Sichelman on The Mathematical Structure of the Law @tedsichelman @USanDiegoLaw

Ted M. Sichelman, University of San Diego School of Law, has published The Mathematical Structure of the Law. Here is the abstract.

Scientific “law” and human-made law (“social law”) are both “laws” in a very general sense—scientific laws “govern” the workings of the material world and social laws govern the behavior of people. Beyond this superficial resemblance, do social laws partake of the same sorts of mathematical structures as scientific laws? Many theorists have proposed formal deontic-oriented logical models of legal rights and other entitlements. Here, leveraging the formalism of Wesley Hohfeld and related work, this article proposes a novel, mathematical model of legal entitlements. This model allows for physical and mathematical properties—such as entropy, indeterminacy, temperature, and modularity—to be adapted to provide for quantitative measures of the properties of legal systems. Moreover, previous logical models exhibit an important feature: if all relevant information is known, legal actors hold determinate sets of legal entitlements. Although theorists have modeled legal entitlements under conditions of incomplete information, which can effectively lead to indeterminacy, this article proposes a model in which—even with complete information—legal entitlements can exhibit indeterminacy. Unlike classical indeterminacy, which is of a stochastic nature, this sort of “inherent” indeterminacy is akin to—and can be readily modeled by—the notion of “indeterminacy” in quantum mechanical formalism. These results have important implications for the nature of legal rules, legal artificial intelligence, game theory and the law, and the ontology of rule-based systems more generally. Of particular note, the formalism suggests a novel approach to the quantum measurement problem, which proposes that measurement is a “second-order” physical process—fundamentally different from ordinary, “first-order” physical processes.

Download the article from SSRN at the link.

Mathematics, Crime, and Los Angeles

Inside Higher Ed notes the publication of  L. A. Math: Romance, Math, and Crime in the City of Angels (Princeton University Press, 2016)  a book by James A. Stein, is a collection of short stories which combines, well, romance, math, and crime. Here's a description of the contents.

Move over, Sherlock and Watson—the detective duo to be reckoned with. In the entertaining short-story collection L.A. Math, freelance investigator Freddy Carmichael and his sidekick, Pete Lennox, show how math smarts can crack even the most perplexing cases. Freddy meets colorful personalities throughout Los Angeles and encounters mysterious circumstances from embezzlement and robbery to murder. In each story, Freddy’s deductive instincts—and Pete's trusty math skills—solve the crime.
Featuring such glamorous locales as Beverly Hills, Brentwood, Malibu, and Santa Barbara, the fourteen short stories in L.A. Math take Freddy and Pete through various puzzles and challenges. In "A Change of Scene," Freddy has to figure out who is selling corporate secrets to a competitor—so he uses mathematical logic to uncover the culprit. In "The Winning Streak," conditional probability turns the tables on an unscrupulous bookie. And in "Message from a Corpse," the murderer of a wealthy widow is revealed through the rules of compound interest. It’s everything you expect from the City of Angels—A-listers and wannabes, lovers and lawyers, heroes and villains. Readers will not only be entertained, but also gain practical mathematics knowledge, ranging from percentages and probability to set theory, statistics, and the mathematics of elections. For those who want to delve into mathematical subjects further, the book includes a supplementary section with more material.

Filled with intriguing stories, L.A. Math is a treat for lovers of romance, crime, or mathematics.

So, the premise is that math can be fun? Ok, I'll bite.

 

Pi Day!

It's Pi Day! March 13 (3/14) is celebrated around the world as the day for venerating the mathematical ratio of a circle's diameter to its circumference. Remember that nugget from your early education? It's (sort of) 3.14 (if you want to calculate it yourself, see some methods here). While various organizations suggest ways to honor the irrational number, including baking Pi pies, there is at least one law and humanities link to Pi.

Now, I have heard at least two different stories purporting to be the truth here (some suggesting that the Indiana legislature was involved and some that it was the Kentucky legislature that tried to redefine the value of Pi). Here's what I have tracked down. In 1897, an Indiana physician and amateur (really amateur) mathetician named Edward J. Goodwin thought he had succeeded in squaring the circle and also demonstrated that the value of Pi was actually effectively 3.2. Now, squaring the circle is a mathematical impossibility, as Ferdinand von Lindemann showed in 1882. However, Dr. Goodwin thought he had done it, and copyrighted his proof. Further, he really wanted children to be educated to understand his great discovery (despite his desire to collect royalties on his proof), so he decided that he would ask the state of Indiana to accept the truth of his discovery. Thus, the state wouldn't have to pay royalties, which would probably have been prohibitive.

He got the attention of some Indiana legislators who introduced House Bill 246 (the Indiana Pi Bill)  during the 1897 session. Then the fun began. The debate on the floor over the advisibility of accepting a set value for Pi got national attention. It also caught the attention of a math professor, Clarence Abiathar Waldo, at Purdue University, who proceeded to educate some of the members of the Indiana Senate on the basics of math, which they seemed to have forgotten. They were successful in putting off a vote on the bill, enthusiasm for it faded away, and as a result, Pi in Indiana does not have an official value of 3.2.

More here from Mental Floss Magazine, here from a personal page by Mark Brader at the University of Michigan.  Read the text of the bill here.