Where does mean collide?

In the Nicomachean Ethics (c. 350 BCE), Aristotle held that each moral virtue is a mean, a balanced middle state of feeling and action lying between a vice of excess and a vice of deficiency: courage, for instance, sits between recklessness and cowardice, and the right amount is fixed relative to the person and the situation. Later writers call this the doctrine of the mean, or the golden mean, and read it as a claim about how good character is structured rather than a rule for splitting the difference. Here the word names a quality of character judged by practical wisdom, not a number computed from data, and not a fictitious body used to keep uniform time.[1]

Unit

One virtue expressed at the right degree, judged relative to the person and situation

Recovery means

Not applicable

Measured by

Appraised qualitatively through practical wisdom and observed conduct, not by a numeric scale

The arithmetic mean is one of the classical means: Nicomachus of Gerasa set it out around 100 CE in his Introduction to Arithmetic as the middle term of a proportion, the value that exceeds one extreme by the same amount it falls short of the other. Its modern role as the best single summary of repeated measurements was fixed by Gauss in 1809, whose work showed that the average minimises squared error under normally distributed noise, and Plackett (1958) traced how the principle of the arithmetic mean took hold across astronomy and metrology. Here the word names a computed average of numbers, obtained by adding the values and dividing by their count, not a balanced trait of character and not a way of reckoning time.[2][3][4]

Unit

A single averaged value on the same scale as the data it summarises

Recovery means

Not applicable

Measured by

Computed by summing the observed values and dividing by their count

Mean solar time is kept by a mean sun, an imaginary body that moves along the celestial equator at a perfectly uniform rate, unlike the real sun, whose apparent motion speeds up and slows across the year. Ptolemy described the underlying correction, the equation of time, in the Almagest around 150 CE, and modern positional astronomy (Urban and Seidelmann, 2013) still defines civil clock time through this fictitious uniform sun rather than the observed one. Here the word names a uniform timekeeping standard built from an averaged rate, not an average of a data set and not a middle state of character.[5][6]

Unit

A uniform time reckoned from a constant-rate fictitious sun, in hours, minutes, and seconds

Recovery means

Not applicable

Measured by

Derived from apparent solar time by applying the equation of time, then referred to a time zone