I love novel ways of looking at arithmetic. I'm fascinated with how computers compute in binary, with tricks for simplifying calculations and with how Vedic mathematicians handle difficult arithmetic efficiently. So, when Princeton University Press sent me a review copy of their new book "Count Like An Egyptian," I immediately fell in love with it. I was delighted to learn even more techniques and the ideas behind them to deepen my appreciation of the beauty of what most consider to be mundane arithmetic.
"Count Like an Egyptian" is a delightful book, full of color illustrations, fun stories, lots of hands-on exercises, and an appreciation for the power of simple but deep ideas.
David Reimer was a pleasure to interview. He is a brilliant mathematician who hasn't lost sight of the power and beauty of mathematics. He taught me and modeled that, despite the stereotype, the more advanced mathematicians are the ones who are more likely to communicate ideas well.
We discussed these questions plus some nice tangents!
1. How did you get interested enough in Egyptian computation to write a book about it? What is the book about and who is the audience?
2. You're a math professor. What courses do you teach and at what level?
3. You researched the Rhind Papyrus to figure out how Egyptians did computations. Where did you get a hold of the Papyrus? How much time did you spend unraveling its secrets?
4. I'm fascinated with the idea that children can learn to do multiplication and division by just learning to double and add numbers. How did we develop such a cumbersome system of multiplication that requires memorizing tables?
5. I find it interesting that computers doing multiplication (and all other arithmetic) in binary equates to Egyptians doubling and adding numbers. Can you connect the dots for our listeners? (Nice video here, btw: https://www.youtube.com/watch?v=EDLLPnfpMfU)
6. Tell us about how Egyptians worked with fractions and why it was so novel.
7. One reviewer said this: "Of course our system is more apt for us (or for machines) to do calculations just following recipes, which need no insight or wit, but what we lose is that the Egyptian system keeps the practitioner sharp, forcing him or her to think about the problem and the result of the calculations." What do you think of the statement?
8. In addition to exploring Egyptian computation you also write about other mathematical systems. Tell us about those.
9. Is there a next book or big project?
10. The question I ask everyone: What advice would you give to a parent whose child was struggling with math in school?
About David Reimer
In high school I was a mediocre student at best. But I did far better on my SATs than was expected. I passed a number of AP exams never having taken any AP courses but learning from published study guides. This got me into Colgate. I started as a computer science major but quickly found that I knew more than my professors, at least in practical computing. I toyed with becoming a physics major, winning the school’s award for the best freshman physics student. I eventually settled on math as everyone in my family did.
Over the summers I worked at Creative Computing, which was then the largest computer magazine in the world and for Prudential Insurance, where I wrote the database for the central office’s purchasing department. I passed two actuarial exams and was offered a job but decided to take a try as a freelance programmer. On one project, which we spent six months on, the company cancelled and refused to pay us. Desperately needing money I taught night school calculus as an adjunct. I immediately knew that this is what I wanted to do for the rest of my life.
I got into the graduate math program at Rutgers. While most grad students taught recitations and graded papers, the department noticed my teaching skill and gave me my own higher level classes even giving me a 300-level course. I finished up my Phd. thesis while making some money as a full instructor first at Rutgers and then at Middlesex Community College. While there I was told that my proof of the Vandenberg-Kesten conjecture won the Polya Prize in Discrete Mathematics which is given every four years to what is considered to be the best work in discrete math during that period. The conjecture is a generalization of a probabilistic proposition often used in percolation, the theory of how things like epidemics and fires spread. Being overly simplistic it basically says that given two events that can happen anywhere but not in the same place, the probability of both happening is less than what would be expected if they were independent events. Based on this theorem I got what most would call a post doc at the Institute for Advanced Study in Princeton (where Einstein worked) and then a job at the College of New Jersey where I am today.
About "Count Like an Egyptian"
(From the Princeton University Press book page)
The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can't be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated--they technically didn't exist in the land of the pharaohs. You'll be counting like an Egyptian in no time, and along the way you'll learn firsthand how mathematics is an expression of the culture that uses it, and why there's more to math than rote memorization and bewildering abstraction.
Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you'll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.
Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation--the precursor to our modern system--and compares ancient Egyptian mathematics to today's math, letting you decide for yourself which is better.