Imaginative Economics

One of my colleagues had posted the question, "Is Imagination more important than knowledge?" He's a good friend, so I asked him about it. He expressed an interesting answer to his own question, which is that the two are complementary, and (at least for research purposes) you need a minimum of both to get anywhere.

He expressed this mathematically, and I corrected a minor error in his math to get:

result = (maximum{imagination - minimum1, 0})^alpha * (maximum{knowledge - minimum2, 0})^beta

That is, if either the imagination or knowledge falls short of its minimum, the net result is zero. If both are above the minimum, then they work together in some proportions, and can partially - but not fully - substitute for one another. Within some constraint, the result will be highest when imagination and knowledge exist in the proportions (alpha, beta) respectively.