Numbers: Their Tales, Types And Treasures by Alfred S. Posamentier & Bernd Thaller (book review)

Numbers. You can’t live without them and I suspect even those of you who don’t see yourselves as numerate can at least count with them from time to time. Alfred S. Posamentier & Bernd Thaller’s book, ‘Numbers: Their Tales, Types And Treasures’ explains all about them, dropping off various facts along the way. I mean, did you know that the number nine is seen as lucky across the world (although I thought China didn’t see it that way), especially to various religions. Even the authors aren’t quite sure why there is such an attraction but it does exist.


Something Posamentier & Thaller will make you pay real attention to is a little talent most of us have in subitizing. That is looking at a pattern and know the number, in this case stars, without counting. It mostly works if the objects are in some sort of order but its an interesting observation. The same for children, as the very young think the distance between the lower numbers is longer than the bigger numbers. Their observation of how numbers are represented in other countries, especially Chinese, is something to behold, as many call them the other way around.

There are a lot of explanations given in this book. The use of base 60, which is used for time and global dimension was helped by the combination of using one hand and the thumb of the other hand for multiples, so you were in effect using base 6 in counting and base 10 was only a middle base to counting that way.

Another is not just telling us about how different types of counting was done but showing example of it. The Chinese used counting boards, splitting numbers up and so their sticks wouldn’t accidentally slip into other boxes, alternated them as horizontal and vertical. It is from the Indian counting that you can see how our current way of writing numbers evolved and it looks like ‘9’ has always been that way. As usual, the catholic church got in the way of the Hindu-Arabic system being taken on in the west until the 15th century but was taken on after the Crusades. Makes you wonder how long it would have taken without the ‘Holy War’. Our English use of the word ‘zero’ came from the Italian word ‘zefiro’ which also reinforces how much of our culture is influenced across the world.

Some things have their wry giggle, like Aristotle ignoring the number one because you don’t count until you get to two. Another I absolutely loved and never realised before is the source of the term ‘square root’ as the authors showed how early mathematicians laid out their spots in squares for visualising and saw the multiples. It’s so obvious but so effective. These same squares where if they don’t have an even number immediately identifies a prime number. Saying that, there is a list of the prime numbers in the first 10,000 numbers in the appendix, as indeed a variety of other unique number ranges. I wonder how many of you will see these as an opportunity for password material.

Numbers come up in all sorts of places, including poetry, although not always in English. All to do with the rhythm beats when you read that particular chapter.

Some of it far more advanced although explained sufficiently to try the examples and do for yourself like with Pascal’s triangles and magic numbers grids. The fact that these started off early shows Man has always had a fascination with numbers. Fibonacci comes up a lot, especially the reminders of his real name, Leonardo da Pisa, that I’m remembering how to spell forever now.

There are some interesting reveals so if you want to know if a large number is divisible by 7, 11, 13 or 17 you are shown the means to do it. Saying that, I do have to wonder under what circumstances that would be important in anything but school. Some of the other number tricks developed from formulas would also give your sprogs or yourselves some practice with your spreadsheet software.

Although I’m less sure about number philosophy in the final chapter, if you have an interest in maths, there’s plenty here on its history that you can try out and experiment with. The length of the review shows how much I picked out from it so think what you might find.

GF Willmetts

August 2015

(pub: Prometheus Books. 389 page enlarged paperback. Price: $19.00 (US), $20.00 (CAN). ISBN: 978-1-63388-030-6)

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released: 11 August 2015

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