“There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.

Charles Hermite

“By keenly confronting the enigmas that surround us, and by considering and analysing the observations that I have made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

M.C. Escher

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You know, I could see you adding your thoughts to these quotes, especially bridging the last four words of the first quote with the second. What is it that forces someone to claim the divinity of the split between ideality and materiality? I don’t even think Whitehead would necessarily agree with such a facile statement. Kant would, no doubt, but only first by proving the impossibility of proving this so-called divinity. But that’s unfair, Kant doesn’t want to prove divinity, he’s making room for faith.

Also, I do not like the use of the word “world” in the first quote. Even something as simple as I described above–the split between ideality and materiality–does not really get at what this fellow means by a split between worlds.

Let us urge this point: not only is he mistaken (two worlds do not exist, and if a world exists it is not de facto…which one could say about the world of capitlaism), but he seems to be hallucinating a usage of the word “world” which only comes about in intense meditative/drug-induced visions.

There exists/there is….both the oldest and most worn out thought, as well as the most formalized (hence mathematics…Badiou’s two operators: existence/universality) and most mystical saying (Levinas, the haunting presence of the there is contaminating the void).

Hermite is interesting for many reasons… Did you know he pens some of the earliest remarks on fractal sets?

He even writes in a letter to a colleague: “I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives.”

A benevolent God surely wouldn’t let such things exist….🙂

Although I am trained in Mathematics, I must say that I agree with Nietzsche:

“Logic, too, also rests on assumptions that do not correspond to anything in the real world, e.g., on the assumption that there are equal things, that the same thing is identical at different points in time: but this science arose as a result of the opposite belief (that such things actually exist in the real world). And it is the same with mathematics, which would certainly never have arisen if it had been understood from the beginning that there is no such thing in nature as a perfectly straight line, a true circle, and absolute measure.”

Hilbert had a brilliant idea when he devised a class of space filling curves.. thus posing a question on what does dimension really mean if a curve can fill a 2D object like a square.. maybe this is what Hermite thought as being monstrous.

You know Joe, I just now understood Laruelle’s references to fractal islands in his definition of non-aesthetics…he talks about the perspectives of non-euclidean geometry, and I didn’t really understand until I was rereading the definition and thinking about talking to you about some of the definitions more or less rigorously, you know, in an interrogative mode. It made me think of your Escher quote, and then, of course I realized Escher perfectly fits the example of an artist taking non-euclidean perspectives….so, in a way, your Escher quote about mathematics would probably fit in a lot with Laruelle’s argument.