The widespread adoption of double entry bookkeeping probably helped to legitimize negative numbers. Alice Adventures in Wonderland may well be a satire of the new mathematics of Carroll's time. Lewis Carroll wrote a book called Euclid and His Modern Rivals. It is a defense of Euclid in the format of play.
Personally, I don't think non-euclidean geometries are logically self contained structures, i.e. logically independent of Euclid -- although this is how they are portrayed. Euclid was the mould in which they were cast, but then the necessity of themould is semantically denied with an obfuscating term like "intrinsic" curvature. I have looked closely at the notion of intrinsic curvature and it is based on the covariant derivative which in turn presuppose the existence of a tangent to a surface, which by definition touches the surface but is not intrinsic to the surface. Harry On Tue, Mar 9, 2021 at 12:14 AM William Beaty <bi...@eskimo.com> wrote: > > > But this resembles the math community's much earlier hatred of Poincare' > infinities, then their earlier hatred of irrationals, and even earlier > hatred of negative numbers. (I remember being in third grade, and having > to tolerate negative numbers while holding my nose; being sure that I'd > grow up to invent a way to avoid ever using them. Gradually I became > accustomed to the stench. Looks like Schrodinger was the same, regarding > complex numbers.) > > Lewis Caroll Dodgson, lover of all things Euclidian, is rumored to have > despised Imaginary numbers, and built criticism into Alice in Wonderland: > https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ > > Never forget, we can't have Mandelbrot set without the imaginary axis. > (Well we CAN, but then it becomes ...clunky and contrived!) > > And also, everyone knows that pi is actually made from ln(-1)/sqrt(-1) > > As for the simulated universe in which we are currently embedded, lots of > computation could be avoided by its algorithms, if they hold their noses > and lower themselves to employing Imaginary numbers. But that layer seems > accessible only indirectly by human perceptions? We experience it as > phase in waves. (A square wave is the same thing as a delta function > impulse, if phase between spectrum peaks is unimportant!) > > > Also: > > The worlds' smartest crow observes two farmers walk into a shed, then > three farmers walk back out again. The crow won't fly down to eat any > corn. > > Obviously it's waiting for one farmer to walk back in ...so the shed > becomes empty! > > Also: > > Two FE-device inventors walk into a bar... > > > > > > On Mon, 8 Mar 2021, H LV wrote: > > > > > https://www.quantamagazine.org/imaginary-numbers-may-be-essential-for-describing-reality-20210303/ > > > > (((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))) > William J. Beaty SCIENCE HOBBYIST website > billb at amasci com http://amasci.com > EE/programmer/sci-exhibits amateur science, hobby projects, sci fair > Seattle, WA 206-762-3818 unusual phenomena, tesla coils, weird sci >
