Sunday, May 29, 2011

Initial Conditions and Predictability

According to physicist, Eugene Wigner (article linked in sidebar), physics is possible because we are able to identify regularities in nature.
The world around us is of baffling complexity and the most obvious fact about it is that we cannot predict the future... It is, as Schrodinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities...
This is surprising, he says, for a few reasons. The first is that it is true everywhere on earth and it will always be true, i.e., it is invariant. The second reason that it is surprising is that this invariance "is independent of so many conditions that could have an effect on it." It doesn't matter where on earth or by whom the rocks are dropped and "there are innumerable other conditions which are all immaterial from the point of view of the validity of Galileo's regularity." He says,
The irrelevancy of so many circumstances which could play a role in the phenomenon observed has also been called an invariance. However, this invariance is of a different character from the preceding one since it cannot be formulated as a general principle. The exploration of the conditions which do, and which do not, influence a phenomenon is part of the early experimental exploration of a field. It is the skill and ingenuity of the experimenter which show him phenomena which depend on a relatively narrow set of relatively easily realizable and reproducible conditions. (Italics added.)
This is important when it comes to understanding the surprising thing about making predictions. Wigner says, "the law of nature is contained in the statement that the length of time which it takes for a heavy object to fall from a given height is independent of the size, material, and shape of the body which drops."

Given certain "easily realizable and reproducible" Initial Conditions (ICs) and a Law of Nature (LN), then a Prediction will follow. (IC & LN) > P. However, 
the laws of nature can be used to predict future events only under exceptional circumstances - when all the relevant determinants of the present state of the world are known. It is also in consonance with this that the construction of machines, the functioning of which he can foresee, constitutes the most spectacular accomplishment of the physicist. In these machines, the physicist creates a situation in which all the relevant coordinates are known so that the behavior of the machine can be predicted. Radars and nuclear reactors are examples of such machines.
The two important points I draw from the preceding exposition are:
  1. In order to apply a law to make a prediction you need to identify the relevant conditions (ICs).
  2. The ability to isolate phenomena whose regularity can be demonstrated with easily reproducible conditions cannot be summed up in a general principle. 
 To those two points I would also add an idea that I think follows from an insight of Stuart Kauffman, author of Reinventing the Sacred (linked on the sidebar) where he says, in analyzing mechanical systems, 
physicists since Newton have put in the constraints..."by hand" as what are called the mathematical "boundary conditions" on a system, rather like the boundaries of a billiard table, that keep the balls from rolling off into infinity or under the table. Given the boundary conditions, physicists state the initial conditions, particles and forces, and solve the equations for the subsequent dynamics...
But in the real universe, we can ask, "Where do the constraints themselves come from?"(pp. 90-91) (italics added.)
Although in principle it might be possible to retroactively determine the sequence of events that gave rise to a naturally occurring phenomenon (then again, there's the problem of infinite regress), no one could specify the relevant conditions in advance of every phenomenon-to-be in this complex world. What would we be looking for?

Kauffman discusses the evolution of life and considers Darwinian preadaptations; e.g., three bones in the jaw of an ancestral fish that become bones in the middle ear in species descended from it. At the time this ancient fish lived, was there any way to predict the role of its bones in later species, let alone what later species would emerge?

This is not just an issue of complexity or chaos; i.e., sensitivity to initial conditions (a.k.a "the butterfly effect"). It is that, as Kauffman says, we can't prestate the relevant conditions  (p. 139 ff). What potentials will become actualities?  In Kauffman's view, this is not just an epistemic limitation, it is an ontological one. He says, "the evolution of life violates no law of physics, but cannot be reduced to physics." Not all of nature is law governed. 

So it seems to Kauffman, and to me, that the "natural law" model of a mechanistic universe has limited applicability; i.e., to "phenomena which depend on a relatively narrow set of relatively easily realizable and reproducible conditions."

We cannot completely predict the future, and generally that idea gives me comfort. Nature has space to play.

Tuesday, May 3, 2011

On Elitism

Why is it that populism props up the ruling elite, while the individualist dream of the enlightenment has gone by the wayside, except as a ridiculous caricature? What does this mean for the possibility of democracy?

We can no longer afford to think in terms of the original "social contract" among rational consenting individuals because, clearly, individuals maintain their identities in terms of their relationship to a real or idealized group, not by means of some inborn identity and a capacity for individual reasoning.  Also, people are born into and conditioned into an existing culture, with its history, its images, and its language . Speech is always historically and culturally conditioned and most people welcome that conditioning, although they may tell you otherwise by way of some fantasy "lone cowboy" image of individualism or something along those lines, equally culturally conditioned.

We are members of real or idealized tribes and in times of rapid change in technology, the precursor to a change in ideology, there is a culture lag. Today we see cultural regression. In some years, this will pass, hopefully with less pain than we might anticipate.

The message, though, is that politics is not about rational choices. It's about tribal allegiances and, in uncertain times, it's the ancient archetype of the alpha male tribal leader, perhaps updated to the archetype of a valiant king, that keeps the lines of power organized and most people aligned to the interests of the oligarchy that directs our economy, regardless of what government regulators may want to do about it. Although our contemporary stories still indicate some deformed attempts to escape some vestigial projection of feudalism, the instinct to submit to the "divine right of kings" across many domains of human endeavour doesn't seem to have abated much.

What is an economy? It is a combination of our technologies, how we are socially organized to make the best use of them (or not) to produce what we need (and much, much more) from nature, and the institutions and stories that sustain that arrangement, and the powers of those who dominate the economy, in whom our powers are vested. We, more often than not, work against our personal advantage (usually unwittingly) and instead maintain the structures that in turn maintain our investment in the powers that sanction the rules and rituals that organize our lives and public relationships. For example, mothers in certain countries make sure that their daughters are "circumcised" in order to ensure their marriageability.

Today though if you dare to dream that reason, morality, art and respect for evidence (science) will help see us through to a more just arrangement, you may be called "elitist". This label is vestige of the hatred of the privileges of the feudal lords. It has nothing to do with today's world. Populism is the vehicle that most acutely and continually sustains the elite today. The next question is, what does that mean for democracy, if the dream of the enlightenment has become something "elitist"?

Of course, it's much more complicated than dreamers of the enlightenment may care to think. There is a deep seated sense that enlightenment dreams represent a kind of hubris on the part of human beings, as if we could rationally organize ourselves or submit our wills to a rational economy (invisible hand, "free"enterprise) to best achieve our increasingly empty ends.  Of course we can't. The the complexity of the world would prevent our being able to do it - although frighteningly, the recent rediscovery of the complexity of nature doesn't prevent our ability to think it. 

What is the alternative? As many are voicing today, the solution is in being adaptive, in our responsiveness and resilience. Rather than fixed universal truths of "human nature" or visions of true science, the just beneficence of some "invisible hand" economics, or various ideological diseases that afflict us today, I think we should rediscover what it means to understand, in all its dimensions, with the proviso that human understanding is ever-provisional.

Today more than ever we need to understand our relationship to the world we burden with the polluting byproducts of our Promethean dreams and our unrelenting, culturally conditioned searches for a better life. We will never arrive at a perfect solution but we can find our way to a more harmonious one, I hope.