• Puzzle 1. Suppose I have a box of jewels. The average value of a jewel in the box is \$10. I randomly pull one out of the box. What’s the probability that its value is at least \$100?
• Puzzle 2. Suppose I have a box full of numbers—they can be arbitrary real numbers. Their average is zero, and their standard deviation is 10. I randomly pull one out. What’s the probability that it’s at least 100?
John Baez and Brendan Fong claim to have answered questions like these, but in a general way that is useful for quantum mechanics:
They’ve written a paper and a blog post.
Paul J. Ferraro and Laura O. Taylor ask, “Do Economists Recognize an Opportunity Cost When They See One? A Dismal Performance from the Dismal Science”
One expects people with graduate training in economics to have a deeper understanding of economic processes and reasoning than people without such training. However, as others have noted over the past 25 years, modern graduate education may emphasize mathematics and technique to the detriment of economic reasoning. One of the most important contributions economics has to offer as a discipline is the understanding of opportunity cost and how to apply this concept to all forms of decision making. We examine how PhD economists answer an introductory economics textbook question that requires identifying the relevant opportunity cost of an action. The results are not consistent with our expectation that graduate training leads to a deeper understanding of the concept. We explore the implications of our results for the relevance of economists in policy, research, and teaching.
Importantly, given four options, only 21.6% of respondents chose the correct one. They performed worse than chance. Some feeble statistical analysis is performed by the authors.
This challenges none of my views about economists: none of them can do maths; none of them can do statistics; what they do has very little rational basis; they are terrible at designing questions for undergrads that don’t require you to make assumptions, often drawing heavily on cultural knowledge.
Found via MetaFilter, which compares the problem to the Monty Hall problem in probability. Nowhere near, in my opinion.
There’s a very interesting article in Foreign Policy on a man called Patrick Ball who uses statistics as a human rights tool.
Could the movements of refugees have been random? No, Ball said. He had also plotted killings of Kosovars and found that both phenomena occurred at the same times and in the same places — flight and death, hand in hand. “I remember well the moment of astonishment that I felt when I saw the killing graph for the first time,” Ball replied to Milosevic. “I assumed I had made an error, because the correlation was so close.”
The article doesn’t just describe Ball’s conclusions – it goes into a good amount of detail about the methods he uses, and the dangers of misinterpreting non-representative data.
A new episode of the Math/Maths Podcast has been released.
A conversation about mathematics between the UK and USA from Pulse-Project.org. This week Samuel and Peter spoke about: Samuel’s ridiculous bus trip; Computer programmes with IQ 150; IBM’s Watson and data analytics; Extracting Dynamical Equations from Experimental Data is NP-Hard; OPERA faster-than-light neutrinos experiment UPDATE 23 February 2012; ‘Invisibility’ cloak could protect buildings from earthquakes; How Bots Seized Control of Carlos Bueno’s Pricing Strategy; Calculus: The Musical!; Who says ‘maths curriculum failing to meet the needs of the 21st century’?; Turing Stamp; & more, and Peter spoke to some of the team behind Maths in the City on the occasion of their inaugural London walking tour. Oh, and Samuel forgot to mention Science Sparring Society’s second fight, but the link is in the show notes anyway.
Get this episode: Math/Maths 87: Faulty Cables, Ridiculous Buses & Intergalactic Steroids
The Jerry Slocum Collection of mechanical puzzles embodies a lifetime pursuit of the intriguing and the perplexing. The result is the largest assemblage of its kind in the world, with over 34,000 puzzles. Unlike word or jigsaw puzzles, mechanical puzzles are hand-held objects that must be manipulated to achieve a specific goal. Popular examples include the Rubik’s cube and tangrams. The puzzles in the collection represent centuries of mathematical, social, and recreational history from across five continents. When complete, this database will allow researchers and puzzle enthusiasts to search and browse the entire puzzle collection.
Archivists at Indiana University are publishing photos and descriptions of the 30,000+ puzzles in the collection donated to them by Jerry Slocum. So far just over 24,000 puzzles have been put online. You can filter the database by date, designer, maker, and type of puzzle.
After almost three months, Ed Pegg has finally added some new material to MathPuzzle.com. He says he’s been working his way through the top 1000 films. It’s a fairly thin update, but maybe he’ll get back in the swing of things.
The OPERA project has identified two possible sources of error in the experiment that appeared to observe neutrinos travelling faster than the speed of light. The CERN press release reads:
The OPERA collaboration has informed its funding agencies and host laboratories that it has identified two possible effects that could have an influence on its neutrino timing measurement. These both require further tests with a short pulsed beam. If confirmed, one would increase the size of the measured effect, the other would diminish it. The first possible effect concerns an oscillator used to provide the time stamps for GPS synchronizations. It could have led to an overestimate of the neutrino’s time of flight. The second concerns the optical fibre connector that brings the external GPS signal to the OPERA master clock, which may not have been functioning correctly when the measurements were taken. If this is the case, it could have led to an underestimate of the time of flight of the neutrinos. The potential extent of these two effects is being studied by the OPERA collaboration. New measurements with short pulsed beams are scheduled for May.
Source: OPERA experiment reports anomaly in flight time of neutrinos from CERN to Gran Sasso: UPDATE 23 February 2012.