Originally posted to 13.7 Cosmos & Culture on 7/30/2014


Last week, I came across George Johnson's piece for The New York Times, "Beyond Energy, Matter, Time and Space," where he writes, in his usually engaging style, about two recent books with opposite viewpoints concerning what we can and cannot know of the world.

On the one hand, we find philosopher Thomas Nagel, and the arguments from his 2012 book Mind and Cosmos. According to Nagel, simple materialism, as we understand it today, is insufficient to make sense of some of the most complex natural phenomena, life included. He proposes an extension of current ideas, still within the material, but into yet unknown modes of thinking.

On the other, we have the überplatonism of MIT physicist Max Tegmark, as explained in his book Our Mathematical Universe. According to Tegmark, math is not just the tool we invent to describe both physical reality and pure rational constructions, but the very essence of nature.

Johnson's concluding paragraph resonates strongly with my own book The Island of Knowledge. The main point is that it is naïve to believe we can have such a thing as complete knowledge of nature. There are two essential reasons for this belief.

The first is simply that to make models of nature we need data. This data comes from tools of all kinds, from microscopes and particle detectors to telescopes and mass spectrometers. Any tool has limits of precision and range. Hence, we are always partially myopic to what goes on. Tools can and will improve. But some shortsightedness will always be unavoidable.

The second reason is that nature itself operates within certain limits: the speed of light and the finite age of the universe delimit how far we can see in space and limit causal relationships; quantum uncertainties delimit what we can say about the position and velocity of submicroscopic objects, and imply in nonlocal correlations through entanglement; math itself has its limits, as Kurt Gödel explores in his incompleteness theorems. The same is true with computers, from Alan Turing's undecidability theorem.

So, the image of an island captures our struggle to make sense of things, surrounded by an ocean of the unknown. As the island grows, so do the shores of our ignorance: as we learn more about the world we are able to ask questions we couldn't have anticipated before.

To know it all we would need to know all questions. And that, of course, is clearly impossible.

Unanswerable questions invoke a feeling of humility, of how science is, in essence, an ongoing mosaic of ideas, a self-correcting narrative of what we can gather of physical reality. This is far from a defeatist view; in fact, it is liberating. What could be more exciting for us to realize that knowledge is an endless frontier?