Quantum mechanics is usually associated with weird and counterintuitive phenomena we can't observe in real life. But it turns out that quantum processes can occur in living organisms, too, and with very concrete consequences. Some species of birds, for example, use quantum mechanics to navigate. Last year we talked to physicists Simon Benjamin and Erik Gauger for our article Flying home with quantum physics, and we found out that studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer.
Now you can read all the technical details as Benjamin, Gauger and their colleagues has just published their research in Physical Review Letters. Their research has also been featured in New Scientist.
You can hear Benjamin and Gauger discuss their work in our podcast, and learn how birds have harnessed quantum physics in the accompanying article.
Negative numbers are easy to imagine if you think of the number line as
a giant thermometer which includes sub-zero temperatures. This makes
addition and subtraction easy, as you just move up or down the number
line by the according amount.
But what about those tricky multiplication rules? Why does positive
times negative give negative, and negative times negative give positive?
Here the number line can help us too.
Suppose you're standing at the point 0, facing in the positive direction
of the number line. You take two steps backwards and you do this 4 times.
You end up at the point -8, showing that -2 steps times 4 is -8, ie (-2)x4=-8.
Now suppose you're back at 0, this time facing in the negative direction.
You take 2 steps forwards and you do this 4 times. You also end up at
point -8, showing that 2 steps times -4 is -8, ie 2x(-4)=-8.
Again, go back to 0, looking in the negative direction. Take 2 steps
backwards and do this 4 times. You end up at the point 8. Stepping
backwards gives you a -2. Facing in the negative direction gives you a
-4. Putting all this together gives (-2)x(-4)=8.
Straight Statistics is a campaign set up by journalists and
statisticians to improve the use of statistics by government, the media,
companies and everyone else who uses stats. On the Straight Statistics
website you can find all sorts of interesting articles responding to
stats as they come up in the news — whether it's lucky house numbers, the
impact of bird flu, or your chance to reach your 100th birthday.
Sixteen-year-old Rebecca Simpson, of Dame Alice Owens School in Potters Bar, has won a national competition to produce a creative photo connected to maths.
Winning entry by Rebecca Simpson.
The competition was run by Maths Inspiration, a great initiative that runs lecture events in theatres around the country, featuring speakers such as the writer and TV broadcaster Simon Singh. The competition, sponsored by Hewlett Packard, was open to all the 6,000 who attended the shows last autumn. Rebecca's entry, entitled Box and whiskers, depicts a cat being measured for its level of cuteness. It's a play on box and whiskers diagrams, which will be familiar to any GCSE maths pupil.
Rob Eastaway, the director of Maths Inspiration (and Plus author), said: "Our shows aim to prove there's more to maths than just taking exams, and humour is an important part of how we present maths. Rebecca's entry really caught the spirit of what we are trying to achieve".
Rebecca wins £200 and a signed copy of the book Fermat's Last Theorem by Simon Singh, while her school receives two top-of-the range Hewlett Packard graphing calculators.
Rob Eastaway has written several articles for Plus:
This is it! The holidays have started, the turkey is defrosting and the presents are all wrapped ... all you have to do now is relax and be kind to one another. And since Christmas is all about love, the very last door of our advent calendar is devoted to it, too. The Plus team wish you a very merry Christmas and a happy new year!
Kissing the frog: a mathematician's guide to mating
What's your strategy for love? Hold out for The One, or try and avoid the bad ones? How long should you wait before cutting your losses and settling down with whoever comes along next? We investigate and save the national grid in the process.
It may seem a bit un-romantic, but when it comes down to it, dating is all about strategy. Find out what happens if, like in the film The beautiful mind, everyone goes for the blonde, and if it's possible to be too attractive.
Safety in numbers
Primes are also what keeps your credit card details safe when you buy something over the internet. Find out how with Simon Singh.
The prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Here are two ways of sieving out all primes up to a given number: Sundaram's sieve and a geometrical method.