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The Banach-Tarski Gyroscope

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Subject: The Banach-Tarski Gyroscope
From: wolfgang...@hs-augsburg.de (WM)
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by: WM - Sun, 5 Dec 2021 10:22 UTC

The Banach-Tarski Gyroscope is an intricate mechanism believed to have been constructed using the Axiom of Choice. On each complete rotation counterclockwise, the Banach-Tarski Gyroscope doubles in volume while maintaining its shape and density; on rotating clockwise, the volume is halved. When first discovered, fortunately in the midst of interstellar space, the Banach-Tarski Gyroscope was tragically mistaken for an ordinary desk ornament. Subsequently it required a significant portion of the available energy of the contemporary galactic civilization to reverse the rotation before nearby star systems were endangered; fortunately, the Banach-Tarski Gyroscope still obeys lightspeed limitations on rotation rates, and cannot grow rapidly once expanding past planetary size. After the subsequent investigation, the Banach-Tarski Gyroscope was spun clockwise and left spinning. [E. Yudkowsky in "The Banach–Tarski paradox", Hacker News (28 Dec 2008)]

Re: The Banach-Tarski Gyroscope

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From: james.g....@att.net (Jim Burns)
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by: Jim Burns - Sun, 5 Dec 2021 22:10 UTC

On 12/5/2021 5:22 AM, WM wrote:

> The Banach-Tarski Gyroscope is an intricate mechanism
> believed to have been constructed using the Axiom of
> Choice. On each complete rotation counterclockwise,
> the Banach-Tarski Gyroscope doubles in volume while
> maintaining its shape and density; on rotating clockwise,
> the volume is halved. When first discovered, fortunately
> in the midst of interstellar space, the Banach-Tarski
> Gyroscope was tragically mistaken for an ordinary desk
> ornament. Subsequently it required a significant portion
> of the available energy of the contemporary galactic
> civilization to reverse the rotation before nearby star
> systems were endangered; fortunately, the Banach-Tarski
> Gyroscope still obeys lightspeed limitations on rotation
> rates, and cannot grow rapidly once expanding past
> planetary size. After the subsequent investigation,
> the Banach-Tarski Gyroscope was spun clockwise and
> left spinning.
> [E. Yudkowsky in "The Banach–Tarski paradox",
> Hacker News (28 Dec 2008)]

Q. What is an anagram of Banach-Tarski?

A. Banach-Tarski Banach-Tarski.

Subject	Author
The Banach-Tarski Gyroscope	WM
Re: The Banach-Tarski Gyroscope	Jim Burns