Selasa, 13 November 2012

Mathematics.. it’s nothing short of magic! (Part 2)

 I started with an example of a think-of-a-number trick which a child regards as magic but an adult normally regards as a "so what?". Curiously, it can sometimes work the other way around. Adults can be surprised by things that children regard as unexceptional.
Here is an example. Let's suppose that the world is a perfect sphere and you have tied a piece of string tightly around it, so tightly that you can't even squeeze a razor blade underneath. Now cut the string and add in an extra metre to it. Compared to the enormous length of string around the earth, you have only inserted a tiny bit of slack. So the question is, how much slack is there? If millions of people spread out all along the string now tried to lift up the string at the same time, would there be enough slack for them all to squeeze a razor blade underneath? Could they possibly even get their fingers under it?
An adult's intuition usually says that even the razor blades would struggle to get through. Which makes the real answer gobsmacking. It turns out that around the earth there would now be enough slack to let millions of rabbits get under the string without even having to squeeze. The answer is so surprising (if you haven't heard it before) that it seems impossible - or magical, depending on your point of view.
Something is only magic if it goes against what your experience tells you to expect. What the two-year-old boy saw was exciting, but no more magical than countless other new experiences he saw every day (like the fact that when you drop a bottle it smashes into hundreds of pieces), whereas what his mother saw went against everything she thought she knew.
In the same way, many maths tricks are only surprising to mathematicians who have spent years encountering results that have led them to expect something else. That's why sometimes clever people can be the easiest to fool.
So magical maths isn't just limited to the minds of primary school children. However far you go in the exploration of this subject, you can be certain that there will be things around the corner waiting to surprise you. – (original text by Rob Eastaway, 2001)