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.)
Controversies
Climate-change
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.
Smoking
Interesting papers by the famous statistician Ronald Fisher who was critical regarding the connection between smoking and cancer can be found here.
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.
String theory:
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:
Bible codes
I had some first-hand experience with the “bible code” debate. (Look here, and here .)
Mozart effect
You can read about the Mozart effect in the Wikipedia article. (I don’t believe it.)
Intelligent design
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.)
Debates
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”.
Combinatorics and more 
What standards are appropriate for publishing supporting data and software, in sufficient detail to permit independent replication of published results?
I recall my roommate in college telling me a story about John von Neumann. Once upon a time, von Neumann wrote a paper in which he developed a novel technique to prove an important result long conjectured but not previously confirmed. Before submitting the paper for publication, he became concerned that the importance of the result might overshadow the importance of his new technique. So he chopped the new technique out of the paper, inserting in its place the phrase, “It follows directly that…”. The flurry of letters to the editor, after publication of the abbreviated paper, of the form “It does not *either* follow directly that…”, ensured that a *second* paper, presenting the new technique, received proper attention.
But v.N. never expected his claim to have proven his result to be accepted on faith.
My impression is that, in mathematics, complete publication, in sufficient detail to permit replication and confirmation, is customary and expected.
The standards in other fields seem to be somewhat different. In “climate science”, for example, this sort of obstructive response to efforts to obtain the information necessary to replicate a claimed result seems to be more or less the norm:
http://www.climateaudit.org/?p=1584
Is this sort of thing acceptable in “science”, as distinct from propaganda?
Dear Rod,
You raise a very important issue. It has some importance in mathematics and other theoretical areas but it is especially important in empirical science. Another important question is: Given the empirical data and softwere in sufficient details, what could be a methodology to check, after the fact, if the experiment was conducted properly.
Math and social seinces.
My personal feeling is that many non psycho9logists have no clue about the scoop and validity of certain psychology quite valid findings.
OTOH, Many psychologists, do not know numbers, yielding some farcical blunders.
I think that only having both in hand is acceptable.
Psychology and economics.
It is hard to escape the psychological effect.
For one to overlook the problems with risk models, psychology plays a central role. It is also the intricates and details of human thinking with its practical limits that plays a large role. The intricates of human mind, I mean also what comes naturally to mind and what not. What takes effort and what not. This is the process throught whihc any opinion and action comes by.
In a sense, one can argue about what exactly is the definition for psychology in this context. Because when someone has a mistake, he maybe using bad models, deviating from certain normative logics (we see it usually in hindsight), and the whole thing starts and goes on throught the psychological aparatus of a human actor.
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