If you’ve ever struggled with equations, cursed algebra or given up hope of improving your arithmetic, then help is at hand. According to London-based maths blogger Alex Bellos, you’re simply not getting the joke. “The ha-ha! in the case of a joke, and the aha! In the case of maths describe the same experience,” he says in the introduction to Alex Through the Looking Glass (Bloomsbury, Rs 399), adding that his aim is simply to help you achieve that satisfying ‘whoosh’ of understanding.
Unlike his first book Alex’s Adventures in Wonderland, this is far more rooted in reality, and consistently gives you practical applications for the concepts that are explored. Take, for example, his demonstration that people consistently assume round numbers to be larger than precise ones. While interesting in itself, his contention stays with you because of how he uses it to explain the world around us. This, he says, is the reason why you’ll pay Rs 399 rather than Rs 400 for the book that you are reading, or why we might be inclined to think that a house priced at $391,534 is a better deal than the same house priced at $390,000. Similarly, discovering that there is mathematical law that governs the frequency with which words appear in any given text will change the way you think about both reading and writing. From a newspaper to a novel, a word’s ‘rank’ is governed by a clear inversely proportional relationship. Wordsmiths, it seems, cannot escape the long arm of mathematics.
We were also particularly taken by the contention that numbers can be personified, and that these ‘personalities’ govern our interactions with them. Why is it that in studies, people consistently attribute female characteristics to even numbers, and male characteristics to odd ones? Or why do we associate the number ten with balance, certainty and reliability, while nine and eleven seem to suggest the opposite? Understanding these unconscious associations helps us understand how brands can manipulate our choices, and why our shopping decisions might not be entirely rational.
Fittingly, the book also acknowledges and explores different cultural contexts – what makes four unlucky in Japan, Korea and China (it’s similar sound to the word for death) does not apply universally, and the Shagun practice of giving a round sum of money with a single rupee added is not widely practiced outside of the Indian subcontinent. Interestingly, though, some numbers do transcend their cultural context – and the centrality of the number seven to different societies across space and time is something to ponder upon. Is it because it is the average number of thoughts a human can simultaneously process? Because ancient societies observed seven planets in the sky? Or simply because it is the only number between one and ten that cannot be multiplied or divided within the group?
Bellos is equally even-handed in his history, and you’ll find Indian thinkers being given appropriate credit for the development of the number zero, the concept of negative numbers as well as one of the earliest examples of a place value number system. Greek, Babylonian and Egyptian number systems also make an appearance, along with specific philosophers and their theorems, giving the book a strong historical context, and providing a good balance against its more theoretical excursions.
The introduction does warn that at times the level of mathematics reaches that of an undergraduate degree, and there are certainly sections that require a few re-reads before they reveal their secrets. Yet this hardly detracts from the book’s claim of reaching out to the lay reader, as each chapter stands alone, and it’s always possible (as, indeed, the author advises) to skim trickier sections that invariably crop up at the end of each section, before going on to something fresh when the next chapter opens.
But if you want to find out why pi is a bit pointless, then we’d advise you to dive into the book yourself.