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.
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.
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