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To: EPS who wrote (28820)	11/7/1999 5:23:00 PM
From: Scott C. Lemon	Read Replies (2) \| Respond to of 42771

Hello Victor, > I am not sure what you mean by chaos theory (something like small > variation of initial conditions could lead to very different > outcomes..contrary to what people seem to infer from the heading > chaos theory the theory is designed to apparently PREDICT > suitable behavior for certain types of nonlinearities..e.g. when > the chaotic complex behavior is generated in a simple way iterating > simple rules..). Inspite of chaos theory we can't predict most > things with certainty...:) I'm not sure that I'll agree with your definitions, and will stick with known experts in the field (as I know that I believe in the theories, but do not claim to be the expert in them ...) I'm not sure that your definition is accurate ... I'll quote from a Duke University source: The very name "chaos theory" seems to contradict reason, in fact it seems somewhat of an oxymoron. The name "chaos theory" leads the reader to believe that mathematicians have discovered some new and definitive knowledge about utterly random and incomprehensible phenomena; however, this is not entirely the case. The acceptable definition of chaos theory states, chaos theory is the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems. A dynamical system may be defined to be a simplified model for the time-varying behavior of an actual system, and aperiodic behavior is simply the behavior that occurs when no variable describing the state of the system undergoes a regular repetition of values. Aperiodic behavior never repeats and it continues to manifest the effects of any small perturbation; hence, any prediction of a future state in a given system that is aperiodic is impossible. Assessing the idea of aperiodic behavior to a relevant example, one may look at human history. History is indeed aperiodic since broad patterns in the rise and fall of civilizations may be sketched; however, no events ever repeat exactly. What is so incredible about chaos theory is that unstable aperiodic behavior can be found in mathematically simply systems. These very simple mathematical systems display behavior so complex and unpredictable that it is acceptable to merit their descriptions as random. My general statement was intended to indicate that I believe that the growth of the computer industry, and the innovations that have occurred, can be characterized as "aperiodic behavior" ... and per the definition above "Aperiodic behavior never repeats and it continues to manifest the effects of any small perturbation; hence, any prediction of a future state in a given system that is aperiodic is impossible." I'm not sure, but I think that we are in agreement that the current state of evolution of the computer industry can not be compared to a potentially better or worse scenario, based solely on the presence or absence of various Microsoft tactics. I (and I think you) understand that direct correlations can not be made. > I don;t think that the issue is to remove MSFT at all but to make > it obey the laws of the land.. ... of the moment. ;-) I guess that this is my point all along. You make the statement above as though laws are "absolutes" ... and yet we all know they are not. They bend, and mutate, into new laws ... or they give birth to new laws. > MSFT is a monopoly and what is perfectly admissible (maybe not nice > but admissible and certainly legal) behavior for most corporations > (and certainly it was perfectly legal when MSFT it was not a > monopoly) it is not (I repeat IS NOT) admissible behavior for a > MONOPOLY. I would have to say that I pretty much agree with your carefully written statement! ;-) This is the root of how evolution works ... "survival of the fittest" until something else becomes the "fittest" ... natural selection at it's best! ;-) So the only area that I am not willing to make such absolute calls on, is that area of exactly what to expect next. The "Findings of Fact" makes the statement of monopoly ... now we have to wait for the rulings, decisions, appeals, etc. to see exactly what will occur. So I'm not sure which specific "behavior" of Microsoft will be required to change ... all ... parts ... it'll be interesting to see! > Please comment on these findings if you have time.. I take it that you've already read the entire Finding? I am already a quarter of the way through it ... started reading Friday night ... ;-) (I want to make sure that we'll be able to discuss it as two people who have read the entire doc!) ;-) Scott C. Lemon