CHRISTIAN TRACTATUS - SECTION 4

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4. The world obeys a number of fairly simple physical laws, which form the modern scientific worldview, which is fundamentally correct.

4.1 A physical law is a means of assigning a probability to a future state of affairs, given the disposition of the relevant portion of the world at the present time.

4.1.1 Physical laws are not necessarily based on the assumptions of strict causality nor of determinism, but only on the observed regularity and predictability of the world.

4.1.1.1 Hence, for example, I am not necessarily committed to any "hidden variable" theories of quantum mechanics.

4.1.2 Laws must be used with caution outside the domain in which they have been demonstrated to be reliable.

4.2 The term simple requires explanation. It has to be understood in its context.

4.2.1 I do not mean by this term "capable of being understood by the man in the street". This is clearly not the case, for instance, with the law of universal gravitation in Einstein's general theory of relativity.

4.2.2 I do, however, retain some of the naive sense of the word simple. Natural laws have turned out to be far simpler than there was any a priori reason to suspect.

4.2.3 In physics, when referring to the world's laws as simple I mean "capable of being described by mathematics".

4.2.3.1 Because mathematics, unlike language, is on the borderline of human capacities, people demonstrate an enormous range of ability and very few find mathematics simple. However, the existence, say, of inverse square laws in gravitation & electrostatics is a remarkable fact, given that any irregular function of distance might have appeared possible a priori.

4.2.4 Laws in sciences other than physics, while they cannot always be totally reduced to mathematical expression, usually have a pronounced mathematical character, as in the statistical characters of the laws of natural selection and of genetics.

4.3 Despite the fact that the world seems to obey a number of simple laws, it cannot yet be demonstrated beyond all contradiction that all of experience may be reduced to law, nor that all of the world's laws are simple, because not all of experience has yet been analysed nor are all of the world's laws yet fully understood.

4.3.1 However, scientific progress to date leads us to expect laws to govern most areas of experience and for as yet undiscovered laws to turn out to be simple.

4.3.1.1 Such expectations govern, for instance, the search for grand unified theories (GUTs) in physics, which seek to unify the four fundamental forces (gravitational, electromagnetic, and the strong & week nuclear forces) into a single super-force (eg. in the theory of superstrings). It is, of course, still an open question whether the fundamental forces of physics can be unified and hence whether there is a limit to the simplifications that can be discovered.

4.4 It might be objected that, since old theories are constantly being replaced by new ones (eg. Newton's theories of dynamics & gravitation by Einstein's special & general theories of relativity; the various theories of the atom; etc.), we should despair of the absolute and final truth of scientific laws. However, the replacements are not random changes of mind, but usually represent either the correction of less accurate models by ones of greater precision or the expansion of the domain of reference of the enquiry.

4.4.1 From the above we may expect that any particular scientific theory is not the last word in its field. It may yet be replaced by one of wider scope or greater precision. This is not to imply, however, that we should abandon the scientific enterprise as futile. An inadequate theory of the atom, for instance, was still sufficient for the development of the technology for the release of nuclear energy.

4.4.1.1 It is to be noted that changes of scientific paradigm are usually in the direction of greater simplicity (as in the successive explanations of planetary motion given by Ptolemy, Copernicus & Newton), often with a corresponding gain in generality. Occasionally, however, simplicity has to be sacrificed to generality (as in the further transition from Newton to Einstein) or in response to more accurate observation (as in Kepler's substitution of elliptical for Copernicus' circular planetary motion).

4.4.2 Because the final form and absolute truth of currently accepted scientific laws are open to doubt, caution should be maintained in the attempted deduction of metaphysical deductions from them.

4.4.2.1 Another reason for resisting the deduction of metaphysical conclusions from scientific theory is that such theory is taken out of its primary domain of reference and hence loses its predictive power.

4.5 The fact that the world displays a regular pattern is the reason we can make some sense of it and our ability to predict its future (when we can) is due to the operation of its laws.

4.5.1 Irregularity would make prediction & learning from experience impossible. It is this fact of routinely successful application of learned experiences to future experience that confirms our belief in a regular world governed by law.

4.5.2 This regular pattern is not made void by quantum theory. While the strict application of the classical rules of cause & effect may break down at the quantum level, future states of affairs may still be assigned probabilities.

4.5.2.1 In quantum mechanics, events may still be described as ordinary or extraordinary. An extraordinary event would be one with a probability orders of magnitude lower than that of other possible events.

4.5.2.2 The extrapolation of quantum uncertainty to attempt explanations of macroscopic "miraculous" events leads to such low probabilities as to be indistinguishable from impossibilities.

4.5.2.3 I am not impressed by arguments to the effect that quantum uncertainties make the universe more open to the intervention of an external creator than was the case with the divine clockwork of the Newtonian (or Laplacian) universe.

4.6 While the basic laws of a system may be simple, their consequences may be very complex; even, in practise, indeterminate.

4.6.1 This is demonstrated by the recent theories of Chaos, ie. theories of non-linear systems that demonstrate a sensitivity to slight variations in initial conditions. These theories show that, because the initial conditions cannot be precisely measured, the simple, but non-linear, equations of motion governing the system magnify these errors so that the state of the system beyond a certain time in the future is completely unknown.

4.6.1.1 Consequently, we cannot deduce that a system obeys no simple laws merely because it appears complex. The theories of Chaos encourage rather than discourage the belief that the world may yet be fully described by a set of simple laws.

4.6.1.2 Hence, we must distinguish between the explanatory & the predicatory powers of laws. Classical physics has the laws to explain the weather even if it cannot predict it.

4.7 A system of beliefs based on extraordinary events, ie. those with no explanation within the the normal framework of physical law, requires a greater level of proof than one based on common experience.

4.7.1 Hence, for example, greater proof is required for us to believe that the sun "stood still in the sky" on a particular day than that the earth continued on its daily revolution as normal.

4.7.2 The reason for our reluctance to accept alleged violation of physical law as the explanation of an event is that this procedure, if routinely followed, would undermine the whole application and validity of physical laws & the methods of physical science.

4.7.2.1 It is because physical laws are routinely found to work and that a patient search for physical explanation within the confines of law is so frequently rewarded, that we are willing to reject explanations outside these confines unless the evidence for the extraordinary explanation is so compelling that we are forced to rule out alternatives.


© Theo Todman 1992 - 2000.
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