For regions like the US with a mm/dd/yy calendar order today gives 3/14/15 -- the first five digits of Pi 3.1415. going a bit further you get the first ten digits - 3.141592653 - at 9:26:53.

Only one day every century has this relation. And that brings up a curious relation with Einstein whose birthday is today. In 1915 he published his paper on General Relativity. To call it remarkable is understatement of the grandest order.

There is a foundational paper published a bit earlier with an astonishing opening paragraph. A non-technical phrasing might be: “Here is my theory of the dynamics of space and time, with an introduction to its mathematical underpinnings, as well as derivations of all the previous laws of physics within this new framework.” He mentions Grossman, but that was help with the math rather than the underlying physics. I doubt we’ll ever see such a dramatic leap penned by an individual for a theory that holds up to experiment. And it has held solidly for a century!

What you need to do is celebrate. He had a sweet tooth and liked vanilla ice cream cones with chocolate sprinkles. He also had a fondness for fruit, particularly cherry, pie - so perhaps a slice of cherry pie with a scoop of ice cream is appropriate. You might throw care to the wind and add some chocolate shavings or sprinkles...

And it is a day to celebrate William Jones - the person who believed (but didn't prove) the ratio of the circumference to the diameter of a circle was irrational and should have it's own symbol.

snip

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the symbol for this ratio known today as π (pi) dates from the early 18th century. Before this the ratio had been awkwardly referred to in medieval Latin as: *quantitas in quam cum multiflicetur diameter, proveniet circumferencia* (the quantity which, when the diameter is multiplied by it, yields the circumference).

It is widely believed that the great Swiss-born mathematician Leonhard Euler (1707-83) introduced the symbol π into common use. In fact it was first used in print in its modern sense in 1706 a year before Euler's birth by a self-taught mathematics teacher William Jones (1675-1749) in his second book *Synopsis Palmariorum Matheseos*, or *A New Introduction to the Mathematics* based on his teaching notes.

Before the appearance of the symbol π, approximations such as 22/7 and 355/113 had also been used to express the ratio, which may have given the impression that it was a rational number. Though he did not prove it, Jones believed that π was an irrational number: an infinite, non-repeating sequence of digits that could never totally be expressed in numerical form. In *Synopsis* he wrote: '... the exact proportion between the diameter and the circumference can never be expressed in numbers...'. Consequently, a symbol was required to represent an ideal that can be approached but never reached. For this Jones recognised that only a pure platonic symbol would suffice.

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I have not come across any indication of Jones' dessert preferences. Then again he was Welsh. Pie in the day was likely meat filled.

## on nash's contribution to economics

A nice

New Yorkerpiece by John Cassidy on John Nash's work in economics.snip

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That’s partly because Nash-influenced game theory isn’t actually a testable scientific theory at all. It is an intellectual tool—a way of organizing our thoughts systematically, applying them in a consistent manner, and ruling out errors. Like Marshallian supply-and-demand analysis or Bayesian statistics, it can be applied to many different problems, and its utility depends on the particular context. But while appealing to the Nash criteria doesn’t necessarily give the correct answer, it often rules out a lot of implausible ones, and it usually helps pin down the logic of the situation.

For these reasons, studying game theory, and learning how to recognize a Nash equilibrium, are highly worthwhile exercises. Once you learn the basics, it is amazing how broadly they can be applied. (Much of the advanced stuff can be safely skipped.) For example, in writing a book about the economics of the financial crisis and trying to figure out why so many people on Wall Street and elsewhere did things that ultimately blew up in their faces, I relied heavily on the Prisoner’s Dilemma, a simple game involving a particular type of Nash equilibrium that shows how certain incentive schemes can promote self-destructive behavior.

My experience wasn’t out of the ordinary. These days, political scientists, evolutionary biologists, and even government regulators are obliged to grasp best-response equilibria and other aspects of game theory. Whenever a government agency is considering a new rule—a set of capital requirements for banks, say, or an environmental regulation—one of the first questions it needs to ask is whether obeying the rules leads to a Nash equilibrium. If it doesn’t, the new policy measure is likely to prove a failure, because those affected will seek a way around it.

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04:46 in General Commentary, math | Permalink | Comments (0)