The link L10n74
(click on the picture to see L10n74’s Braid representation, its Morse link presentation, its Alexander and Jones polynomials, its Khovanov homology, and more, much more.)
Here are some links and further comments regarding the last four posts. (Mainly for the post about controversies.)
This is probably the most important issue as far as direct policy implications. (And it is a clear-cut scientific debate.) I have very little first-hand knowledge on the climate change debate. I found links to two blogs on “shtetl-optimized” (Both representing the common views regarding the issue – namely that global warming is caused by humans). The first is RealClimate (that made a good impression on me), and the second is Climate change denial (that did not make a good impression on me).
An interesting paragraph from the second blog in a post about “Israeli climate change denial” (written by Lucy Michaels) is:
“A further aspect of Israeli climate denial, argued by [Pinhas] Alpert and supported by my own research, is that there is a relatively high number of climate skeptics in Israel such as astrophysicist Nir Shaviv who still persists with his Cosmic Ray theory despite it being roundly rebutted by the scientific community. A personal friend at the Israel Meteorological Service is yet to be convinced of the anthropogenic causes. Alpert argues that climate skepticism in Israel represents a Jewish trait based on traditions of Jewish critical learning – to constantly dispute and find alternative explanations. This, I think, is a polite way of saying that Israelis in general are an argumentative and contrary bunch.”
Hmm! (Actually I know Nir Shaviv quite well, here is his blog.) The notion “climate denial” is especially cute.
Our local Institute for Advanced Study will hold starting today a large workshop on “Reducing the Uncertainty in the Prediction of Global Warming” about (mainstream) climate-change science.
Economics, games and psychology
A very skeptical view on the normative or descriptive value of economic theory and game theory (even in principle) is expressed by Ariel Rubinstein (here, and here). Robert Aumann has a very different view. (Look at this paper .)
Rationality and psychology. - my opinion is that while the behavioral effects are significant and important, it is even more important to develop further modeling and analysis based on the standard rationality assumptions. (Or on “neutral” assumptions.) A similar remark applies to the “game theory revolution” in theoretical economics. It contributed important insights and at the same time made it impossible to work out large examples to the extent that interest was shifted away from traditional issues of theoretical economics.
An interesting question is: Are psychological aspects important in understanding the last financial crisis? I doubt if psychology is the crux of matters as many claims (e.g. look at this NYT article: “In Modeling Risk, the Human Factor was Left Out”). It looks that there are even more basic problems in current risk models, and there may well be some fundamental impossibilities to have a riskless risk assesement.
The scrolls of Qumran
The twelve competing theories and the “correct one” can be found in this paper by Magen Broshi and Hanan Eshel.
The blog debate about it was quite interesting. (Especially so since much of it had little to do with string theory.) Here is a cluster of relevant posts from “Asymptotia”. These with the following post on “cosmic variance” and many posts on Peter Woit’s blog and Lubos Motl’s blog can give a good picture of the nature of this debate. Here is a short Hebrew article by string theorist Barak Kol.
Mathematics in social science
The debates regarding the role of mathematics in social science, especially in political science, and sociology is quite heated. (I will try to find and add some interesting links.)
Moving to more pseudo-scientific corners:
You can read about the Mozart effect in the Wikipedia article. (I don’t believe it.)
Let me not even start to give links except one. Olle Haggstrom wrote a paper about a certain mathematical argument, the “no free lunch theorem” which is prominent in the intelligent design argument. (It is also interesting to compare the two versions of Olle’s paper; here is the early version. Our papers on the “bible code” passed a similar transformation.)
Kobi Glazer and Ariel Rubinstein wrote several papers about modeling debates. Here is one.
Impossibilities and possibilities:
Voting theory: This topic is close to my research interests and I will probably blog about it at some point. Here is a provocative post in “Secret Blogging Seminar” followed by an interesting discussion.
Solving equations by radicals: Before the successful impossibility results by Abel and Galois there was an incomplete argument by Paolo Ruffini . (This tells us that in scientific debates the scientific quality of an argument is more important than the “bottom line”.) The significant achievement of Galois is that his theory goes well beyond explaining why the earlier goal of solving equations by radicals cannot be achieved, and his theory paved the way to modern algebra. Impossibility claims are more exciting as well as more likely to be convincing if they go further than just claiming “it won’t fly”.