Friday, July 30, 2010
Vital Statistics
07 Sep 2007
Book Review: ZERO: The Biography of a Dangerous Idea by Charles Seife (2000)
Dr Ganesh Nana
ZERO: The Biography of a Dangerous Idea
by Charles Seife (Penguin Books, 2000)
Number geeks of the world unite! From chapter zero all the way to chapter ∞, this book is a fun way to learn about what is my favourite number. Just co-incidentally, of course, it is also the most important number in the universe.
Zero, of course, is a unique number – it is the only number which when added to a number doesn’t change the original number. But, if you add something to something then that latter something must change. So, zero transgressed this seemingly immutable law of nature. And when you take zero away from a number, again, that number remained unchanged. Meanwhile, multiplication just threw everything away to a single zero and division became incomprehensible with a zero – it all pointed to zero being some heretical, devil-inspired concept (in today’s language, think terrorist) – a concept that would need to be banished by all civilised societies.
That zero survived these assaults to now be at its rightful place at the very centre of the number line is indicative of its importance to the development of human knowledge.
The book is readable – even for non-geeks – thanks to the author skipping chapters nine to ∞-1. However, I must admit that chapters 7 and 8 were a bit dry – primarily because they were all about what scientists did to zero and we all know how unexciting that lot (physicists in particular) are, don’t we?
But, left in the hands of the philosophers and mathematicians (chapters 0 to 6), the story of zero is mixed with intrigue, emotion and the joys of discovery that only true explorers and researchers can relate to.
Beginning from the original counting implement (a wolf bone of 30,000 years ago) the story detours to the Greeks and the Egyptians (and latterly the Romans). Their mathematical prowess based on geometry (shapes) resulted in problems due to their banishment of zero. For example, there was Zeno who really couldn’t figure out how Achilles could never catch a tortoise.
Meanwhile, the Babylonians found counting a lot easier with a zero, but the true role and centrality of zero was still to be recognised.
This was left to Indian mathematicians who played the central role in humankind’s great leap forward. With some influence from the Greeks, Egyptians, and Babylonians – courtesy of Alexander the Great – Indian mathematicians were not so much fussed about geometry. They were more interested in arithmetic. They devised easy methods to add, subtract, multiply and divide – without the use of, the then calculator of choice, the abacus.
Arabic influences were also present – with Mohammed ibn-Musa al-Khowarizmi and his treatise Al-jabr wa’l muqabala, for example. So, now we had algebra (Al-jabr) and algorithms (al-Khowarizmi).
These of course required zero to take its rightful place, before 1, in the scheme of things. This, of course, led not only to negative numbers (a logical inevitability when one is engaged daily in subtracting numbers from other numbers), but also to the heretical irrationals. Curiously, 0 remains in the wrong place (to the right of, or after, 9) on most keyboards, telephones and calculators of today. Are we still afraid of zero’s mystical powers?
But wait … there’s more … murder (Pythagoras having to deal with the troublesome and irrational Hippasus); war crimes (the Romans contribution being the killing of Archimedes despite his being in the midst of proving a theorem); historical contradictions (the elevated importance of the golden ratio[1] despite it being an irrational number); banks, tally sticks, stockholders; Aristotle and the many proofs of God’s existence; and Pascal and his advice to believe in God (based on probabilities and, of course, zero). And that’s not to mention Descartes and his Cartesian coordinates; imaginary numbers[2] (which are the reason we had to grapple with complex numbers in 7th form calculus); Newton and his dirty tricks; Cantor and Kronecker; and everybody’s favourites from School Certificate days … trigonometry, differentiation and integration.
And, of course, no book about zero would be complete without assigning true blame for the “start of the millennium” fiasco on those who ignored zero and its rightful role.
And whatever you do, don’t miss the proof that:
2 = 1
This proof provides convincing evidence that zero, used without the utmost care that it rightly deserves, can lead you to look extremely stupid.[3]
Happy reading … and counting ….
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