Music of the spheres?
Interview with Gerald S. Hawkins
by Monte Leach
A radio astronomer reports on the mathematical relationships within the elements of crop circles in England.
Gerald S. Hawkins earned a Ph D in radio astronomy with Sir Bernard Lovell at Jodrell Bank, England, and a D Sc for astronomical research at the Harvard-Smithsonian Observatories. His undergraduate degrees were in physics and mathematics from London University. Hawkins’ discovery that Stonehenge was built by neolithic people to mark the rising and setting of the sun and moon over an 18.6-year cycle stimulated the new field of archaeoastronomy. From 1957 to 1969 he was Professor of Astronomy and Chairman of the Department at Boston University, and Dean of the College at Dickinson College from 1969 to 1971. He is currently a commission member of the International Astronomical Union, and is engaged in research projects in archaeoastronomy and the crop circle phenomenon.
Monte Leach: How did you get interested in the crop circle phenomenon?
Gerald Hawkins: Many years ago, I had worked on the problem of Stonehenge, showing it was an astronomical observatory. My friends and colleagues mentioned that crop circles were occurring around Stonehenge, and suggested that I have a look at them.
I began reading Colin Andrews’ and Pat Delgado’s book, Circular Evidence. I found that the only connection I could find between Stonehenge and the circles was geographic. But I got interested in crop circles for their own sake.
ML: What interested you about them?
GH: I was very impressed with Andrews’ and Delgado’s book. It provided all the information that a scientist would need to start an analysis. In fact, Colin Andrews has told me that that’s exactly what they intended to happen. I began to analyse their measurements statistically.
The major scale
ML: What did you find?
GH: The measurements of these patterns enabled me to find simple ratios. In one type of pattern, circles were separated from each other, like a big circle surrounded by a group of so-called satellites. In this case, the ratios were the ratios of diameters. A second type of pattern had concentric rings like a target. In this case, I took the ratios of areas. The ratios I found, such as 3/2, 5/4, 9/8, ‘rang a bell’ in my head because they are the numbers which musicologists call the ‘perfect’ intervals of the major scale.
ML: How do the ratios correspond with, for instance, the notes on a piano that people might be familiar with?
GH: If you take the note C on the piano, for instance, then go up to the note G, you’ve increased the frequency of the note (the number of vibrations per second), or its pitch, by 1 1/2 times. One and one-half is 3/2. Each of the notes in the perfect system has an exact ratio — that is, one single number divided by another, like 5/3.
ML: If we were going to go up the major scale from middle C, what ratios would we have?
GH: The notes are C, D, E, F, G, A and B. The ratios are 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, finishing with 2, which would be C octave.
ML: How many formations did you analyse and how many turned out to have diatonic ratios relating to the major scale?
GH: I took every pattern in their book, Circular Evidence. I found that some of them were listed as accurately measured and some were listed as roughly or approximately measured. I finished up with 18 patterns that were accurately measured. Of these, 11 of them turned out to follow the diatonic ratios. Colin Andrews has since given me accurate measurements for one of the circles in the book that had been discarded because it was inaccurate. That one turned out to be diatonic as well. We finished up with 19 accurately measured formations, of which 12 were major diatonic.
The difficulty of hitting a diatonic ratio just by chance is enormous. The probability of hitting 12 out of 19 is only 1 part in 25,000. We’re sure, 25,000 to 1, that this is a real result.
ML: Could this in some way be a ‘music of the spheres’, so to speak?
GH: I am just a conventional scientist analyzing this mathematically. One has to report that the ratios are the same as the ratios of our own Western invention — the diatonic ratios of the (major) scale. We have only developed this diatonic major scale in Western music slowly through history. These are not the ratios that would be used in Japanese music, for instance. But I am not calling the crop circles ‘musical’. They just follow the same mathematical relationships.
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