BARBURY CASTLE CROP CIRCLE

Crop circle designs developed in phases over 30 years, beginning with simple circles in the 1970's then expanding into pictorial designs (pictograms) in the late 1980's, complex geometries in 1991 and binary number designs in 2001. The Barbury Castle crop circle exemplifies the mathematics that are hallmarks of genuine formations. These mathematics point to the beginning of modern mathematics with mathematician-healer Pythagoras and his mentor, Apollo, in Greece.

The trail from modern crop circles to the foundational mathematics of our civilization starts with Gerald Hawkins, radio astronomer and former chair of the Department of Astronomy at Boston University. Hawkins identified four theorems first demonstrated by Euclid, 3rd century BCE mathematician at Alexandria. Hawkins had extensively studied Stonehenge, the megalithic site where crop circles first appeared in the 1970's, and written a book, Stonehenge Decoded, proving that numerous astronomical alignments were the basis of Stonehenge's design. Stonehenge's northeast orientation pointing to the rising sun on the longest day of the year, the summer solstice, was among the most obvious alignments that had intrigued astronomers for centuries.

The calculations to prove that extensive astronomical alignments were inherent in Stonehenge's design were too complex to be easily proven before the advent of super computers. Gerald Hawkins was able to gain access to a super computer in the 1960's to run the calculations to prove that Stonehenge was a highly structured, sophisticated astronomical observatory built by Neolithic people almost 5,000 years ago.

Hawkins said he first looked into crop circles because of their appearance near Stonehenge, but he was unable to find any correlations except geographic. Even though he did not find specific correlations with Stonehenge in the crop circles he examined, Hawkins found a pattern of relationships and ratios in crop circles that expressed four Euclidean theorems. A theorem is an expression of a rule or relationship in terms of a formula or symbols.

Four Euclidean rules that Hawkins identified in 12 of 19 crop circles enabled him to derive a fifth rule that Euclid had not expressed but was a logical extension of the first four. Hawkins appealed to the teachers and students who read Mathematics Teacher magazine to ask if anyone knew of published reference to a fifth rule derived from the four Euclidean theorems he had identified in 12 of 19 crop circles he had studied. None of the teachers and students who read Mathematics Teacher knew of any reference Euclid had made to such a theorem. A crop circle demonstrating the fifth rule Hawkins had derived from earlier crop circles was made the next year.

These ratios can be translated into musical notes and scales using Pythagoras' musical theory of the Lambdoma, a multiplication and division table that is the basis of diatonic scales used in Western music. Pythagorean theorems in crop circles point back to an era when the olden gods taught the mathematical foundations of Western civilization to Pythagoras. Reaching back 2,600 years into history, the timeless principles Pythagoras taught are renewed in crop circles.

Pythagoras spoke of different sorts of music to which the Lambdoma's ratios could be applied. Musica instrumentalis is the ordinary music made by playing the seven-string ancestor of the guitar the Pythagorean's invented; musica humana, is the music made by the human organism, especially the resonance between soul and body beyond the range of human hearing; and musica mundana, is the music of the cosmos, which would come to be known as the music of the spheres.

The basis of the Music Of The Spheres, according to Pythagoras, is that all matter vibrates and vibration produces sound that could be heard if were within the range of human hearing or perception. The Pythagoreans used mathematics to train the mind and sensitize perception to attune to the Ideal that Pythagoras postulated.

Pythagoras spent 22 years in Egypt as a priest of the temple before Cyrus the Great, King of Persia, burned the temples of Memphis and Thebes in 527 BCE and took him to Babylon as a prisoner. After returning to Greece Pythagoras founded the first of the Greek wisdom schools. Pythagoras and his students revered Apollo as their mentor in the tradition of the ancient mystery schools that acquired information from oracles and were sworn to vows of secrecy. The mathematician-healer Pythagoreans taught their principles with a stringed instrument called the cithara, which was the forerunner of the modern guitar.

Pythagoras literally means "Place of Apollo's Temple" in the ancient Greek language, formed from the words "pithias" which means "Apollo's Temple" and "agora" for "Place". Apollo is the only Greek deity who was not native to Greece, yet he represents order, harmony, and civilization in a way that most other Olympian deities cannot equal. Apollo is associated with music and medicine, and his role as the leader of the Muses establishes him as a patron of intellectual pursuits. His symbols include the musical lyre, the bow, and the swan representing Cygnus.

According to the Greek poet Hesiod, Apollo is the son of the Olympian Zeus and the Titan Leto the brother of the goddess Artemis. When Zeus's wife, Hera, found that Zeus had impregnated another goddess, the Titan Leto, she would not allow Leto to bear the children. Leto was forced to take shelter on the island Delos, which means "brilliant". Apollo was also identified with Helios, the all-seeing Sun god, and was worshipped in many places, particularly Corinth and Rhodes, after 450 BCE. Earlier accounts of Helios related that he was the son of Titan Hyperion and the Titaness Theia and was brother of Selene (the Moon) and Eos (Dawn).

We find an account of Apollo's birth on the distant northern island of Hyperborea, according to the 1st century BC historian, Diodorus Siculus, who quoted an earlier 3rd century historian, Hecataeus of Abdera: "There is a magnificent sacred precinct of Apollo and a notable temple which is spherical in shape" on an island inhabited by the Hyperboreans. Hyperborean is a Greek term for a people who lived in the distant north and worshiped the Greek Apollo. This often cited reference attributed to Hecataeus was taken from a 3rd century book that has now been lost except for an index but which Diodorus Siculus was familiar with in the 1st century BCE. The Dorian musical scale first developed on a lyre, called the hearpa in Old English, is commonly heard in Irish jigs and Gregorian chants and may have been the instrument that accompanied Anglo-Saxon poems and stories such as Beowulf. Depictions of lyres over 3,000 years show two main types: one with seven or fewer strings and one with more than seven strings. The lyre was one of Apollo's primary symbols in Greece where the Pythagoreans used the seven-string cithara.

Another account of the sun god's birth on an island is found in Egypt where Apollo was known as Horus. As Apollo appeared in Greece after the Dorian invasion, Horus appeared in pre-dynastic Egypt after his followers invaded there. The Egyptian form of Horus, Heru, can become Helu with the "l" and "r" interchangeable. This gives us the Greek solar god Helios, or Apollo. In Egypt Horus signified, "He who is above," from the Egyptian word "Hor", which translates as "face."

In his most popular form, Horus was known as "He who has on his brow Two Eyes," the sun and moon representing his eyes. He became part of Egyptian religion and was associated with the sun god, Ra. Horus was so important to Egyptian religion that Pharaohs were considered his human manifestation and even took on the name Horus. In the Osiris cults, Horus was the son of Osiris and Isis. He was conceived magically after the death of Osiris and brought up by Isis on a floating island in the marshes of Buto. As a child he was in constant danger from his uncle Seth, who had murdered his father Osiris, and who sent serpents and monsters to attack him. His mother, Isis, warded off the evil sent to him. As a young man, Horus avenged his father Osiris's death by victoriously waging war against Seth.

In Greece, England and Egypt, Apollo-Horus was associated with the appearance of mathematics and science that still confounds modern technology.

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