C. Auguste Dupin discussing Dupin's method in the light of Charles Sanders Peirce's logic of making good guesses or "abductive reasoning," Nancy Harrowitz first quotes Poe's definition of analysis and then shows how "Poe the semiotician is running the gamut of possibilities here—inferences, reasoning backwards, visual, sensual and aural signs, reading faces. Playing cards with the man would have been an interesting experience." There is considerable controversy about the philosophical nature of Dupin's method. According to biographer Joseph Krutch, Dupin is portrayed as a dehumanized thinking machine, a man whose sole interest is in pure logic. However, Krutch has been accused elsewhere of
Dupin cyclide of Dupin cyclides is invariant under the larger group of all Lie sphere transformations; any two Dupin cyclides are Lie-equivalent. They form (in some sense) the simplest class of Lie-invariant surfaces after the spheres, and are therefore particularly significant in Lie sphere geometry. The definition also means that a Dupin cyclide is the envelope of the one-parameter family of spheres tangent to three given mutually tangent spheres. It follows that it is tangent to infinitely many Soddy's hexlet configurations of spheres. A further special property of a cyclide is: An elliptic cyclide can be represented parametrically by the following formulas