Saturday, March 5, 2011

An Imagined World

Over the past centuries science has pushed humankind from its pedestal several times. First Copernicus showed that the earth is not at the center of the universe, then Darwin showed that humans are the product of evolution and direct descendants of the apes. What else awaits us? With the advance of fast and more intelligent computation we will see the realization that computers can be far smarter than humans. We passed a few thresholds: Deep Blue beating Kasparov in chess, and now Watson becoming the new champion in the television show Jeopardy. As time goes on, we will see many more of these landmarks happen. There will be a time when we will be second to computer systems in almost any imaginable task. Are there even stranger revolutions that await us?

Although it is exceedingly difficult to look in a crystal ball, there are signs that an even bigger philosophical shock awaits us. Physicist believe that the true ontological degrees of freedom are far fewer than the ones we usually entertain to describe our world. In fact, there are signs that we could pack all the degrees of freedom on a two-dimensional plane, instead of in a three dimensional world. What then are these surplus unphysical degrees of freedom? My claim is that they are imagined: they live in our head in order to make sense of our world. Remember that all our brain is concerned with is predicting the future. If you can predict better you have an edge in survival. Now imagine that the ontological degrees of freedom have very complicated laws of dynamics, i.e. their future is very hard to predict from the past. Then lets imagine that by introducing a bunch of auxiliary variables this prediction task may become easier. This is not such a far fetched thought. In fact in statistics people do it all the time. Adding variables can simplify the description of a problem. However, in physics this is also a well understood phenomenon. Almost any modern theory has so called "gauge symmetries". These are transformations that change one description of the world into another description of the world without changing the actual state of the world. For instance, Einsteins general relativity allows one to transform between two frames of references (observers) that accelerate relative to each other. One observer interprets the state of the world as "gravitational pull" while the other as acceleration.

These symmetries lead to conservation laws (Noether's famous insights). Conservation laws are constraints between variables. They simply express that we have have used too many variables to describe the state of the world and hence some variables can be solved from other variables (and in fact removed). So there are two types of variables in a theory: variables whose state can only be solved from the world state in the past and variables whose state can be solved from the state of other variables at the same time. The second type is redundant, but often very useful in writing down nice concise equations to describe our world. What I predict will happen is that we have completely underestimated the number of these spurious variables in our theories. I believe, supported by the holographic principle which states that all real degrees of freedom can be stored on a surface, that there are vastly more unphysical degrees of freedom in our theories than physical ones.

Now let's take this one step further. Our brain is also in the business of making models of our world. Everyone of us is a physicist, if you like it or not. I now propose the following leap of faith: the way we view the world is also largely made of unphysical degrees of freedom. We have evolved to use these over-parametrized models because they lead to easier prediction at the macroscopic scale in which we live and survive. But they are largely an illusion, a fantasy of our minds that we all share (like the ability to speak language this illusion has been hardwired in our brain through evolution). This is the new revolution that I anticipate: we will come to realize we live in a fantasy world.

What are the potential consequences, if what I propose is true? While the auxiliary variables may work well at the macroscopic level, they may not work all that well at the microscopic world. I believe the brain has introduced new variables that follow simple laws of dynamics themselves. In particular, together with the real degrees of freedom they make up a consistent system where (usually) cause precedes effect. However, for the unphysical degrees of freedom there is no reason why this should be enforced. In general, there may be glitches in this framework in situations that are not important to survival. These glitches in consistency may for instance involve apparent reversed causality for the unphysical degrees of freedom, but in such a way that they will not affect the strict causality necessary for the physical degrees of freedom. We should not be able to receive a message from our yet to be born daughter who instructs us to kill ourselves so she will not be born (unless all the degrees of freedom that govern this daughter are unphysical of course).

All of this is compete speculation, and I make no claims that there is evidence for it. But oftentimes, a half true story might help one to keep an open mind to explore or embrace new ideas.