Book Report — The Old Math

IMG_1379IMG_1380I just finished How to Become Quick at Figures, which was, as the graphic shows, published late in the 19th century. I found the attitude of the book fascinating. For instance, this, not a cover page, appeared immediately before the Table of Contents:

MEN WANTED

“It has been truly said that the great want of the age is men. Men of thought; men of action. Men who are not for sale. Men who are honest to the heart’s core. Men who will condemn wrong in friend or foe — in themselves as well as others. Men whose consciences are as steady as the needle to the pole. Men who will stand for the right if the heavens totter and the earth reels. Men who can tell the truth and look the world and the devil right in the eye. Men who neither swagger nor flinch. Men who are Quick at Figures. Men who can have courage without whistling for it, and joy without shouting to bring it. Men through whom the current of everlasting life runs still, and deep and strong. Men too large for certain limits, and too strong for sectarian bands. Men who know their message and tell it. Men who know their duty and do it. Men who know their place and fill it. Men who mind their own business. Men who will not lie. Men who are not too lazy to work, nor too proud to be poor. When in office, the workshop, the counting room, in the bank, in every place of trust and responsibility, we can have such men as these, we shall have a christian civilization — the highest and best the world ever saw.

And then this, right after the Table of Contents:

DO SOMETHING

Do not spend your precious time in wishing, and watching, and waiting for something to turn up. If you do, you may wish and watch and wait forever. You can do it if you wish, but you must put forth the effort. Idleness and indifference never accomplished anything. It takes energy and push to make headway in the world, and an active, energetic, persevering man is sure to succeed. If he can not do one thing he will do something else. If he can not succeed in one direction he will in some other. He will do something. He will not waste his time in idleness. There is no lack of work, no lack of opportunities. Do what comes to your hand, and do it well. True progress is from the less to the greater. You must begin low if you would build high. Work is ordinarily the measure of success. Quit resolving and re-resolving and go and do something. —  School Supplement.

The author or sponsors of this book obviously felt that men worthy of leadership were in short supply. When aren’t they?

The author could be S. Stone, cited in the bibliography of Revelations of a Spirit Medium, a book to debunk charlatans published in 1922, or John Scott, listed author of a 1915 book that appears to be an updated edition of this one.

The book’s contents begin with many methods and special cases of arithmetic problems common in the mid- to late-19th century business world. There are then specific and brief chapters about business applications like simple and compound interest. The book includes references for the many different systems of measurement in use at the time, including avoirdupois, Troy, Imperial, and the nascent (at the time) Metric Systems. The last pages of the book feature parlor tricks and puzzles for entertainment purposes. It seems that this section was a resource for the book that cited it above in debunking numerological hocus-pocus.

As the tone of the block quotes above suggests, the book is designed for self-improvement at a time when the U.S. was growing rapidly in territory, population, and wealth. The 1880s were a period of recovery after the longest period of continuous economic contraction in U.S. history, 1873-1879, which, at 65 months, was actually longer than the period of contraction recorded for the depression between the 20th century’s two great wars. People of the time called this the “Great Depression.” It was not as severe in depth as the depression of the 1930s, but it was statistically longer. In 1883, a young man looking to make his fortune would have been encouraged by the continuing Second Industrial Revolution and the increase in settled territory where commerce would become more feasible, relatively continuously, for the next thirty years.

I also found it fascinating that the author or authors of the quotes above called up so many virtues that we might — or at least, I do — associate with honorable military service. The U.S. was still reeling culturally from the Civil War less than two decades earlier, and the leaders of businesses would have been people who lived through those difficult years and many of them would have been veterans. I’ve spent significant time around veterans of the U.S. armed forces, and they always seem to be wishing that the young people they encounter had more of these qualities. This may be something I hear more often because I am a teacher and like to have conversations with them about my work.

The arithmetic methods were fascinating to me. Many are very mechanical and specific. For instance: to square a two-digit number ending in 5 (useful for exactly 9 calculations), multiply the tens’ digit by one more than itself and append 25. So 75 squared is 5,625. I recognize in others basic content from my algebra courses: to multiply two mixed numbers, add the product of the whole numbers, the product of the first fraction and the second whole number, the product of the second fraction and the first whole number, and the product of the fractions. If we were to write the mixed numbers as the sums of whole numbers and fractions and apply the FOIL method, this is exactly the result we would get. The author is exhorting the student to do all of this mentally. My students would convert the mixed numbers to fractions, multiply the fractions, and the convert the product back to a mixed number, if that is appropriate. I can do that in my head, and I can do the method presented in the book in my head … but I wouldn’t challenge students in my classes to do it.

As I move on to my next book — I’m hoping to read one book per week and write about each one here — I am pondering how an updated version of this book would look in today’s context. Machines do all of this for us now, instantly. Most of us do not desire to know how the machines work or how the machines are programmed to do the work. This makes modern math seem like a kind of magic, perhaps even more than it seemed to be 140 years ago, at a time when an estimated one-sixth of the U.S. population, including 70% of its non-White population, could not read. I don’t like that math seems like magic. I’d like to do something about that. Hmmm…

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