I have a theoretical question. What do you think is the absolute fastest time possible for a human being in the 100 yard freestyle. One way I was looking at it was to start at 1.00 second and say, will anyone ever be able to swim it in 1.00 sec. No. Will anyone ever be able to swim it in 2.00 seconds. No...so on and so on. At what time do you stop and say, hmmm, maybe someday someone would be able to swim that fast.
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Elaine (What does the "S." stand for, BTW) -
Sort of and no.
For past events, if you have no knowledge other than the date a record was set and the time, all you can do is see how far it deviates from what might have been "expected" at that time and then set a threshold beyond which we decide that something earthshaking has occured. For example, if we go back far enough to when the 100m record was done as breastroke and then see the first time the record was set as crawl (or some variant), I'd bet the this would give a deviation on the extrapolation of the breaststroke curve that would be very sharp. But without knowledge of exactly what occured to get that deviation you can only give a mathematical interpretation of "paradigm shift". With knowledge of all paradigm shifts, then you can come up with a closer definition of these shifts, but again, you can't define them with certainty even then. (Example: A genetic mutation, a la the Foundation Trilogy, occurs.)
As to the future, although you can look at the effect of a change of x.x standard deviations off an extrapolated curve, it presupposes that this will, or even can, occur. So, for example, if we presuppose that a new technique will be invented that supercedes the crawl, we can get a rough approximation based on the past. But, is it likely and is it likely to be of that magnitude? Probably not.
If I have some time on Monday, I will try to investigate this a bit.
-LBJ
Elaine (What does the "S." stand for, BTW) -
Sort of and no.
For past events, if you have no knowledge other than the date a record was set and the time, all you can do is see how far it deviates from what might have been "expected" at that time and then set a threshold beyond which we decide that something earthshaking has occured. For example, if we go back far enough to when the 100m record was done as breastroke and then see the first time the record was set as crawl (or some variant), I'd bet the this would give a deviation on the extrapolation of the breaststroke curve that would be very sharp. But without knowledge of exactly what occured to get that deviation you can only give a mathematical interpretation of "paradigm shift". With knowledge of all paradigm shifts, then you can come up with a closer definition of these shifts, but again, you can't define them with certainty even then. (Example: A genetic mutation, a la the Foundation Trilogy, occurs.)
As to the future, although you can look at the effect of a change of x.x standard deviations off an extrapolated curve, it presupposes that this will, or even can, occur. So, for example, if we presuppose that a new technique will be invented that supercedes the crawl, we can get a rough approximation based on the past. But, is it likely and is it likely to be of that magnitude? Probably not.
If I have some time on Monday, I will try to investigate this a bit.
-LBJ
