Every Indiana Jones movie has its own MacGuffin, an object of importance that has the main good guys and bad guys busy searching and getting into wacky adventures.
In the latest film – Dial of Destiny – that object is, you guessed it, an ancient object called the dial of destiny. The movie refers to the dial, inspired by the real-life Antikythera mechanism, as the Dial of Archimedes, or Archimedes Dial.
This being an Indiana Jones movie (think of the holy grail in Last Crusade or the Ark in Raiders of the Lost Ark) the dial ends up having some ridiculous properties, which we won't go into due to spoilers. The real device, often described as the world's oldest analog computer, has puzzled since it was retrieved from a shipwreck off the Greek coast in 1901. Dating to around 100 BCE, the 30-gear mechanism is believed to be a device to predict astronomical events, after examination of the object and inscriptions on it.
A central historical character in the film is Archimedes, who the film's characters believe created the dial, which Indy then uses centuries later for its true intended purpose. In real life, Archimedes has been suggested to have been the originator of the Antikythera mechanism. However, a later study found that the device used an Epirote calendar, rather than Syracuse, where Archimedes lived out his life.
In real life, not much is known about Archimedes, though we know enough to call him one of the greatest mathematicians of ancient times. Anyone who has seen the movie in question (we shall be as oblique as possible here) may be interested in knowing that he has been credited with a number of designs for defenses of the city of Syracuse, including an "Archimedes claw" aimed at latching onto ships and then upturning them.
He has also been credited with improvements to catapults, used to defend against a siege on the city in 214 BCE, and an "Archimedes death ray" – a system of mirrors used to focus the Sun's heat and burn enemy ships, though there is much skepticism that this was ever built or used and it does not appear in Archimedes' own work.
You likely know of Archimedes for the Archimedes principle, and the supposed "eureka" moment that came from it. According to Vitruvius, writing in the first century BCE, a crown had been made for King Hiero II of Syracuse to place in a temple for the gods. After it had been made, however, the maker was accused of substituting some of the gold in the crown for silver. Archimedes was asked to crack the case, with the extra stipulation that he couldn't damage the crown, e.g. by melting it down to see what it was composed of.
While thinking about the conundrum, Archimedes supposedly took a bath and noticed that the more he lowered himself into the bath, the more water was displaced.
"As this pointed out the way to explain the case in question, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking," a translation of Vitruvius reads, "for he as he ran he shouted repeatedly in Greek, 'Eureka, eureka'."
According to the account, Archimedes realized that the amount of water displaced showed him the volume of the object, and dividing the volume by the object's mass would reveal the object's density. Comparing this density to gold would let him know if the crown had been cut with silver, which the story says it was, and he was able to catch the maker out.
Though a cute story and method, it has been questioned whether this is the method Archimedes used, and whether he really ran through the city yelling about his scientific achievements to people whose main question was, "Ok, but why are you naked exactly?". For one, the crown was so light it would displace little water, making accurate measurement at the time unlikely.
Galileo later created a hydrostatic balance that could be used to measure the density of objects, inspired by the tale of Archimedes. Having created it, though, he came to believe that he was beaten to it.
"I think it probable that this method is the same that Archimedes followed," Galileo wrote, "since, besides being very accurate, it is based on demonstrations found by Archimedes himself."