Source: Michael Nielsen blog, Feb 2016
Exploration and discovery require a logic that is different to, and at least as valuable as, conventionally “correct” reasoning. The idea of semi-concrete reasoning is a step toward media to support such exploration and discovery, and perhaps toward new ways of thinking about mathematics.
Alan Kay has asked “what is the carrying capacity for ideas of the computer?” We may also ask the closely related question: “what is the carrying capacity for discovery of the computer?” In this essay we’ve made progress on that question using a simple strategy: develop a prototype medium to represent mathematics in a new way, and carefully investigate what we can learn when we use the prototype to attack a serious mathematical problem.
In future, it’d be of interest to pursue a similar strategy with other problems, and with more adventurous interface ideas. And, of course, it would be of interest to build out a working system that develops the best ideas fully, not merely prototypes.