This point has been disputed by Arkady Plotnitsky (one of the authors mentioned by Sokal in his original hoax). Plotnitsky says that "some of their claims concerning mathematical objects in question and specifically complex numbers are incorrect," specifically attacking their statement that complex numbers and irrational numbers "have nothing to do with one another." Plotnitsky here defends Lacan's view "of imaginary numbers as an extension of the idea of rational numbers—both in the general conceptual sense, extending to its ancient mathematical and philosophical origins...and in the sense of modern algebra." The first of these two senses refers to the fact that the extension of real numbers to complex numbers mirrors the extension of rationals to reals, as Plotnitsky points out with a quote from Leibniz: "From the irrationals are born the impossible or imaginary quantities whose nature is very strange but whose usefulness is not to be despised."