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The practical value of category theory (and art)

April 12, 2014 3 comments

After my presentation “A category-theoretic view of model-driven” (slides forthcoming through the conference web site) during this year’s Code Generation conference, I got the question what the practical value of category theory was. In the heat of the moment, I chanced upon an analogy with art which very soon found its way to Twitter as:

Felienne CT-tweet

This got some retweets and also some responses to the tune of me being completely wrong. Although the above is what I said, my actual opinion on this is a bit more nuanced. (As an aside: Félienne was kind enough to write a live-blog post about my presentation.)

First of all, art has quite some practical value: it improves people’s lives in a myriad ways by triggering deeply-felt emotional responses. Category theory (or CT, in short) doesn’t quite work like that in general although for some of its practitioners it might come close. CT certainly has value in providing its practitioners a mental framework which guides them to the sort of abstractions that work really well in mathematics and, increasingly, in functional programming to think and reason more effectively.

What didn’t quite made it to the tweet was my assertion that in practice CT does not relieve you of the hard work. Or to put in another way: there’s no substitute for thought. Framing something in the CT language and framework doesn’t “magically” give you the answers for the questions you might have. It can certainly help in reaching those answers more efficiently and phrasing them (much) more elegantly – which is precisely what proper abstraction should achieve. But at the same time, once you have these answers, it’s perfectly possible to “desugar away” from the use of CT. At the end of the day, everyone has to consider his/her ROI on learning enough CT to be able to take this route.

For the same reason I have a problem with the tendency in certain circles to outright declare adequate knowledge of CT as a criterion for admittance to those circles. (I hinted somewhat obliquely and humorously to this in my presentation.) It’s an entirely artificial entry barrier with those enforcing it doing so for not entirely autarkic reasons.

In conclusion: yes, CT can certainly have practical value but it requires the right context and considerable upfront effort to achieve that and does not constitute a prerequisite.

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