These days that question is easy to answer. If in doubt, pull out your smart phone and check your coordinates. But it's not so long ago that people died for not knowing where they were. Many ships got lost at sea, crashed into rocks or ran aground because sailors couldn't figure out their longitude.
The book Longitude by Dava Sobel tells the fascinating story of that tricky coordinate, why a prize was put on its head and how the puzzle was finally solved by means of a clock. This "true-life thriller" is one of our favourite popular science books ever!
If you've already read the book, or need to pass the time until it turns up under the tree on Christmas day, then read about the maths of navigation on Plus:
Time and motion tells you why getting from A to B is harder than you think.
David, our favourite statistician, has guided us through many a sticky statistical situation and has met many of his own making, including an excellent round on Winter Wipeout. He wrote a column here at Plus and is responsible for the excellent website Understanding Uncertainty, as well as many other activities. Michael, journalist, author and radio producer, is the person who first introduced us to the world of radio and podcasting. He created the fabulous BBC Radio 4 show More or Less.
You can read more about the maths of networks on Plus, including the networks behind our brains, rapping, crime fighting and the best parties. And to find out how this all started, why not watch our oscar-worthy movie below!
You can read more about the bridges of Königsberg here.
Beck creates those beautiful geometrical shapes by walking through the snow. The shape you see above is based on the Von Koch snowflake. To create the full shape, you start with an equilateral triangle and replace the middle third of each side by a "spike" consisting of two sides of a smaller equilateral triangle. Now do the same for each of the twelve straight-line segments of the resulting shape and repeat, ad infinitum. The Von Koch snowflake is an example of a fractal, a mathematical shape that is infinitely intricate and self-similar: it exhibits the same structures over and over again as you zoom in on smaller and smaller pieces. You can find out more about fractals here.
Beck can't produce the Von Koch snowflake exactly, of course, because it involves an infinite process. But he has created an amazingly good approximation, which comes from using the first few iterations of the process. He gets the shape down in the snow by counting steps to measure distances and using a compass when changing direction to make sure he gets the correct angles between straight-line segments. "In the case of the Koch shape, I found I was soon able to judge the 60 degree angles and do it quicker to an acceptable level of accuracy without using the compass," he says.
If you like the pictures, you can see more of them in Beck's new book, Snow Art, which you can purchase from his website. Here are a few more samples:
An image taken by the Hubble Space Telescope, courtesy NASA, ESA and E. Sabbi (ESA/STScI).
How important are experiments in science? Scientists use experiments
to check whether a theory's predictions match up with
reality, so without them you can't pick out bad theories.
theoretical physics, however, there are many theories that cannot be
tested. Not only because our experimental tools are nowhere near good
enough, but also because there's some fundamental reason that stops us
exploring some of the predictions those theories make. Examples are string theory, M theory and the various multiverse theories. Should we
pursue them anyway, or dismiss them as speculation?
This debate, featuring one of our favourite theoretical physicists, David Tong (among others), explores this question and asks whether physics has strayed too far from experiment. It's been produced by the Institute of Art and Ideas in London.