Alien Dawn: A Classic Investigation into the Contact Experience (8 page)

It so happened that, on the other side of the Atlantic, another scientist had been corresponding with Zuckerman and was following his advice.
Gerald S.
Hawkins was a British radio astronomer who had been professor of astronomy at Boston University, and had achieved international celebrity through his book
Stonehenge Decoded
in 1965.
In 1960, he had used a computer to investigate an idea that had been planted in his head when he attended a lecture on Stonehenge at London University in 1949: that Stonehenge may be a complex calendar or computer to calculate moonrise and sunrise over the 18.6-year moon cycle.
The idea, which caused fierce controversy at the time, is now generally accepted, and has become the basis of the new science of archaeoastronomy—the study of ancient peoples’ knowledge and beliefs about celestial phenomena.
Subsequently he went on to apply the same techniques to the pyramids of Egypt.

Hawkins started Boston University research in 1989, the year that
Time
magazine published a long article on the crop-circle controversy.
He was intrigued by the photographs, and by the comment of a few colleagues that perhaps the circles might provide him with another problem for computer analysis.
After all, they were mostly in the same county as Stonehenge.
Later that year, on a visit to England, he picked up a copy of
Circular Evidence
by Andrews and Delgado—which had become an unexpected bestseller, demonstrating that the phenomenon was now arousing worldwide interest.

Andrews and Delgado had carefully measured eighteen of the circles, and included the measurements in their book.
A glance told Hawkins that this was not suitable material for computer analysis.
The obvious alternative was a mathematical or geometrical approach—to compare the size of the circles.

As a typical scientist, Hawkins had already plodded through
Circular
Evidence
page by page.
Being an astronomer, he was treating the book like a star catalogue.
Andrews and Delgado had measured twenty-five circle patterns with engineering precision, and gave them in order of appearance.
The first forty pages were large circles with satellites, and the diameters revealed a musical fraction, accurate to one percent.
Anyone can check this from the book by just taking a pocket calculator and dividing the large by the small.
One percent, by the way, is high precision for the circle maker.
It is only just detectable in a symphony orchestra, and totally unnoticeable in a rock group.

But after 1986 things changed.
From this time on circles appeared with rings around them.
Hawkins found the simple fraction was now given by the
area
of the ring divided by the
area
of the circle.
From schooldays we recall that ancient area formula, pi-r-squared.
Modern computer experts would say, ‘Ha!
Data compression.
We get a larger ratio from the same sized pattern’.

The first step in his reasoning was that, if the first circles had been made by Meaden’s vortices, then all patterns involving several symmetrical circles must be ruled out, since a whirlwind was not likely to make neat patterns.
Which meant that the great majority of circles since the mid-1980s must be made by hoaxers.
But would hoaxers take the trouble to give their patterns the precision of geometrical diagrams?
In fact, would they even be capable of such precision, working in the dark, and on a large scale?
They would be facing the same kind of problem as the makers of the Nazca lines in the desert of Peru—the great birds, spiders and animals drawn on the sand—but with the difference that the Nazca people worked by daylight and had an indefinite amount of time at their disposal, whereas the circle makers had to complete their work in the dark in a few hours.

Hawkins began by looking closely at a ‘triplet’ of circles which had appeared at Corhampton, near Cheesefoot Head on 8 June 1988.
To visualise these, imagine two oranges on a table, about an inch apart.
Now imagine taking a small, flat piece of wood—like the kind by which you hold an ice lolly—and laying it across the top of them.
Then balance another orange in the centre of the lolly stick, and you have a formation like the Cheesefoot Head circles of 1988
.

Now even a nonmathematical reader can see that the lolly stick forms what our teachers taught us to call a tangent to
each
of the oranges.
And, since all the oranges are spaced out equally, you could insert two more lolly sticks between them to make two more tangents.
The three sticks would form a triangle in the space between the three oranges.

That is a nicely symmetrical pattern.
But, of course, it does not prove that the circle makers were interested in geometry.
Perhaps they just thought there was something pleasing about the arrangement.

When he had been at school, Hawkins had been made to study Euclid, the Greek mathematician, born around 300 BC, who had written the first textbook of geometry.
Euclid is an acquired taste; either you like him or you don’t.
Bertrand Russell had found him so enjoyable that he read right through the
Elements
as if it were
Alice in Wonderland.

As an astronomer, Hawkins had always appreciated the importance of Euclid, in spite of having been brow beaten with him at school.
So now he began looking at his three circles, and wondering if they made a theorem.
He tried sticking his compass point in the centre of one circle, and drawing a large circle whose circumference went through the centres of the other two circles.
He realised, to his satisfaction, that the diameter of the large circle, compared with that of the smaller ones, was exactly 16 to 3.

So now he had a new theorem.
If you take three crop circles, and stick them at the corners of a small equilateral triangle, then draw a large circle that passes through two centres, the small circles are just three sixteens the size of the larger one.

He looked up his
Elements
to see if Euclid had stumbled on that one.
He hadn’t.

Of course, it is not enough to work out a theorem with a ruler: it has to be proved.
That took many weeks, thinking in the shower and while driving.
Eventually, he obtained his proof—elegantly simple.

After this success, he was unstoppable.
Another crop-circle pattern, in a wheatfield near Guildford, Surrey, showed an equilateral triangle inside a circle—so its vertices touched the circumference—then another circle
inside
the triangle.
Hawkins soon worked out that the area of the bigger circle is four times as large as the smaller one.

Another circle used the same pattern, but with a square instead of a triangle.
Here, Hawkins worked out, the bigger circle is now twice as large in area as the smaller one.

When another circle replaced the square with a hexagon, he worked out that the smaller circle is three-quarters the size of the larger one.

Now so far, you might say, he had proved nothing except that crop-circle patterns—which might have been selected by chance, like a child doodling with a pair of compasses and a ruler—could be made to yield up some new theorems.
But, early in the investigation, he had stumbled upon an insight that added a whole new dimension.

It so happened that his wife, Julia, had always had an ambition to play the harp.
So Hawkins bought her one.
And, although he was not a musician, he decided to tune the harp himself.
Which in turn led him to teach himself the elements of music.

The musical scale, as everyone knows, has eight notes—doh, re, mi, fa, so, la, ti, doh.
The top doh completes it, but also begins a new octave.
These are the white notes on a piano keyboard—we also call them C, D, E, F, G, A, B and top C—and we feel that they are somehow natural and complete.
But of course the keyboard also has black notes, the semitones.
Hawkins found that the harp sounded better if he tuned it according to the white notes—which are also known as the diatonic scale—and used mathematical fractions.

Now the reason that each sounds different is that they all differ in
pitch,
which is the number of times the piano string vibrates per second.
The doh in the middle of a piano keyboard is 264 vibrations per second.
And the top doh is exactly twice that—528 vibrations per second.
And since, to our Western ears, the remaining six notes sound ‘perfectly spaced’, you might expect each note to increase its vibrations by a jump of one seventh, so that re is one and a seventh, mi is one and two-sevenths, and so on.
But our Western ears deceive us—the notes are not perfectly spaced.
In fact, re is one and an eighth, mi is one and two-eighths, fa is one and a third, soh one and a half, la one and two-thirds, and ti one and seven-eighths.

However, the points is that these
are
simple fractions.
The black notes are a different matter.
While re is one and an eighth above doh, the black note next to it (called a minor third) is 32 divided by 27, which no one could call a simple fraction.

Now, as Hawkins went on measuring and comparing crop circles, he discovered that most of the ratios came out in simple fractions—and, moreover, the fractions of the diatonic scale, listed above.
The 16:3 of the Cheesefoot Head formation was the note F.
Three well-known circle formations yielded 5:4, the note E, 3:2, the note G, and 5:3, the note A.
A few, where circles and diameters were compared, yielded two notes.

If Doug and Dave, or other hoaxers, had been responsible for the crop circles, then the odds were thousands to one against this happening (Hawkins calculated them as 25,000 to 1).
In fact, Hawkins studied a number of circles that Doug and Dave admitted to, and found no diatonic ratios in any of them.

Now it is true that not every circle revealed this musical code.
Out of the first eighteen Hawkins studied, only eleven were ‘diatonic’.
The answer may be that Doug and Dave had made the other seven.
Or that some of the ‘circle makers’ were not musical.
Yet almost two-thirds was an impressive number, far beyond statistical probability.

So Hawkins felt he had stumbled on a discovery that was as interesting as any he had ever made.
If the ‘circle makers’ were human hoaxers, then they had devised a highly sophisticated code.

But why bother with a code?
Why not simply spell out the message, like the WEARENOTALONE inscription, which is claimed by Doug and Dave?
An obvious answer suggests itself.
WEARENOTALONE sounds like Doug and Dave.
But a code of diatonic ratios is almost certainly beyond Doug and Dave.

Following the advice of Lord Zuckerman, Gerald Hawkins sent off an account of his findings to
Nature,
the prestigious magazine for publishing new and yet-to-be-explained discoveries.
In 1963,
Nature
had published his work on Stonehenge, but now in July 1991 the editor balked, saying: your findings do not ‘provide a sufficient advance towards understanding the origin of crop circles to excite immediate interest of a wide scientific audience’.

It was like asking an astronomer to explain the origin of the stars, sun or moon.
Hawkins, like any careful research scientist, does not rush in with a theory.
He looks at the facts that are there.
Edmund Hilary did not ask for the theory of origin of Mount Everest, he climbed it because it was there.

Even now as I prod and poke, I cannot get Hawkins to come out with an origin.
For him, the game’s afoot.
He continues to investigate the theory of hoaxers as Zuckerman suggested, but what he has found in the intellectual profile has made him even more cautious.
Now he talks about ‘circle makers’, a tautology that neatly covers hoaxers and all possible origins.

But let us go back to the basic question.
If
there is a complex geometry hidden in the circles, does this not suggest that
nonhuman intelligences are trying to communicate with us?
If Hawkins’s geometry leads us to conclude that the answer is yes, then we have decided a question that has been preoccupying scientists for well over two centuries: the question of whether we are alone in the universe, or whether there are other intelligent beings.