Mathematics

If you are going to use 'entanglement' to teleport quantum information on a practical scale, it needs to be worked out how entanglement could be 'recycled' to increase the efficiency of these connections. Writing in  Physical Review Letters , a group has done just that - mathematically. They have also devised a generalized form of teleportation, which allows for a wide variety of potential applications in quantum physics. Long a staple of science-fiction, teleportation became a 'it might work in principle' idea in 1993, when theoretical physicists calculated that teleportation could…

Regulars to this blog know I am partial to game theory. The very idea that mathematical reasoning can teach us a thing or two about the strategies we deploy in social interactions, is most intriguing. Game theory recognizes that humans do possess rational and selfish characteristics, and builds models describing human decisions based on no more than these two characteristics. This minimalistic approach teaches us a lot about the character of economic behavior and the emergence of strategies build on cooperation, retaliation, etc. At the same time, game theory forces us to think deeper about…

It's statistical polling...for science.  A paper in Nature Climate Change uses structured expert elicitation and mathematically pools experts' opinions to forecast future sea level rises from melting ice sheets. Soliciting and pooling expert judgments is used in eruption forecasting and the spread of vector borne diseases - with questionable accuracy - and in their paper Professor Jonathan Bamber and Professor Willy Aspinall from the University of Bristol try to model the uncertainties in the future response of the ice sheets.  The ice sheets covering Antarctica and Greenland…

Why do people skip the queue, obstruct, cause traffic jams, and create delays for everyone? Who are these anonymous creatures lacking cooperation skills? And more importantly: are you sure others don't classify you as such? Game theory models the behaviors that emerge in situations of conflict, and predicts how rational individuals driven by selfish motivations compete and cooperate. The predicted outcomes can be disappointing. PD, the Prisoner's Dilemma, is a prototypical model in game theory used to demonstrate that the interaction of two rational individuals each attempting to optimize…

2013 will be the year of Mathematics of Planet Earth. This global initiative was spearheaded by Professor Christiane Rousseau of the University of Montreal, and it was fitting that the first national launch of MPE2013 was held in Canada on the 7th December 2012.   MPE2013 enjoys the patronage of UNESCO and is endorsed by the International Council of Science (ICSU), the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathematics (ICIAM) .  "More than 100 academic institutions and scholarly societies have joined in a major world-wide…

Srinivasa Ramanujan was a self-taught Indian mathematician known for intuiting extraordinary numerical patterns and connections without using proofs or modern mathematical tools. Instead, the devout Hindu genius said that his findings were divine and were revealed to him in dreams by the goddess Namagiri. A group of number theorists decided to mark the 125th anniversary of his birth by exploring his writings and imagine how his brain may have worked. Like being a mathematical anthropologist, they say, and they came up with a formula for mock modular forms that solves one of the greatest…

In the history of statistics, economy and decision theory, the St. Petersburg paradox plays a key role. This lottery problem goes back a full three centuries to the mathematician Nicolas Bernoulli who first formulated the problem in 1713. Twenty five years later, in 1738, his nephew Daniel Bernoulli presented the problem to the Imperial Academy of Sciences in St. Petersburg. That presentation not only gave the paradox its name, it also created a lot of commotion amongst mathematicians. And even today, following three centuries of discussion and debate, the problem continuous to intrigue…

We all love paradoxes, those seemingly consistent logical brain-teasers where we sort out what can and should and might and must happen and that invariably lead to self-contradictory arguments. If you are like me and my friends, there is nothing you enjoy more than sitting around during half-time of the Steelers game and arguing over Maxwell's Demon - the many ways to violate the Second Law of Thermodynamics, namely that heat transfer happens, from warmer to colder, until equilibrium is reached.  If I put an ice pack next to Ben Roethlisberger's blazing hot 145 third down QBR (Total…

The most startling thing to me about the election of 2012 was how spookily accurate polls were.  Social scientists in one camp want to dismiss determinism while the other camp has biology-envy but either the deterministic side got a big boost on Tuesday or the opposing sides in this election were so entrenched there was virtually no reason to vote, other than to see who had the best Get Out The Vote campaign. As I discussed in How Accurate Are Those Political Polls?, that is where the magic happens.  Could polls predict how successful a Get Out The Vote campaign is? Maybe. I know…

Nate Silver, a sports statistician, made waves when he accurately projected the results of the presidential election in 2008.  So a few days go when he predicted that President Obama was 75% likely to win when polls only showed the candidates were about even, it set atwitter those people who think statistical models of polls are meaningful.  They were vindicated, the age of scientific projections had arrived, in a baseball cap. They thought that because they don't understands polls or statistical models. After I wrote on Twitter that 'polls are bad models', Razib Khan of the GNXP…