A Society based on the Letter of the Law

Quoting Russian writer Aleksandr Isayevich Solzhenitsyn (b. 1918):

I have spent all my life under a Communist regime and I will tell you that a society without any objective legal scale is a terrible one indeed. But a society based on the letter of the law and never reaching any higher fails to take full advantage of the full range of human possibilities.

The letter of the law is too cold and formal to have a beneficial influence on society. Whenever the tissue of life is woven of legalistic relationships, this creates an atmosphere of spiritual mediocrity that paralyzes man’s noblest impulses.

This passage was taken from A World Split Apart, the commencement address delivered by Solzhenitsyn at Harvard University on June 8, 1978. I urge you to read it. It’s really worth it.

Solzhenitsyn was awarded the Nobel Prize in Literature in 1970. He was exiled from the Soviet Union in 1974. In 1994, he returned to Russia with his wife, Natalia.

Gödel, Escher, Bach: A Mental Space Odyssey

One of the books that I have been planning to read for a long time is Douglas Hofstadter’s Pulitzer Prize-winning Gödel, Escher, Bach: an Eternal Golden Braid (GEB), a book which is powerful enough to change the lives of those who read it (those are the good books!) and beautiful enough to be itself a work of art.

Recently, my friend Shubhendu Trivedi informed me that there was a Summer course at MIT based on the GEB book. This course was named Gödel, Escher, Bach: A Mental Space Odyssey.

[ image courtesy of Justin Curry and Curran Kelleher ]

The course’s lecture notes and video lectures are available online thanks to the awesome MIT OCW program. An excerpt of the course’s description:

What do one mathematician, one artist, and one musician all have in common? Are you interested in zen Buddhism, math, fractals, logic, paradoxes, infinities, art, language, computer science, physics, music, intelligence, consciousness and unified theories? Get ready to chase me down a rabbit hole into Douglas Hofstadter’s Pulitzer Prize winning book Gödel, Escher, Bach. Lectures will be a place for crazy ideas to bounce around as we try to pace our way through this enlightening tome.

I have been watching the video lectures. Quite interesting indeed. They discuss isomorphisms, recursion, paradoxes, infinity, logic, formal systems, fractals, and how self-reference and formal rules allow systems to acquire meaning despite being made of “meaningless” elements. I must warn you that the course’s material is not easy to absorb (that is what makes it so interesting).

The Creativity Machine

[ image courtesy of Imagination Engines Inc. ]

Stephen Thaler founded a company named Imagination Engines Inc. to explore the possibilities of the Creativity Machine, a “thinking” machine based on artificial neural networks. If the machine works the way Thaler describes it, it’s indeed a beautiful, ingenious idea.

Here’s a documentary on the Creativity Machine:

The Patriot Missile Failure

In February 2003, shortly before the Gulf War II started, I found a very interesting article explaining what went wrong with the Patriot Missile Defense System on February 25, 1991, during Gulf War I. The failure was caused by bad numerical computing, which led to a catastrophic accumulation of round-off errors and, consequently, to a failed interception.

[ PAC-3 missile - image courtesy of Boeing ]

The Patriot missile battery at Dhahran (in Saudi Arabia) had been in operation for around 100 hours, and after such a long time the system’s internal clock had already drifted approximately 0.34 seconds. Given that a tactical ballistic missile such as the Scud is a very fast moving target (approx. 1600 m/s), a timing error of “only” 0.34 seconds was equivalent to a position error of approximately 600 meters. No wonder the Patriot missile failed to intercept the target.

Nothing is more vexing than…

A really wonderful passage from Fyodor Dostoevsky’s “The Idiot“:

Indeed, nothing is more vexing than to be, for instance, wealthy, of good family, passable in looks, fairly well educated and intelligent, and even kindly, and yet to possess no talent, no outstanding feature or even quirk, not a single idea of one’s own, and to be positively “just like anybody else”.

There is wealth, but far less than the Rothschilds possess; the family is an honorable one, but has never won the least distinction; one’s looks are pleasant enough, but express nothing in particular; one’s education is quite sound, but one has no idea of what to direct it towards; one has intelligence but no ideas of one’s own; one has a kind heart but no magnanimity, and so and so forth, on all counts. There is a vast multitude of such people in the world, and even far more than may seem. Like all other people, they fall into two categories: those of limited intelligence, and those that are “far cleverer than most”. The former are the happier.

I came across this passage on David Siska’s blog. Thanks to David for letting me know from which book the passage was taken.

Possily related:

• Satisfying one’s curiosity

The Purpose of Computing

Quoting U.S. mathematician Richard Hamming (1915-1998):

The purpose of computing is insight, not numbers.

I totally agree. It might shock some purists, but I find numerical computing extremely useful to prove that a given conjecture is false. Proving analytically that a conjecture is true / false is much, much harder than proving that it is false via numerical computing. That is Experimental Mathematics. Yes, Mathematics can also be an experimental science!

 

The Hungarian System

Quoting renowned U.S. computer scientist Donald Knuth (b. 1938):

The Hungarian educational system has been the most successful in pure mathematics.

The other day I was chatting with a friend who’s a grad student in Computer Science at the Univ. of Chicago, and we were commenting how intriguing it is that Hungarians seem to dominate Discrete Mathematics. Graph Theory and Combinatorics, especially. Paul Erdős (1913-1996) and Alfréd Rényi (1921-1970) were prime examples of such dominance.

And let’s not forget John von Neumann (1903-1957) who many believe to have been the most intelligent being who ever lived on this planet. The examples are abundant: George Pólya (1887–1985), László Kalmár (1905-1976), John George Kemeny (1926-1992), Endre Szemerédi (b. 1940), Béla Bollobás (b. 1943), László Babai (b. 1950), Éva Tardos (b. 1957), etc. Hungary even has an algorithm named after itself: the Hungarian Algorithm.

Some papers on Hungarian Mathematics:

• The Emergence of Modern Number Theory in Hungary (by Michael Coons)

• A Panorama of Hungarian Mathematics in the Twentieth Century: Non-Commutative Harmonic Analysis (by Jonathan Rosenberg)

• Some Facts and Tendencies in Hungarian Mathematics Teaching (by Tibor Szalontai)

• The Social Construction of Hungarian Genius (by Tibor Frank)

And if we think of Physics, it’s easy to recall a few more Hungarians: Theodore von Kármán (1881-1963), Cornelius Lanczos (1893-1974), Paul Nemenyi (1895-1952), Leó Szilárd (1898-1964), Eugene Wigner (1902-1995), Edward Teller (1908-2003), Albert-László Barabási (b. 1967), among many others.

There’s a “legend” about the Hungarians working in the Manhattan Project: it seems that sometimes, small teams of physicists would gather to brainstorm… and then they would realize that they were all Hungarian, so they would start speaking Magyar instead of English. That might be an urban myth, but there’s strong evidence that it may have happened a few times.

Rudolph Kalman (b. 1930) is Hungarian too. Ernő Rubik (b. 1944), the inventor of the famous cube that bears his name, is also Hungarian. The inventor of the modern ballpoint pen, László Bíró (1899-1985), was Hungarian.

For such a small country, Hungary has indeed contributed enormously to the advancement of Science and Technology. And Hungary contributed also in the artistic arena. Think Franz Liszt (1811-1886) and Béla Bartók (1881-1945).

Long live Magyarország

Related:

• John von Neumann: 104th birthday (by Luboš Motl)

• Von Neumann Memorial Lectures

• Interview with Eugene Wigner

I love Python

I recently started to learn Python, and I must admit that I really love it! Python is powerful yet readable, it has a clear syntax, it’s versatile… and quite sexy. While some other programming languages seem to have been developed by hardware engineers, Python seems to have been developed by mathematicians / computer scientists.

When coding in some other languages, I feel somewhat like a “slave” of that language. When coding in Python, I have the impression that I am unbeatable, and that I can solve any small-sized problem with only a few lines of beautiful code. I also feel that if I can’t solve a small-sized problem with a few lines of Python code, then I have no-one to blame but myself…

… in fact, this feeling must be kind of similar to what the US Air Force F-4 Phantom pilots experienced when they switched from the F-4 to the F-15 Eagle in the 1970s. They must have felt invincible. They could go over Mach 2, they could accelerate while flying up vertically, they could pull tight high-G turns, etc. It’s a whole new world full of possibilities.

Algorithmic Game Theory

I have been reading Algorithmic Game Theory, a great book edited by Noam Nisan, Tim Roughgarden, Éva Tardos, and Vijay Vazirani. A non-printable version of the book can be downloaded here (PDF - 5.17 MB).

[ image courtesy of Éva Tardos, and Vijay Vazirani ]

Prior to reading this book, my knowledge of Game Theory was pretty much non-existent. Now, at least I know a tiny, tiny bit on the subject. I am somewhat intrigued by the fact that even very simple two-player strategic games can be so hard to analyze. Moreover, Nash equilibria are sometimes quite hard to find.

I have also been playing around with Gambit, a library of game theory software and tools for the construction and analysis of finite extensive and strategic games. When analyzing two-player strategic games in which each player has a lot of strategies to choose from, Gambit is quite helpful and fun to use.

Some papers on the computation of equilibria:

• Computation of Equilibria in Finite Games (by Richard McKelvey, Andrew McLennan)

• Computing Equilibria for Two Person Games (by Bernhard von Stengel)

• Computing Equilibria in Multi-Player Games (by Christos Papadimitriou, Tim Roughgarden)

• Smoothing techniques for computing Nash equilibria of sequential games (by Samid Hoda, Andrew Gilpin, Javier Pena)

Some papers on graphical games:

• Game Networks (by Pierfrancesco La Mura)

• Graphical Models for Game Theory (by Michael Kearns, et alia)

• Correlated equilibria and graphical games (by Sham Kakade et alia)

• Nash propagation for loopy graphical games (by Luis E. Ortiz, Michael Kearns)

• An Efficient Exact Algorithm for Singly Connected Graphical Games (by Michael L. Littman, Michael Kearns, Satinder Singh)

• Multi-Agent Algorithms for Solving Graphical Games (by David Vickrey, Daphne Koller)

Some courses on Algorithmic Game Theory:

• Algorithmic Game Theory (Cornell CS 684)

• Computational Game Theory (UPenn CIS 620)

• Seminar on Algorithmic Aspects of Game Theory (Berkeley CS 294)

• Topics in Algorithmic Game Theory (Caltech CS/SS 241a)

• Game Theory with Engineering Applications (MIT 6.254)

Some interesting PhD theses:

• Selfish Routing (by Tim Roughgarden, 2002)

• Non-cooperative Games (by John Nash, 1950)

Last but not least, some non-technical articles:

• The Complexity of Competition (by Prof. Christos Papadimitriou)

• The Network Game (by Prof. Asuman Ozdaglar)

New Ideas

Quoting influential science fiction writer, inventor and futurist Sir Arthur C. Clarke (1917-2008):

New ideas pass through three periods: 1) It can’t be done. 2) It probably can be done, but it’s not worth doing. 3) I knew it was a good idea all along!

Sir Arthur C. Clarke passed away in Sri Lanka on March 19, 2008.