Zero

"Unlike Ifrah, Charles Seife is a brilliant popular science writer who has here written the ‘biography’ of zero. And even though he doesn’t talk that much about India, it works well as a handbook to Ifrah’s sections on India. Because Seife talks about how zero is mathematically very close to the idea of infinity, which is another mathematical idea that the Indians thought about differently. Seife gives you the context and it explains why, really, without zero, you can’t do anything. The difficulty of understanding zero is similar to the difficulty of understanding infinity. The Greeks had no zero, Roman numerals have no zero, and they had no infinity. He plays with this idea that we were afraid of infinity and then gradually we learnt not to be afraid of it. There is an energy to the way Seife writes about maths, using a strong narrative, which is very difficult to pull off: but he knows exactly how to do it. You finish each chapter and you really want to go on to the next one and ‘find out what happens’. There were different reasons, but fear of mathematical infinity is probably best expressed by Zeno’s paradoxes, the most famous of which is probably that about Achilles and the tortoise. Imagine Achilles in a race with a tortoise, with Achilles starting behind. By the time Achilles reaches the tortoise, the tortoise has got a little bit further. This happens the next time he reaches the tortoise and again and again, so he will never beat the tortoise. How can that be? To understand this paradox you have to be able to cope with infinity, because you are counting an infinite number of time units and you are assuming that an infinite number of time units goes on for ever. But in fact it can be finite. Only with calculus and Newton did mathematicians harness the power of infinity rather than run away from it. But Seife says the other reason, spiritually or religiously, that we were afraid of infinity and zero and the reason that India got zero, was that Western religions thought there has to be God everywhere. Nothingness, or the void, is frightening, because it’s a world without God. Whereas in Indian religious thought, that’s nirvana. Yes, so this religious thought provoked the mathematical thought. The Seife is a rip-roaring page-turner about the history of zero, but it is great to read it with Ifrah so that you can just stare at all the lovely information on India alongside."