Brilliant AF.
One of the hardest things to do is make difficult processes and systems accessible. This article achieves that with a simple discussion of building a staircase (no mean feat, first time) to step up to the springboard for a much larger idea. It's almost as if observing the staircase details renders a scaleable model fractal that gets to measurement of a learning curve.
I wonder if, by observing the details of one's own most difficult task, focusing on the time to learn each detail and assemble one's own model, an overall speed for learning ANY difficult task, done by a particular person could be calculated. That could be a valuable tool for measuring human potential, particularly in apprentice-type learning.
The value of the time and the effort put into the apprenticeship -- to both the apprentice and the master craftsman -- could be assessed before hand. Achievement baselines could be set closer to reality; or it could be decided that the apprenticeship would not be worth the time and effort. But that last decision could be made on firmer ground, data-wise.
Da Vinci, I would suggest, was a great observer of detail; he was also pretty good at math, science, engineering, and architecture. But it all started with drawing -- observing the most minute of detail, in all it's imperfection, then transferring that to paper. As an artist, he also learned to sort of standardize many of the imperfections -- or at least the use of the tool to represent those imperfections on paper or canvas. The painting method he galvanized, sfumato, eschewed hard lines in nature, and worked hard to achieve the soft edge. I wonder if da Vinci saw the irrationality of pi as evidence that a circle has no true "edge," but that a circle was instead equidistant points stretching out in a small infinity, particular to a specif object
The downside of observation might be wrapped up in this last, though. Because the casual observer of a circle, presuming that there is a definite, finite edge to a circle could lose their faith in the dimensional space we've grown up perceiving (four dimensions.) This might be okay for a mathematician, a scientist, or an artist. To a suburban husband with a mortgage and a minivan, it might be terrifying. The observation might completely unmoor him, and send him drifting off.
Nature is like that. The infinite diversity of nature, at say, the class, order, genus, species, or individual level can be maddening to try to take in. Looking above, at "animal, mineral, vegetable" compounds that exponentially. How those pieces work together to build a staircase, or a giraffe, or a seam of granite, or the savanna of Africa, is the heart of scientific -- and artistic -- inquiry.
Thanks, John Salvatier, for a provocative and insightful article.