Math is beautiful and fractals are among the most elegant objects in all of mathematics. I have to admit that I am a bit obsessed with them. For those who are interested in learning more about fractals … this Ted Talk from 2007 by Ron Eglash offers both a useful overview and an application to African design.
Albert-László Barabási, in his usual creative fashion, has produced an interesting game to help publicize his new book, Bursts: The Hidden Pattern Behind Everything We Do.
Read their description of the game below and check it out if you’re interested!
BuRSTS is a performance in human dynamics, a game of cooperation and prediction, that will gradually unveil the full text of Bursts. In a nutshell, if you register at http://brsts.com, you will be able to adopt one of the 84,245 words of the book. Once you adopt, the words adopted by others will become visible to you — thus as each words finds a parent, the whole book will become visible to the adopters. But if you invite your friends (and please do!) and you are good at predicting hidden content, the book will unveil itself to you well before all words are adopted. We will even send each day free signed copied of Bursts to those with the best scores.
April 15th is Tax Day! Unless you’ve filed for an extension or you’re a corporation on your own fiscal year, you’ve hopefully finished your taxes by now!
While you were filing your return, you may have noticed references to the Internal Revenue Code (IRC). The IRC, also known as Title 26, is legal slang for the “Tax Code.” Along with the Treasury Regulations compiled into the Code of Federal Regulations (26 C.F.R.), the Internal Revenue Code contains many of the rules and regulations governing how we can and can’t file our taxes. Even if you prepared your taxes using software like TurboTax, the questions generated by these programs are determined by the rules and regulations within the Tax Code and Treasury Regulations.
Many argue that there are too many of these rules and regulations or that these rules and regulations are too complex. Furthermore, many also claim that the “Tax Code” is becoming larger or more complex over time. Unfortunately, most individuals do not support this claim with solid data. When they do, they often rely on either the number of pages in Title 26 or the CCH Standard Federal Tax Reporter. None of these measures take into consideration the real complexity of the Code, however.
In honor of Tax Day, we’re going to highlight a recent paper that we’ve written that tries to address some of these issues – A Mathematical Approach to the Study of the United States Code. The first point to make is that this paper is a study of the entire United States Code. Title 26, the Tax Code, is actually only one small part of the set of rules and regulations defined in the United States Code. The United States Code as a whole is the largest and arguably most important source of Federal statutory law. Compiled from the legislation and treaties published in the Statutes at Large in 6-year intervals, the entire document contains over 22 million words.
In this paper, we develop a mathematical approach to the study of the large bodies of statutory law and in particular, the United States Code. This approach can be summarized as guided by a representation of the Code as an object with three primary parts:
Given this representation, we then calculate a number of properties for the United States Code in 2008, 2009, and 2010 as provided by the Legal Information Institute at the Cornell University Law School. Our results can be summarized in three points:
The figure above is an actual image of the structure and interdependence of the United States Code. The black lines correspond to structure and the red lines correspond to interdependence. Though visually stunning, the true implication of this figure is that the United States Code is a very interdependent set of rules and regulations, both within and across concept categories.
If you’re interested in more detail, make sure to read the paper –A Mathematical Approach to the Study of the United States Code. If you’re really interested, make sure to check back in the near future for our forthcoming paper entitled Measuring the Complexity of the United States Code.
From the abstract: “How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate.”
This weekend we participated in the Society for Evolutionary Analysis in Law (SEAL) annual meeting at William & Mary Law School. For those not already familiar, SEAL is devoted to the integration of the life sciences and social sciences into legal scholarship and teaching. Relevant topics include but are not limited to evolutionary and behavioral biology, cognitive science, complex adaptive systems, economics, evolutionary psychology, primatology, etc. SEAL boasts over 400 members from 30 countries — including the 2009 Economics Nobelist Elinor Ostrom. Anyway, this weekend witnessed a very interesting and exciting set of presentations …. we are looking forward to more great presentations at SEAL 12.
Above is a link to a new release highlighting Constantinos Daskalakis and his important work. Together with Paul Goldberg and Christos Papadimitriou, Constantinos received the Game Theory and Computer Science Prize for his paper “The Complexity of Computing a Nash Equilibrium.” The prize is awarded once every four years at the World Congress of the Game Theory Society. A shorter and simpler version of the paper is available here.
The question of what computer science can teach social science disciplines such as economics is a constant discussion here at Michigan CSCS. I would say the consensus is that there exists real opportunities for meaningful cross-fertilization. For example, take the results presented in this paper. Now, consider a group of agents/players with ranges of different cognitive limitations and information sets playing all types of different games on a multi-dimensional graphs …. now imagine we did not assume the system in question had a fixed point attractor. Rather, assume we allowed for the possibility of a limit cycle attractor or even a strange attractor. Under such conditions, the richness of the problem might encourage one to put aside their pencil and paper and consider what computation might be able to bring to the problem ….
From the LOC Website … “The Law Library of Congress began harvesting legal blawgs in 2007. The collection has grown to more than one hundred items covering a broad cross section of legal topics. Blawgs can also be retrieved by keywords or browsed by subject, name, or title.” To access our visualization of the legal blogosphere (pictured above) … please click here.
I have to admit that I got totally suckered by this April fools day post over at the Faculty Lounge. I did not carefully read all of the supporting details. So, (a) kudos for them for this great prank and (b) shame on me for skimming!
So I have been mulling it over a little bit … and although it was pitched as a joke … the MIT School of Law sounds like very interesting idea …
I guess part of why I was so willing to believe this post is because, in my estimation, it represented a good assessment of the state of the market for legal education. Namely, MIT School of Law seems like a plausible effort to capture and arguably better serve one particular subset of the market.
We live in the petabyte era and the impacts of the era of ‘big data’ are already remaking many sectors of the economy. It cannot be too long until the scope of available information fundamentally alters the market for legal services. Specifically, in terms of leveraging information technology to improve the quality and efficiency of legal services … my bet is on someone with an interest in attending the MIT Law School.
So, I know what you might be thinking… Isn’t it the case that lots of institutions offer courses and programs that would generally parallel those offered by MIT Law School? Well, yes.
However, I believe that an MIT law school would arguably differ from existing offerings in two important ways:
(1) Given a selective pool of students with prior technical training … the emphasis upon science and technology, etc. could be much more extensive. Indeed, one could imagine a legal curriculum that strongly emphasized science, technology, statistical training, mathematical and computational modeling, etc. There is a growing market for lawyers with this class of skills (but those jobs are currently in non-traditional places).
(2) Like in many other fields, a non-trivial amount of the substantive education is generated through peer-to-peer interaction outside of the classroom. A culture that was exclusively or nearly exclusively devoted to the integration of law, technology, applied math, computer science as well as the social and physical sciences could arguably do a better job of nurturing the development of a particular subset of the broader law student population.
I want to make sure it is clear that this post is not a general affront to state of American legal education. There are some serious issues in American legal education but I will leave this broader reform question to more qualified folks. Instead, this post is related to better serving a narrow slice of the market (i.e. law students with particular class of prior technical training).
Anyway, while this is probably not likely to come to pass … I still thought the idea was worthy of some sort of brief sketch … I mean if one thinks UC-Irvine has stormed the scene … seriously, think about what a MIT law school might be able to do!
Tomorow is the Law.gov meeting at Colorado Law School. I am looking forward to it. Thanks to Paul Ohm and Carl Malamud for organizing the event. I know that we will have a very meaningful discussion! For those interested, click on the image above and you will be directed to the agenda for the meeting.
The United States Supreme Court has recently launched its newly redesigned website. Given the significant limitations associated with the prior website, this launch had been highly anticipated. Indeed, many had hoped for a website that would reflect well upon the Court. While we applaud the decision to move away from the prior design, a review of the Court’s new website reveals a product which still falls far below the mark.
One of the very disappointing aspects of the new interface is that it appears to have been created with little regard for the overtures offered by folks such as the Sunlight Foundation. Specifically, in an effort to improve the experience of end users, the Sunlight Foundation offered a very constructive mockup redesign for the website. Unfortunately, the current redesign does not reflect most of their ideas.
For those interested in additional thoughts on this matter, the good folks over at Law Librarian Blog offer a number of constructive suggestions for improvements. These include unlocking PDF documents by simultaneously making their content available in friendly formats such as XML / HTML. Anyway, we hope that this is merely one step in the direction of genuine improvement …. but given the current state of affairs … the path to a 21st century website for the United States Supreme Court looks to be quite long.
