Looking at Numbers

Authors: Johnson, Tom, Jedrzejewski, Franck

  • Mathematics and music from a platonic point of view     
  • Numbers as Pythagoras might have seen them       
  • Numbers producing images  and music too    ​
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About this book

Galileo Galilei said he was “reading the book of nature” as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a technical, professional way, we tend to overlook their basic attributes, the things we can understand by simply “looking at numbers.”

Tom Johnson is a composer who uses logic and mathematical models, such as combinatorics of numbers, in his music. The patterns he finds while “looking at numbers” can also be explored in drawings. This book focuses on such drawings, their beauty and their mathematical meaning. The accompanying comments were written in collaboration with the mathematician Franck Jedrzejewski.

About the authors

Tom Johnson (1939) is considered a minimalist, since he works with simple forms, limited scales, and generally reduced materials, but he proceeds in a more logical way than most minimalists, often using formulas, permutations, predictable sequences and various mathematical models. He is particularly well known for his operas. The Four Note Opera (1972) has been presented in 11 different languages since its premier 40 years ago. Riemannoper has been staged more than 30 times in German-speaking countries since its premier in Bremen in 1988. Often played non-operatic works include Bedtime Stories, Rational Melodies, Music and Questions, Counting Duets, Tango, Narayana's Cows, and Failing: a very difficult piece for solo string bass. His longest work is the Bonhoeffer Oratorio for four soloists, two choruses and orchestra, presented in Maastricht (1996), Berlin (1998) and New York (2000). The book Conversations avec Tom Johnson, in collaboration with Bernard Girard, was published in 2011.

Franck Jedrzejewski is a researcher in mathematical physics at the
CEA Saclay and has also a PhD in philosophy and musicology. He
teaches at the INSTN as well as in the University of Paris Sud and
Versailles-Saint-Quentin.

Reviews

“T. Johnson and F. Jedrzejewski’s book Looking at numbers presents a dual perspective (musical and mathematical) on making sense of a large set of drawings created by Johnson to illustrate self-discovered patterns in finite collections of numbers. … Overall, for a non-expert in the overlap of music and mathematics, the book is interesting and fairly well written.” (Guadalupe I. Lozano, Mathematical Reviews, June, 2015)


Table of contents (11 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-0348-0554-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-3-0348-0553-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Looking at Numbers
Authors
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0554-4
DOI
10.1007/978-3-0348-0554-4
Softcover ISBN
978-3-0348-0553-7
Edition Number
1
Number of Pages
XVII, 120
Number of Illustrations and Tables
138 b/w illustrations, 1 illustrations in colour
Topics