Newton and the mean

Ok this is really an excuse to put Isaac Newton in a post, but still this is kind of fun:

Newton did something unusual, and even, as Alan Shapiro notes, “almost [we would say entirely] unprecedented in the 17th century”: he averaged all of the differences….None of this reached print….Newton certainly avoided hinting in print that his law of arithmetical progression was adduced by anything other than the most skillful and precise of measurements.

….Newton’s “mean”—the average—was the weapon with which he slew the invevitable dragons of sensual errors. It was a most paradoxical weapon for the times, because it amounted to a method by which error seems to be reduced by committing it repeatedly. No such method appears elsewhere at the time, and it would certainly have seemed odd, to say the least, to most practitioners of the period.

….We have no contemporary record of the reasoning by which he justified this unusual method….Yet Newton used averages early on; he used them frequently and, it seems, consistently….Why did Molyneux and Flamsteed, a decade or two later, do so as well?….Is there some evidence as to what underpinned the average, decades before statistical notions became widespread?

Apparently the answer to that last question is no. The authors produce a bit of evidence that Newton thought of the average as akin to measuring a center of gravity, but that’s about it. It appears that Newton never explained himself, but just quietly went ahead with his use of  averages several decades before anyone else. It was the secret behind his famously accurate observations.

I’m not sure this is true, as Wikipedia says that Tycho Brahe did the same thing. I can’t find any primary source that says that Brahe did (in a Google search), so I don’t know if he did. Anyway …. Isaac Newton.

 

 

 

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