Science in School - the best in science teaching and research
The third issue of the magazine Science in School is just out, and as usual is a fascinating read about all areas of science. Plus particularly enjoyed Richard West's reminiscences of discovering a comet, and the articles on the power behind the Sun and the advances of Muslim scientists during the Dark Ages in the West.
Science in School aims to promote inspiring science teaching across Europe. It's published quarterly, and you can either subscribe to the printed edition or read it free online at http://www.scienceinschool.org.
In the recent Queen's Speech to Parliament there was one point that went largely unnoticed, but that may drastically alter the nature of political argument: the government's plan to set up an Independent Statistics Board. The board will "reinforce the independence, integrity and quality of statistics produced in government". So why is this necessary? As always with statistics, it's not
necessarily their quality that gives cause for concern, but their presentation. At the moment, the Office of National Statistics reports straight to ministers — and ministers get hold of the outcomes of statistical surveys and studies ahead of everyone else. So what reaches us when results are released is not just the numbers, but also the ministers' interpretation of them.
With the proposed Statistics Board in place, ministers would no longer get these sneak previews. Statistics would not only be produced, but also analysed and interpreted by independent experts that have no links with policy makers. Their interpretations would be understandable for the general public. Politicians, who would get the results at the same time as everyone else, would find spinning
them a whole lot harder than they do now. Statistics are a critical measure of a government's performance on pretty much everything, including health, education and the economy. They are a crucial tool in political debate. So, who knows — maybe politics is just about to get more honest.
Mathematical moments - Taking chances with De Moivre
Abraham De Moivre
Born on the 26th of May 1667 in Vitry-le-Francois, France
Died on the 27th of November 1754 in London, England
When De Moivre first came across Newton's famous work the "Principia" he was so struck by its depth and rigour that he immediately bought a copy and cut it into pieces - carrying just a few pages at a time was the only way he could study the work while making his rounds tutoring private students in London.
But it wasn't just dedication that gained him full marks. Since an early age he had been interested in maths, especially in games of chance, and he is today known as a pioneer of probability theory and of analytic geometry. His "Doctrines of chance" presented the broadest and most rigorous treatment of probability of its day, and he is credited with deriving the normal curve and developing the
concept of standard deviation. His name is famously attached to a formula that gives geometric meaning to powers of complex numbers by expressing them in terms of trigonometry.
De Moivre's eminence as a mathematician was recognised by many of his most prominent contemporaries, including Newton, who he was friends with, and Leibniz. Interestingly, the Royal Society called upon him to referee Newton and Leibniz's dispute about who had first invented the calculus.
Sadly, though, De Moivre's genius was never rewarded professionally. As a French national who had been expelled from France (after a prison sentence) because of his protestant religion, he remained a foreigner in London. Despite the support of his prominent friends he was never employed by a university. He made a living as a private tutor and died in poverty.
Death played an important role in his mathematics. Together with Halley, who gave his name to the comet, he set about investigating mortality statistics, laying the foundations for actuary theory used by life insurances.
Most curiously, De Moivre is said to have used maths to predict his own death. He had noticed that he was sleeping 15 minutes longer every day. Analysing the arithmetic progression 15, 30, 45, .... , he calculated that on the 27th of November 1754 he would sleep through the full 24 hours. He was right - it was the day he died.
Plus's favourite radio show on all things mathematical is back on the air. More or Less has two series a year on BBC Radio 4, exploring maths in politics, health, avalanches, and much more. In the first shows of this season they have already covered drug testing in sport, the economics of climate change, uncovered the
games behind hospital waiting times, and the perverse nature of randomness.
The show is produced in association with the Open University, which provides additional material on their site. You can hear all the past shows online at the More or Less site, and listen live every Monday at 4.30pm on BBC Radio 4.
You can read more about More or Less from presenter Andrew Dilnot in a past article on Plus.
The famous mathematical family, the Bernoullis, produced an astounding eight mathematicians over three generations. The sheer number of them, and the family habit of using the same first names, required the numbering system you see above to keep track of them all. And given the family's mathematical success, you would think that each generation was actively encouraged to study the subject. But
instead the mathematical members of the family often had to study mathematics and astronomy against the wishes of their parents. Indeed there were enough quarrels, backstabbing and even untimely deaths among the Bernoullis to script a soap opera.
Jacob (I) Bernoulli was the first member of the family to study maths, and taught his brother Johann (I) who had been forced to study medicine. The brothers worked on similar topics, such as calculus (Jacob was the first mathematician to use the term 'integral') and studying families of curves such as the catenary, the curve of a suspended string. However, in what would prove to be typical
behaviour in the family, the brothers soon went from collaborators to rivals, publicly criticising each other's intellect and competing to solve the same mathematical problems.
Jacob and Johann taught their nephew, Nikolaus I, mathematics, and Nikolaus assisted his uncle, Jacob, in publishing his works. Nikolaus is known for posing the probability problem the "St Petersburg paradox", which describes a gambling game that no-one would reasonably play, despite a possibly infinite prize.
Nikolaus's cousin Daniel (son of Johann) provided an explanation of the St Petersburg paradox. Daniel, probably the most famous mathematician of the family, did his most important work on fluid dynamics, and gave the Bernoulli principle. However, continuing the family's bitter history, Daniel had a difficult relationship with his father Johann, who did not want him as a mathematical
competitor. Johann tried to stop Daniel from studying mathematics, and even attempted to plagiarise Daniel's greatest work, "Hydrodynamica".
Johann I's other two sons were also mathematicians. His favourite Nikolaus II worked on the problem of trajectories, and the mathematical arguments behind Newton and Leibniz's dispute over who had invented calculus. Johann II worked in mathematical physics.
Johann II also had two mathematical sons. Johann III was a child prodigy, and was just 19 years old when he was appointed to the Berlin Academy. He produced work in astronomy and probability, but his accounts of his travels in Germany had a greater impact historically. Jacob II worked on mathematical physics at the St Petersburg Academy of Sciences, and married Euler's granddaughter. Sadly he
drowned in the Neva River when he was only 29 years old.
The Bernoulli family, despite its infighting and bitterness, dominated mathematics in the 17th and 18th centuries. Together with their contemporaries Newton, Leibniz, Euler and Lagrange, they laid many of the foundations of mathematics and physics that we still use today.
"There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician." - Daniel Bernoulli