A beautifully told story with colorful characters out of epic tradition, a tight and complex plot, and solid pacing. -- Booklist, starred review of On the Razor's Edge

Great writing, vivid scenarios, and thoughtful commentary ... the stories will linger after the last page is turned. -- Publisher's Weekly, on Captive Dreams

Monday, February 1, 2010

Chance and Causation

Demons from the Vasty Deep

In the  previous post, we looked at the question of how can something immaterial [gravity] could affect something material [matter]. This generated much discussion in the LiveJournal version of this blog.  Check out the comments here.

This was bound up in the problem of whether gravity is a substance, composed of matter and form, that swims outward from a mass (like sperm, perhaps) to attract other masses.  But if gravity were a substance, then a gravitating body would lose mass over time as the gravitational fluid left the body.  It would also be hard to explain how the gravitational fluid pressing out would attract other masses in.  Also, since gravity is produced by all matter -- and that included "energy"; even light rays have gravity -- then gravity to the extent it consisted of matter, would have gravity.  [And this gravity would have its own gravity, ad inf.] 

The modern vision of gravity as a warping of space-time by the presence of mass -- a particular state of the Ricci tensors -- is no less problematical, since space and time, under general relativity, have no objective existence themselves.  We are faced with the problem of how a material thing [matter] can affect an immaterial thing [space-time]. 

In neither case do we have a problem saying it does.  We just don't know how it does it.  Recall Newton's words: "we have explained the phænomena of the heavens ... by the power of gravity, but have not yet assigned the cause of this power."  The Aristotelian answer is that gravity is not a force, per se, but a natural property of matter itself.  (Einstein is more in line with Aristotle.)  Thus, to ask how an immaterial concept like "gravity" could cause the motion of "matter" is akin to asking how a mental abstraction like three-sidedness could cause a real life triangle.   

Newton also noted the difference between gravity and mechanical forces: "This is certain, that [gravity] must proceed from a cause ... that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes use to do), but according to the quantity of the solid matter which they contain."  That is, it doesn't matter how big a surface area is attracted; it only matters how big the attractor is.  This is a hint that gravity is not a force in the same sense that being hit with a hammer is a force.

This led, by insensible increments to the denial of causation itself, with the usual invocation of quantum mechanics, and the conjuring up of Chance from the vasty deeps. 

Now the claim that quantum theory involves uncaused effects is seldom backed up with an example of one of these uncaused effects.  Sometimes people say: Particles can appear from nothing!  But this conflates the meaning of "nothing" with the meaning of "zero."  When pressed, the admission is that particles come from fluctuations in the quantum state of the vacuum energy.  In which case, there is not nothing: there is vacuum energy; there are quantum states. 

Then, too, I am told by my physicist friends that quantum mechanics consists of many equations and these equations work out to with precision.  This could not be if there were no causation at the quantum level. 

Now, what about CHANCE, that great bugaboo that is sometimes invoked to deny causation. 
Aristotle wrote that chance is simply the intersection of two independent lines of causality.  Suppose a man walking past a construction site is hit on the head by a falling brick.  He is not walking past by chance.  He has decided to eat lunch at a diner down the street, and he has chosen this route because it is the most direct.  He is walking past at this particular time because it is his lunch time from the office.  (Notice that causation is not determination.  He could have chosen to eat elsewhere, brought his lunch,etc.)  Meanwhile, the brick is falling under Newton's immutable laws - gravity, again.  It was set on its way by the foot of a workman on the scaffolding who decided it was time for his break and in standing accidentally kicked the brick.  But note that the workman standing in just such a manner caused his foot to nudge the brick which caused the brick to tip from the scaffold which caused the brick to fall at 32 ft/sec^2, with a final velocity of sqrt(64*distance) and to strike with a kinetic energy of 0.5mv^2 = 32m*distance.  At no point is chance involved in a causal sense. 

Basically, we invoke "chance" when the cause system is so complex, consisting of so many minor causes, so much uncertainty in the measurement of them, that it is inherently impractical to identify them all, let alone measure them with sufficient precision without interfering with the system itself. 

Quality control engineers are accustomed to dividing variation in the data into those variations that are individually assignable to specific, special causes, and the variation that is ascribed to "a constant system of common causes" which are impractical or uneconomical to separate.  The usual demonstration of random variation is by means of a quincunx.  Beads drop down a funnel into a system of pins arranged in quincunxial patterns.  They bounce left or right off the pins depending on initial conditions and accumulate in slots below in the familiar bell-shaped, normal distribution.  The normal curve is the result of a great many small causes the effects of which accumulate additively: Y = X1+X2+....+Xn.  But the pins (and the balls and the funnel) are the causes, not "chance."  It's just no use asking which particular pin caused the bead to end in this particular slot.  The same result could obtain from other combinations of pins. 

Chance, per se, is not a cause of anything.  An appeal to "chance" is a direct appeal to irrationality.  It is, in fact, the "chance of the gaps" theory. 

Then, too, there are causes outside the system.  When two particular billiard balls strike each other, it may seem like a chance event, if we confine our attention to the balls and the felt and the table.  But if we pull back to include Minnesota Fats, we can see that there was no chance at all.  Similarly, a physicist (as I've said before) may explain the boiling water in a kettle by reference to Boyle's Law or Charles' Law, to vapor pressure, burner temperature, caloric content, and all what have you.  The one thing it will not discover is that Miss Marple wanted to have a cup of tea.  Natural science, by its methodological restrictions, is incapable of "seeing" causes that are outside its boundaries.  What if focuses on, it sees very clearly; but it cannot see at all anything outside that focus.  Tolstoy once wrote that to discover what makes a locomotive move one must study "the laws that regulate steam, bells, and the wind" until discovering "the ultimate cause of the motion of the locomotive in the steam compressed in the boiler."  The historian John Lukacs remarks dryly, "It did not occur to Tolstoy that the main 'cause' of the motion of the locomotive might be its driver."

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