# (Roughly) Daily

## “Games are a compromise between intimacy and keeping intimacy away”*…

… Maybe, as Greg Costikyan explains, none more so than Rochambeau (or “Rock-Paper-Scissors” as it’s also known)…

Unless you have lived in a Skinner box from an early age, you know that the outcome of tic-tac-toe is utterly certain. At first glance, rock-paper-scissors appears almost as bad. A four-year-old might think there’s some strategy to it, but isn’t it basically random?

Indeed, people often turn to rock-paper-scissors as a way of making random, arbitrary decisions — choosing who’ll buy the first round of drinks, say. Yet there is no quantum-uncertainty collapse, no tumble of a die, no random number generator here; both players make a choice. Surely this is wholly nonrandom?

All right, nonrandom it is, but perhaps it’s arbitrary? There’s no predictable or even statistically calculable way of figuring out what an opponent will do next, so that one choice is as good as another, and outcomes will be distributed randomly over time — one-third in victory for one player, one-third to the opponent, one-third in a tie. Yes? Players quickly learn that this is a guessing game and that your goal is to build a mental model of your opponent, to try to predict his actions. Yet a naïve player, once having realized this, will often conclude that the game is still arbitrary; you get into a sort of infinite loop. If he thinks such-and-so, then I should do this-and-that; but, on the other hand, if he can predict that I will reason thusly, he will instead do the-other-thing, so my response should be something else; but if we go for a third loop — assuming he can reason through the two loops I just did — then . . . and so on, ad infinitum. So it is back to being a purely arbitrary game. No?

No…

Read on for an explanation in this excerpt from veteran game designer Greg Costikyan’s book Uncertainty in Games: “The Psychological Depths of Rock-Paper-Scissors,” from @mitpress.

* Eric Berne

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As we play, we might send carefully-plotted birthday greetings to Vilfredo Pareto; he was born on this date in 1848. An engineer, mathematician, sociologist, economist, political scientist, and philosopher, he made significant contributions to math and sociology. But he is best remembered for his work in economics and socioeconomics– particularly in the study of income distribution, in the analysis of individuals’ choices, and in his studies of societies, in which he popularized the use of the term “elite” in social analysis.

He introduced the concept of Pareto efficiency (zero-sum situations in which no action or allocation is available that makes one individual better off without making another worse off) and helped develop the field of microeconomics. He was also the first to discover that income follows a Pareto distribution, which is a power law probability distribution. The Pareto principle ( the “80-20 rule”) was built on his observations that 80% of the wealth in Italy belonged to about 20% of the population.

source

Written by (Roughly) Daily

July 15, 2023 at 1:00 am

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## “If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one”*…

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history.

Mathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was both consistent — never leading to contradictions — and complete, serving as the building blocks of all mathematical truths.

But Gödel’s shocking incompleteness theorems, published when he was just 25, crushed that dream. He proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency.

His incompleteness theorems meant there can be no mathematical theory of everything, no unification of what’s provable and what’s true. What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring.

In the 89 years since Gödel’s discovery, mathematicians have stumbled upon just the kinds of unanswerable questions his theorems foretold. For example, Gödel himself helped establish that the continuum hypothesis, which concerns the sizes of infinity, is undecidable, as is the halting problem, which asks whether a computer program fed with a random input will run forever or eventually halt. Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but — in some ill-understood way — reality…

A (relatively) simple explanation of the incompleteness theorem– which destroyed the search for a mathematical theory of everything: “How Gödel’s Proof Works.”

* John D. Barrow, The Artful Universe

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As we noodle on the unknowable, we might spare a thought for Vilfredo Federico Damaso Pareto; he died on this date in 1923.  An engineer, sociologist, economist, political scientist, and philosopher, he made several important contributions to economics, sociology, and mathematics.

He introduced the concept of Pareto efficiency and helped develop the field of microeconomics.  He was also the first to discover that income follows a Pareto distribution, which is a power law probability distribution.  The Pareto principle,  named after him, generalized on his observations on wealth distribution to suggest that, in most systems/settings, 80% of the effects come from 20% of the causes– the “80-20 rule.” He was also responsible for popularizing the use of the term “elite” in social analysis.

As Benoit Mandelbrot and Richard L. Hudson observed, “His legacy as an economist was profound. Partly because of him, the field evolved from a branch of moral philosophy as practised by Adam Smith into a data intensive field of scientific research and mathematical equations.”

The future leader of Italian fascism Benito Mussolini, in 1904, when he was a young student, attended some of Pareto’s lectures at the University of Lausanne.  It has been argued that Mussolini’s move away from socialism towards a form of “elitism” may be attributed to Pareto’s ideas.

Mandelbrot summarized Pareto’s notions as follows:

At the bottom of the Wealth curve, he wrote, Men and Women starve and children die young. In the broad middle of the curve all is turmoil and motion: people rising and falling, climbing by talent or luck and falling by alcoholism, tuberculosis and other kinds of unfitness. At the very top sit the elite of the elite, who control wealth and power for a time – until they are unseated through revolution or upheaval by a new aristocratic class. There is no progress in human history. Democracy is a fraud. Human nature is primitive, emotional, unyielding. The smarter, abler, stronger, and shrewder take the lion’s share. The weak starve, lest society become degenerate: One can, Pareto wrote, ‘compare the social body to the human body, which will promptly perish if prevented from eliminating toxins.’ Inflammatory stuff – and it burned Pareto’s reputation… [source]

Written by (Roughly) Daily

August 20, 2020 at 1:01 am

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