A new post is available over at Second-Rate Minds by Samuel Hansen.
Why your friends have more friends than you do. That is the rather provocative title of a 1991 paper by Purdue University sociologist Scott Feld. While the title is rather provocative, thankfully it turns out that the statement is built on a solid foundation. It turns out that your friends having …
Read the full post: “The True Importance of Friends“
Ian Stewart gives us a taste of his new book Seventeen Equations That Changed the World in a Guardian article about the Black-Scholes equation. This, he says:
provided a rational way to price a financial contract when it still had time to run… It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.
So what went wrong? Stewart explains that “the equation itself wasn’t the real problem”, going into some detail about how the equation was derived, how it works and what assumptions are included. He concludes:
Was an equation to blame for the financial crash, then? Yes and no. Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.
Ultimately, Stewart argues, “the financial sector performs no better than random guesswork”, with the system “too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don’t represent reality adequately”, a situation that requires “requires more mathematics, not less”.
Guardian: The mathematical equation that caused the banks to crash.
A conversation about mathematics between the UK and USA from Pulse-Project.org. This week Samuel and Peter spoke about: Every odd integer larger than 1 is the sum of at most five primes; No pardon for Alan Turing; more super bowl math; Early results from the Met Office weather game; Trends in Race/Ethnicity and Gender Representation in the Mathematical Sciences; Wolfram|Alpha Pro; more on Elsevier boycott; & more.
Download or stream via pulse-project.org.
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Last summer the Met Office launched an online game to understand how best to present probabilities in weather forecasts. This game was collecting data for a project on perception of probabilities.
The Met Office reports game was played more than 11,000 times. A blog post presents some initial findings:
When faced with straightforward decisions, providing probabilities doesn’t confuse people.
For more complex situations, on average people are able to make better decisions using probabilities.
People make the best decisions when more detailed information on forecast uncertainty is provided.
Data analysis continues.
Met Office: Early results from our record-breaking weather game.
Stephen Wolfram writes what Wolfram|Alpha Pro does and what it will cost you. He says:
Over the two and a half years since we first launched, Wolfram|Alpha has been growing rapidly in content and capabilities. But today’s introduction of Wolfram|Alpha Pro in effect adds a whole new model for interacting with Wolfram|Alpha—and brings all sorts of fundamentally new and remarkable capabilities.
Broadly speaking, this adds capabilities around inputting into and download and customise the output from the system.
Announcing Wolfram|Alpha Pro.
The Advisory Committee on Mathematics Education have a call for views on post-16 education. This says:
In a speech at the Royal Society in July 2011, the Secretary of State Michael Gove stated his wish that within ten years, all young people would be studying some form of mathematics post-16. ACME is seeking views on how we can make this a reality.
A paper giving some background information & details of how to submit your views are available via the website.
ACME: Bridging the Mathematics Gap : Have Your Say.
Terence Tao has uploaded to the arXiv a paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. He says this result is:
in the spirit of (though significantly weaker than) the even Goldbach conjecture (every even natural number is the sum of at most two primes) and odd Goldbach conjecture (every odd natural number greater than 1 is the sum of at most three primes). It also improves on a result of Ramaré that every even natural number is the sum of at most six primes. This result had previously also been established by Kaniecki under the additional assumption of the Riemann hypothesis, so one can view the main result here as an unconditional version of Kaniecki’s result.