We just found a 1963 reprint of W.W. Sawyer’s little book Mathematician’s Delight at Mostly Books, a family-owned bookstore on 529 Bainbridge Street in Philadelphia. In chapter 2 of his book, which was first published in 1943, Prof. Sawyer notes “the connexion between reason and imagination,” stating that “reason is … an experiment carried out in the imagination.” (What an amazing and beautiful phrase; the italics are Sawyer’s.) He also describes — and defends — simple models this way (again, emphasis in original):
It is impossible to imagine any event in perfect detail. In attacking any problem, we simplify the situation to a certain extent. We do not bother about those facts which seem unimportant. The result of our reasoning will be correct if the picture in our imagination is, not exactly correct, but sufficiently correct for the purpose in hand.
In other words, abstraction, parsimony, and reduction are not only necessary and unavoidable in solving problems logically. Abstraction, reduction, etc. can be helpful too.
Preaching to the choir?
