Do mathematics reveal a designer?
Rauser takes aim at atheism in this next section of the book by positing that the "unreasonable effectiveness" of mathematics is evidence that a rational mind is behind the design of the universe. This is a favorite topic of mine (as I'm a big fan of cognitive linguist George Lakoff and his book Where Mathematics Comes From, which posits a wholly physical and cognitive origin of mathematics), and Rauser stumbles out of the gate with his very first erroneous example—one that to my surprise, Schieber does not object to.
That example is the famed Fibonacci number sequence. The contention is that this number is readily observable, as Rauser claims, "throughout nature, ranging from the spiral structure of seashells and pinecones to pinwheel galaxies". He then makes a similar claim about the numbers pi and phi (closely related to the Fibonacci sequence), claiming that examples of them are abundant in nature. The problem is, this is not actually true. There is ample literature on this common misconception, so I'll simply leave some references: [1, 2, 3, 4, 5, 6, 7, 8]. Even the claim that the "golden ratio" is abundantly found in human architecture is a myth. It's disconcerting to see Rauser begin with examples that aren't just wrong, but are easily found to be so with cursory research. It's equally disconcerting that Schieber did not pounce on this opportunity to thoroughly and aggressively undermine Rauser's argument. Instead, the authors spend several pages debating whether Rauser's examples are actually evidence for God—which they cannot be, since they are not actually true in the first place. And frankly, I see no reason to give this argument any further attention.
Rauser's second argument is that "the extraordinary degree to which mathematics generally maps onto physical reality" is evidence that a rational mind designed the universe. He opines, "This calls out for an explanation, and a mind is precisely the kind of explanation that accounts for the phenomenon." Schieber's rebuttal in this section is on track. He says, "I think you are right to appeal to a mind when thinking about the relationship between mathematics and the sciences, but I think you've got the direction of explanation backward." He later expounds, "we impose various systems of mathematics onto our prior accumulated observations and come up with elegant explanations that both fit the data and make predictions about future observations." As the stalemate between the authors arises again, I find myself remembering the thesis of Lakoff's work: that the embodied mind maps mathematical concepts through metaphor. This is a rich topic unto itself and I strongly recommend further reading.
My own objection to Rauser, again, is conceptual in nature. He hastily concludes that a rational mind would impose a mathematical structure onto the universe; but per Lakoff, much of our understanding of mathematics derives from our embodiment and neural structure. It's not clear, then, how an unembodied mind (not withstanding its many other conceptual ambiguities) would think about mathematical concepts, nor is it clear that our embodied understanding of mathematical concepts would overlap with these, for lack of a better term, "divine mathematics". Rauser is again, despite his objections to Schieber elsewhere, relying on a heavily anthropocentric conceptualization of God to make his point. This exposes a pattern with Rauser's argumentation I find frustrating: God is sufficiently ineffable and mysterious in his omni-being when Rauser wants to insist that evidence underdetermines His existence or nature, and sufficiently humanlike when Rauser wants to invoke natural theology or speculate about His motives. This could have been avoided if Rauser had given us a less ambiguous conceptualization of God to begin with.