DARING INVENTION OF LOGARITHM

I became acquainted with the author through our shared love of aviation. This book is extremely well researched and was a joy to read.

There are numerous books written about the development of logarithms, most never getting to the basics of how the concept was developed. This book saves the day -- answers the question nicely. The book is quite readable, too. And, the price is a real bargain.

Most mathematicians are aware of the logarithm tables of John Napier, the definition of the logarithm function by Johannes Kepler, and its modern version by Leonard Euler. But there is so much more to the invention of logarithms that have marked a revolution in physics, in particular astrophysics, in the 17th century.In the early 17th century, numerical computations in astrophysics required addition, subtraction, multiplication, division, computation of powers, and extraction of roots. Computations were done by hand, and the first known machine has been created in 1623 by Wilhelm Schickard whose motivation was to support Kepler in his tedious computations. But while his and a later independent machine by Blaise Pascal supported addition and subtraction very well, all the other operations remained very tedious, even with machine support. The logarithm essentially reduces the effort to efficient additions and subtractions, and it has been the basis for a leap in scientific progress.Klaus Truemper takes us back to an unknown period between 1600 and 1609, when Jost Bürgi completed his seminal work on logarithm tables, well before John Napier. First he sets the stage: The known mathematics at this time, in particular no concept of the logarithm function, not even the term “logarithm”, and only very cumbersome notation of decimal fractions. Then he describes the work of Bürgi by “looking over his shoulder”. He emphasises how Bürgi optimised the computational effort in creating his tables, and he points out how close he came to inventing slide rules and similar devices that have been instrumental for numerical calculations for centuries to come; they were replaced by pocket calculators not before the 1970s. He even includes an imaginary “interview” with Jost Bürgi. Then he covers the independent work of John Napier, who used a different approach to logarithm tables, and finally Henry Briggs, who build on the work of Napier and produced the kind of logarithm tables that were popular until the 1970s. Finally, Klaus Truemper interprets his findings on a solid philosophical basis.I hope the above motivates you to read this book. I have been a professor of Mathematics and a professor of Computer Science, and I have learned a lot. But you don’t need such a background at all: If you have only very basic mathematical skills, you will enjoy this book. Admittedly, there are a few “dangerous bends”, but Klaus Truemper warns you just in time, and you can skip that and still enjoy this remarkable journey!

When I was doing a little reading about the development of logarithm ideas, I was confused because the early publications of tables by Bürgi, Napier, and Briggs had different purposes and used different approaches.Truemper's terse volume helped bring me into the mindset of these thinkers and the ways they advanced computation algorithms by using logarithms. Truemper examines how the choices these thinkers made led to different tables all of which worked as huge computational time-savers.One of the strengths of this book is that Truemper makes scaled tables that clarify the exponential bases used by each thinker, and he employs modern-day notation regarding exponents and decimal points when it is helpful in the service of clarifying things.

Would have liked even more detail, but this is a very good account. And the author is engaging and interesting. I like the style.The Burgi treatment is especially good.