We have two players playing in turns. Each player can decide to stop in which case the game is stopped and the two players can go on with their lives, or to act.
The player that acts gains and the other player loose twice as much.
So in the first round: player I can stop the game, if he acts he gets 1 and the other player II gets -2.
If the games continues in the second turn player II can stop the game, if he acts he gets 1 and player I gets -2.
If the games continues in the third turn player I can stop the game, if he acts he gets +1 and player II gets -2.
How to play this game?
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. Continue reading
Happy new 2009, everybody!
An understanding of our fundamental limitations is among the most important contributions of science and of mathematics. At the same time, various fundamental limitations stated by many great minds turned out to be wrong, sometimes rather quickly.
There are quite a few cases where things that were considered to be impossible turned out to be possible. Immanuel Kant claimed: “No finite Reason can hope to understand the production of even a blade of grass by mere mechanical causes.” This quote is from the Critique of Judgment (1790). Elsewhere Kant wrote: “It is absurd to hope that another Newton will arise in the future who shall make comprehensible by us the production of a blade of grass according to natural laws which no design has ordered.”
Auguste Comte claimed: “Of all objects, the planets are those which appear to us under the least varied aspect. We see how we may determine their forms, their distances, their bulk, and their motions, but we can never know anything of their chemical or mineralogical structure; and, much less, that of organized beings living on their surface …” (The Positive Philosophy, Book II, Chapter 1 (1842)).
Spectroscopy was developed by Gustav Kirchhoff in the 1840s, and the first spectroscopic analysis of the sun appeared about ten years later, less than 20 years after Comte’s statement.
A slightly different example relates to the philosopher Wittgenstein. Continue reading