Video Series & Companion Book


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book cover

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Rediscover a forgotten mathematical relic

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.

Over 150 stunning full-color photos not seen in the video series

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.


Photos from the Book as Posters!

Download a PDF preview of all four posters

book cover

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Four posters: Study the machine

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.

Visual table of contents to maximize understanding

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.

Extensive labelling to aid you

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.

Part-by-part we guide you through the machine

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!

Extensive sample output to deepen understanding

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.

Eight stunning spreads let you “walk” around the entire machine

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.

Primer on Mathematics of Fourier Methods

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.

Michelson’s original paper announcing the machine

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.

Bonus video: Commentary on every page

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.


Link to analysis video