A proof is a proof. What kind of a proof? It’s a proof. A proof is a proof, and when you have a good proof, it’s because it’s proven.
Jean Chretien
A proof is a proof. What kind of a proof? It’s a proof. A proof is a proof, and when you have a good proof, it’s because it’s proven.
Jean Chretien
Tim Gowers has a weblog, imaginatively entitled Gowers’s Weblog. I find it difficult to imagine this will be anything other than a fascinating read.
“Mathematicians are like Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.”
Johann Wolfgang von Goethe
The 14th Carnival of Mathematics is up at Vlorbik on Math Ed.
I particularly recommend this article by Polymathematics about John Conway’s soldiers in the desert problem. I’d never actually seen a proof of this before.
Prof Servetto died in a private plane crash on July 24. The IEEE Information Society has more information.
Since I haven’t even finsihed explaining the optional stopping theorem yet, I thought I’d point you towards a very good post on Good Math, Bad Math explaining the max-flow min-cut theorem.
In a fascinating article Who want airbags? (PDF) from 2005, Mary Meyer and Tremika Finney argue that the statistics show the airbags cause more deaths than they save.
Broadly speaking, Meyer and Finney argue that the statistics tell the following two stories. First, in very serious accidents, airbags save many lives. However, when airbags go off accidentally or incorrectly – not in serious accidents – the act of the airbag exploding can be very dangerous, even fatal. They argue that government bodies have paid too much attention to the first statistic, to the detriment of the latter, even though this may happen more often. To quote:
Here is an analogy to help understand this: If you look at people who have cancer, radiation treatment will improve their probability of survival. However, radiation treatment is dangerous and can actually cause cancer. Making everyone in the country have airbags and measuring effectiveness only in the fatality group, is like making everyone have radiation treatment and looking only at the cancer group to check efficacy. Within the cancer group, radiation will be found to be effective, but there will be more deaths on the whole.
It’s well worth a read, and includes some discussion from a dissenter at the end.
Who want airbags? (PDF)
Mary C MEYER and Tremika FINNEY
Chance, 18:2, 3-16, 2005
Ok, that was all a little short-lived last time. But now that I’m a proper PhD studentTM, maybe I’ll have another go. And see if it lasts any longer this time…
Sally Clark, the solictor wrongly imprisoned between 1999 and 2003 for the murder of both her young sons, died this morning, according to BBC News.
Her conviction, and subsequent acquittal, became very famous in the UK, particular because of some of the statistics offered by an expert witness, Sir Roy Meadow. Meadow’s evidence was, basically, that the chance of both of Sally Clark’s sons dying of natural causes was so slim, that one had to assume that they were murdered. The structure of his argument was as follows:
Aliens invade the earth and threaten to obliterate it in a year’s time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world’s best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack.
