine a viewpoint where this makes sense, any expectation that a significantly large swath of present-day society will agree on a set of principles (never mind virtues!) seems insanely optimistic. The table nevertheless provides much good food for thought.

Taleb states that he has constructed antifragile financial strategies using insurance to control downside risks. But he also states on page 6 “Thou shalt not have antifragility at the expense of the fragility of others.” Perhaps Taleb figures that few will shed tears for any difficulties that insurance companies might get into, perhaps he is taking out policies that are too small to have material effect on the insurance company in question, or perhaps his policies are counter to the insurance company's main business, so that payouts to Taleb are anticorrelated with payouts to the company's other customers. One presumes that he has thought this through carefully, because a bankrupt insurance company might not be all that effective at controlling his downside risks.

Appendix I beginning on page 435 gives a graphical summary of the books main messages. Figure 28 on page 441 is good grist for the mills of those who would like humanity to become an intergalactic species: After all, confining the human race seems likely to limit its upside. (One counterargument would posit that a finite object might have unbounded value, but such counterarguments typically rely on there being a very large number of human beings interested in that finite object, which some would consider to counter this counterargument.)

The right-hand portion of Figure 30 on page 442 illustrates what the author calls local antifragility and global fragility. To see this, imagine that the x-axis represents variation from nominal conditions, and the y-axis represents payoff, with large positive payoffs being highly desired. The right-hand portion shows something not unrelated to the function x^2-x^4, which gives higher payoffs as you move in either direction from x=0, peaking when x reaches one divided by the square root of two (either positive or negative), dropping back to zero when x reaches +1 or -1, and dropping like a rock as one ventures further away from x=0. The author states that this local antifragility and global fragility is the most dangerous of all, but given that he repeatedly stresses that antifragile systems are antifragile only up to a point, this dangerous situation would seem to be the common case. Those of us who believe that life is inherently dangerous should have no problem with this apparent contradiction.

But what does all of this have to do with parallel programming???

Well, how about “Is RCU antifragile?”

One case for RCU antifragility is the batching optimizations that allow many (as in thousands) concurrent requests to share the same grace-period computation. Therefore, the heavier the update-side load on RCU, the more efficiently RCU operates.

However, load is but one of many aspects of RCU's environment that might be varied. For an extreme example, RCU is exceedingly fragile with respect to small perturbations of the program counter, as Peter Sewell so ably demonstrated, by running emacs, no less. RCU is also fragile with respect to timekeeping anomalies, for example, it can emit false-positive RCU CPU stall warnings if different CPUs have tens-of-seconds disagreements as to the current time. However, the aforementioned bones and muscles are similarly fragile with respect to any number of chemical substances (AKA “poisons”), to say nothing of well-known natural phenomena such as lightning bolts and landslides.

Even when excluding hardware misbehavior such as auto-perturbing program counters and unsynchronized clocks, RCU would still be subject to software aging, and RCU has in fact require multiple interventions from its developers and maintainer in order to keep up with changing hardware, workload, and usage. One could therefore argue that RCU is fragile with respect to perturbations of time, although the combination of RCU and its developers, reviewers, and maintainer seem to have kept up reasonably well thus far.

On the other hand, perhaps it is unrealistic to evaluate the antifragility of software without including black-hat hackers. Achieving antifragility in that sort of environment is still very much a grand challenge problem, but a challenge that must be faced. Oh, you think RCU is to low-level for this sort of attack? There was a time when I thought so. And then came rowhammer.

So please be careful, and, where possible, antifragile! It is after all a real world out there!!!