numerals; they were too easy to change to other numerals and therefore easy for crooks to ‘tamper’ with. The next great mathematician to address the concept of zero was Rene Descartes, the founder of the Cartesian coordinate system. Descartes defined coordinates relative to the point (0, 0). Although zero was now becoming more common, the developers of calculus, Newton and Leibniz, would make the final step in understanding zero. Although adding, subtracting and multiplying by zero are relatively simple, division has confused even the greatest minds throughout history. Unfortunately, the answer is not well-established. However, this concept is the key to calculus. For example: You are driving to the supermarket. The speed of the car is never constant, due to traffic lights, traffic jams and different speed limits. How would you find the speed of the car at one particular instant? Zero and calculus both enter the picture here. If you wanted to know your speed at a particular instant, you would have to measure the change in speed that occurs over a set period of time. By making that set period smaller and smaller, you could reasonably estimate the speed at that instant. Effectively, as the change in time gradually approaches zero, the ratio of the change in speed to the change in time because more and more similar to ‘x’ (distance travelled) over zero. This is the same problem that Brahmagupta pondered ‘over, and Newton solved independently in the 1600s. We have seen that the supposedly simple concept of nothing is in fact fiendishly complex. However, we have to try to further our understanding on this ‘nothing’, just like all the great mathematicians have aspired to do so in the past. One day, a long time ago (around 14 billion years ago to be exact), there really was nothing… absolutely nothing. And maybe, one day in another 14 billion years’ time, there will be nothing once more. Nil, naught, nada, cipher, zilch; so many words for a concept so many do not fully understand. But does it really matter that they don’t? Does it really matter that they know nothing about nothing? It is true, if you look closely, nothing is everywhere. So, instead of reading this maths article and then contemplating over the dull, dis-heartening subject of zero... close this magazine, step outside and enjoy what there is now.
References http://www.geom.uiuc.edu/~huberty/math5337/groupe/overview.html http://www.exploratorium.edu/pi/history_of_pi/
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