One of the things that I would like to do is break the cycle of repeated arguments, that tend to exist after mostly the same people cover mostly the same territory. One thought I had was triggered by the use of the word "rational" in several posts. I started thinking about framing the argument in terms of axiomatic systems, seeing what is derived from various sets of axioms, and what just appears to be derived from a casual use of the axioms.
>From this, possibly, a more fruitful discussion might emerge. In addition to this, it would be worthwhile to discuss indeterminacy, chaos, and complexity with regards to physical systems, humans, and social systems. There are a lot of ideas concerning this thrown about in this discussion, and differences in understanding these can lead to don't loop arguments (keeps on looping and don't do nutting). First, let us consider randomness and chaos. My favorite example of this is a random number generator. Remember when you just started division with whole numbers and used remainders? For example, 7/3 = 2, remainder 1. Random numbers are typically generated in this manner. The overflow of the 32 bit unsigned integer is usually used. That is to say, one obtains c = a* b, where a, b, and c are all integers. With a 32 bit unsigned integer, clock arithmetic is commonly used. So, when this is done on a computer, we automatically get c/2^32= d remainder e. We are not interested in d, but e is the next random number. We then get f = a*e, f/2^32 = g remainder h. h is the next random number. This is a random number generator because there is no correlation between e and h. If one looked at the h(e-1) and h(e+1), one would find the same pattern one would see of one looked at h(e-49724835) or h(50928345083). This is also a chaotic system. A change in only 1/(2^32) of the full range results in a number that has a flat probability distribution over the full range. Further, this random number generator is not really random: it is pseudo-random. That is to say, if one runs it a thousand times, starting with the same a & b values, one gets the exact same sequence every time. That is why varying the seed is always an option. Some random number generators also allow one to vary a. Random number generator quality is determined by two factors: the lack of correlations and the periodicity. The one I've given has a periodicity of 2^32, which is good enough for most purposes. The book on random number generators that I used to write my first generator (the standard DEC ran() function wasn't pseudo-random) has a very illustrative example of how one needs to be very structured in setting up a random number generator. He gave an example of doing about 10 different "random" things, like taking the sine, an exponential, etc. of the number before returning it as the seed for the next calculation. He ran it, and found it had a periodicity under 20. Seemingly "random" actions ended up in establishing a very tight pattern. These random numbers describe chaotic behavior. Minimal changes in the input value can result in full scale changes in the output value. There is no way to predict the next state of the system from the present state, or the present and previous state, the present and the two previous states, etc. (except by knowing the algorithm.) There are physical systems that are like this. I've given some examples of this before. Even if one were to assume that air molecules were classical perfectly elastic hard spheres, we see that the we need to know the position of air molecules in a 1 meter cube with (practically) infinite precision to know if the position of a given molecule is closer to the left or the right, to the top or the bottom, to the front or the back of this cube at 1 second. Both the random number generator and the model of air molecules as little hard spheres are examples of classical chaos. In theory, one could make the predictions (with the random number generator one actually could), but the complexity gets in the way. With real air molecules, of course, one cannot do this even in principal. Quantum effects insure that the results are indeterminant. Quantum mechanics is truly random. Let us consider a thin slit experiment, where the light source is dim, and emits one photon at a time. (I tried an ASCII drawing of this, but it didn't parse right.) Knowing everything possible to know about the source, we cannot determine where the photon will hit. We have a probability distribution, given by the one slit diffraction pattern, but that is just a probability pattern. It is impossible to know where a given photon will hit. When QM was first developed, this caused some discomfort. People like Einstein thought that there must be some underlying determinism (God does not roll dice with the universe). But, after >75 years, experimental and theoretical advances have shown that it is impossible to have a local hidden variable theory underlying QM. That is to say, if these hidden variables actually exist, they must either violate special relativity by traveling faster than light, or travel backwards in time. Thus if one assumes that QM will survive as no less than a special limit value case of a more advanced theory (the way Newtonian mechanics is a special limit value case of QM and SR), then one has to drop the idea of local determinism. Finally, having discussed indeterminancy and chaos, it is worthwhile to discuss complexity. Complexity is on the edge between chaos and order. Patterns emerge out of chaos, apparently having properties that did not exist before things became complex. That is only sorta true; the example of the "random" operations causing a short cycle is a good example of what is going on. Even with a random number generator, one can generate a set of algorithms that obtains order out of the chaos. Nothing comes out of the blue, the potential for the order is in the nature of the operations and the random number generator. Rather, results that are counter-intuitive can emerge. It's not intuitive that picking operations out of the air could cause a random number generator to turn into a short cycle. But, one can see, if one thinks about it, how such a thing could happen. We can turn to thermodynamics for a second example. I can state, with some confidence, that a perpetual motion machine, based on classical thermodynamics and classical mechanics cannot be built. There are many classes of perpetual motion machine: a perpetual motion machine of the first kind creates energy out of nothing, a perpetual motion machine of the second kind takes heat from a reservoir and turns it into mechanical energy without transferring a minimal fraction of that heat to a colder reservoir. The first kind violates conservation of energy, the second violates the principal of entropy: the entropy of a closed system must always increase. Therefore, if I am told that someone has invented a perpetual motion machine, I can dismiss it out of hand without considering the details of his machine. No matter how the inventor explains that perpetual motion is an emergent property that comes out of the complexity of the system; my knowledge of the underlying physics allows me to rule it out. Indeed, the existence of such a machine, no matter how complex, would overturn physics at its most basic levels. Having said this with confidence, it doesn't mean that counter-intuitive things cannot happen. For example, creationists have argued that entropy is inconsistent with evolution. One way to look at evolution is that more and more complex and ordered systems evolve from less complex and ordered systems. Since the principal of entropy states that things naturally become less ordered, this cannot happen. There is a hole in this reasoning, of course. The law of entropy is for a closed system. There is no reason why the entropy of an open system cannot be reduced.as long as the entropy of other systems that are connected to this system rise at least as much as that system falls. So, localized drops in entropy, which appear paradoxical to the casual observer, can be seen to be very compatible with the laws of physics. This gives us a rule for the use of complexity. Complexity can result in phenomena that are counter-intuitive to one who just thinks in general about basic principals. Complexity cannot result in phenomena that are at odds with the basic principals. Well, this post has gotten long while giving us just one axiom. But, I think it helps lay the groundwork for explaining my thinking. I'd welcome any critique of this analysis. Dan M. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
