Necker Cubes & Multiple Worldviews
So this didn’t really start out as an idea for a blog post, rather I was just explaining something to a friend of mine earlier today and decided to put it down in writing. She expressed a concern that she lacked a natural aptitude for physics to which I responded that I thought that the concept of natural aptitudes for particular fields of science was largely hokum. Except for claims of sucking at quantum physics and relativity. We all suck at quantum physics and relativity. Oh sure, you can train yourself in the thought patterns necessary to excel in those fields, but it is an uphill climb. While there are many things that are non intuitive, very few things actually as counter intuitive as these two fields (well, okay we can probably toss in some non-Euclidean geometry as well).
To understand this, we have to start with vision. A simple and elegant explanation for this involves the Necker Cube. The cube is, to begin with, not really a cube. Take a look at the picture and your brain will fly into action interpreting it. And it will be wrong. The first thing our brains are programmed to do is to grant the illusion of depth to a two dimensional image, and interpret as right angles several lines that are really no such thing. This is a perfectly understandable reaction for an organ that has evolved to function in a world with more than two dimensions. The more interesting error comes after we have granted depth to the figure. If you look long enough, behold! It inverts! In fact, with the least amount of effort the cube can be shifted back and forth at will. What’s going on here?
As Peter Watts puts it (and I haven’t heard a better summation of it than this): We are, as a species, incapable of holding multiple simultaneous worldviews. That is to say that when we are confronted with an ill-posed problem (a problem with multiple equally valid solutions barring the addition of any additional information) our brains arbitrate and select one possible solution. We are incapable of holding all possible solutions as simultaneously true. Oh, of course we can know that they are all equally valid, just as we know that no one view of the Necker cube is more valid, but that has no bearing on what we see. It should here be noted that the Necker cube is one of the best examples of this phenomenon because it is simple and relatively un-‘sticky’. Certain other demonstrations of the same thing, such as the spinning dancer illusion, can be much harder to swap back and forth or even see the other possible interpretations in the first place.
It should be fairly apparent why this is. We are machines with two very specific operating parameters: survive and reproduce. Neither of these is aided by coming across an ambiguous situation and standing there overwhelmed at all the pretty interpretations. In the interest of action, our brains pick an interpretation for us. Presumably this is based on certain hard wired precepts like the ones Helmholtz outlined (faces are usually viewed upright, light generally comes from above, we often don’t look at objects from below) mixed with lessons learned from personal experience. Now, such quick and some may even say arbitrary decision making in the face of ambiguity might in fact be lethal for an individual, but natural selection works on populations. For instance with the dancer illusion above, about 2/3 of people see the dancer as rotating clockwise, research into this has pointed to a bias to interpreting things as viewed from above. Which makes sense for creatures known for their upright posture, in the wild it seems likely that many things early man was interested in were located below eye level (food, spawn, the breasts of early woman, etc.).
What this has all been getting to in a roundabout way, is that one of the reasons many people struggle with relativity with its multiple shifting reference frames and quantum physics with its wave equations and probability, is that we are biologically predisposed to pick one interpretation and act on it. To beat a possibly dead cat, lets examine Schrödinger’s classic illustration: to the human mind the idea that something exists in two states simultaneously is absurd. To truly understand that situation it would be like seeing both interpretation of the Necker cube, or being able to see the dancer moving both clockwise and anti-clockwise simultaneously. When we look at the Copenhagen interpretation of quantum theory, and are told that there is a superposition of possible states that only resolve when an observation takes place, we find that we are simply not wired to think in that fashion however true it might be.
However, we are very clever. Over the years many people have trained themselves to work quite dexterously within these realms of physics despite this vestigial limitation of the mind (In some ways it is very like how we can discuss the mathematics of occurrences in any set of dimensions ‘n’ despite not being able to picture or indeed work within physical dimensions beyond the familiar three). Although I can’t but wonder if our cognitive limitations are related to the fairly slow going in physics these days.