On the Essential Unity of Mathematics, Science, and Art: The Justice Evaluation Function and the Golden Number

This paper describes how some basic scientific ideas—fairness/comparison/reference-dependence, deficiency and excess, loss and gain—coalesce, unexpectedly revealing a link to the Golden Number, which itself links mathematics and art. Fairness, comparison, and reference-dependence are mathematically equivalent. So are deficiency aversion—deficiency relative to the just amount is felt more keenly than comparable excess—and loss aversion—loss relative to the reference amount looms larger than comparable gain. Representing the outcomes (the justice evaluation J and the value V) by zero (for zero deficiency/excess or loss/gain), negative numbers (for deficiency or loss), and positive numbers (for excess or gain) leads naturally to a contrast between the negative and positive outcomes (deficiency and excess in one case, loss and gain in the other). This contrast can be expressed as a difference or a ratio. The ratio of the absolute value of the negative outcome to the positive outcome thus expresses the deficiency aversion coefficient or loss aversion coefficient. This ratio increases as the deficiency/excess or loss/gain k increases, crossing 2—deficiency is felt twice as keenly as excess and loss looms twice as large as gain—when k equals 5-1/2 (≈0.618) of the just or reference amount. School of Athens painted by Raphael in 1509–1511 in the Apostolic Palace in the Vatican. (Adapted with permission from https://upload.wikimedia.org/wikipedia/commons/4/49/%22The_School_of_Athens%22_by_Raffaello_Sanzio_da_Urbino.jpg). The code of this chapter is 01000111 01101111 01101100 01100100 01100101 01101110 00100000 01001110 01110101 01101101 01100010 01100101 01110010.