Highly Composite Journal

Posting every day has become a ritual though not on a schedule like breakfast or bedtime. It’s something I do in between those two daily milestones and have been doing for almost a year. I really would have preferred to walk from a milestone in Manchester to end at the start of the Via Appia in Rome. More significantly, like you, I wish none of us were in the middle of a two year pandemic.

This is the 360th daily post.  If you know your angles and your times, you’ll know to nod in gratitude to the Sumerians in Iraq. Their cuneiform-inscribed clay tablets have lasted some three thousand years, recording their world view in sexagesimal counting. We use base 2 to convert thought to electricity to writing like you are reading now. Coders often read these binaries as hexadecimal base 16 while we count most things like money and bananas in decimal base 10. Number systems are hidden deep in your daily life, and Cobol (born 1959) is what messes up your banking (but that’s another story – see below).

You know that time and angles are based on circles. Old clock faces were round for a reason. Even a sun dial is round. No one knows exactly why Sumerians adopted base 60 but it is likely that the moon, the tides and divisibility were major influences.

Seasonal time seemed to repeat in twelve cycles so the wise in Sumer came up with a year of twelve months. The tidal cycles and the moon seemed to be related and repeated in patterns of 30 that they called days. That’s 360 right there.

A positive integer with many divisors is considered a highly composite number. 60 is highly composite, having 12 divisors.

The Sumerians split each of these days into 12 units that could be calibrated with water or sand flowing from one vessel to another, like your egg timer does today.  Eventually they went to 24 hour days but now you know that Sumerians gave you the 12 hour clock face. They called the 12 hours ‘watch’ and went one step further, they sub-divided the watch into 360 units called ‘gesh’. I guess (sic) that’s where our angles come from.

And so it goes. There is certainty of timing calibrated to predictable astronomical events. The Babylonians refined it and formalised it, making rules about the positions of the numbers and of course, they only used two symbols to write the whole base 60 system. So clever that we’ve inherited this notion of two symbols (base 2, binary, 1 and zero) and the positions of say 789 that have contracted from to 7X100 and 8X10 and 9X1. Leap years and precise lunar cycles notwithstanding, this ancient sexagesimal system has truly passed the test of time.

I suppose that a mathematically inclined Sumerian or Akkadian before them would have tried to measure the circumference of a circle. Or a tiler tried to work out the surface area of a circular design in order to have enough inventory on hand.

And here we are, three thousand years on, using computers (base 2) and competing to calculate the uncertainty of Pi in order to be precise ‘The most accurate value of pi is 50,000,000,000,000 digits, and was achieved by Timothy Mullican (USA) in Huntsville, Alabama, USA, on 29 January 2020’.

And yet, minor numerical errors aside, NASA has just landed on Mars with a lander that has its own semi-autonomous drone helicopter, powered by commercial smartphone components and smartphone chip.

I mentioned Cobol for a reason – CitiBank and Revlon – read this and weep.

Tomorrow at 9.30 UT, we’ll be in court (via Zoom) in The Arches Court of Canterbury in the matter of an Application for a Faculty for a memorial in the Churchyard of St Giles, Exhall, Diocese of Coventry.