That’s what I took the point to be. The initial descriptions of what Simplicio and Salviati accomplished make them sound comparable. It wouldn’t occur to most that one was overwhelmingly superior to the other. But working it out shows otherwise.
It’s true that a lot is buried in the line “Salviati instead tries to measure X, and finds a variable Z which is experimentally found to have a good chance of lying close to X.” What was required to establish this “experimental finding”? It might have taken labors far in excess of Simplicio’s. But now we know that, unless Salviati had to do much, much more work, his approach is to be preferred.
I think the superiority will be obvious to anyone who’s ever seen a few scatterplots of correlated variables, and who can imagine a graph of X against X + noise where sd(noise) = 0.1*sd(X), and who thinks for a moment. Of course many people, much of the time, won’t actually think for a moment, but that’s a very general problem that can strike anywhere.
Suppose the story had gone like this: Simplicio measures X, and does it so well that his measurement has a correlation of 0.6 with X. Salviati examines lots of pairs (X,Y) and finds that X and Y typically differ by about 0.1 times the s.d. of X. Then the result would have been the same as before. Would that be a reason to say “measurement is no good; use probability and statistics instead”? Of course not.
Suppose the story had gone like this: Simplicio measures X, and does it so well that his measurement has a correlation of 0.6 with X. Salviati examines lots of pairs (X,Y) and finds that X and Y typically differ by about 0.1 times the s.d. of X. Then the result would have been the same as before. Would that be a reason to say “measurement is no good; use probability and statistics instead”? Of course not.
Indeed. What matters is not what the procedures are called, but how they compare. Salviati’s results completely trump Simplicio’s.
That’s what I took the point to be. The initial descriptions of what Simplicio and Salviati accomplished make them sound comparable. It wouldn’t occur to most that one was overwhelmingly superior to the other. But working it out shows otherwise.
It’s true that a lot is buried in the line “Salviati instead tries to measure X, and finds a variable Z which is experimentally found to have a good chance of lying close to X.” What was required to establish this “experimental finding”? It might have taken labors far in excess of Simplicio’s. But now we know that, unless Salviati had to do much, much more work, his approach is to be preferred.
I think the superiority will be obvious to anyone who’s ever seen a few scatterplots of correlated variables, and who can imagine a graph of X against X + noise where sd(noise) = 0.1*sd(X), and who thinks for a moment. Of course many people, much of the time, won’t actually think for a moment, but that’s a very general problem that can strike anywhere.
Suppose the story had gone like this: Simplicio measures X, and does it so well that his measurement has a correlation of 0.6 with X. Salviati examines lots of pairs (X,Y) and finds that X and Y typically differ by about 0.1 times the s.d. of X. Then the result would have been the same as before. Would that be a reason to say “measurement is no good; use probability and statistics instead”? Of course not.
Indeed. What matters is not what the procedures are called, but how they compare. Salviati’s results completely trump Simplicio’s.
Correlation, maybe?