(Roughly) Daily

Posts Tagged ‘randomness

“Everything we care about lies somewhere in the middle, where pattern and randomness interlace”*…

True randomness (it’s lumpy)

We tend dramatically to underestimate the role of randomness in the world…

Arkansas was one out away from the 2018 College World Series championship, leading Oregon State in the series and 3-2 in the ninth inning of the game when Cadyn Grenier lofted a foul pop down the right-field line. Three Razorbacks converged on the ball and were in position to make a routine play on it, only to watch it fall untouched to the ground in the midst of them. Had any one of them made the play, Arkansas would have been the national champion.

Nobody did.

Given “another lifeline,” Grenier hit an RBI single to tie the game before Trevor Larnach launched a two-run homer to give the Beavers a 5-3 lead and, ultimately, the game. “As soon as you see the ball drop, you know you have another life,” Grenier said. “That’s a gift.” The Beavers accepted the gift eagerly and went on win the championship the next day as Oregon State rode freshman pitcher Kevin Abel to a 5-0 win over Arkansas in the deciding game of the series. Abel threw a complete game shutout and retired the last 20 hitters he faced.

The highly unlikely happens pretty much all the time…

We readily – routinely – underestimate the power and impact of randomness in and on our lives. In his book, The Drunkard’s Walk, Caltech physicist Leonard Mlodinow employs the idea of the “drunkard’s [random] walk” to compare “the paths molecules follow as they fly through space, incessantly bumping, and being bumped by, their sister molecules,” with “our lives, our paths from college to career, from single life to family life, from first hole of golf to eighteenth.” 

Although countless random interactions seem to cancel each another out within large data sets, sometimes, “when pure luck occasionally leads to a lopsided preponderance of hits from some particular direction…a noticeable jiggle occurs.” When that happens, we notice the unlikely directional jiggle and build a carefully concocted story around it while ignoring the many, many random, counteracting collisions.

As Tversky and Kahneman have explained, “Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not ‘corrected’ as a chance process unfolds, they are merely diluted.”

As Stephen Jay Gould famously argued, were we able to recreate the experiment of life on Earth a million different times, nothing would ever be the same, because evolution relies upon randomness. Indeed, the essence of history is contingency.

Randomness rules.

Luck matters. A lot. Yet, we tend dramatically to underestimate the role of randomness in the world.

The self-serving bias is our tendency to see the good stuff that happens as our doing (“we worked really hard and executed the game plan well”) while the bad stuff isn’t our fault (“It just wasn’t our night” or “we simply couldn’t catch a break” or “we would have won if the umpiring hadn’t been so awful”). Thus, desirable results are typically due to our skill and hard work — not luck — while lousy results are outside of our control and the offspring of being unlucky.

Two fine books undermine this outlook by (rightly) attributing a surprising amount of what happens to us — both good and bad – to luck. Michael Mauboussin’s The Success Equation seeks to untangle elements of luck and skill in sports, investing, and business. Ed Smith’s Luck considers a number of fields – international finance, war, sports, and even his own marriage – to examine how random chance influences the world around us. For example, Mauboussin describes the “paradox of skill” as follows: “As skill improves, performance becomes more consistent, and therefore luck becomes more important.” In investing, therefore (and for example), as the population of skilled investors has increased, the variation in skill has narrowed, making luck increasingly important to outcomes.

On account of the growth and development of the investment industry, John Bogle could quite consistently write his senior thesis at Princeton on the successes of active fund management and then go on to found Vanguard and become the primary developer and intellectual forefather of indexing. In other words, the ever-increasing aggregate skill (supplemented by massive computing power) of the investment world has come largely to cancel itself out.

After a big or revolutionary event, we tend to see it as having been inevitable. Such is the narrative fallacy. In this paper, ESSEC Business School’s Stoyan Sgourev notes that scholars of innovation typically focus upon the usual type of case, where incremental improvements rule the day. Sgourev moves past the typical to look at the unusual type of case, where there is a radical leap forward (equivalent to Thomas Kuhn’s paradigm shifts in science), as with Picasso and Les Demoiselles

As Sgourev carefully argued, the Paris art market of Picasso’s time had recently become receptive to the commercial possibilities of risk-taking. Thus, artistic innovation was becoming commercially viable. Breaking with the past was then being encouraged for the first time. It would soon be demanded.

Most significantly for our purposes, Sgourev’s analysis of Cubism suggests that having an exceptional idea isn’t enough. For radical innovation really to take hold, market conditions have to be right, making its success a function of luck and timing as much as genius. Note that Van Gogh — no less a genius than Picasso — never sold a painting in his lifetime.

As noted above, we all like to think that our successes are earned and that only our failures are due to luck – bad luck. But the old expression – it’s better to be lucky than good – is at least partly true. That said, it’s best to be lucky *and* good. As a consequence, in all probabilistic fields (which is nearly all of them), the best performers dwell on process and diversify their bets. You should do the same…

As [Nate] Silver emphasizes in The Signal and the Noise, we readily overestimate the degree of predictability in complex systems [and t]he experts we see in the media are much too sure of themselves (I wrote about this problem in our industry from a slightly different angle…). Much of what we attribute to skill is actually luck.

Plan accordingly.

Taking the unaccountable into account: “Randomness Rules,” from Bob Seawright (@RPSeawright), via @JVLast

[image above: source]

* James Gleick, The Information: A History, a Theory, a Flood


As we contemplate chance, we might spare a thought for Oskar Morgenstern; he died on this date in 1977. An economist who fled Nazi Germany for Princeton, he collaborated with the mathematician John von Neumann to write Theory of Games and Economic Behavior, published in 1944, which is recognized as the first book on game theory— thus co-founding the field.

Game theory was developed extensively in the 1950s, and has become widely recognized as an important tool in many fields– perhaps especially in the study of evolution. Eleven game theorists have won the economics Nobel Prize, and John Maynard Smith was awarded the Crafoord Prize for his application of evolutionary game theory.

Game theory’s roots date back (at least) to the 1654 letters between Pascal and Fermat, which (along with work by Cardano and Huygens) marked the beginning of probability theory. (See Peter Bernstein’s marvelous Against the Gods.) The application of probability (Bayes’ rule, discrete and continuous random variables, and the computation of expectations) accounts for the utility of game theory; the role of randomness (along with the behavioral psychology of a game’s participants) explain why it’s not a perfect predictor.


Written by (Roughly) Daily

July 26, 2021 at 1:00 am

“In the space between chaos and shape there was another chance”*…

Prince Hamlet spent a lot of time pondering the nature of chance and probability in William Shakespeare’s tragedy. In the famous “To be or not to be” speech, he notes that we helplessly face “the slings and arrows of outrageous fortune” — though a little earlier in the play he declares that “there’s a special providence in the fall of a sparrow,” suggesting that everything happens because God wills it to be so.

We can hardly fault the prince for holding two seemingly contradictory views about the nature of chance; after all, it is a puzzle that has vexed humankind through the ages. Why are we here? Or to give the question a slightly more modern spin, what sequence of events brought us here, and can we imagine a world in which we didn’t arrive on the scene at all?

It is to biologist Sean B. Carroll’s credit that he’s found a way of taking a puzzle that could easily fill volumes (and probably has filled volumes), and presenting it to us in a slim, non-technical, and fun little book, “A Series of Fortunate Events: Chance and the Making of the Planet, Life, and You.”

Carroll (not to be confused with physicist and writer Sean M. Carroll) gets the ball rolling with an introduction to the key concepts in probability and game theory, but quickly moves on to the issue at the heart of the book: the role of chance in evolution. Here we meet a key historical figure, the 20th-century French biochemist Jacques Monod, who won a Nobel Prize for his work on genetics. Monod understood that genetic mutations play a critical role in evolution, and he was struck by the random nature of those mutations…

Carroll quotes Monod: “Pure chance, absolutely free and blind, at the very root of the stupendous edifice of evolution: This central concept of modern biology is no longer one among other possible or even conceivable hypotheses. It is today the sole conceivable hypothesis, the only one that squares with observed and tested fact.”

“There is no scientific concept, in any of the sciences,” Monod concludes, “more destructive of anthropocentrism than this one.”

From there, it’s a short step to the realization that we humans might never have evolved in the first place…

Preview(opens in a new tab)

The profound impact of randomness in determining destiny: “The Power of Chance in Shaping Life and Evolution.”

See also: “Survival of the Luckiest.”

* Jeanette Winterson, The World and Other Places


As we blow on the dice, we might send carefully-calculated birthday greetings to Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French mathematician and physicist who is probably (if unfairly) better known as Voltaire’s mistress; she was born on this date in 1706.  Fascinated by the work of Newton and Leibniz, she dressed as a man to frequent the cafes where the scientific discussions of the time were held.  Her major work was a translation of Newton’s Principia, for which Voltaire wrote the preface; it was published a decade after her death, and was for many years the only translation of the Principia into French.

Judge me for my own merits, or lack of them, but do not look upon me as a mere appendage to this great general or that great scholar, this star that shines at the court of France or that famed author. I am in my own right a whole person, responsible to myself alone for all that I am, all that I say, all that I do. It may be that there are metaphysicians and philosophers whose learning is greater than mine, although I have not met them. Yet, they are but frail humans, too, and have their faults; so, when I add the sum total of my graces, I confess I am inferior to no one.
– Mme du Châtelet, to Frederick the Great of Prussia


“Real randomness requires an infinite amount of information”*…


If you have ever tossed dice, whether in a board game or at the gambling table, you have created random numbers—a string of numbers each of which cannot be predicted from the preceding ones. People have been making random numbers in this way for millennia. Early Greeks and Romans played games of chance by tossing the heel bone of a sheep or other animal and seeing which of its four straight sides landed uppermost. Heel bones evolved into the familiar cube-shaped dice with pips that still provide random numbers for gaming and gambling today.

But now we also have more sophisticated random number generators, the latest of which required a lab full of laser equipment at the U.S. National Institute of Standards and Technology (NIST) in Boulder, CO. It relies on counterintuitive quantum behavior with an assist from relativity theory to make random numbers. This was a notable feat because the NIST team’s numbers were absolutely guaranteed to be random, a result never before achieved.

Why are random numbers worth so much effort? Random numbers are chaotic for a good cause. They are eminently useful, and not only in gambling. Since random digits appear with equal probabilities, like heads and tails in a coin toss, they guarantee fair outcomes in lotteries, such as those to buy high-value government bonds in the United Kingdom. Precisely because they are unpredictable, they provide enhanced security for the internet and for encrypted messages. And in a nod to their gambling roots, random numbers are essential for the picturesquely named “Monte Carlo” method that can solve otherwise intractable scientific problems…

Using entanglement to generate true mathematical randomness– and why that matters: “The Quantum Random Number Generator.”

* Tristan Perich


As we leave it to chance, we might send learned birthday greetings to Athanasius Kircher; he was born on this date in 1602.  A scholar, he published over 40 works. perhaps most notably on comparative religion, geology, and medicine, but over a range so broad that he was frequently compared to Leonardo Da Vinci (who died on the date in 1519) and was dubbed “Master of a Hundred Arts.”

For a look at one of his more curious works, see “Wonder is the beginning of wisdom.” And his take on The Plague (through which he lived in Italy in 1656), see here.

220px-Athanasius_Kircher_(cropped) source

Written by (Roughly) Daily

May 2, 2020 at 8:44 am

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