Lancelot Hogben and his Mathematics for the Million

Want to know about the mathematics of Stonehenge? Diophantus? James Bernoulli? Fermat? The Binomial Theorem? De Moivre’s Theorem? Maclaurin’s Theorem? Pascal’s triangle? Spherical triangles?

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"A Learned Man in All Philosophie, Astronomie and the Other Mathematiks”
[ Up-front Popularizers No. 1 ]
— Tony Rogers

Copyright

I first tried to read it in my teens, and have recently been delighted to rediscover it in a 1993 American reprint. Lancelot Hogben's Mathematics for the Million: How to Master the Magic of Numbers, first published in England in 1937, with later revised editions up till 1967. My copy (a reissue of the fourth edition) has an ISBN of 0 393 31071 X.

As its title implies, its main purpose is to explain mathematics in a simple way for those adults hitherto off-put by the subject. Nothing but the most basic of knowledge is assumed, yet Hogben manages to cover everything from elementary arithmetic to the maths of navigation and logarithms.

Hogben (1895-1975) was born and educated in England. He held several academic appointments, including professorships in zoology and medical statistics. He was the author of at least seven books, the best known and most popular, apart from Mathematics for the Million, being Science for the Citizen.

Another book with which his name is now always associated was Frederick Bodmer's The Loom of Language, which Hogben edited. Though trained as a scientist, Hogben was passionately interested in matters linguistic, and was one of those language addicts who proposed his own international language. In Hogben's case it was "Interglossa", an artificial concoction which he based on Greek and Latin roots together with a syntax resembling that of Chinese, and the principles of which he set out in The Loom of Language.

(By the way, Harlish Goop, how about something for Bikwil on Interglossa, Esperanto, Volapük and their other synthetic cousins?)

There was a slight political edge to Hogben’s writings, principally relating to his strong belief in the power of education, such as his book of essays entitled Dangerous Thoughts. A couple of quotes of his I found on the Internet follow.

To be proud of intellectual isolation from the common life of mankind and to be disdainful of the great social task of education, is as stupid as it is wicked.

People who have to rely on experts, will be subjugated.

So what do I like about Mathematics for the Million?

Primarily, its social perspective. From the very start of his Prologue, Hogben has us appreciating the historical evolution of whatever aspect of maths he is explaining. He begins, appropriately enough I suppose, with Zeno's Paradox of Archilles and the Tortoise, which he uses as a engaging and easy-to-understand launch pad to

. . . narrate how the grammar of measurement and counting has evolved under the pressure of man's changing social achievements, how in successive stages it has been held in check by the barriers of custom, how it has been used in charting a universe which can be commanded when its laws are obeyed, but can be never propitiated by ceremonial and sacrifice.

Later in the Prologue he speaks of his approach in these terms:

The customary way of writing a book about mathematics is show how each step follows logically from the one before without telling you what use there will be in taking it. This book is written to show you how each step follows historically from the step before and what use it will be to you or someone else if it is taken. The first method repels many people who are intelligent and socially alive, because intelligent people are suspicious of mere logic, and people who are socially alive regard the human brain as an instrument for social activity.

From then on, we are treated to the following chapter topics:

One chapter definitely worth reading is The Dawn of Nothing, which, as you may have guessed, is partly about the invention of Arabic (strictly, Hindu) numerals, in particular the concept of a symbol for zero. Incidentally, did you know that the word "algebra" is derived from the name of an ancient Arab mathematician? He was Abu Al Khwarizmi, who worked in Baghdad in the 8th century, (not the 13th, as Hogben claimed, which was when his writings became known in Europe in Latin).

Another passage of fascinating interest is Hogben's discussion of the sectarian uses arithmetic was put to during the period of the Reformation:

Peter Bungus, a Catholic theologian, wrote a book of 700 pages to show that the number 666 of the Beast was a cryptogram for the name of Martin Luther . . . Luther replied by interpreting it as a prophecy of the duration of the papal regime, which was happily approaching its predestined end . . .

Perhaps the most "useful" section of the book is Hogben's very serviceable method for translating problems "in the language of everyday life into the language of algebra". It could well be used in high schools, where many a young person has difficulty knowing even where to start when confronted with something like the following:

A train leaves London for Edinburgh at one o'clock, going at 50 miles per hour. Another train leaves Edinburgh for London, going at 25 miles per hour. If Edinburgh is 400 miles from London, when do they meet?

Or, worse:

When I am as old as my father is now, I shall be five times as old as my son is now. By then my son will be eight years older than I am now. The combined ages of my father and myself are 100 years. How old is my son?

But it doesn't stop there. Want to know about the mathematics of Stonhenge? Diophantus? James Bernoulli? Fermat? The Binomial Theorem? De Moivre’s Theorem? Maclaurin’s Theorem? Pascal’s triangle? Spherical triangles?

Be of good cheer: all such things are possible with Hogben’s help.

Assuming you've mastered all that, you are now invited by Hogben to seat yourselves at High Table and to partake of some really cryptic mathematical cuisine. Namely, a repast of heady treats like imaginary numbers, differential calculus, permutations and combinations, probability theory . . . As the Gershwins were more than once heard to remark, "Who could ask for anything more?"

Seriously, though, folks . . .

For such a book to get reprinted so often (I fancy it’s never been out of print), many others must have liked it as much as I have. As a convenient exit, two obvious ones had better be quoted — Albert Einstein ("It makes alive the contents of the elements of mathematics") and H.G. Wells ("A great book, a book of first class importance").

(The above article's title is from a 16th century history of Scotland by Raphael Holinshed. His Chronicles enjoyed great popularity in Elizabethan times, and indeed formed the basis for many of Shakespeare’s historical plays.)

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