"If you're like me, you probably recall Voltaire's satirical novel Candide as one of the more enjoyable 18th century novels you were forced to read in high school. Its fast-moving and rather silly plot involves a young man who is tutored by an optimistic philosopher named Pangloss. Pangloss insists that they are living in the best of all possible worlds, despite losing an eye and an ear, catching syphilis, being sold into slavery, and experiencing disasters such as a fire, earthquakes, and a tsunami. But did you know that the philosophy that Pangloss parodies is directly related to the development of calculus?
This connection comes from the fact that Gottfried Leibniz, the co-inventor of calculus, was also a well-respected philosopher. You may recall that one of the key achievements of calculus is the ability to find a maximum value of a function. This works because calculus lets us look at the slope of a curve, which measures how steeply it is rising or falling, at any infinitesimal point. When a curve has stopped rising and is about to fall, its slope is 0, and it has achieved a local maximum. So if you can calculate the point where the slope of a curve is 0, you can find a maximum.
In mathematics, this idea is not very controversial. But Leibniz extended this accomplishment into the domain of philosophy. As a basic premise, he started with his Christian religion, which asserted that there was an omniscient and omnipotent God who designed the universe. Most likely, an omniscient or all-knowing God would know calculus, and probably a much more powerful divine super-calculus than what Leibniz had developed. And being all-knowing, he would also know all the variables that would go together to describe the universe, and be able to define some infinitely complex function that would describe how good the universe is. Since God is also supposed to possess infinite goodness, it stands to reason that he would apply his super-calculus to the universe's goodness function, and achieve an overall maximum. Therefore if something local seems bad, it's only because in combination with the other variables of the universe, it needs to be that way to achieve the overall maximum.
Actually, I find it kind of hard to argue with this reasoning. In the centuries since Leibniz, many complicated functions have been defined, which we don't have algorithms to optimize in a reasonable time, but God would know all the mathematical techniques he needs, and wouldn't care about time limits. After all, if there is truly an all-powerful divine being who likes to create universes, he may as well take his time doing it, even if he has to spend several eons executing an NP-complete optimization algorithm. So if your religion admits the existence of an all-powerful and all-knowing Creator, then Leibniz and Pangloss were both right, and we really do live in the best of all possible worlds.
And this has been your math mutation for today."
To listen to the it yourself, then click the Calculus In Candide