More evidence is accumulating, and so to dispose some of the anxiety of soon having to leave the dear world of tennis, addiction and myths of feral babies, I take some time off the story and its footnoted branches, and instead review some new occurrences of numeral confusion, and a possible explanation, to boot.
In the odd insert of Himself’s fond look back upon his younger years, the event of a sheared off doorknob leads him into his future work in annulation, or at least is presented as a foundation for this future work. The description of the rotation of the circle on a stalk on the hard floor is faultless, and the mathematical discussion of the cycloid that ensues, is quite flawless until this bit of information intrudes: “But since here, on the bedroom’s floor, a circle was rolling around what was itself the circumference of a circle, the cycloid’s standard parametric equations were no longer apposite, those equations’ trigonometric expressions here becoming themselves first-order differential equations.”
So we have a parametric description of the curve a point on a ring will go through as the ring rolls in a straight line. This is the cycloid. And since here a ring is really rolling in a circle itself, being restricted by the attached stalk, something is different. All of this is true. But why would the same parametric equations not be applicable along the circular path of the doorknob? As far as I can see, they would, and Himself telling us this story should be well aware of that.
The second new piece of evidence comes from one of the end notes, where Pemulis briefs Hal on how to obtain derivatives. x to the power of n derives to, he claims, nx+x^(n-1), which is finally absurd enough to turn suspicion into certainty: this is not noise, it is signal. This signal, however, not carrying simple narrative, because once again the person speaking both clearly knows the correct answer and also has no reason to deceive, or to expect a deception to be undetected, derivation of a polynomial being your pretty basic analytical bread and butter for high school kids.
And then, a few notes down, we witness Pemulis say this to a snivelling Possalthwaite: “Todd, trust math. As in Matics. Math E. First order predicate logic. Never fail you. […] The vital statistics of God or equivalent. When all else fails […] You can fall back and regroup around math.” This is followed by some lemma on line integrals that is indeed (and somewhat confusingly) true.
So if math is considered the one unwavering basal truth, yet is bent out of shape almost every time it comes up in the fabric of the novel, along with the laws of optics in the case of the shadows in the desert, which please recall is also a field of expertise of Himself, as is annulation, the weirdly absurd process of waste negating waste, it all seems to point to the fact that James Incandenza maybe found a way to infect everything he touched with some sort of existential rot, eroding the foundations of truth itself, just like any good father will.