Welcome to part one of a three-part series on building a working Antikythera mechanism out of LEGO. In this post, we’ll go through the device’s history and talk about the maths behind how it works. You can also skip to part two (buying the parts) and part three (building the machine) if you have no interest in its origin story.
Many thanks to the original builder of the LEGO Antikythera mechanism, Andrew Carol. Without Andrew’s fantastic work, this post would not have been possible. You can see Andrew’s original machine in action on YouTube.
The Antikythera mechanism is an ancient analog mechanical computer built around the first or second century B.C. It can calculate the position of both the Sun and Moon in addition to calculating future solar and lunar eclipses. Researchers have suggested that it could also calculate the relative positions of known planets at the time; however, this has never been proven. The technology and craftsmanship used to construct the device are especially interesting, as the skills were not thought to exist until at least the fourteenth century – up to 1,500 years after its construction.
The device was discovered in 1901 by a team of sponge divers buried in a shipwreck on the Greek island of Antikythera. In 1903, an archaeologist named Valerios Stais noticed that the corroded lump of bronze and wood had a gear embedded within it. Stais suggest that the device may be an astronomical clock; however, scholars at the time ruled this an impossibility due to the age of other items found on the wreck.
The mechanism sat in the museum as nothing but a curiosity for the next 50 years. It wasn’t until the 1950s that a physicist named Derek J. de Solla Price became interested in studying the device more closely. In 1971, Price and a Greek nuclear physicist named Charalampos Karakalos made X-ray and gamma-ray images of the device, which had now split into 82 fragments, likely due to excessive handling and exposure to air over the previous 70 years.
How it works
The device, enclosed in the remains of a wooden box 30 cm high by 20 cm wide, contained more than 30 bronze gears and was covered in Greek inscriptions. The front of the device featured a large circular dial with two concentric scales. The first scale featured the months of the year and was divided into 365 days. The second scale featured the 12 signs of the zodiac and was divided into 360 degrees. Pointers moving around the dial showed the date and the relative position of the Sun and the Moon at the time. A revolving ball painted half black and half white showed the phases of the Moon.
On the back of the device were two more spiral dials. The top dial displayed a repeating 235-month calendar. The number 235 is significant as after 235 synodic months, or 19 years, the distribution of new moons in the solar year is the same. The bottom dial represented a 223-month eclipse cycle – known as a saros cycle. Symbols within each division provided more information on what type of lunar eclipse to expect and at what time of the day it would occur.
Synodic months and the saros cycle
Before diving into the maths, let’s define some astronomical terms. A synodic month is the average period of the Moon’s orbit with respect to the line joining the Sun and the Earth. This corresponds with each lunar phase, as the Moon’s appearance from Earth depends on the position of the Moon with respect to the Sun. On the other hand, a sidereal month is the time it takes for the Moon to return to the same position with respect to the stars. This distinction is important, as the dials on the Antikythera mechanism track synodic months – critical for eclipse prediction.
As mentioned above, a saros cycle is 223 synodic months, 18 years, 11 days and 8 hours. Knowledge of this cycle is built into the mechanism and allowed the ancient Greeks to predict future eclipses with some degree of accuracy.
Mathematical limitations of LEGO
Fortunately, a LEGO mastermind named Andrew Carol has already built a version of the Antikythera mechanism out of LEGO. Below we’ll explain the maths behind his version and then begin the construction process.
There are several important constants that need to be represented in the LEGO version of the machine. Firstly, the relationship between the Sun, Moon, and Saros cycles. If we imagine an axle, which we’ll call Y, one full rotation of the axle equals one year. One half-turn of the axle equals six months – one quarter-turn equals three months etc. The important relationships are as follows:
- Sun = Y
- Moon = Y * 254 / 19
- Saros cycle = Y * 235 / (223 * 19)
This means the constants we need to represent in LEGO so far are 19, 223, 235, and 254.
The actual Antikythera mechanism consists of five winds of the spiral on the back face of the device. It would be impossible to represent 223 lunar months on a single dial without overlapping a lot of information, so Andrew’s version of the LEGO mechanism uses four winds of the spiral, matching the full moon cycle. This modification from five to four spirals means the Saros cycle calculation also needs a slight modification:
- Saros4 cycle = Y * 4 * 235 / (223 * 19)
We derive 235 by multiplying 5 and 47 and 254 by multiplying 2 and 127. Therefore, the required constants needed in LEGO are now 2, 4, 5, 19, 47, 127 and 223.
LEGO gear ratios
The easiest gear ratios to represent in LEGO are 1, 3, and 5. We say easiest as some gears provide fractional ratios, which aren’t particularly useful for our application. Some of our constants are also prime numbers, which means they aren’t easily derived with just 1, 3 and 5.
Fortunately, we can solve this problem with a differential gear. Wikipedia defines a differential as:
… a gear train with three shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others, or a fixed multiple of that average.
We’ll use differentials to create the gear ratios that we need to derive our constants. The formula for a two-input shaft differential is:
- C = (A + B) / 2
This means the average wheel speed of A plus B equals the output speed of C. The make the formula more useful, we can reformat it as:
- A = 2 * C – B
This now means if C is 3 and B is 25, we get:
- -19 = 2 * (3) – (5 * 5)
The negative value means the axle is rotating in the opposite direction. We can easily reverse the direction of a shaft by adding an identically sized gear alongside it.
Based on the above assumptions and Andrew’s work, we can now define our required differentials as follows:
|Input shaft C||Input shaft B||Output shaft A |
(2 * C – B)
|3||5 * 5||-19|
|5 * 5||3||47|
|-1||5 * 5 * 5||-127|
|1||5 * 5 * 3 * 3||-223|
We now have the required constants to construct the machine: 2, 4, 5, 19, 47, 127 and 223.
In part two, we’ll buy the parts we need to build the machine out of LEGO.
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