Descartes' Chart

Science uses systematic observation to yield objective understanding. That perception distorts observation, however, makes objectivity highly suspect. We do well to look out for personal biases, but the problem is more pernicious. Some biases belong not to individuals but to the human species or, worse, any observer whatever. Thus, we have two modes of distortion.

  1. Personal circumstance influencing perception and observation.
  2. The apparent perception made by any human contradicting deeper facts.

Solutions to problems generated by the first mode include using peer review, promoting open discourse, and keeping the bar high for hard evidence. In other words, maintaining a scientific culture. The second mode poses a more ambiguous threat. For these distortions become apparent with further investigation, but it is not clear what to make of them. Regardless, we cannot ignore them.

When you look at Google Maps or Apple Maps, you are looking at the Mercator projection, which is only one of many options for displaying the surface of the Earth.

Gauss' Theorema Egregium tells us that no projection from a sphere to a plane can completely perserve the sphere's curvature; therefore, every flat map contains distortions. While the Mercator projection is desirable because it preserves angles, which is helpful for navigation and orientation, it makes objects far from the equator look bigger than they should. Tissot's indicatrix gives us a visual sense for this distortion by seeing how the projection modulates circles that are the same size on the globe. As you can see, the circle near Greenland is larger than the circle near Africa, so we know Africa is in reality much larger than Greenland (verify for yourself).

By acquainting ourselves with other projections, we can break out of the provincial view of the Mercator projection. But the misperception caused by something as benign as a map begs the question: how do we know we're seeing reality? If my perception can verifiably fail me, when can I trust it?

That's the question Descartes asked, albeit more abstractly. He wanted his view of reality to depend only upon principles which he could not doubt. It would not be a stretch to say that modern philosophy comes out of responses to his line of reasoning. But Kant points out the gap between the phenomenal world, which contains things as we sense them, and the noumenal world, which contains the things-in-themselves, independent of our senses. In his view, we see things as spatially or temporally extended because that's how our perceptual apparatus is structured. In Beyond Good and Evil, Nietzsche critiques Descartes' famous cogito ergo sum as a confusion stemming from grammar.

The inability to access reality might be disheartening to some. I do not think so. Even if we could obtain a complete description of reality, we should wonder whether we want it. Borges' short story "On Exactitude in Science" describes a map of the same size as the territory it represents. Such a full-sized map is useless because the utility of a map is that it reduces the Earth to only what is relevant for navigation. The title of the story makes the point clear. Science wants science to be exact. People need science to be comprehensible, pragmatic, perhaps even enlightening.


This post was inspired by What caused the hallucinations of the Oracle of Delphi?