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Many famous machines have been built to do math -- like Babbage’s Difference Engine for solving polynomials or Leibniz’s Stepped Reckoner for multiplying and dividing -- yet none worked as well as Albert Michelson’s harmonic analyzer. This 19th century mechanical marvel does Fourier analysis: it can find the frequency components of a signal using only gears, springs and levers. We discovered this long-forgotten machine locked in a glass case at the University of Illinois. For your enjoyment, we brought it back to life in this book and in a companion video series -- all written and created by Bill Hammack, Steve Kranz and Bruce Carpenter.
In 128 pages filled with over 150 beautiful photos, this book reveals the secrets of Albert Michelson’s harmonic analyzer. One reader told us “the minute depth of these photographs and the stunning clarity and the beauty of the images are really incredible.” Another shared that “the detail in the images brings the machine to life.” When immersed in the book’s gorgeous photos you’ll be transported to an era before silicon and logic circuits; a time when computers could only be made of polished brass, iron, wood and leather.
We’ve made four posters for you to enjoy. The photo array poster contains 43 images of the machine all taken from the book. The single view on white shows the entire machine -- from the base to the very top of the spring. The white poster composed of four views of the analyzer shows the front, right side, back and left side of the machine. The single view of the analyzer on black is taken from the cover of the book. It shows the machine at it’s largest -- nearly 70% actual size. On the right side, it contains a pictures of the machine’s parts with their respective page numbers in the book so this poster doubles as a table of contents! Download a PDF preview of all four posters.
The book opens with a detailed three-part visual table of contents that links together the machine’s motions to their mathematical function. We take you through each part of the equations being used for calculations and point you to the section of the book that implements that particular mathematical operation.
Subtle labels on the photographs guide you through the book. Set in inconspicuous, yet readily readable type, they both identify the parts and keep you oriented.
The book takes you through the machine’s operation part-by-part in order. The tour starts with the crank and describes fifteen separate parts, including the cone gear set, the rocker arms, the amplitude bars, and the magnifying wheel. It concludes with the output at the front of the machine. Each stop on the tour is illustrated in a two-page spread -- or more!
To help you understand deeply the machine we show you 44 configurations and the output produced. We show you all twenty sinusoids produced by the machine, and then show how to set the machine and its output for many mathematical functions: among them square waves, sincs, Bessel functions, and beats.
The book features eight two-page spread that show the machine from eight key angles. A reader described these as “simply beautiful.” Yet beyond mere beauty these detailed, rich views help you understand the machine in its entirety. They put in context every detail of the machine described in the book.
Two pages go deeper into the mathematics underlying the machine’s operation. They allow you to understand the machine more fully: you can understand the simplifications and approximations made by the machine when calculating. These pages used the notation of modern mathematics and so are a bridge to more formal discussions of Fourier analysis.
A facsimile of Albert Michelson’s 1898 paper on an 80-wheel version of this harmonic analyzer -- a machine four times the size of the one in this book -- shows over 30 examples of the kind of output one can make with more sinusoids. You can read in Michelson’s own words how he conceived of the machine, and how he thought about the machine.
In the video below Bill Hammack, the Engineer Guy, comments on every page of the book. He highlights subtle details, shares information that didn’t make it into the videos or this book, and even takes you behind the scenes a bit.
Albert Michelson's Harmonic Analyzer: A Visual Tour of a Nineteenth Century Machine That Performs Fourier Analysis
Bill Hammack, Patrick Ryan, & Nick Ziech
128 pages | 6 x 9 | 150 illustrations
Publisher Articulate Noise Books | firstname.lastname@example.org
Hardcover | ISBN 978-0-9839661-6-6 | 8.25 x 9.75
Paper | ISBN 978-0-9839661-7-3 | 8.5 x 8.5
Audience 01 — General Trade
MAT000000 MATHEMATICS / General
SCI000000 SCIENCE / General
MAT015000 MATHEMATICS / History & Philosophy
COM080000 COMPUTERS / History
Description Albert Michelson’s Harmonic Analyzer celebrates a nineteenth century mechanical calculator that performed Fourier analysis by using gears, springs and levers to calculate with sines and cosines—an astonishing feat in an age before electronic computers. One hundred and fifty color photos reveal the analyzer’s beauty though full-page spreads, lush close-ups of its components, and archival photos of other Michelson-inspired analyzers. The book includes sample output from the machine and a reproduction of an 1898 journal article by Michelson, which first detailed the analyzer. The book is the official companion volume to the popular YouTube video series created by the authors.