How does Aristotle's theory of the Golden Mean relate to reason?

Answer 1

There are two ideas more important to philosophy than any others.
One is: A is.
(Existence exists; space-time is real).
The second is: Aristotle's golden mean.
Most people quote it as "nothing in excess".
But the idea behind the calculation of how much of something/anything is useful, good, productive of happiness etc. involves the most basic function of the mind--to study reality, learn about it, evaluate it, think up a pan and then invest life capital or "personally controlled values" wisely--to produce a profit;.
And the Golden mean also involves the categorizing or scientific-level definition of how things work in Nature (or the prioritized internal workings of man-made structure of things used for human purposes).
Knowing how much of something is needed in any case and in what exact condition it needs to be kept in order to do what specific normative function--that's what knowledge means, in a nutshell. The use of "reason".
The Golden Mean also applies to acting on knowledge without overdoing or omitting necessary steps to success.

Answer 2

It has something to do with average(means) balance of things important to the harmony of life. As in the book called The Eternal Golden Braid. Where the great art works of Escher, the great musical works of Bach, and the great mathematics of I think Euclid are braided into an example of what harmony is. And philosophicaly speaking if you were to average these works, one might come up with a reasonable answer.

Answer 3

Aristotle's Golden Mean refers to the optimum position between two extremes. For example, Courage and Fear are opposite extremes. The ideal position is the 'perfect' (golden) balance point in the middle (mean) of the two. Courage which is not tempered by reason is extreme and can lead to nasty consequences. Fear can be debilitating and, therefore, also create nasty consequences. The ideal position is a balance of fear to stimulate reasoning and courage to create action.

Best wishes.