2681: Archimedes Principle

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Archimedes Principle
"I've always wanted to run naked through town, but I don't want to get in trouble with the king or be remembered by history as a weirdo. I wonder how I could ... EUREKA!"
Title text: "I've always wanted to run naked through town, but I don't want to get in trouble with the king or be remembered by history as a weirdo. I wonder how I could ... EUREKA!"


Archimedes was tasked by his tyrant king, Hiero II of Syracuse, with determining whether a votive crown made by a local goldsmith actually contained all the gold the king had provided for it, or whether the goldsmith had substituted an equal weight of silver for the more-valuable gold. Archimedes knew he could solve this problem if only he could compare the crown's weight to its volume; since any silver in it, being only about half as dense, would occupy more volume than the gold. Despite knowing this, Archimedes didn't know how to measure the volume of the crown, which was highly irregularly shaped. According to legend, as Archimedes was getting into a bath one day, the bath overflowed. Archimedes realized that the volume of water displaced by any immersed object, including his body and the crown, was equal to the submerged volume of the object, and thus he could establish the crown's volume; a crown made with substituted silver of equal mass would displace more water than the supposed gold version would. This insight led him to solve the king's problem (and determine that the goldsmith had in fact cheated the king out of some gold). Legend also says[1] that upon having this insight, he went running naked down the streets of Syracuse shouting "eureka!", Greek for "I have found it!" - a word now associated with sudden insights.

In the comic, Archimedes' insight doesn't involve science, but is a plan for self-enrichment. Evidently, he has concealed a less-valuable gold-plated or gold-alloy crown in the tub of liquid, and plans to swap it for the real crown when 'measuring the volume'. This implies that the king's crown turns out to be, in fact, pure gold, but Archimedes will report it to be adulterated with silver, in order to steal the gold crown for himself. This is claimed to be the invention of the heist. While theft has no doubt existed since property has existed, a "heist" implies a complex plan, often based on deception and carefully planned operations, as is typical of heist films.

The title of the comic, "Archimedes Principle", refers to a different but related insight of Archimedes, that the upward buoyant force that is exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces. It may also relate to the particular twist of morality being observed by this version of Archimedes, in that it seems not to be against his principles to defraud a king, and (incidentally?) besmirch a particular master-craftsman.

According to the title text, Archimedes's eureka moment wasn't when he discovered how to measure the crown's volume, but when he realized that he could use this discovery as a pretext for running naked through town, something he'd always wanted to do.


[Megan is leaning over a large bucket standing on the floor. She is resting one hand on the bucket and holding a crown in other other hand, which she has pulled partially up over the top of the water filled bucket. The water is now splashing over the edge of the bucket and dripping from the still partially immersed crown. Behind her back, with his back toward hers, Archimedes sits on a chair at a desk. He is depicted as a balding man with a white beard, and he is writing on a piece of paper, while a stack of papers lies in front of him.]
Megan: Uh, Archimedes, why is there a bucket of water with a gold crown hidden in the bottom?
Archimedes: It's mostly silver. Replica of the King's crown. He's coming here later, and I have a plan.
[Caption beneath the panel:]
Archimedes invents the heist.

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I started an explanation, but I can't really figure out what Archimedes' "plan" is. I guess it has something to do with swapping out the fake crown with the king's real gold crown. Heist movies and TV shows always confuse me (I liked "Leverage" for the characters, but could never understand the plans). Barmar (talk) 23:12, 5 October 2022 (UTC)

Under the guise of demonstrating the displacement principle (the buoyancy effect has no real part in this, given the non-floating nature of any crown... I think the focus in the explanation should just be upon the displaced volume of liquid which traditionally would quantify the volume of an object of known weight and a density to be tested to ensure it is that of the purported substance) he will dunk the real crown in the water. Then either:
  • extract the fake crown, now 'proven true', satisfying everyone but leaving him the really-true crown, or,
  • extract the fake crown, possibly fudging the interpretation (how much water sloshes out) to make it seem like a fake crown went in (and the fake that came out can now be destructively examined to confirm this, now having just cause to utterly ruin the craftwork in the process, and framing the original artisan for fraud), again leaving him with the crown he was given for testing.
If the original crown was itself already fake then it might not be worth it (or have to lean towards the latter outcome with a bit of extra care not to 'upgrade' the fake) but that's probably covered by the typical Batman Gambit of a typical heist movie characterm 00:37, 6 October 2022 (UTC)
The first of the two options makes way more sense. I don't like this plan at all though. How do you hide a colored shiny thing in a bucket of transparent water?!? I feel like we're missing something obvious. 01:53, 6 October 2022 (UTC)
Megan says "hidden IN the bottom" , so I think there is some kind of false floor/double bottom at play here; allowing the fake crown to be hidden from view and allowing for a crown-swap in the middle of the demonstration. Flekkie (talk) 02:02, 6 October 2022 (UTC)
Nobody said that it was clear water.  Pond water could be dirty or murky enough that the scam would work without the need of a false-bottomed bucket. RAGBRAIvet (talk) 04:24, 6 October 2022 (UTC)
According to legend, Archimedes is given the king's crown in order to test for its purity without breaking it; he suspects that the goldsmith he hired replaced most of the gold with silver and kept the excess to himself. Archimedes uses his displacement principle to measure the volume (figuring the principle out in his "Eureka" moment) and weighs the crown to determine its density; his results imply that the crown is in fact fake.
Here it's implied that the real crown is actually gold, and Archimedes is taking advantage of the king's paranoia; he's likely planning to switch it out, perform his experiment on the fake crown, and keep the real gold to himself. --Account (talk) 03:50, 6 October 2022 (UTC)
Which could indicate that the successful execution of Archimedes' plan is what leads to the legend as we have it today.MarquisOfCarrabass (talk) 05:40, 6 October 2022 (UTC)
Yes agreed. The King was paranoid and his crown made of gold. And the reason the legend says he proved the crown to be false, is that he did this heist to steal the real gold crown. So for a bit of gold and some silver he gained the same volume of gold, that could be either melted or sold to a secret bitter --Kynde (talk) 14:04, 6 October 2022 (UTC)
The buoyancy does matter, the buoyant force is still there regardless of whether it is greater than the weight of the crown or not. If you place a crown weighing one pound and a one-pound bar of gold on a scale, they will balance in the air, but in the water if the crown is part silver the buoyant force on it will be greater and the gold bar will show as being heavier. In ancient Greece without precision measuring glassware, this would be much easier to do than measuring a small difference in the displacement if only a small part of the crown was replaced with silver. 00:33, 21 October 2022 (UTC)
xkcd does Archimedes's Heureka, Gotlib does Newton's apple...any more examples of (not necessary comic medium) parodies of famous science history anecdotes? 06:27, 6 October 2022 (UTC)

Why is the image on here so blurry? I'd edit it, but I'm not sure how to do so myself. 18:18, 30 October 2022 (UTC)

Ironically, I think it's a result of the _2x image being downloaded but being displayed at 'low'-res size (theusaf has channged the procedure, recently, to grab the bigger image but then put in the directive to show at the smaller dimensions).
Comparing this page on one tab and the two "source" images on other tabs, at least in my browser (if it's not how the wikimedia gets served - I haven't dug deeper into that just yet) it seems to downscale slightly less nicely than the 'preshrunk' standard version.
But that may be as much my eyes/screen. I suppose I should screengrab and examine those pixels in a further zoom level to try to get a definitive idea of where the 'problem' lies.
That said, I don't find it notably detrimental... Didn't really think there was a problem until I saw your comment and did the above comparison for myself. 19:14, 30 October 2022 (UTC)