Brilliance over 2,200 years ago and Brilliance in 2021.

Will Keys

The James Webb Telescope.

On the 28th December 2021, the fantastic, incredible, and brilliant James Webb Telescope (“JWT”) will be launched into space from French Guiana, on an Ariane 5 rocket.  It has taken over twenty years and over nine billion dollars, but in a few days, the JWT will hopefully become a reality.  I take this opportunity to compare the JWT with the ancient Antikythera Mechanism (“AKM”) discovered at the turn of the 19th century.  Both are works of astounding mathematics and brilliant engineering.

I will report on the JWT, after it has unfolded and become functional at the 2nd Lagrange point, which is over 1.2 millions kilometres from earth. 

The Antikythera Mechanism.    

Acknowledgements:  The research for this article came out of my original fascination in the NOVA production about the Antikythera Mechanism (“AKM”) and I acknowledge NOVA and further acknowledge that this article is heavily based upon their research and their reporting found on Youtube.  My wife and I travelled to Athens, Greece, to see the AKM first hand.    

In October 1900, a team of sponge divers decided to wait out a severe storm off the Greek Island of Antikythera.   They took the opportunity to dive anyway.  In those days the standard diving dress was a canvas suit with a copper helmet.  A diver donned the gear and descended, about 60 meters to the seafloor.  He quickly signalled to be pulled up.  He described seeing human bodies and a horse on the sea bed.

The sponge divers had discovered the wreckage of an ancient Roman ship  The Greek Education Ministry and Hellenic Navy were advised, and they recovered artefacts and sculptures.  One of the artefacts was a severely corroded piece of bronze that had indecipherable inscriptions and an apparent complex clock-work cog-gear mechanism at its core.  The object would become known as the Antikythera Mechanism (“AKM”)  andis on display in the National Archaeological Museum in Athens. 

The AKM has been carbon-dated to be +/- 300 years BC old.  It remained below the ocean surface all that time.  Such an extremely sophisticated mechanism cannot be invented overnight.  It required mathematical brilliance that was millennia ahead of its time.  The almost unbelievably skillful engineering, to transfer cosmological observations into a laptop-size digital mechanism is only believable because it exists, and is on display.    

Over the past 100 years, scientists have tried to decipher the purpose and inner workings of the AKM.  Only now, 100 years after its discovery, has x-ray technology evolved to enable the inscriptions and inner workings of the AKM to be observed and partially understood.      

The AKM had in all some +/- 60bronze cog-gear wheels.  These cogs were so tightly packed together that they resembled the inner workings of a complicated clock.  The entire mechanism was fitted into a small box the size of a laptop computer.  It had two external dials; one would later be termed the Saros dial.  These dials manipulated the inner workings of the mechanism.

The ancient Babylonians, and the Greeks, were apparently capable of advanced mathematics far beyond that which has been reported in history.   They plotted heavenly bodies and in so doing discovered that the number 235 was a key to calculating the cycle of the moon.  From one new moon to the next is a time averaging 29.5 days.  This was a problem because to have 12 months in every year meant that 12 x 29.5 = 354, which is 11 days short of a natural/solar year.

The Greeks also knew that 19 solar years = 235 lunar months. This meant that a calendar year would remain perfectly in line with the seasons.  The Greeks called it the Metonic Calendar and mechanical computation of the cycle was built into the AKM.

(Considering a year to be ¹⁄₁₉ of this 6,940-day cycle gives a year length of 365 + ¹⁄₄ + ¹⁄₇₆ days (the unrounded cycle is much more accurate), which is slightly more than 12 synodic months.)

The ancient Greeks realised that it takes the moon 29.5 days to orbit the earth and catch up to the sun.  However, it took only 27.3 days to orbit the earth to get back to the same star in the sky.  They did the arithmetic and found that it meant that over a period of 19 years, there will be 254 orbits.  The ancients decided that 254 teeth was a lot of teeth, so they reduced 254 by half and created a gear of 127 teeth.  They then used another gear to multiply the effect up to 254.  The calculation involved two prime numbers 19 and 127. The AKM required a re-writing of the history of ancient technology.  It was clear that things were going on in the 2^nd century BC that we know nothing about. 

They discovered that the front gear was a planetarium of the Greek Cosmos and was geo-centric of the earth.  In other words, everything circled the earth.   The ancient Greek calendar was organized according to the moon.  Luna predictions affected everyday life, for example, debts became payable on the new moon.  The calendar was reconciled with the year and controlled by the sun, and the months by the moon.  

It was often the case that although a gear could be identified, the exact number of teeth on the gear had eroded, thus the reasoning was not known. 

In modernity, advanced technology-enabled investigators to look beneath the surface and for the first time, see inscriptions on the metal parts.  One inscription confirmed that there was a large gear wheel at the back of the AKM that had 223 teeth, another prime number.  

Although most of the mechanism had been recovered in a corroded mass, there were a number of fragments that had been recovered separately.  The investigators knew that these fragments were part of the mechanism but they were unable to figure out which parts.   The inscription pointing to a 223 tooth gear was a valuable clue.  Using virtual engineering software, with what was marked as fragment ‘F’, the position of the 223 gear became apparent.  It was located at the back of the mechanism.   

In 646 BC Babylonian mathematicians had written about the number 223.  It referred to the 18 year period (223 months = 18 years) this was also known as the Saros Cycle.  The 18 year period was used to predict eclipses.  Investigators called the inscriptions ‘glyphs’ because they looked like Egyptian Hieroglyphs.  These glyphs were inscriptions of the date, and hour of eclipses and whether it was to be a lunar or solar eclipse.

The investigators concluded that the large 223 gear was directly connected to the Saros dial.  They had found something remarkable.  They had discovered a machine that could look into the future and very accurately predict eclipses.  In other words, this was the world’s first computer. Not only did the AKM predict eclipses in the future to the hour, but it also predicted the direction that the shadow was going to cross and the color of the eclipse.

As mentioned, the Greeks considered eclipses to be omens and attributed causation far beyond what was justified. They used eclipses to predict travel arrangements etc.  This led to some terrific mistakes and misjudgments.  An example was the destruction of the Athenaeum fleet at Syracuse, Sicily, in the 3^rd or 4^th centuries BC.

One of the biggest challenges faced was to explain how the AKM dealt with the orbit of the moon around the earth.  The orbit is not a perfect circle, it circulates in an elliptical fashion.  When the moon is closer to the earth, it travels faster and when it is further it travels slower.

There is nothing easy about the motion of the moon.  In modern terms, we know that the moon goes around the earth in an elliptical orbit but the ellipse is not stationary.  The ellipse rotates very slowly, in elevation, over a period of about 7 years.  

One of the investigators noticed a shadow on an x-ray of the 223 gear that indicated some kind of ‘pin and slot mechanism’ in the gear.   The gear with the pin turned at the centre, at a slightly different pace, to the gear as a whole.  This extra mechanical device introduced variability in one of the gears.  Amazingly the ‘pin and slot device’ accurately followed the variable motion of the moon.  The slot deals with the ‘elipse’ and the pin with the ‘elevation’. 

Based on cycles (Metonic & Saros) the investigators deduced that the ancient Greeks had calculated the annual rate of rotation of the moon to nine decimal places, that is, exactly 0.112579655.  The investigators were incredulous that the AKM could conceivably calculate to that precision.  Nevertheless, this was the case.   

The investigators had followed the trail of prime numbers 19 – 127 – 223 – 53 to understand how the AKM was made and how it worked. They thought that they may find the identity of the inventor inside the mechanism itself.  They worked out from inscriptions that there were four months of the year written in the ancient language of Corinth.  The conclusion was that the inventor had to have been from Corinth itself, or from one of the colonies i.e. Syracuse in Sicily. 

In the 3 & 4^th centuries BC, Syracuse was the second biggest city-state in the Greek world.  Syracuse was also the home of Archimedes (3^rd century BC).   As an astronomer, Archimedes accurately figured out the distance between the earth and moon.  He showed how to calculate the volume of a sphere and discovered the fundamental number Pi.  The investigators concluded that only a mathematician of Archimedes stature and status could have been the original inventor of the AKM.  No doubt it further evolved and was reduced in size until it was the size of a modern laptop computer.   

According to the Roman historian Plutic, after the Romans had invaded Sicily, the Commander (Marcus Claudius Marcellus) ordered the city to be sacked but Archimedes life to be spared.  A Roman soldier came upon an old man drawing circles in the sand and when challenged he failed to show the required deference.  The soldier ran his sword through him.  

Cicero the Roman historian, in his commentaries, wrote about the incredible machines made by Archimedes and the Ionians.  He described and confirmed that cosmological machines had been invented that could predict eclipses.  Few people at the time took his comments seriously.  They thought he was exaggerating.  

Medieval two-dimensional drawings (in cross-section) of the known universe could only have come from information provided out of the AKM.   

As the Roman Empire expanded the AKM technology moved eastwards to the Byzantine Empire.  Later it entered the sophisticated world of the Islamic sciences.  A much simpler mechanism (520 AD) was sold to the London Museum.  The complexity of clockwork gears found their way back into Europe through the Moors in Spain in the 13^th century.

During the Renaissance in the 14^th century, highly sophisticated clockwork gears appeared and proliferated and all the future advances followed the same pattern and principles found in the AKM.  On its front face, the universe as they understood it, with the five (5) planets; the sun and the moon.  On its near face was a Greek calendar that accurately predicted eclipses.

All modern-day watches have a genesis in the AKM.

By Will Keys