Make Category Theory Intuitive! by Jocelyn Ireson-Paine.
From the post:
As I suggested in Chapter 1, the large, highly evolved sensory and motor portions of the brain seem to be the hidden powerhouse behind human thought. By virtue of the great efficiency of these billion-year-old structures, they may embody one million times the effective computational power of the conscious part of our minds. While novice performance can be achieved using conscious thought alone, master-level expertise draws on the enormous hidden resources of these old and specialized areas. Sometimes some of that power can be harnessed by finding and developing a useful mapping between the problem and a sensory intuition.
Although some individuals, through lucky combinations of inheritance and opportunity have developed expert intuitions in certain fields, most of us are amateurs at most things. What we need to improve our performance is explicit external metaphors that can tap our instinctive skills in a direct and repeatable way. Graphs, rules of thumb, physical models illustrating relationships, and other devices are widely and effectively used to enhance comprehension and retention. More recently, interactive pictorial computer interfaces such as those used in the Macintosh have greatly accelerated learning in novices and eased machine use for the experienced. The full sensory involvement possible with magic glasses may enable us to go much further in this direction. Finding the best metaphors will be the work of a generation: for now, we can amuse ourselves by guessing.
Hans Moravec, in Mind Children [Moravec 1988].
This is an essay on why I believe category theory is important to computer science, and should therefore be promoted; and on how we might do so. While writing this, I discovered the passage I’ve quoted above. My ideas are closely related, and since there’s nothing more pleasing than being supported by such an authority, that’s why I’ve quoted it here.
Category theory has been around since the 1940s, and was invented to unify different treatments of homology theory, a branch of algebraic topology [Marquis 2004; Natural transformation]. It’s from there that many examples used in teaching category theory to mathematicians come. Which is a shame, because algebraic topology is advanced: probably post-grad level. Examples based on it are not much use below that level, and not much use to non-mathematicians. The same applies to a lot of the other maths to which category theory has been applied.
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An interesting essay with many suggestions for teaching category theory. Follow this essay with a visit to Jocelyn’s homepage and the resources on category theory cited there. Caution: You will find a number of other very interesting things on the homepage. You have been warned. 😉
Spreadsheets too! What is it with people studying something that is nearly universal in business and science? Is that why vendors make money? Pandering to the needs of the masses? Is that a clue on being a successful startup? Appeal to the masses and not the righteous?
If you try the Category Theory Demonstrations, be aware the page refreshes with a statement: “Your results are here” near the top of the page. Follow that link for your results.
In a thread on those demonstrations, Jocelyn laments the lack of interest among those who already understand category theory in finding more intuitive ways of explaining it. I have no explanation to offer but can attest to the same lack of interest among lawyers, academics in general, etc. in making their knowledge more “intuitive.”
So how do you successfully promote projects designed to make institutions or disciplines more “transparent?” A general public interest in “transparency” doesn’t translate easily into donations or institutional support. Suggestions?