The Mystery of Knowledge

This morning, I sat next to an autistic man on the metro. We chatted a bit, and then he grabbed a scrap of paper and scrawled on it:

“JOBFAIR=1979”

“GAO=2009”

He then concatenated the numbers, and wrote:

19792009

His pen lingered above the piece of paper for thirty seconds or so. The man seemed deep in thought, utterly lost in the wonders of the integer he had just written down. Then he completed the thought:

19792009 IS PRIME

I did a double-take. No way that a human being can test the primality of an eight-digit integer in under a minute. As soon as I got to work, I checked if the claim was true. It was. 19,792,009 is a prime number.

It was only at that point that I realized both that the story I’ve recounted is a tragic one, and that it serves as a beautiful allegory for the larger tragedy of modern, mutilated science. Whether or not the number 19,792,009 is prime is what a mathematician would call a trivial or uninteresting claim. What meaning it had for my traveling companion must have resided in the meanings of the cryptic phrases “JOBFAIR” and “GAO” and in whatever algorithm he had used to turn these phrases into numbers. The same is true of the scientist – without that mystic light that gives meaning and depth to those shadows in our minds called concepts we are doing nothing more than chasing those shadows and shuffling meaningless symbols on a piece of paper.

And yet, as Joseph Bottum points out in an essay published here at First Things in 1994:

In the real psychology of conversion, no one comes to believe merely for the sake of guaranteeing knowledge.

This is undoubtedly true, yet most mathematicians continue to believe, at the very least, in an underlying order to the universe. Bottum continues :

This has an analogue in the theological realization that God is not mastered by the thought of Him, but discovered by thought to be beyond thought: He is silent where thought most needs Him to speak. And it has an analogue in the epistemological realization that the Divine defeats knowledge for the sake of which we suppose the Divine: God (posited as a transcendental condition for the possibility of knowing) must Himself be unknowable—else we would need to posit some further God as the condition for the possibility of knowing Him. And it has its most accurate analogue in the historical realization that we are not premoderns: we cannot cease to be moderns by rebelling against modernity.

To this I would add a fourth analogue: that of Godel’s sentence ‘G’, which is by its very nature unprovable and yet by the nature of our system of mathematical inquiry must both exist and be true. Like Bottum’s epistemological analogue, creating a condition for the provability of ‘G’, for instance by adding an axiom specifying its truth, does nothing more than to require the existence of a further ‘G’ as a necessary condition of the power and consistency of our truth-seeking system.

I think the analogy is even stronger than I have described it as being, but a description of why would require a journey into some fairly technical reasoning. The important question that remains is how given a thing that is intrinsically unknowable, we can still believe in our ability to pursue intimations of the thing. Indeed, if I were asked to come up with a concise statement of the “mathematician’s creed” it would be the following:

Patterns are the way in which our limited minds interpret symmetries in the deeper underlying reality.

Ultimately then, in Bottum’s language, the existence of knowledge rests not only on a faith in the transcendental condition for the possibility of knowing, but in a further faith that, even if such a transcendental condition is ultimately unknowable, we can trace those reflected rays that illuminate the world around us back to their source.

P.S. Bottum’s entire essay is well-worth reading. Available here .