The book Sparks of Genius, which dives deeply into the variety ways in which we know, devotes one chapter to transformational thinking, the ability to apply various techniques to change the character of a problem. The chapter lists a variety of such transformations, but this passage on one medical advance stood out:
One of the most intriguing data-sound transformations has been made by a team of biochemists, musicians, and computer programmers at Michigan State University to improve urinalysis. In the standard procedure, a machine measure the different amounts of each wavelength of light that passes through the urine. The amount of light tells how much of each type of chemical is present. But herein lay a problem. The team found that many different urine samples give visual traces so similar to one another that the human eye has difficulty distinguishing among them. To find out if the ear could do better, they sent the output of the chromatograph to a computer instead of a chart recorder. The computer implemented various rules regarding signal intensity, time, and other parameters to transform the data into a form readable by a sound synthesizer. The computer also converted the sound signals into musical notation, which could be turned into a musical score. The results were spectacular. People could hear differences between one urinalysis and another that their eyes could not see. The transformation of numerical data into information observed aurally produced a significant and useful increase in patter discrimination.
Now I don't expect my doctor to slip in some ear buds on my next visit, but the point is made. The simultaneous or serial use of different thinking tools to transform thedata set can result in an insight unavailable to the user of a single set of tools, whether the tool be abstraction, analogy, empathy, imaging, modeling, logic - take your pick.
The point is that there is more than one way to problem solve. Sometimes by seeing, or in this case, by hearing the problem, differently, a breakthrough can occur.
Similarly, on occasion it is the question, not the answer, that matters.