Wednesday, September 4, 2019

Institutionalization and Reform

Most innovations probably arise from intuitions; the intuitions are triggered by external observations of reality or changes in society. How did calculus come to be invented at roughly the same time by Newton (b. 1643) and by Leibnitz (b. 1646); the occasion was a desire to predict mathematically points on a geometrical curve. It’s easy to predict the location of a point on a line; but when the damned thing is sloping away from you in an ark, not easy. The desire in both cases was powerful, the need to get good answers pressing. The new math worked! In due time we’ve come to formalize its procedures into calculus. And now it is institutionalized; it is taught in school. The reason why most people frown, their features signaling unease, when calculus is mentioned is because the method has become institutionalized. People taking calculus don’t have the burning need to understand curves in order, say, to understand the orbits of planets. Institutionalization makes it relatively easy to learn an art; no invention is necessary, no repetitive testing, frustration, torn up sheets, and back to the start. At the same time, if the art is a difficult one—and is taught because it’s part of some grand scheme (you want to graduate in some science eventually); it is rarely taught in answer to a burning urge.

Looking around I can at least imagine some time in the future when much of what we now experience as twenty-first century culture may have been largely lost, especially the complicated parts. Then some people in the future may meet the problem of the curve again. Those experiencing the difficulties will once more be powerfully motivated to find the math to help them. Imagine such a group when one of its members bursts into a laboring group; he’s  holding some ancient book. “It’s been done before,” he cries. “And it’s all in here. A little hard to understand, but it’s the answer.” The mood in the room can almost be felt. And it represents what I’d call Reform: the renewal of an art that began as an intuition, got institutionalized, and now will be reformed. The reform will be present because this new group will make additional innovations to the math while trying to understand that ancient text.

This subject is of value in the context of my current ponderings. Everything we live now was once an innovation; many things have become ritualized so they no longer live in us as driving needs. And institutionalization is followed by decay. Reform, however, has no doubt already begun—even if we don’t fully see it yet.

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