Babbage's Insight

I spent Monday reading Charles Babbage's autobiography, Passages from the life of a Philosopher. Calling it an autobiography is a bit of an exageration: it's more like Surely you're joking Mr. Feynmann, or Boy. He's quite funny, though some of his puns haven't held up so well. He held the Lucasian chair at Cambridge, and while he was there he successfully got them to switch from Newton's fluxions notation (represented with a dot) to Leibniz's superior notation (the familiar dx/dy style of writing derivatives). He published a pamphlet to sway people to his cause: The principles of pure D-ism in opposition to the Dot-age of the university.
Because computation had always been done by the mind before, Babbage and his collaborators were very aware that they were building a kind of artificial intelligence. This is a fascinating topic that I will talk about more in my book. But here I wanted to mention something else that interested me.
Babbage wrote a program that would calculate based on one formula for one million iterations, then switch to a second formula, and continue with a new law. He presented it to some friends from Ireland:
"this succession of a new law, coming in and continuing during any desired time, and then giving place to other new laws, in endless but known succession, might be continued indefinitely."
"I remarked that I did not conceive the time ever could arrive when the results of such calculations would be of any utility. I added, however, that they offered a striking parallel with, although at an immeasurable distance from, the successive creations of animal life, as developed by the vast epochs of geological time. The flash of intellectual light which illuminated the countenances of my three friends at this unexpected juxtaposition was most gratifying. "
"Encouraged by the quick apprehension with which these views had been accepted, I continued the subject, and pointed out the application of the same reasoning to the nature of miracles... "
"A further illustration may be taken from geometry. Curves are represented by equations. In certain curves there are portions, such as ovals, disconnected from the rest of the curve. By properly assigning the values of the constants, these ovals may be reduced to single points. These singular points may exist upon a branch of a curve, or may be entirely isolated from it; yet these points fulfil by their positions the law of the curve as perfectly as any of those which, by their juxtaposition and continuity, form any of its branches. Miracles, therefore, are not the breach of established laws, but they are the very circumstances that indicate the existence of far higher laws, which at the appointed time produce their pre-intended results."
So already the idea of the universe as a simulation was being considered, with God sitting outside programming the universe. I like the idea of the Atonement as a kind of moral singularity, where the laws of the universe suddenly shift (in harmony with a higher law.) There is a passage from Alma that touches on this. The prophet has explained that it doesn't matter if you kill one man or ten men to make up for a sin: each individual death has zero effect on righting the injustice of the original wrong. But when you multiply zero by infinity, there is a singularity: the old laws no longer hold. "Wherefore, there must needs be an infinite atonement..."