I hate multiplication when one of the multiplicand or multiplier heads into double digits and beyond.  I’d rather shoot myself when both parts become larger numbers.

Fortunately, Russian peasants and the Ancient Egyptians were kind enough to impart the knowledge of how to handle these numbers and come up with an answer with very little effort involved.

Thanks to a book that I’m reading from 1955 I’ve now discovered an even easier way, however large the numbers involved happen to be, which was used by the Mesopotamians.

The only thing you need to have in advance is a table of squares to use for reference.  You know what these are:

Obviously you’ll need to have one of those that is a little more extensive, but I don’t think that that is too much to ask if you happen to live in a world without calculators.  After all, using a washing machine to clean your clothes with the minimum of fuss is great, but they’re only any good providing that someone has gone to the trouble of building it and you’ve bought it and installed it first

Here’s an example in action, for finding the product of 102 and 96:

1) Add 102 to 96 and divide the result by 2 to get the average: 99

2) Take 96 from 102: 6

3) Find half of the difference that you calculated in 2: 3

4) In step 1 you found the average, 99.  Use your table of squares to find the square of it: 9801

5) In step 3 you found half of the difference between the two numbers whose product you’re seeking, 3. Use your table of squares to find the square of it: 9

6) Take the small square, 9, from the larger square, 9801, and you find the correct answer: 9792

And that’s just one of the interesting things from this book, which I seem to have finished off by accident in no time at all, so highly readable it is.

Man Must Measure: The Wonderful World Of Mathematics by Lancelot Hogben

So much about this book screams vintage, making it stand out in comparison to the flood of titles to which we have access fifty years later.

It’s outsize, an impressive 34 cm by 25 cm. It’s bright, the cover and each page bearing hand-drawn illustrations, indicative of a bygone age. Last, but not least, the name of its author lends an authority that we don’t get nowadays, when Ians and Daves are producing books at a prolific pace: Lancelot Hogben.

Hogben holds a special interest for me anyway, as the author of the constructed language Glossa. In his colourful life he was imprisoned as a conscientious objector during WW1, before latterly holding positions in such academic institutes as the London School of Economics. The man, deceased in 1975, had pedigree.

I have read more than a handful of books on mathematics over the last few years, all costing considerably more than the fifteen shillings that this one was selling for. I’ve been leafing through a book on maths that runs over a thousand pages during the last few months. It doesn’t hold a candle to this one.

In fact, I’d consider this one probably the best maths book that I’ve read. Bearing in mind the esteem in which I hold Petr Beckmann’s A History Of π and Eli Maor’s e: The Story Of A Number this should come as high praise.

Sure, the other books document in much more detail, but this isn’t what Hogben was aiming at. He provides a great insight into the progress of mathematics over the course of millennia, in flawlessly written, sharp paragraphs.

I learned so much, it came across as though I was saying “Ah” to myself every other minute. I’ve read entire books on longitude without knowing exactly how the parallels are set, yet Hogben covers it here in easy-to-follow English in the space of a couple of anecdotes, complemented by beautiful illustrations.

Honestly, the presence of so much complementary colour is magnificent. Why don’t modern books emulate this style, instead of reproducing page after page of text?

The book spans eight chapters, each progressing chronologically and geographically, and each given a specific header.

We start off with a short chapter which introduces us to the first recordings of time, which would have been done long ago by the use of moons. I always wondered how it was that so many separate ethnic groups ended up with calendars of 360 days and the base-60 counting system. Now I know, and it was presented to me in a few seconds.

Ancient Greece is our next stop, where we encounter the building of the pyramids. With such scale, there is plenty of room for error, yet the builders constructed the pyramids perfectly. The wherefores are explained simply, again complemented by brilliantly colourful illustrations.

I’m going to stop waffling on about the individual chapters at this point, simply because I can’t do them justice. This book is a joy to read and, interestingly, I can’t tell whether it’s supposed to be for children. That’s a great indicator of superb penmanship. Kids, I’d wager, could follow this without a problem, yet this particular adult, who already has a background in maths, was intrigued by it too.

I’m not sure how I could recommend this anymore. If you want to spend a few hours familiarising yourself with mathematics, this is the way I think you should do it. This book will take pride of place on my bookshelf. It was a joy and, at one penny plus postage, an absolute bargain.

Tags: Lancelot Hogben

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