M
mdkluge
Guest
Helen wrote (after consulting with Setterfield???):
And the latter is a fair statement of Setterfield's situation as you describe it in 1981. He had n data points, where n < 163 that he has had since 1987. Also, in 1981 his n >> 2! It is true that if it were given that you had n (n > 2) points fitting a curve perfectly, and you added m more points, then the probability of those m + n points fitting the curve perfectly is very small (unless the m points were chosen in advance to perfectly fit the curve.)
However, one seldom, if ever, has n (n > 2) EXPERIMENTAL points that perfectly or near perfectly fit a curve. EVERY scientist knows this--good, bad, and ugly. But Setterfield didn't. He had some large number of experimental measurements of c (2 << n < 163) in 1981, he KNEW that they didn't all lie on the same curve, and yet he believed his computer when it told him that their r value was .99999999+. That was unreasonable. That was his blunder. With many more than two points which he KNEW did not all lie upon his fitting curve, he still failed to immediately see that his r value could not possibly be .99999999+.
Sure, any programmer could have made the programming mistake that caused his computer to calculate r at the wrong place in his analysis algorithm. It is Setterfield's unique shame to have failed to cach such egregious an error prior to its publication. The only pre-publication pressure that might justify such a blunder might be that of standing in front of a firing squad with the alternatives "publish or perish!"
No, Helen. While it is true that if you have exactly two distinct points there is a unique line fitting them, and that if you add a third point you will not in general be able to fit a line to all three points, it is not true that if you have three points and you add a fourth that the line fitting the four points will fit less well than the line fitting the three. Nor is it true that if you have a line fitting (imperfectly) through n points and you add m more points, that the line of best fit through the n + m points will in general fit the m + n points more poorly than the line fitting the n points.Mark, if you draw a line between two points, you have a perfect fit for those two points. The more points you have, the less likely you are to have a perfect fit for a line or a curve or any function you like. It was a simple logical statement. Please don't take it to be something it was not meant to be.
And the latter is a fair statement of Setterfield's situation as you describe it in 1981. He had n data points, where n < 163 that he has had since 1987. Also, in 1981 his n >> 2! It is true that if it were given that you had n (n > 2) points fitting a curve perfectly, and you added m more points, then the probability of those m + n points fitting the curve perfectly is very small (unless the m points were chosen in advance to perfectly fit the curve.)
However, one seldom, if ever, has n (n > 2) EXPERIMENTAL points that perfectly or near perfectly fit a curve. EVERY scientist knows this--good, bad, and ugly. But Setterfield didn't. He had some large number of experimental measurements of c (2 << n < 163) in 1981, he KNEW that they didn't all lie on the same curve, and yet he believed his computer when it told him that their r value was .99999999+. That was unreasonable. That was his blunder. With many more than two points which he KNEW did not all lie upon his fitting curve, he still failed to immediately see that his r value could not possibly be .99999999+.
Sure, any programmer could have made the programming mistake that caused his computer to calculate r at the wrong place in his analysis algorithm. It is Setterfield's unique shame to have failed to cach such egregious an error prior to its publication. The only pre-publication pressure that might justify such a blunder might be that of standing in front of a firing squad with the alternatives "publish or perish!"