Sunday, September 12, 2010

More Thinking about Thinking

WARNING:  There is almost nothing in this post about Italy, and no pictures.  It's just stuff I have been thinking about for the last few decades.

I take it for granted that the brain has evolved to help us make sense of the world, involving some trade-off between the two goals of maximum accuracy and minimum uncertainty.  Maximum accuracy leads to rapid automatic assessment of sensory information and its similarities to past experience, and the possibility of more leisurely analysis of the less-obvious.  Minimum uncertainty means the willingness to make snap decisions and act on them, rather than worrying about the subtleties of the situation.

Based on my experience with control systems, I believe the first problem the brain faces in interacting with the world is to detect the presence or absence of something.  Once you can do that, you can develop a processor or analyzer to determine the magnitude of what has been detected, and what else it is related to.  So the yes-no, true-false system is basic, and that has developed into our capacity with logic.   The analysis of how-much leads to mathematics on one hand,  and to analysis of the relationship to other things on the other hand.  Relationships between things tend to be similar to other relationships between other things, so metaphor and analogy are the basis of much thinking, and the same neural processes can be reused in many ways.

All this is was evolved and culturally developed in dealing with, first, the external world of things, and second, the relationship to other people.

Starting with the world of things, it is interesting to see what happens when we run into things that never happened to our evolutionary ancestors, that do not follow the same rules.  I am thinking here of quantum mechanics.  The world of the very small (electrons and photons and such) is well understood in the sense that we have mathematical theories that predict exactly what will happen in a given experimental setup.  It is poorly understood in the sense that the rules just seem flatly impossible to our instinctive ways of thinking.

The basic puzzle of quantum mechanics is the wave-particle duality.  Classically, every object is a particle or collection of particles.  If you know where it is now and how it interacts, you can calculate where it will be in the future and where it was in the past.  There are, of course, experimental limits to just how accurately you can do that.

In quantum mechanics, it turns out that the mathematics of the classical model does not work to make predictions from the present to other times.  The mathematics that has been found to give accurate predictions of quantum systems effectively assumes that the particle is some kind of (manifestation of some kind of) wave that travels in time, with all the interference patterns and lack of specific location a wave has, which can give only statistical probabilities about where it will be in the future.  Then, of course, when you detect the particle again, measure its position, it is a particle that is at some one point in that probability distribution and not at any other.  All that is required to derive this is the recognition that the limit on accuracy is not just an experimental limit, it is a fundamental feature of nature;  theories assuming that every thing can (in principle) be specified to arbitrary accuracy are incorrect.  These quantum theories lead to funny ideas when people try to make sense of them, and I believe that is because our brains aren't built for it.

There is a popular model, or interpretation, which most science writers seem to believe, which says that the probabilistic wave is all there is until someone looks at it, leading to speculations about the fundamental role of consciousness in creating reality.  To counteract that interpretation, there is the famous Schroedinger's cat.  A cat is put in a box with a radioactive source, a detector, and some poison.  When the detector catches a decay particle, the poison is released and the cat is dead.  If you wait a suitable time, there is a 50% chance the cat is dead, but you don't know until you open the box and look.  But if you really believe the model that says the system isn't defined until you look, then before you look the cat is in a kind of "superposition of states" and isn't either really dead or alive until you look, because the detection of the decay particle is only probabilistic until observed..  This was intended to illustrate the fallacy of that interpretation, but is now seriously represented as something that would actually happen.  Einstein is supposed to have asked someone "Do you seriously believe that the moon is not there if no one is looking at it?"

The reason this model is taken seriously is because any theory that says things really are deterministic, not just probabilistic, has to be able to match the experimental results.  The probabilistic models match experiment, and anything else would have to be more complicated without changing experimental predictions.  One of the books I have brought on this trip, which I am slowly working on, is a book about "hidden variable" theories.  They are called hidden variables because the variables which specify exactly what will happen must be hidden from view, unable to be specified and measured.  If the "hidden variables" weren't hidden from view they could be specified and measured, and then the theory wouldn't match experimental results known to date.  It was written in 1956, and I bought it 30 years ago.  One of the things it says is that future experiments might be able to distinguish these theories.  I think that might now have been done.

One of the subjects much in the scientific news lately are various experiments that show that faster-than-light-speed communication might work, because it is possible to prepare wave-particle pairs (photons) that then separate themselves, and you can do an experiment on one of the pair which amounts to forcing the wave function to collapse, giving a specific value to both the particles, and the other particle takes on its complimentary value faster than light could travel from one to the other, so the second somehow knows instantaneously what the other has done.  That is presented as really weird and exciting, but only within the wave-collapse-generates-values model.  Normally, a requirement for faster than light communication speed is taken to indicate a serious impossibility.  I think this experimental result is, rather, an experimental demonstration that a hidden variable theory is needed and the existing quantum mechanical theory is simply wrong in asserting that the unmeasured values are truly undefined until observed.

The point of all this is that modern science has demonstrated that either things are really not determined until you look, which makes looking somehow special, or that things are determined but if you know some of them the others are inherently unknowable, but it is possible to choose which is which.  We aren't built for that.  To think about things we need theories that somehow tie everything down.  We need a solid foundation to work from, and if we are given an incomplete set of information we will complete it in some way that matches some pattern that seems plausible.

This has no relevance to our trip to Italy, except as a partial answer to the question of what I am thinking about in addition to circa-Renaissance religious painting.  I am concerned about how we create mental representations, or modes of thinking about and understanding, for things that are unquestionably real (in some sense of the word reality) but outside the direct range of our senses, and therefore outside the range of our evolved mental modeling capabilities.  They are things that we can model and think about only in terms that are generally a metaphor or analogy to our real concern.  A basic problem in communicating these ideas is that the available metaphors don't really fit because they are derived for different subject matter.

One of our basic needs is to see things in true-false, yes-no pairs.  What must we do to become comfortably able to deal rationally with ambiguity?  I say rationally, because the emotional responses are all automatic and hence based on the evolved models, and the evolved models simply do not cover the range of the phenomena of interest.  With practice, quantum mechanical thinking can become normal, and the "How can it be like that?" response dies out, or at least is repressed enough to let us get on with the analysis of what is happening.  Then the intuitive recognition that something is right or wrong, based on whether or not it matches the expectation of a mental model, can work with the derived and learned model without being tied to the automatic involuntary models.

We can somehow satisfy the felt need for a firm basis for our beliefs by regretfully giving up the idea of a solid foundation of unquestionable truth, and replacing it with a global positioning system which we can use to navigate between familiar landmarks. 

The method of analysis and understanding by observing the phenomena and deducing relations without grounding them in a concrete physically intuitive model should work for other things, as well as quantum mechanics.  So that's part of how I'm looking at pictures in Italy.

No comments:

Post a Comment