[Kevin] You can't find it be_cause_ it's not there (in the second paragraph above). But it (the word "cause") is in the third paragraph above (mine) and in the paragraph immediately preceding this one (yours). I won't speak for your instance of the word but the word appears in my paragraph be_cause_ I did something. I pressed the keys c, a, u, s and e and the word "cause" appeard on my monitor. Pressing the keys was the cause. The word appearing on the monitor was the effect. How did your instance of the word get there? [Case] Oh yeah, sorry about that. Edward Lorenz discovered that butterfly effect while running very primitive weather model in the 60's. His model did a string of calculation that produced a string of numbers. This process took a very long time and produced a long set of numbers.
One day the while the model was running something caused it to shut down and rather than restart it from the beginning Lorenz plugged in the last number it generated and let it run again. Later he discovered that the figures generated after the restart varied from the series produced if the model ran all the way through. At the point where he plugged in the number, the numbers started out about the same then began to vary wildly. Lorenz eventually realized that the divergence stemmed the fact the computer calculated number to say 4 decimal places but printed them out to two decimal places. It was not that the rounding error "caused' the divergence it was that in order for any model to be able to predict the weather it would need to have infinite precision. Laplace's vision of perfect determinism would require such infinite precision on a cosmic scale. What Lorenz showed was that it is only possible to develop short term models. He showed that the world can be purely deterministic and yet purely unpredictable at the same time. So the rounding error does not "cause" the butterfly effect but the butterfly effect is the result of rounding error. As for irrational numbers, the square root of 2 was among the first discovered by the Greeks. I have not hand calculated a square root since the invention of the calculator but as I recall the process involved guessing and calculating and guessing again and calculating until you either get it exactly or close enough. With irrational numbers you never get it, you just get closer and closer. The irrational numbers can only be expressed approximately. What this suggests to me is that the future is "in principle" unpredictable. It is not just that our knowledge of the present state of every particle in the universe is limited in fact, which it is. We can not ever know the position and momentum of every particle in the universe because of the uncertainty principle. Even God can not know the position of every particle in the universe. I conclude that even God can not know the future. As I suggested in another thread God must watch the process unfold through what Whitehead called his Consequent Nature. I have also suggested a couple of times that this process also works in reverse. So that you could never go back in time to the same place as to get there you would have to rewind every particle in the universe with infinite precision. Some have said, using old school ideas, that the past somehow calcifies out of present and is fixed and unchanging in our wake. I maintain that the past is as unknowable as the future. In fact I maintain that for an omniscient being able to transcend time and space and move backwards and forwards in time it would be like watching a movie that ends differently every time you rewind and replay it. moq_discuss mailing list Listinfo, Unsubscribing etc. http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org Archives: http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ http://moq.org.uk/pipermail/moq_discuss_archive/
