Golden ratio: proof positive?

by Paul Burmeister

Mathematician George Markowsky wrote an article in 1992 (The College Mathematics Journal, Vol. 23, No. 1) that debunked popular misconceptions about the golden ratio. I'd like to note two items included in his article.
First, a major point of Markowsky's critique of misconceptions is: since "measurements of real objects can only be approximations," and since "inaccuracies in measurements lead to greater inaccuracies in ratios," then most demonstrations of the golden ratio are enthusiastic and convenient rather than methodical and provable.
Second, Markowsky calls into question, rightly so, the precise role of intention in historical designs, as intentions are self-proved by retrospective speculations and demonstrations. For purposes of his rigorous disproving, modern speculations and their attendant demonstrations regarding designs of the Parthenon and Leonardo's St. Jerome are easy targets. Neither example falls within his acceptable tolerance of ±2% for ratio.

While Markowsky's careful mind catches sloppy or sensational claims made for famous examples, his eye is blind to the intuitive process of the skilled designer. Never mind that Markowsky's own methods can be problematic, he seems unwilling to acknowledge that designing minds intuitively select approximations of the golden ratio because the approximations are functional and pleasing.