a meditation on Hofstadter’s Law

In Godel, Escher, Bach: An Eternal Golden Braid, a book that is on my list of books to reread, Douglas Hofstadter set forth what has since become known as Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.

There are many reasons that I ponder Hofstadter’s Law, or as I (perhaps inappropriately) prefer to refer to it, Hofstadter’s Principle. One very tangential reason is the context in which I first encountered it, through my reading of Hofstadter’s book. I have always had a soft spot in my heart for the perspective bending art of Escher, and in fact my area of mathematical research is reflected in some of his works such as Angels and Devils. Perhaps there is scope for exploring this internal connection in some future post.

A second and much less indirect reason is the recursive, self referential nature of the Principle. As we work through the details of a situation or a task, we sometimes find ourselves enmeshed in the details contained within the details, the grit that can on occasion create the grinding friction that emerges as we work to refine our approach to the details. I spend a part of each day pondering grit and its consequences, and the truth of the Principle makes itself felt every day.

But perhaps the main reason is the extent to which modifications and variations of the Principle also makes themselves known and felt. It’s harder than you expect, even when you take into account the Principle. It always requires more attention to detail than you expect, even when you take into account the Principle.

In aikido, part of what we are working to do is to retrain the ways our bodies react when we’re attacked, when we’re held. We react by instinct blazingly quickly some times, and so yes, this retraining takes longer than we expect when we first start (or at least longer than I naively expected when I started), even when I began to appreciate the application here of the Principle.

When teaching, we spend a significant chunk of our preparation time cutting paths through the tangle of material that constitute the jungle of a discipline, grown tall and green through the work of scholars over decades or centuries. We then act as guides for the neophyte students encountering the jungle for a first time, and one of several things we need to keep in mind as teachers is that for our students, the Principle applies and we need to give them the time and support to come to their own understanding of the material we are presenting to them.

So for me, Hofstadter’s Principle and its variants form some of the bedrock of how I encounter the world. I work to minimize its impact but I recognize it is always there, watching from the shadows. Waiting, like one of our house panthers, for its moment to strike.

~ by Jim Anderson on 6 December 2020.

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