Eureka (Ancient Greek: εὕρηκα, romanized: héurēka) is an interjection used to celebrate a discovery or invention. It is a transliteration of an exclamation attributed to Ancient Greek mathematician and inventor Archimedes.
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Transcription
When you think of Archimedes' "Eureka!" moment, you probably think of this. As it turns out, it may have been more like this. In the third century BC, Hieron, king of the Sicilian city of Syracuse, chose Archimedes to supervise an engineering project of unprecedented scale. Hieron commissioned a sailing vessel 50 times bigger than a standard ancient warship, named the Syracusia after his city. Hieron wanted to construct the largest ship ever, which was destined to be given as a present for Egypt's ruler, Ptolemy. But could a boat the size of a palace possibly float? In Archimedes's day, no one had attempted anything like this. It was like asking, "Can a mountain fly?" King Hieron had a lot riding on that question. Hundreds of workmen were to labor for years on constructing the Syracusia out of beams of pine and fir from Mount Etna, ropes from hemp grown in Spain, and pitch from France. The top deck, on which eight watchtowers were to stand, was to be supported not by columns, but by vast wooden images of Atlas holding the world on his shoulders. On the ship's bow, a massive catapult would be able to fire 180 pound stone missiles. For the enjoyment of its passengers, the ship was to feature a flower-lined promenade, a sheltered swimming pool, and bathhouse with heated water, a library filled with books and statues, a temple to the goddess Aphrodite, and a gymnasium. And just to make things more difficult for Archimedes, Hieron intended to pack the vessel full of cargo: 400 tons of grain, 10,000 jars of pickled fish, 74 tons of drinking water, and 600 tons of wool. It would have carried well over a thousand people on board, including 600 soldiers. And it housed 20 horses in separate stalls. To build something of this scale, only for that to sink on its maiden voyage? Well, let's just say that failure wouldn't have been a pleasant option for Archimedes. So he took on the problem: will it sink? Perhaps he was sitting in the bathhouse one day, wondering how a heavy bathtub can float, when inspiration came to him. An object partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. In other words, if a 2,000 ton Syracusia displaced exactly 2,000 tons of water, it would just barely float. If it displaced 4,000 tons of water, it would float with no problem. Of course, if it only displaced 1,000 tons of water, well, Hieron wouldn't be too happy. This is the law of buoyancy, and engineers still call it Archimedes' Principle. It explains why a steel supertanker can float as easily as a wooden rowboat or a bathtub. If the weight of water displaced by the vessel below the keel is equivalent to the vessel's weight, whatever is above the keel will remain afloat above the waterline. This sounds a lot like another story involving Archimedes and a bathtub, and it's possible that's because they're actually the same story, twisted by the vagaries of history. The classical story of Archimedes' Eureka! and subsequent streak through the streets centers around a crown, or corona in Latin. At the core of the Syracusia story is a keel, or korone in Greek. Could one have been mixed up for the other? We may never know. On the day the Syracusia arrived in Egypt on its first and only voyage, we can only imagine how residents of Alexandria thronged the harbor to marvel at the arrival of this majestic, floating castle. This extraordinary vessel was the Titanic of the ancient world, except without the sinking, thanks to our pal, Archimedes.
Etymology
"Eureka" comes from the Ancient Greek word εὕρηκα heúrēka, meaning "I have found (it)", which is the first person singular perfect indicative active of the verb εὑρίσκω heurískō "I find".[1] It is closely related to heuristic, which refers to experience-based techniques for problem-solving, learning, and discovery.
Pronunciation
The accent of the English word is on the second syllable, following Latin rules of accent, which require that a penult (next-to-last syllable) must be accented if it contains a long vowel. In the Greek pronunciation, the first syllable has a high pitch accent, because the Ancient Greek rules of accent do not force accent to the penult unless the ultima (last syllable) has a long vowel.
The initial /h/ is dropped in modern Greek and in several other European languages, including Catalan, French, Italian, Spanish, Portuguese, Dutch, and English, but preserved in others, such as Finnish, Danish, and German.
Archimedes
The exclamation "Eureka!" is attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed "Eureka! Eureka!" after he had stepped into a bath and noticed that the water level rose, whereupon he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. (This relation is not what is known as Archimedes' principle—that deals with the upthrust experienced by a body immersed in a fluid.[2][3]) He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse.
Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown; he had given his goldsmith the pure gold to be used, and correctly suspected he had been cheated by the goldsmith removing gold and adding the same weight of silver. Equipment for weighing objects with a fair amount of precision already existed, and now that Archimedes could also measure volume, their ratio would give the object's density, an important indicator of purity (as gold is nearly twice as dense as silver and therefore has significantly greater weight for the same volume).
Authenticity
This story first appeared in written form in Vitruvius's books of architecture, two centuries after it supposedly took place.[4] Some scholars have doubted the accuracy of this tale, on the grounds that the votive crown was a fine item, thus an impure crown would displace water only minutely, compared to a pure one. Precise means needed to measure this minute difference was not available at the time.[5][6] For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: using a balance, compare the weight of the crown against pure gold. While they are still suspended from the arms of the balance, simultaneously submerge the crown and the gold in water. If the volumes are the same, the balance remains in equilibrium, meaning that their densities are the same and therefore the crown must be pure gold. But if the density of the crown is less (due to being alloyed with another metal like silver), increased buoyancy of the crown results in imbalance.[7] Galileo Galilei himself weighed in on the controversy, suggesting a design for a hydrostatic balance that could be used to compare the dry weight of an object with the weight of the same object submerged in water.[8]
Names and mottos
California
The expression is also the state motto of California, referring to the momentous discovery of gold near Sutter's Mill in 1848. The California State Seal has included the word eureka since its original design by Robert S. Garnett in 1850; the official text from that time describing the seal states that this word's meaning applies "either to the principle involved in the admission of the State or the success of the miner at work". In 1957 the state legislature attempted to make "In God We Trust" the state motto as part of the same post WWII anti-Communist movement that successfully added the term "under God" to the American Pledge of Allegiance in 1954, but this attempt did not succeed and "Eureka" was made the official motto in 1963.[9]
The city of Eureka, California, founded in 1850, uses the California State Seal as its official seal. Eureka is a considerable distance from Sutter's Mill, but was the jumping off point of a smaller gold rush in nearby Trinity County, California in 1850. It is the largest of at least eleven remaining US cities and towns named for the exclamation, "eureka!". As a result of the extensive use of the exclamation dating from 1849, there were nearly 40 locales so named by the 1880s in a nation that had none in the 1840s.[10] Many places, works of culture, and other objects have since been named "Eureka"; see Eureka (disambiguation) for a list.
Australia
"Eureka" was also associated with a gold rush in Ballarat, Victoria, Australia. The Eureka Stockade was a revolt in 1854 by gold miners against unjust mining license fees and a brutal administration supervising the miners. The rebellion demonstrated the refusal of the workers to be dominated by unfair government and laws. The Eureka Stockade has often been referred to as the "birth of democracy" in Australia.[11]
Mathematics
Another mathematician, Carl Friedrich Gauss, echoed Archimedes when in 1796 he wrote in his diary, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive integer could be expressed as the sum of at most three triangular numbers.[12] This result is now known as Gauss' Eureka theorem[13] and is a special case of what later became known as the Fermat polygonal number theorem.
See also
- Heuristic – Problem-solving method
- Eureka effect – Human experience of suddenly understanding a previously incomprehensible problem or concept
- Serendipity – Unplanned, fortunate discovery
References
- ^ εὑρίσκω. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project
- ^ "IGCSE Physics Notes: Using Archimedes Principle to Find the Density of an Object". A Star Maths & Physics Tutors. Retrieved 2012-06-06.
- ^ Tom Clegg (2001-04-08). "Eureka!". Retrieved 2012-06-06.
- ^ Vitruvius on Architecture, IX: Introduction: 9–12, translated into English and in the original Latin.
- ^ "EXHIBIT: The First Eureka Moment". Science. 305: 1219. 27 August 2004. doi:10.1126/science.305.5688.1219e.
- ^ Biello, David (December 2006). "Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath". Scientific American. Retrieved 4 March 2024.
- ^ Tipler, Paul A.; Mosca, Gene (2003), Physics for Scientists and Engineers (5th ed.), Macmillan, p. 403, ISBN 9780716783398.
- ^ Rorres, Chris. "The Golden Crown: Galileo's Balance". Drexel University. Retrieved 2009-03-24.
- ^ Official state law defining the motto. Accessed February 26, 2007. Archived June 28, 2009, at the Wayback Machine
- ^ California Place Names, by Erwin Gudde, p. 105
- ^ West, Barbara A. (2010). A Brief History of Australia. Infobase Publishing. pp. 66–67. ISBN 9780816078851.
- ^ Bell, Eric Temple (1956). "Gauss, the Prince of Mathematicians". In Newman, James R. (ed.). The World of Mathematics. Vol. I. Simon & Schuster. pp. 295–339. Dover reprint, 2000, ISBN 0-486-41150-8.
- ^ Ono, Ken; Robins, Sinai; Wahl, Patrick T. (1995). "On the representation of integers as sums of triangular numbers". Aequationes Mathematicae. 50 (1–2): 73–94. doi:10.1007/BF01831114. MR 1336863. S2CID 122203472.
This page was last edited on 26 March 2024, at 01:57