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.
How did you get interested in the crop circle phenomenon?
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.
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
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
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.
we were going to go up the major scale from middle C, what ratios would
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.
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.
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.
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.
Who done it?
established that there's a 25,000 to 1 chance that these ratios are
random occurrences. What about natural science processes?
science processes, left to their own devices, like whirlwinds, rutting
hedgehogs, and bacteria have no relationship to the diatonic ratios.
They (the diatonic ratios) are human-invented. They are the human response
to sound. The only place I can find diatonic ratios in nature are bird
calls and the song of the whale. I don't think the birds made the circles,
nor did the whales.
we've eliminated natural phenomena. What about Douglas Bower and David
Chorley (Doug and Dave), the two Englishmen who claimed last year that
they created the circles. Could they have formed these diatonic ratios?
GH: They could
have, if they knew about the diatonic scale, and wished to put it in
the circles. But I think we have to quote their reason for making the
circles. They said they "did it for a laugh." That's fine.
If they did it for a laugh, then it doesn't fit with putting in such
an esoteric piece of information. I did write to them. They never replied.
wrote to them saying what?
did you put diatonic ratios in?"
they didn't reply.
GH: No. I
think we can eliminate them. It's so difficult to make a diatonic ratio.
It has to be laid out accurately to within a few inches with a 50 foot
circle, for example.
many if not all of these circles were created at night.
Mostly they seem to be created at night.
eliminates natural processes and Doug and Dave. What's left?
GH: Lord Zuckerman
[former science adviser to the British Government] wrote a review of
Colin Andrews' and Pat Delgado's book. He said that before we start
building theories we should first investigate what would be perhaps
the most pleasant solution for scientists, which is that the formations
were made by human hoaxers. In a way, he's not stating that that is
his notion. He thinks it would be the simplest explanation. In fact,
I am not supporting the theory that they are made by hoaxers. I am only
investigating the theory that it's done by hoaxers to see if that makes
GH: Yes, but
now I've upgraded the investigation, because I've found an intellectual
profile. This means I've eliminated all natural science processes, so
I don't have to consider any of those any more. The intellectual profile
narrows it down.
have you found in terms of this intellectual profile?
GH: My mathematical
friends have commented on my findings. The suspected hoaxers are very
erudite and knowledgeable in mathematics. We have equated the intellectual
profile, at least at the mathematics level, as senior high school, first
year college math major. That's pushing it to a narrow slot. But there's
more to this than just the diatonic ratios.
GH: The year
1988 was a watershed because that was when the first geometry appeared.
It is in Circular Evidence. These geometrical patterns were quite
a surprise to me. There are only a few of them.
are in addition to the circles you investigated in terms of the diatonic
GH: The geometry
is really 'the dog', and the diatonic ratios of the circles are 'the
tail.' That is, there is much more involved in the geometry than in
those simple diatonic ratios in the circles, although, interestingly,
the diatonic ratios are also found in the geometry, without the need
for measurement. The ratio is given by logic - mind over matter.
did you find from these more complex patterns?
GH: Very interesting
examples of pure geometry, or Euclidean geometry.
found Euclidean theorems demonstrated in these other patterns?
are plane geometry, Euclidean theorems, but they are not in Euclid's
13 books. Everybody agrees that they are, by definition, theorems. But
there's a big debate now between people who say that Euclid missed them,
and those that say he didn't care about them - in other words, that
the theorems are not important. I believe that Euclid missed them, the
reason being that I can show you a point in his long treatise where
they should be. They should be in Book 13, after proposition 12. There
he had a very complicated theorem. These would just naturally follow.
Another reason why he missed them was that we are pretty sure that he
didn't know the full set of perfect diatonic ratios in 300 BC.
are theorems based on Euclid's work, but ones that Euclid did not write
down himself. But they are widely accepted as fulfilling his theorems
GH: Only widely
accepted after I published them. They were unknown.
on your analysis of these crop circles, you discovered the theorems
GH: Yes. A
theorem, if you look it up in the dictionary, is a fact that can be
proved. The trouble is, first of all, seeing the fact, and then being
able to prove it. But there's no way out once you've done that. The
intellectual profile of the hoaxer has moved up one notch. It has the
capability of creating theorems not in the books of Euclid.
It does seem that
senior high school students can prove these theorems, but the question
is, could they have conceived of them to put them in a wheat field?
In this regard, we've got a very touchy situation in that there is a
general theorem from which all of the others can be derived. I stumbled
upon it by luck and accident and colleagues advised me to not publish
it. None of the readers of Science News [which published an article
on this subject] could conceive of that theorem. In a way, it does indicate
the difficulty of conceiving these theorems. They may be easy to prove
when you're told them, but difficult to conceive.
I would assume that the readers of "Science News" would be
pretty well versed in these areas.
GH: It's a
pretty good cross-section. The circulation is 267,000. We found from
the letters that came in that Euclidean geometry is not part of the
intellectual profile of our present-day culture. But it is part of the
culture of the crop circle makers.
about the more recent formations?
GH: Now we
enter the other types of patterns - the pictograms, the insectograms.
Exit Gerald S. Hawkins. I don't know what to do about those.
investigations leave off at the geometric patterns.
GH: The investigations
are continuing, but I haven't gotten anywhere. I see no recognizable
mathematical features. I'm approaching it entirely mathematically, because
there is the strength of numbers. There's the unchallengeability of
a geometric proof of a theorem, for example. The other patterns involve
other types of investigation, such as artistry and images.
I've told you here shows that we've got a developing phenomenon, starting
from the very simple arrangement of diatonic ratios, to a very intricate
way of showing diatonic ratios in the geometries, and now to something
which I think hardly anybody would claim to understand - the pictograms,
insectograms, and so forth.
the major focus of your work right now is looking into these?
GH: Yes. It's
totally absorbing. It's not a joke. It's not a laugh. It's not something
that can be just brushed aside.
there anybody else who is investigating it seriously in terms of your
GH: No. It
boils down to two factors. You wouldn't get a grant to study this sort
of thing. And, two, it might endanger your tenure. It is as serious
as that. There are whole areas in the scientific community that are
not informed about the crop circle phenomenon, and have come to the
conclusion that it is ridiculous, a hoax, a joke, and a waste of time.
It's a difficult
topic because it tends to raise a knee-jerk solution in people's minds.
Then they are stuck. Their minds are closed. One can't do much about
it. But if they can keep an open mind, I think they'll find they've
got a very interesting phenomenon.