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"It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory of machine learning will be deeply ingrained in probability theory, we will derive and analyze probabilistic learning algorithms, and our entire treatment of mathematical finance will be framed in terms of random variables."

SANTA BARBARA-"Maybe we're just too dumb," Nobel laureate physicist David Gross mused in a lecture at Caltech two weeks ago. When someone of his level wonders whether the unification of physics will always be beyond mortal minds, it gets you worried. Since his lecture, I've been learning about a theory that seems to confirm Gross's worry. It is so ridiculously hard that it could be the subject of an Onion parody. But at the same time, I've been watching how physicists are trying to power through their intimidation, because the theory promises a new way of understanding what space and time really are, at a deep level.

Ever since his grad student days at Hebrew University of Jerusalem, Amir Ronen, now a scientist at IBM Research -  Haifa, has been thinking about the intersection of game theory and computer science. In fact, he's one of the leaders in a sub-discipline, called algorithmic game theory, which lies at the intersection of the two fields.

Synthesis is a think-tank devoted to using the emerging paradigm of complex networks in the social sciences to tackle social and public policy concerns. Over the past 20 years or so, social scientists have increasingly made use of advances in the natural sciences to make better sense of social systems. Fields such as network theory, non-linear mathematics and systems theory, which we refer to as the study of complex networks, give us much greater insights that help us make sense of social systems. Armed with a greater understanding, this collection of paradigm-changing toolboxes can help us to make better policy decisions, in the public, private, and "third" sectors.

"Someone points me to this report from Tilburg University on disgraced psychology researcher Diederik Stapel. The reports includes bits like this: When the fraud was first discovered, limiting the harm it caused for the victims was a matter of urgency. This was particularly the case for Mr Stapel's former PhD students and postdoctoral researchers . . . However, the Committees were of the opinion that the main bulk of the work had not yet even started. . . . Journal publications can often leave traces that reach far into and even beyond scientific disciplines. The self-cleansing character of science calls for fraudulent publications to be withdrawn and no longer to proliferate within the literature. In addition, based on their initial impressions, the Committees believed that there were other serious issues within Mr Stapel's publications . . . This brought into the spotlight a research culture in which this sloppy science, alongside out-and-out fraud, was able to remain undetected for so long. . . . The scientific literature must be cleansed of everything that is fraudulent, especially if it involves the work of a leading academic. Sounds familiar? I think it also applies to recipients of the Founders Award from the American Statistical Association. There's more: The most important reason for seeking completeness in cleansing the scientific record is that science itself has a particular claim to the finding of truth. This is a cumulative process, characterized in empirical science, and especially in psychology, as an empirical cycle, a continuous process of alternating between the development of theories and empirical testing. . . . My first reaction was that all seems like overkill given how obvious the fraud is, but given what happened with comparable cases in the U.S., I suppose this "Powell doctrine" approach (overwhelming force) is probably the best way to go."

The eminent British scientist James Lovelock, back in the 1970s, formulated his theory of Gaia, which held that the Earth was a kind of super organism. It had a self-regulating quality that would keep everything within that narrow band that made life possible. If things got too warm or too cold-if sunlight varied, or volcanoes caused a fall in temperatures, and so forth-Gaia would eventually compensate. This was a comforting notion. It was also wrong, as Lovelock himself later concluded. "I have to tell you, as members of the Earth's family and an intimate part of it, that you and especially civilization are in grave danger," he wrote in the Independent in 2006.

A refrain running through the debate over global warming suggests we need to nothing to slow it, because after all, the climate science predicting more warming could turn out to be wrong. Giordano Bruno was burned at the stake, and Galileo almost was, for objecting to the scientific doctrine that the Sun revolves around the Earth. For two thousand years people believed in systems of physics and astronomy that turned out to be incorrect. And for a few more centuries after that they held to a new celestial mechanics only to see it displaced by relativity theory.