Mathematics And The Real World by Zvu Artstein (book review).

April 24, 2015 | By | Reply More

The title sense of Zvu Artstein’s book, ‘Mathematics And The Real World, comes from its extended sub-title ‘The Remarkable Role Of Evolution In The Making Of Mathematics’. This doesn’t mean other members of the animal kingdom can do complex mathematical equations but more in terms of being able to do simple arithmetic in their day-to-day lives. His contention is that this has contribution to an animal’s survival and not something that we primates suddenly developed just made more complex.


There is some comparison to humans where he cites that children only start getting good at calculating when they reach the age of seven, although I suspect that’s only an average number. Unlike other members of the animal kingdom, human brains tend to be less developed when born and take a while to develop.

Not all of this book is about maths. Artstein explains how some people have a fear of clowns because their exaggerated feet and face painting is equivalent of a primeval fear of being taken for prey and alerting parents to their danger. Considering that we don’t all have this fear suggests it can’t have been very useful on an evolutionary basis.

Of course, much of this book is the history of maths but this time in its application to science. They have to go hand in hand really because if you’re trying to work out distance or time, then you need a counting system that works. Some of it has to be unintentional. Although Artstein isn’t totally clear on this, I doubt if the early measure of a drawing a circle took into account pi because 3.1417 isn’t a number you suddenly dream up, you just drew a circle of the right dimensions and got it as perfect as you could. Try it yourself.

What is fascinating is the various number bases that were used. It’s understandable how base 10 caught on because of the number of digits on your hands although it wasn’t used across Europe until the 17th century, but base 20 was also used, so I guess the counting went onto the toes. The Babylonians used both base 60 and even base 24 although when I considered those particular numbers, I had to think of the division of time. There are far more other base numbers tried out so things were pretty hit and miss for a long while that I wondered if traders and accountants used them to conceal what they were doing.

Going back to science. The Greeks caught onto illusions pretty quickly, and the Műller-Lyer illusion where <─> and ›─‹ confuses the length of the dash quickly got them measuring than trusting their eyes. Indeed, on page 70, there is even an example of how geometric shapes were literally developed from dots that could break a shape up into smaller versions of itself.

Just in case you didn’t know, statistics developed because people wanted to work out the odds in gambling. Artstein shows that and if you thought statistics was boring, this might…er…raise the odds against your normal disinterest. One gamble of the winner takes it all if there are 5 tosses of a coin that comes up heads or tails can theoretically win after three successive wins. I think if I was there at the time, I think I would have changed the rules a little and kept tossing the coins until there was five of one side or the other in a row or at least until that number was reached. Bearing in mind early coins had more of raised surface than they do today, I would think one side might be favoured more than the other. Artstein doesn’t get you too caught up in formulas, just the history of their development and their usage. If you want to understand how the odds are played for getting an accident or illness, you will see how people use the numbers. This also extends to how the brain misinterprets information because it relies on intuition too much compared to probability. My own scientific background tends to rely on numbers first and only then use intuition or memory to recall information that might change the decision or widens the possibilities that might have been overlooked.

There is also a satisfactory discussion on Game Theory which is how the odds stack up in the real world decision-making. I did think one of his examples was rather too simplified. If a married couple can’t decide on a shared night out between football and opera and assuming tickets have been bought for both, surely it would make sense to attend separately and choose a different night to do something together or, better still, neither are to use the tickets bought and sell them on. Artstein does expand the arguments with other options later for other choices so maybe I just go through the options differently but, hey, I’m a writer, I look at many decisions at a time.

Don’t think Artstein doesn’t tackle some pure maths occasionally. He voices an old view from Bertrand Russell that mathematicians don’t know if what they are saying is true although I suspect it tends to mean that they aren’t afraid to take chances. After all, when Artstein examines the use of negative numbers, it’s understandable that there isn’t anything like it in the real world but needed for some calculations that has to take it into account.

Towards the end of the book, Artstein voices his dissatisfaction with how maths has been taught at school in his native Israel where, from what he says, they didn’t consider how smart kids were. I suspect other similar dumbing down has been done across the world as well. Are the people leading this just poor at maths and think everyone else is in a similar boat to themselves? It would be interesting to have had him explore why some kids who then grow into adults don’t fully understand maths, especially as we depend on it so much in life. This doesn’t mean everyone needs to know how to do things like calculus all their lives but being able to do sums without a calculator quickly isn’t a bad thing to know.

If you need a book to appreciate maths when applied to science, then this book will serve as a good primer as both subjects do go hand in hand. There is a lot of information to absorb so don’t expect a light read but you will certainly come away from it suitably informed.

GF Willmetts

April 2015

(pub: Prometheus Books, 2014. 426 page indexed hardback. Price: $26.00 (US), $27.50 (CAN). ISBN: 978-1-61614-091-5)

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About UncleGeoff

Geoff Willmetts has been editor at SFCrowsnest for some 21 plus years now, showing a versatility and knowledge in not only Science Fiction, but also the sciences and arts, all of which has been displayed here through editorials, reviews, articles and stories. With the latter, he has been running a short story series under the title of ‘Psi-Kicks’
If you want to contribute to SFCrowsnest, read the guidelines and show him what you can do. If it isn’t usable, he spends as much time telling you what the problems is as he would with material he accepts. This is largely how he got called an Uncle, as in Dutch Uncle. He’s not actually Dutch but hails from the west country in the UK.

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