The Minaretic Octave

July 30, 2009

It was octarine, the color of magic. It was alive and glowing and vibrant and it was the undisputed pigment of the imagination, because wherever it appeared it was a sign that mere matter was a servant of the powers of the magical mind. It was enchantment itself. But Ringworld always thought it looked sort of greenish-purple.
—Terry Pratchett, The Color of Magic

Octarine, the Color of Magic

Octarine is also the color of Mardi Gras

Eight Immortals provided life and wealth in Ancient China

the Star of Chaos

Dharmacakra, the Wheel of Time; the Buddhist Noble Eightfold Path

Minarets are tall spires with octagonal, onion-shaped domes at the top. The Qutub Minar in Delhi India

Minarets appear often in Muslim architecture. Originally the minaret served as an illuminated watchtower and in current times the ‘Lighthouse’ is the vantage point for the muezzin’s call to prayer. Most lighthouses are actually octagons too.

Castle De Haar in Holland features the common octagonal turret. The turret is a small tower that projects vertically from a building, most notably in medieval castles. Breckles Church with a tower in Norfolk, England

The ‘Freedom Tower’ or One World Trade Center

There are 8 planets in our solar system if you don’t count Pluto.

Four terrestrial planets and four gas giants.

Musica universalis means universal music, or music of the spheres.  It was an ancient philosophy about the proportion of movement of the heavenly bodies, or planets.  The idea is generally attributed to Pythagoras. Johannes Kepler believed that the Music of the Spheres was what united Geometry, Cosmology, Astronomy, and Harmony through Music. 

Augustus Octavius was the first Emperor of Rome after the death of Julius Caesar.

The 8th Month, August, was named after Augustus.

In the Pagan Wheel of the Year, August is Lugnasadh or Lammas.

In music, an octave is the interval between one musical pitch and another with half or double its frequency.The octave “relationship” is a natural phenomenon which has been referred to as the ‘basic miracle of music'”, the use of which is common in most musical themes.

88 keys on a piano…

The compass determines direction related to the magnetic poles of the Earth.

Nobody knows for sure who first came up with the octal system, but the same can be said of all base systems. You might as well ask who invented counting. In order to count, there has to be some basis to the count which requires some formal understanding of base numbers, whether it be 2, 8, 10 or 60. 

The decimal system we use today began development in India around 1AD and spread to Europe via the Western Arabs, hence it is known as the Hindu-Arabic numeral system. But prior to that, decimal systems were largely dismissed because of their lack of factoring; the number 10 has only two factors: 2 and 5. By contrast, 60 has five consecutive factors: 2, 3, 4, 5 and 6. Thus base-60 (sexagesimal) was favoured by the ancient Sumerian civilisation 5,000 years ago and is still used to this day: circles still have 360 degrees and the 24-hour clock still has two periods of 12 hours with 60 minutes per hour. Ultimately, any civilisation that can perform highly complex calculations in base-60 would have to have been more than familiar with all other bases, even if only to know why they were unsuitable in the first place. 

Base-8 is clearly no better than base-10 in terms of factoring (2 and 4), but its close relationship to base-2 (binary) is hard to miss, even by ancient Sumerian standards. Indeed, the same can be said of all bases that are a power of 2 and if you can notate sexagesimal then you can certainly notate all bases below 60. 

We do know that the Native American Yuki and Mexican Pamean cultures used an octal system because they counted using the spaces between the fingers rather than the fingers themselves. But this does not equate to an understanding of octal in the same way an ancient Sumerian understood sexagesimal. If anything, it merely demonstrates a complete ignorance of all other bases and almost certainly wasn't used to perform complex calculations. 

But as to who actually invented octal first, nobody can possibly say for sure. I fancy the clever money would be on the Sumerian.