"Oh, nobody said that! For, indeed, it does seem to me I have heard of this Praxagorean system of mathematics, though, I confess, I have never studied it."
"Our school, madame, postulates, first of all, that since the science of mathematics is an abstract science, it is best inculcated by some concrete example."
Said the Queen: "But that sounds rather complicated."
"It occasionally leads to complications," Jurgen admitted, "through a choice of the wrong example. But the axiom is no less true."
"Come, then, and sit next to me on this couch if you can find it in the dark; and do you explain to me what you mean."
"Why, madame, by a concrete example I mean one that is perceptible to any of the senses—as to sight or hearing, or touch—"
"Oh, oh!" said the Queen, "now I perceive what you mean by a concrete example. And grasping this, I can understand that complications must of course arise from a choice of the wrong example."
"Well, then, madame, it is first necessary to implant in you, by the force of example, a lively sense of the peculiar character, and virtues and properties, of each of the numbers upon which is based the whole science of Praxagorean mathematics. For in order to convince you thoroughly, we must start far down, at the beginning of all things."
"I see," said the Queen, "or rather, in this darkness I cannot see at all, but I perceive your point. Your opening interests me: and you may go on."
"Now ONE, or the monad," says Jurgen, "is the principle and the end of all: it reveals the sublime knot which binds together the chain of causes: it is the symbol of identity, of equality, of existence, of conservation, and of general harmony." And Jurgen emphasized these characteristics vigorously. "In brief, ONE is a symbol of the union of things: it introduces that generating virtue which is the cause of all combinations: and consequently ONE is a good principle."