Gödel, Escher, Bach

An Eternal Golden Braid

Thirty-six years ago, one of the greatest books of its decade was published — Douglas Hofstadter’s Gödel, Escher, Bach.

It’s hard to describe how this book affected a certain kind of person. You had to have an interest in logic, recursion, and self-reference in the fields of mathematics, music, and the visual arts, for starters. But if it caught you at the right stage in your life, when these interests were important to you and you had some familiarity with at least Escher and J. S. Bach, then there was nothing like this book. Anywhere.

And that’s still true. Even Hofstadter’s other books, fascinating and improbable as they all are, don’t come close.

It’s a tour de force — both witty and compelling.

There’s little original I can write on the topic, but here are some highlights…

The basics — Wikipedia and Amazon.

Here’s the reasonable (if not entirely sympathetic) review from the New York Times in 1979 by Brian Hayes. (Some readers just don’t seem to appreciate the linguistic humor, the playfulness with which Hofstadter approaches his subjects.)

In looking for good reviews, I was especially interested in recent ones, to see how the book is still received. I was quite happy to find this gem: A discarded review of ‘Godel, Escher Bach: an Eternal Golden Braid’. Not only do I advise you to read it (the comments section illuminates the variation in fans vs non-fans), but inside I found a surprise — a reference to a paean by Eliezer Yudkowsy, whose deliciously intelligent fan-fiction Harry Potter and the Methods of Rationality is a treat in its own right:

This is simply the best and most beautiful book ever written by the human species…

I’m not alone in this opinion, by the way. For one thing, Gödel, Escher, Bach won a Pulitzer Prize. Or just pick a random scientist and ask ver what vis favorite book is, and 1 out of 5 will say: “Gödel, Escher, Bach“. No other book even comes close.

It is saddening to contemplate that every day, 150,000 humans die without reading what is indisputably one of the greatest achievements of our species. Don’t let it happen to you.

Sure, if you’re just an average person, you might not understand everything in this book – but when you’re done reading, you won’t be an average person any more.

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Lessons from a foxhunting photo essay

The full photo essay is here.


29 - Portrait
Continuous horizontal curves

This is not the conventional head pose for this formal pack shot, but I was struck by the lines of horizontal arcs.  The eye travels from the rump’s inverted “U” curve to the “U” curve of the coat’s skirt and back to the inverted curve of the horse’s neck.  The echo of the coat’s curve with the belly provides stability.  The combination conveys balance and permanence.

35 - Portrait
Vertical curves in motion

The horse on the right, by contrast, has vertical arcs, particularly the tail closely echoing the rear.  Unlike the shallow stable arcs in the first picture, these are deeper.  We know the hind leg will straighten, so we see the deep curve as a spring that will uncoil, driving the horse forward.  We also know the matching curve of the tail is impermanent, and that increases the sense of a fleeting second caught and frozen, adding to the sense of motion.

A massive spring
A massive spring

The curves of the Belgian in the next photo are like clock springs tightening and loosening.  The mass of the horse is emphasized by the glimpse we get of her chest, and though she’s trotting she almost seems to be trotting in place and not moving forward.  The obvious coiled power encourages that illusion, and we see the curves, correctly, as engines of stored energy.

Rising like the phoenix
Rising like the phoenix

The estate at Long Branch has two pairs of gate pillars surmounted by old eagles.  The pose is triumphant rather than ascendant, but with the view from below and the maples like flame behind, the curves of the wings look ready to thrust it aloft like the phoenix reborn.

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The path not taken


Let’s start with something simple. What makes this photo so appealing?

This comes from a recent January meet with the Nantucket-Treweryn Beagles in the Shenandoah Valley of northern Virginia. It’s a view of an interior road of a largish farm in a rural area. Despite the timeless air to the place, I know these oaks are less than 100 years old, and that the path probably intersects a public road not far from where it vanishes here, but none of that matters to how the picture registers with me.

There are formal elements that are pleasing — the straight lines of the fences contrasted to the winding line of the lane, the various vertical angles, the flat lane against the low hillocks in the distance, the proportions of sky to land. But I find I have projected personalities and narrative into the scene, and that is the foundation of its appeal to me.

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