Historical accuracy and precision

Accuracy refers to closeness of measurements to the true value. Precision refers to variation of measurements to each other. So precision is relative but accuracy is absolute.

Accuracy and precision can apply to statements as well as measurements. For example, if I say, “Today is Tuesday. This is the third day of the week.” but it is Thursday, the two statements are not very accurate, though they would be more accurate than saying it is Monday. Since the two statements are synonymous, they exhibit precision. A statement such as “It is early in the week.” is less precise than specifying a specific day because it contains ambiguity about exactly which day is specified.

There is something of a trade-off between precision and meaningfulness. A very precise statement such as “The dial reads 2.698” doesn’t say much. For some purposes, that’s all that’s desired. But as part of a larger conversation, much more could no doubt be said. What was the investigator hoping to accomplish, scientifically and professionally? Will this instrument reading make much difference? And so forth.

The definition of “information” by Shannon and others shows this trade-off. Statements that are more surprising, more unexpected have more information than other statements. But precise statements contain a lot of redundancy so they don’t have much information in this sense. On the other hand, a literary work will likely contain many surprises and multiple meanings that stir the heart and imagination.

We have come to expect historical accounts to include specifics such as dates that are tied to a solar-year calendar, places with widely-recognized names, people with specifics about place and time of birth, death, and other significant events, and contextual information about culture and political system.

A traditional account such as the Bible is less precise than histories written today because it lacks many of the specifics expected. However, it can be, and is accurate. It contains primarily qualitative rather than quantitative accounts so prized by science. By following Ockham’s razor science minimizes qualities and allows quantities to expand indefinitely. So Konrad Lorenz was right, “Scientists are people who know more and more about less and less, until they know everything about nothing.”