Tuesday, May 6, 2014


Nothing hinders certain things happening by luck or by chance, if compared to their proximate causes: but not if compared to Divine Providence, whereby "nothing happens at random in the world," as Augustine says. 
-- St. Thomas Aquinas


A comment on a recent post generated a conversation, at the commenter's own blog, on the nature of chance.  Here I continue that discussion by posting my ideas on chance at greater length.

To begin with, I think the best way to approach the mystery of chance is in the context of several similar mysteries, the first of which is free will.   One important aspect of free will is that we cannot predict exactly and with certainty what another person will do, even if we know his entire history and all the influences in creation that might be acting upon him.  If we could, he would be a mere automaton.  Since we might indeed expect subatomic particles to be precisely automatons, it is counterintuitive that the same statement should be true of them -- that there is an absolute limit to our ability to predict what they will do -- yet such is the case.  (This sort of "coincidence" happens all the time, where there is a tenuous but recognizable stylistic similarity between Christian doctrines and the best understanding of the material world science can provide -- almost as if they have the same Author.)

The best analogy I have heard reconciling God's complete control of the universe with free will is that of a work of art.  For example, in The Lord of the Rings, did Saruman betray his fellow wizards by his own free choice, or because Tolkien wrote it that way?  Both, obviously.  Nothing happened in the book that Tolkien did not intend, yet Tolkien's "influence" is of a completely different nature than that of any of the characters in the book -- Gandalf, Galadriel, or even Sauron.  When Saruman rebelled, it was a decision that came from within him, even though it came as a part of Tolkien's story.  Saruman had free will.  This is one of the reasons Tolkien referred to "Middle Earth" as a "sub-creation".

Other works of art can illustrate related ideas.  

One often notices in movies scenes that seem to have nothing much to do with the main characters or plot trajectory, but obviously the scene must be there for some reason.  If we can guess the reason that scene was included -- if, for example, it points to a secret weakness in the villain that the hero can be expected to exploit -- the scene is analogous to what has come to be known as Providence.  Of course, in principle everything that happens can be said to be ordained by Providence, using definition 1a from the Merriam-Webster dictionary ("divine guidance or care"), and the word has even come to be used as a title of God Himself, but most often it is used to describe the ordering of the chain of natural causes in order to produce a divinely intended purpose that we think we recognize.  Almost always this purpose is favorable to the one who calls it Providence.  An American, then, would see the thick fog that allowed Washington to escape New York in 1776 as an example of Providence.

The fine flying weather on September 11, 2001 that helped inexperienced terrorist pilots crash passenger jets into the World Trade Center we would not call Providence.  There could have been storms over New York City leading to microbursts downing the planes in relatively uninhabited areas; if this had happened, we would then have said that weather was providential. 

Aquinas would definitely have included the "Providence" referred to above in his discussion of Fate, but the idea of Fate often comes unaccompanied by the presumed understanding and positive feelings of Providence. OK, yes, it is often invoked in a prideful way; every fan of the University of Alabama felt in 1992 that the Tide was fated to win a national championship that year, when the hundredth anniversary of football (a "Century of Champions") was being celebrated at Alabama.  On the other hand, Fate is also used in situations that are more mysterious or unpleasant, but that look somehow artificial, like they must indeed be part of some larger story.  Any number of examples may be taken from history, but for a light example take the ending to the 2013 game between Alabama and Auburn:
This was not like a normal loss -- the loss to Oklahoma in the Sugar Bowl, for example.  The whole last 5 minutes or so of the game were surrealistic, with both coaches making strange decisions.  To quote the song by the Sons of the Pioneers, "Nothing could have saved us; this was our destiny."

Well, what about Chance, then? Perhaps the best artistic equivalent is Pointillism, as shown in the painting below, A Sunday Afternoon on the Island of La Grande Jatte – 1884.

  A Sunday on La Grande Jatte, Georges Seurat, 1884  

  • Every dot in the painting is intended by the painter. 
  • Knowledge of what is depicted is not sufficient to accurately predict where each dot must be.  From within the painting, the size, position, and perhaps the color of each dot contains an irreducibly random element.
    Notably, this is different from the pixels on a TV screen.  Each pixel has a fixed size, shape, and color; only the intensity varies, and that variation is likely to be rather smooth.
  • The dots dot not make any profound statement about the artist.  Conversely, knowledge of the artist will not make it possible to predict the size and position of the dots.

According to quantum mechanics, there are similar elements in the physical world that, from our perspective as creatures and not the Creator, are entirely random.  The evolution of wave functions is entirely deterministic -- until an observation is made (or information is leaked into the "outside" that would make an observation possible in principle), at which time the wave function "collapses" into an eigenstate of the operator for the observable.  Generally speaking, it will be more probable that the wave function collapses into some eigenstates than into others, just as it is more likely that two fair dice will sum to 7 than to 2, but as with the dice, the probabilities can be calculated. 

Making this more complicated, some observables are incompatible with each other, so that an observation of one observable destroys information about another observable.  (There is no state which is an eigenstate of both observables.)  This is what gives rise to the famous Heisenberg Uncertainty Principle, according to which it is impossible to measure the position and momentum of a particle simultaneously to arbitrary precision, even though either one alone may be measured to (in principle) arbitrary precision.  Such a question, it seems, has no meaning for what "particles" like electrons really are; they are neither classical particles nor classical waves, but quantum particle-waves.

Classical physics has particles and waves, but it has nothing like incompatible observables and no fundamental role for chance.  Quantum physics is different.  It defies our intuitions in troubling ways.  It reminds us that we did not create the universe -- we certainly would not have made a world like this.

It is at this point that the liberal arts major may feel tempted to shake his head sadly and say, "You scientists!  You don't realize it, but you are really describing epistemology, not metaphysics!  You are describing limits to what we can learn about the world, not the nature of the world itself!"  

As far as that goes, it is a true statement.  Furthermore, any Catholic (or Orthodox Christian) knows something that appears, to any physical measurement, to be one thing, but is another:  the Eucharist.  However, in the absence of public revelation to the contrary, we have no choice but to assume that what can be measured in careful observations is a true clue to the underlying reality.  After all, the only reason we have for understanding and being comfortable with classical physics is the fact that macroscopic objects obey classical physics (to a very very very very good approximation).

Thursday, May 1, 2014

April Fools!

Laughing Fool  
Today is April Fools' Day.  At least, it feels like April 1, not May 1.  In normal years, of course, we would have January, February, March, April, and then May.  This year we have had January, Second January, February, March, and now April.