Illusions

It seems to me that half of being strong is knowing where we’re weak.

Constructing an accurate model of reality is hard. The Universe is almost-infinitely complex, endlessly detailed, and rapidly changing. Our ability to acquire data about reality is profoundly limited. Consider vision. Light reflecting off 3-dimensional reality enters our eyes and creates a 2-dimensional patch-work of color on our retinas; Annie Dillard’s “unpeached peaches”. Different regions of the pattern have no intrinsic information about the distance to the object that reflected it, nor the color of the light that initially struck the object. In chapter 4 of How the Mind Works, Steven Pinker tells us that constructing a 3-dimensional model of the world around us from the 2-dimensional image cast on our retinas is not just difficult, but impossible. There isn’t enough data on our retinas to do the job.

Yet we unconsciously and nearly-instantaneously create a 3-dimensional model of our surroundings that is accurate enough that we can successfully walk, run, ski, drive, surf, and fly aircraft without bumping into walls, trees, rocks, coral, bridge abutments, or mountains. How do we do it?

Pinker tells us that it is through the magic of assumptions. By assuming that light is generally uniform, that two objects don’t, by chance, have exactly the same edges, nor are those those edges likely to line up perfectly, and a host of other built-in beliefs about how the world is organized, we can construct a 3-D model from 2-D information.

These assumptions are pretty good. It turns out that there are some aspects of reality here on Earth that are pretty consistent, and which don’t have to be actively queried every time we open our eyes. Those of our predecessors that possessed visual computational circuits that made good assumptions were able to rapidly construct accurate 3-D models; avoid cliffs and poisonous snakes; and navigate successfully to food, shelter, water, and a mate. They become not just predecessors, but ancestors. As copies of these ancestors, we too possess these “firmware” beliefs about the nature of reality. And they serve us well.

But, like many of us, I was introduced early on to optical illusions, drawings, like the one below, that “fooled” our visual system.

Both of the cylinders are the same size by the ruler, but no matter how many times we measure it, no matter how deeply we know it, our visual system tells us that the upper one is larger. In order to deliver a good model in real time, our visual system utilizes hard-wired, and thus extremely fast, assumptions about perspective, distance, and, in this example, size. And because it is hard-wired, it can’t be changed through learning any more than we can learn to have three or four legs instead of two.

So we see that optical illusions occur when our most-of-the-time accurate assumptions about the nature of reality are violated. In the example above, the cylinders aren’t actually in a hallway, but the grid work on the left and right is interpreted by our visual system as such. By violating our evolutionary assumptions we can reveal what they are and see how the “magic” is performed.

This fascinates me. Contained in my moment-to-moment living, in opening my eyes and seeing the 3-dimensional arrangement of objects around me, are the deaths of our predecessors who did not have accurate assumptions, and the unbroken chain of sex (and I hope some measure of love-making) of my ancestors who did. These assumptions reveal the nature of the Universe to us, are a built-in model of reality, with which I was born, seemingly for free. An extraordinary feat of computational prowess that even now, 60 or so years into the age of serious computing, we still have trouble matching. Talk about having a super-fast GPU! How cool is that?

Pinker further illuminates the world of “intuition”, the built-in assumptions we possess about the world that give us a leg-up on its navigation. Intuitive physics, intuitive psychology, intuitive statistics, intuitive biology, and more. These are models of the reality in which we have very high confidence; so high that they are hard-wired into our genetics, and though we may, with great effort, over-ride them on occasion, it seems impossible to escape them. To unpeach Dillard’s peaches.

And, in what I find one of the wonders of Civilization and of being human, we are able to observe and understand how our built-in beliefs work. To discover that we have them in the first place. In addition to the shear joy of knowing our own natures and its computational and engineering marvels, we can also improve our models of reality: in knowing that we make assumptions, that we posses genetic beliefs, that were often-enough true historically to be written into our DNA — and that they aren’t true in every circumstance. Our hard-wired beliefs about the world can be wrong; the assumptions can be violated as they are in the drawing above. Sometimes this happens when we encounter a rare circumstance, or when the world changes. Or when other folks use knowledge of human assumptions to redirect our energies in service of their own goals. Knowing a bit about our assumptions gives us a chance at adjusting for violations. To know that the cylinders will, despite my visual system’s screams to the contrary, fit through the same round hole.