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 that the class of Dupin cyclides is invariant under Möbius (or conformal) transformations. In complex space formula_2 these three latter varieties can be mapped to one another by inversion, so Dupin cyclides can be defined as inversions of the torus (or the cylinder, or the double cone). Since a standard torus is the orbit of a point under a two dimensional abelian subgroup of the Möbius group, it follows that the cyclides also are, and this provides a second way to define them. A third property which characterizes Dupin cyclides is that their curvature lines are all circles (possibly through