Is More Sex Safe? A book review.

I was asked by the Notices of the AMS to review the book “More Sex is Safe Sex: The Unconventional Wisdom  of Econmics” by Steven E. Landsburg.  My review entitled “Economics and Common Sense”, will appeared in the June/July issue of the Notices and you can find it here. (And in the August issue of the AMS Notices, there is will be a book review by Olle Häggström on John Allen Paulos’ new book: “Irreligion”.)

In his book, Steven E. Landsburg uses the “weapons of evidence and logic, especially the logic of economics” to draw surprising insights which run against common sense. “If common sense tells you otherwise,” says Landsburg, “remember that common sense also tells you that the Earth is flat”.

I will include a few little sectionettes from the review here in this post. Some of the issues raised in this book are related to many discussions and debates we had over the years at the Center for the Study of Rationality of the Hebrew University of Jerusalem. Questions regarding “efficiency,” “subsedies,” “monopolies,” “labor union,” “differential salaries,” “law and economics,” “rationality and the judicial system,” and various other related topics were amply discussed at the Center, and some of these topics and discussions are related to issues raised in Landsburg’s book.

The Armchair Economist

Sometime after writing my review, I saw in the Yale book store, along with several copies of Landsburg’s new book, a copy of his older book from the early 90s, “The Armchair Economist”. I bought it and read some of the chapters. So before quoting excerpts from my book review on the new book let me first talk a little bit about the older book. Several chapters are devoted to describing some classic teachings of economics, such as general equilibrium theory, and they are very good. I liked Landsburg’s explanation of the notion of “efficiency” – it is the best popular explanation of “efficiency” I read or listened to.

The Peltzman Effect

Armchair Economist starts with an interesting finding from the 1970s by Sam Peltzman, a U. of Chicago economist, asserting that safety seat belts have led to an increase in the number of car accidents, and that the net effect on death from car-accidents, which is reduced by the direct effect of seat belts and other safety measures, but which at the same time is increased by the indirect effect of drivers taking more risks because of these safety measures, is close to zero. Peltzman’s study also asserts that seat belts have raised pedestrian death toll caused by accidents.

Nati’s Influence

When do we say that one event causes another? Causality is a topic of great interest in statistics, physics, philosophy, law, economics, and many other places. Now, if causality is not complicated enough, we can ask what is the influence one event has on another one.  Michael Ben-Or and Nati Linial wrote a paper in 1985 where they studied the notion of influence in the context of collective coin flipping. The title of the post refers also to Nati’s influence on my work since he got me and Jeff Kahn interested in a conjecture from this paper.

Influence

The word “influence” (dating back, according to Merriam-Webster dictionary, to the 14th century) is close to the word “fluid”.  The original definition of influence is: “an ethereal fluid held to flow from the stars and to affect the actions of humans.” The modern meaning (according to Wictionary) is: “The power to affect, control or manipulate something or someone.”

Ben-Or and Linial’s definition of influence

Collective coin flipping refers to a situation where n processors or agents wish to agree on a common random bit. Ben-Or and Linial considered very general protocols to reach a single random bit, and also studied the simple case where the collective random bit is described by a Boolean function $f(x_1,x_2,\dots,x_n)$ of n bits, one contributed by every agent. If all agents act appropriately the collective bit will be ‘1’ with probability 1/2. The purpose of collective coin flipping is to create a random bit R which is immune as much as possible against attempts of one or more agents to bias it towards ‘1’ or ‘0’. Continue reading

Is Mathematics a Science?

Many people do not regard mathematics as a science since it does not directly probe our physical reality; some mathematicians even like to think about mathematics as being closer to art, music or literature. But is there really a big difference between exploring the physical reality and exploring the logical/mathematical reality?

It is perhaps too early to have an open discussion thread on this blog but let me try anyway. What do you think? Is mathematics a science?

(This post was influenced by a recent post on Peter Woit’s blog where he referred to an article by Robert Matthews entitled: “Do we need to change the definition of Science?”)

Updates: (June 18; June 30 ) A related very successful discussion titled “What is Purity” is taking place Continue reading

Mathematics to the Rescue

It was my first day as a postdoc at MIT, and after landing at Logan Airport I took a taxi to a relative in Beverly, north of Boston, where I was going to stay for a few days while looking for a place to live for me and my family who were arriving a week later. The taxi driver had some difficulties locating the address and when we arrived the taximeter was on 34 dollars and fifty cents. “With the tip I will give you forty,” I told the driver and handed him a 100 dollar bill. “Sorry,” said the driver, “don’t you have smaller bills? I have only 40 dollars on me for change.” Hmm, I thought but could not find any small bills except for 10 notes of one dollar each. The problem seemed unsolvable. Can mathematics come to the rescue?

Local Events, Turan’s Problem and Limits of Graphs and Hypergraphs

I will write a little about how hectic things are now here at HU, and make two (somewhat related) follow-ups on previous posts: Tell you about Turan’s problem, and about Balázs Szegedi’s lecture from Marburg dealing with limits of graphs and hypergraphs.

Local Events

The second semester at HU started on Sunday, May 11th and it will run until August. This is due to the 3-months Israeli Professors’ strike at the beginning of the academic year. Issues regarding the strike and Israeli academics are quite interesting and we may come back to them. Let me make just one little remark: There is an initiative to transform Israeli universities to a more “market-based” structure. US universities and the new evaluation system in the UK are mentioned as examples, and the Australian academic reforms are often regarded as an act to follow. I was always quite negative about this initiative and skeptical even about the Australian example, and the following post by Terry Tao is telling regarding the Australian reforms. (See also the new blog mathematics in Australia.)

Thia semester I am teaching the basic course in combinatorics and a seminar in probabilistic combinatorics. Continue reading

Jerusalem Combinatorics ’93

Jerusalem Combinatorics ’93 is the title of a conference I organized that took place fifteen years ago in May 9-17, 1993 at the Hebrew University of Jerusalem. It was a conference that was devoted to all areas of combinatorics. The other organizers were Noga Alon, Hélène Barcelo, Anders Björner, and Edna Wigderson. Altogether there were around thirty plenary talks, and about fifty additional invited talks in 10 sections representing various subareas of combinatorics. There were also four special talks for a large audience. Overall, it was a fruitful and a very nice event that I think people enjoyed.

A special aspect of the conference was the unusually large number of female speakers. 16 out of the 30 main plenary speakers were women, and also many of the additional speakers,  special session organizers, and other participants. The four large audience lecturers were Vera Sós, who talked about irregularities of distributions, Mireille Bousquet-Mélou who talked about polyominoes, Hillel Furstenberg who talked about Ergodic theory and Combinatorics, and Joan Birman who talked about the combinatorics of finite-type invariants for knots.

collection of papers   by participants of the conference, edited by Barcelo and myself, appeared as Volume 178 of Contemporary  Mathematics.

The poster of the conference also has an interesting story behind it. Continue reading

Rationality, Economics and Games

1. The “Center for Rationality”

“Founded in 1991, the Hebrew University’s Center for the Study of Rationality  [at first it was simply called “Center for Rationality”] is a unique venture in which faculty, students, and guests join forces to explore the rational basis of decision-making. Coming from a broad sweep of departments — mathematics, economics, psychology, biology, education, computer science, philosophy, business, statistics, and law — its members apply game- theoretic tools to examine the processes by which individuals seeking the path of maximum benefit respond to real-world situations where individuals with different goals interact.”

Game theory was always strong at the Hebrew University of Jerusalem, and a nice aspect of it is the combination of mathematics and debating. As an undergraduate I was quite interested in game theory along with combinatorics and convexity, and my first published paper was on game theory, with Michael Maschler and Guillermo Owen. Later I moved in other directions, but more recently, in part because of my membership in the Center for the last ten years and in part because of my collaboration with economists Ariel Rubinstein (who was my classmate in my undergraduate years) and Rani Spiegler, I am trying to do research and write papers in theoretical economics. Not having the basic instincts of an economist, and lacking some basic background, makes it especially difficult.

Let me also mention that there are very interesting connections between computer science and economics and a very large emerging research community.

2. Many many controversies

Among the many issues discussed and debated in seminars at the Center (the regular ones are the “Game Theory Seminar” on Sundays and the “Rationality on Friday” seminars on… Fridays,)  roundtables, the annual retreat, Sunday’s sandwich gatherings, and ample debates over e-mail were:

The controversy over expected utility theory (we will come back to it below); (Little updates: May, 21)

The role of psychology in economics;

The relevance of “neuroeconomy”;