Hints of Trigonometry on a 3,700-Year-Old Babylonian Tablet

Suppose that a ramp leading to the top of a ziggurat wall is 56 cubits long, and the vertical height of the ziggurat is 45 cubits. What is the distance x from the outside base of the ramp to the point directly below the top? (Ziggurats were terraced pyramids built in the ancient Middle East; a cubit is a length of measure equal to about 18 inches or 44 centimeters.)”


Venus, The Rose and the Heart

This is the ‘dance’ of Venus, as viewed from earth.

“Venus has an eight-year rhythm, which formed the subject of the world’s oldest astrological text, a Venus-tablet from Nineveh. It was part of a series called Enuma Anu Enlil, the ‘Book of the Gods of Heaven and Earth’, and was dated to the 17th century BC. It effectively recorded the five synodic periods of Venus, giving a series of ten omens over the eight-year cycle through the pattern of Venus’s appearance and disappearance from view.

“To the astronomer Johannes Kepler, the musical interval generated by Venus and Earth was a ‘sixth’, given by dividing a string in the fraction 5/8.  He said the relation was a ‘marital’ one and varied between the ‘masculine sixth’ G# – E and the ‘feminine’ one of Gb – E. This ratio of 5 to 8 is the key to the pattern traced by Venus against the stars.

“Venus traces a pentagon shape in the sky over ten meetings with the Sun; it does this by moving, between each ‘inferior’ conjunction, exactly 1.6 times around the zodiac, and the time it takes to do this, 584 days, is its synodic period. The pentagon shape is traced around the zodiac in five such synodic periods, which is 7.993 years or 8 years to a fraction of a day. Venus returns to the same portion of the zodiac after ten solar conjunctions, over a period of exactly 8 years.

“The rotation rate of Venus on its own axis was not discovered until 1967 by means of radar. This was able to peer through the dense mists surrounding the planet, and find a rotation period of precisely two-thirds of an Earth-year, or 243 days. Strangely enough, it was in the opposite direction to its rotation around the Sun. This meant that, in an eight-year period, Venus revolves exactly twelve times on its own axis. The numbers 5, 8 and 12 are here interacting. “

Nick Kollerstrom

Coltrane’s Circle of Fifths

From Open Culture:

Physicist and saxophonist Stephon Alexander has argued in his many public lectures and his book The Jazz of Physics that Albert Einstein and John Coltrane had quite a lot in common. Alexander in particular draws our attention to the so-called “Coltrane circle,” which resembles what any musician will recognize as the “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in his seminal text, Repository of Scales and Melodic Patterns. Where Lateef, as he writes in his autobiography, sees Coltrane’s music as a “spiritual journey” that “embraced the concerns of a rich tradition of autophysiopsychic music,” Alexander sees “the same geometric principle that motivated Einstein’s” quantum theory.

Neither description seems out of place. Musician and blogger Roel Hollander notes, “Thelonious Monk once said ‘All musicians are subconsciously mathematicians.’ Musicians like John Coltrane though have been very much aware of the mathematics of music and consciously applied it to his works.”

The Timbuktu Manuscripts 13C+


Timbuktu Manuscripts or (Tombouctou Manuscripts) is a blanket term for the large number of historically important manuscripts that have been preserved for centuries in private households in Timbuktu, Mali. The collections include manuscripts about art, medicine, philosophy, and science, as well as priceless copies of the Quran. The number of manuscripts in the collections has been estimated as high as 700,000.


The majority of manuscripts were written in Arabic, but many were also in local languages, including Manding, Songhay and Tamasheq. The dates of the manuscripts ranged between the late 13th and the early 20th centuries (i.e., from the Islamisation of the Mali Empire until the decline of traditional education in French Sudan). Their subject matter ranged from scholarly works to short letters. The manuscripts were passed down in Timbuktu families and were mostly in poor condition.[4] Most of the manuscripts remain unstudied and uncatalogued, and their total number is unknown, affording only rough estimates. A selection of about 160 manuscripts from the Mamma Haidara Library in Timbuktu and the Ahmed Baba collection were digitized by the Tombouctou Manuscripts Project in the 2000s.


With the demise of Arabic education in Mali under French colonial rule, appreciation for the medieval manuscripts declined in Timbuktu, and many were being sold off. Time magazine related the account of an imam who picked up four of them for $50 each. In October 2008 one of the households was flooded, destroying 700 manuscripts.

from Wikipedia via Muslim Culture