When I was 10 years old (5th grade), circa 1963, I thought I might have discovered some new principle of numbers, but it was almost impossible for me to find out. There was no one to ask, and no references I could find.
My father would take me to his office (attached to a flour milling operation) on the weekend to give my mother a break, and there I would wander around entertaining myself by admiring the sailfish mounted on one man’s wall, and the manual plug-in switchboard. There were, of course, many desks in an open area for clerical work, and many of those desks had calculators.
We are part of nature, an animal like other animals, and our minds preserve that heritage.
I’m conscious of this every time that I’m startled by a grouse shaking the bush along my path when it erupts and I take an involuntary step backward, preparing to fight or run, once I determine what threat is coming my way. My rational mind knows it’s ridiculous, but I’m the product of thousands of ancestors who decided that sometimes it really is a lion, and it’s better to treat it that way, and laugh about it afterward. The ones who didn’t, after all, were sometimes wrong enough that they left no trace.
What do animals do? They observe. They watch the behavior of their mother and siblings, the way their herd, or pack, or flock treats its members. They watch their prey, if they are predators. And vice versa.
Humans, well, we watch everything. We’re fascinated by animals from our very earliest age. Not just our own family and tribe, but all animals. We can spend hours and days just watching them.
What do we learn when we watch animals? We learn, species by species and circumstance by circumstance, just what they are likely to do — depending on the season, the environment, the weather, their state of health, or lust, or maternity. We know they make their own choices, within circumscribed limits. We might not know why, exactly, but we know what — they’re like us, or they seem to be, even the alien ones like bugs. We learn how to predict what they will do. We are wired, I would say, to pay attention to animals this way, just as they pay attention to each other. They have agency, and we want to understand how they work.
I’m an early adopter of technology, esp. software. It’s an essential component of my self-image that began with mathematics in grade school. Back in the 70’s I entered early computer businesses after college and made my entire career in a variety of young companies in the software, support, and consulting wings of the tech industry.
Outside of business, in my personal tool kit, I eagerly embraced home computers for general use, and specialist devices and software for hobbies like music and photography. I immersed myself in evolving standards for good user design and knowledge management philosophies. I studied the engineering principles of mainframe operating systems. By today’s standards I may not be a tech expert, but I am, by god, an experienced technology user.
And I am paying for it. Every day. With the only currency that matters — time.
Among other things, I’m a fiddler of folk music — have been for 25 years or more. Unusually, for an American, I specialize in traditional music from Scandinavia — Sweden, Norway, Denmark, and Finland — instead of Irish, Scottish, or Appalachian. It’s a very rich tradition, with roots in the Baroque and earlier, and a number of interesting bowed string instruments besides the violin, namely the nyckelharpa and the hardingfele.
Except for a handful who grew up in a Scandinavian musical tradition in America (very few), we almost all come from outside the ethnic culture, inspired by the love of the music itself.
Most of us play for dancers or are associated with people who do so. There are a number of thriving dance groups in America — the ones that have local musicians dance to live music, and the rest dance to recordings. These are social dance groups, by and large, not performance groups — it’s like having a local square dance. Both the musicians and the dancers are tightly connected with their counterparts in Sweden and Norway, and instructors travel regularly to America to lead workshops and teach at dance and music camps.
At a guess, there are maybe a couple of hundred musicians who dabble seriously in Scandinavian fiddle music in the USA, and perhaps a thousand or so dancers. That’s a small community, small enough that the musicians who’ve been around a while pretty much all know each other, as do the leaders of the dance groups.
In a traditional community in Sweden, the locals would have had a dozen or so dances, and the musicians would have played tunes in those genres. In America, where it’s an adopted tradition, the dancers tend to have a collector’s mentality: “Ooh, let’s learn that dance next!” So, while a fiddler tied to a village in Sweden might have mastered a few genres of tunes for dances (and many tunes for each type), a fiddler for a modern American dance group needs to be able to cover, say, forty dance genres, with at least two tunes each. A typical free-for-all dance party for Scandinavian dancers might require a basic repertoire of eighty tunes, to just barely cover an evening (80 x 3 minutes each = 240 minutes = 4 hours), and that’s assuming all the ad hoc musicians know all the same tunes.
One of my early Swedish mentors recommended that I specialize in the tunes of a particular district (almost any area has dozens or hundreds of tunes). I explained to him that, as an American Scandie fiddler, I was already specializing — I wasn’t playing Irish or Scottish. Different worlds.
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…
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.
When I was 10 years old (5th grade), circa 1963, I thought I might have discovered some new principle of numbers, but it was almost impossible for me to find out. There was no one to ask, and no references I could find.
