Before this magnificent website existed, I published four editions of what was then known as The Internet Maths Aperiodical at Samuel Hansen’s site ACME Science.
You can find those earlier works in their own category at ACME Science.
You're reading: Posts By Christian Lawson-Perfect
The Turing Digital Archive is online
The Archivist at King’s College, Cambridge has put their collection of material by and about Alan Turing online at www.turingarchive.org.
This clipping of a newspaper report about Turing’s death, with annotations from his mother, is enormously sad.
A Noether Theorem for Markov Processes
• 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:
Perspectives of the regular solid
BibliOdyssey has posted some very old perspective drawings of polyhedra and other geometric shapes.
A Dismal Performance from the Dismal Science
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.
The Body Counter
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.
Causa Efecto by Ana Soler
[youtube url=http://www.youtube.com/watch?v=NoK79YmbGao]