"Suppose we are seeking to determine a curve by observing some of the points on it. The practical man who looked only to immediate utility would merely observe the points he required for some special object; these points would be badly distributed on the curve, they would be crowded together in certain parts and scace in others, so that it would be impossible to connect them by a continuous line, and they would be useless for any other applications, The scientist would proceed in a different manner. Since he wishes to study the curve for itself, he will dsitribute the points to be ovserved regularly, as as soon as he knows some of them, he will join them by a regular line, and he will then complete the curve. But how is he to accomplish this? If he has determined one extreme point on the curve, he will not remain close to this extremity but will move to the other end, after the two extremities, the central point is the most instructive, and so on.
Thus when a rule has been established, we have first to look for the cases in which the rule stands the best chance of being found in fault. This is one of many reasons for the interest in astronomical facts and of geological ages. By making long excursions in space and time, we may find our ordinary rules completely upset, and these great upsettings will give us a clearer view and better comprehension of such small changes as may occur near us, in the small corner of the world in which we are called to live and move. We shall know this corner better for the journey we have taken into distant lands where we had no concern. " Poincare page 20 Science and Method "I can not dwell further on this point, but these few words will suffice to show that the scientist does not make a random selection of the facts to be observed. He does not count lady-birds, as Tolstoy says, because the number of these insects, interesting as they are, is subject to capricious variations. He tries to condense a great deal of experience and a great deal of thought into a small volumne, and that is why a little book on physics contains so many past experiments, and a thousand times as many possible ones, whose results are known in advance. " Poincare, Science and Method, page 23. Factorial designs allow for the organization of this great deal of experience and thought, and they allow the anticipation of future experiments, just as Piaget says that lattice structures do. Concretistic people are too concerned with immediate gratification to grasp the long term impact of such abstraction. They do not take the long journeys into time and space to fill out the lattice and the factorial and do not see the exceptions that break the ignorant rules. And futher more, Poicare says Bill "The scientist does not study nature because it is useful to do so. He studies it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of that beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more itimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp. It is this that gives a body a skeleton, so to speak, to the shimmering visions that flatter oursenses and withot this support the beauty fo these fleeting dreams would be imperfect because it would be indefinite and ever elusive. Intellectual beauty, on the contrary, is self-sufficing, and it is for that the scientist condemns himself to long and painful labours." Boys, its time to get back to work. Now which part of CR do you not understand? Bill . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
