A Tangled Tale · Chapter
§1: The Buckets explained
The chapter presents a puzzle about a small bucket floating in a larger one, challenging Lardner's statement that a solid displaces an equal bulk of fluid.
What happens
The chapter presents a puzzle about a small bucket floating in a larger one, challenging Lardner's statement that a solid displaces an equal bulk of fluid. Various correspondents offer flawed explanations, and the author provides the correct interpretation: 'displaces' means occupying space that could be filled with water without altering surroundings. No class-list is published due to insufficient correct answers.
Themes in this chapter
Mathematical Reasoning
The chapter centers on a physical paradox about buoyancy and displacement, requiring precise logical interpretation of Lardner's statement.
Logic and Paradox
The floating bucket problem presents a logical puzzle where common assumptions about displacement lead to contradictions, resolved by clarifying the definition of 'displaces.'
Characters to notice
- Hecla
Argues that only the submerged portion of the floating bucket displaces an equal bulk of water, but this view is shown to be incorrect.
- Jane E.
As Magpie, claims the fallacy is assuming one body can displace another from where it isn't, and that Lardner's assertion only holds if the vessel was originally full to the brim.
- Old King Cole
Takes the same view as Hecla regarding displacement.
- Tympanum
Assumes 'displaced' means 'raised above its original level' and explains the water rise, but ends up in the same flawed position as Hecla.
- Vindex
Shares Tympanum's assumption about displacement and lands in the same erroneous boat.
Key passages
“Lardner states that a solid, immersed in a fluid, displaces an amount equal to itself in bulk. How can this be true of a small bucket floating in a larger one?”
Lardner claims a submerged solid pushes aside its own volume of fluid. But how does that apply when a small bucket floats inside a larger bucket?
Introduces the central paradox of the chapter.
“Lardner means, by 'displaces,' 'occupies a space which might be filled with water without any change in the surroundings.'”
Lardner's 'displaces' actually means the solid takes up a volume that could be replaced by water without altering the rest of the water.
Clarifies the correct interpretation of Lardner's statement.
“If the portion of the floating bucket, which is above the water, could be annihilated, and the rest of it transformed into water, the surrounding water would not change its position: which agrees with Lardner's statement.”
If the part of the bucket above water vanished and the submerged part turned to water, the water around it would stay exactly as it is—this matches Lardner's meaning.
Explains the correct reasoning behind the puzzle.