» the jsomers.net blog.

For the last few months I’ve been feeling very uncreative. I try to sit down to write every day, but lately these sessions have ended prematurely, after ten or twenty minutes scouring what feels like an empty brain. I peruse my notes, but even there, it seems like I’ve been doing a lot more consuming than thinking. I’ve been bereft of ideas, of that feeling of teeming, the wonderful elastic looseness that accompanies a bustling inquisitive mind.

And then I started reading Hofstadter again. I first fell in love with him when I picked up Godel, Escher, Bach: An Eternal Golden Braid (GEB) in my sophomore year at Michigan, on the implicit recommendation of a friend who had it lying on his dorm room floor. That book rebuilt me: I came out of it with a thousand new interests, a new vocabulary, a massively expanded conceptual toolkit, a more playful attitude, and a remarkable feeling of clarity, like the mental equivalent of a cleansed palette. If you haven’t read it yet, you must.

Just a few weeks ago, I dove into his Le Ton Beau de Marot: In Praise of the Music of Language, a tome ostensibly “about” translation which of course turns out to be nothing short of an annotated, illustrated garden path through the totality of Hofstadter’s mind. Taking Clément Marot’s short poem “A une demoiselle malade” as its kernel, it unfolds a story of language, of Hofstadter’s personal life, of puzzles and puns and palindromes, of frames and templates and analogical structures, of “recursion, computation, reduction, holism, meaning, ‘jootsing’ (Jumping Out Of The System), ’strange loops,’ and much, much more”—all presented with the usual “family of elaborate (and lovingly elaborated) analogies”, “structural puns”, and in general a feeling of childish delight that makes reading any of his books an incomparable joy. [1]

Enough gushing. The point is, after just one or two sittings with Le Ton Beau, I’ve been re-invigorated. And I think I know why.

Hofstadter’s writing—all of it—is littered with little anecdotes about sets of afternoons here and there where he dives into some intellectual adventure: translating a Stanislaw Lem story from Polish to English, pointing camcorders at televisions to investigate recursion, training himself to speak backwards (he calls it “Hsilgne”), etc. It’s hard not to be inspired by these informal experiments: what else can you do, after Hofstadter tells you that he wrote the preceding paragraph without using the letter “E”—he was making a point about the way constraints drive creativity—than to try it yourself? [2]

That’s why reading Hofstadter is so much fun, because he challenges you on every page. I said earlier, for example, that Le Ton Beau de Marot had Clément Marot’s short poem “A une demoiselle malade” as its “kernel”; what Hofstadter did was to ask a whole slew of his friends to translate that poem as best they could under certain constraints, mainly the requirement that they respect something of the original’s content, tone, and basic metric structure. When his friends began responding in spades, Hofstadter found the submissions so delightful, and the issues they raised—about languages, analogies, constraints, creativity, translation, and “transculturation”—so rich and interesting, that he decided to build an entire book around them. So Le Ton Beau’s expository chapters are interleaved with small showcases of notable translation efforts, just as GEB’s “regular” chapters were interposed between dialogues. The effect is wonderful and, again, it’s virtually impossible to go through without wanting to take a stab yourself. (Here’s mine.)

And that’s the trick. Hofstadter gradually ropes you in with his games and puzzles; he’s always demonstrating the very concepts he’s describing, always coaxing you to play along. In GEB, for instance, his dialogue, “Crab Canon”, about retrogressive palindromic structures in music, art, and biology, is itself palindromic: each speech is repeated twice, with the two halves of the dialogue mirror images of one another. The effect works because he specifically (and painstakingly) collected phrases with ambiguous meanings, like “Not at all!”—which can mean either “Definitely not!” or “No sweat!”—or “One has no frets”—which could either be about guitar strings or worries, depending on the context.

In Le Ton Beau, to take another example, one of the overriding themes is the relationship between form and content, and in particular on the way in which each influences and constrains the other. But rather than just talk about this problem, Hofstadter lives it, not just in little games like the “E”-less paragraph mentioned earlier—though there are plenty of those throughout—but in the construction of the book itself. From the introduction:

Above, I very casually remarked that I have enjoyed total control over page-breaks and such things; yet the truth of the matter would be far more accurately captured by turning the phrase around and saying that the page-breaks and word spacing and such things have enjoyed total control over me! By this, I mean that I have been forced to rewrite and rewrite and rewrite passages in order to make a page boundary come out exactly where I wanted it. It is not just by some happy accident, for instance, that the poems inside chapters are never, ever broken across page boundaries.

The amount of influence exerted on my text by concerns of purely visual esthetics is incalculable — and by “my text”, I don’t merely mean how I wound up phrasing my ideas, I mean the ideas themselves. Content has been determined by considerations of elegant form so often that I couldn’t begin to imagine it. Every single line of text, for instance, is characterized by its spacing — how wide the blanks between words are. I can clearly see the spacing as I type on my screen, and I rewrite and rewrite in order to make sure that no line is too tightly or too loosely spaced. In the course of such rewritings — here extracting a word, there using a shorter or a longer one, elsewhere inserting a word where none was — words and phrases that I would otherwise not have thought of pop to mind, suggesting ideas I would not have thought of, and those ideas suggest unexpected paragraphs, and those paragraphs are in turn linked to other ones, and so on…

It’s this feature—Hofstadter’s habit of taking fairly abstract concepts like “the battle between form and content” or “level-crossing feedback loops” and engaging them at every turn, in the selfsame sentences he uses to describe them—that most contributes, I think, to his ability to spark the reader’s creativity. Because the effect of his incessant demonstrations and illustrations is to gradually train you to think like him, to transform you into a little fledgling version of himself. Which is great, because as Dan Dennett puts it,

What Douglas Hofstadter is, quite simply, is a phenomenologist, a practicing phenomenologist, and he does it better than anybody else. Ever. For years he has been studying the processes of his own consciousness, relentlessly, unflinchingly, imaginatively, but undeludedly. [1]

That is, he’s a student of his own mind, a mind that is unstoppably inquisitive, and we benefit from his struggle to articulate its intricate workings, first because we’re exposed to his innumerable interests and second, because we too become students of those processes—analogy-making, constraint-satisfaction, conceptual slippage, etc.—that he uncovers as the basis of his creativity.

This first feature, the simple fact that his books cover a lot of ground and therefore activate in the reader all sorts of dormant swaths of brain, is probably best illustrated by a simple tour of GEB’s wonderful annotated bibliography. Picking three starred entries basically at random, we find:

1. Mikhail Bongard’s Pattern Recognition. Hofstadter remarks that “In his book, [Bongard] sets forth a magnificent collection of 100 ‘Bongard problems’ (as I call them)-puzzles for a pattern recognizer (human or machine) to test its wits on. They are invaluably stimulating for anyone who is interested in the nature of intelligence.” His enthusiastic recommendation led me to this webpage, an index of 280 Bongard problems, including 56 from Hofstadter himself. Solving these is not only a fun way to chew on difficult questions regarding cognition and AI, but also an excuse to kill four or five afternoons!

2. The proceedings of a conference on Communication with Extraterrestial Intelligence. I found this in the New York Public Library and was so blown away by the one chapter I had time to read that I immediately bought it. The conference was broken into distinct sessions organized, roughly, by terms in the Drake equation, which is used to estimate the number of intelligent alien civilizations in our galaxy. So each session is this wonderful discussion among top scientists—a few Nobelists, guys like Freeman Dyson, Carl Sagan, Francis Drake, etc.—trying to home in on a reasonable estimate for a given term, say, L, the length of time an average intelligent civilization lasts, sometimes defending their hunches with sophisticated technical arguments and sometimes with nothing more than hand-wavy intuitions. It’s an absolutely fascinating read, not only because the question of extraterrestrial life itself is so fertile, but also because we get to see such talented scientists at work.

3. Howard Bergerson’s Palindromes and Anagrams, a strange little book that boasts perhaps the world’s most complete collection of top-notch palindromes and anagrams (duh), along with several chapters discussing the art of anagrammatical-palindromic thinking, and diversions into other forms of wordplay, like “vocabularyclept poetry”, in which writers are challenged to craft a poem using the complete set of words from another poem that they haven’t seen before (interesting questions there include, How much will this new poem resemble the old one? and Do the two poets connect their (shared) words into phrases in the same way? and How much of a poem’s DNA is contained just in the words it uses, ignoring their placement and order?) Fun, fun, fun.

Three books chosen from more than one hundred, and all of them rich enough to set off about two weeks of intellectual exploration; I could easily write at length about each, with any feeling I used to have of “an empty mind” replaced by a sense of overflowing activity.

I think Hofstadter’s books range so broadly—that is, they touch on so much of the world—because he wants to drive home two points: first, that so much of the world is connected, and second, that analogy-making—the process of seeing an X as a Y—is the crux of thought, and creative thought in particular.

The following is from a section entitled Creativity and Randomness from page 673 of GEB:

Just as science is permeated with “conceptual revolutions” on all levels at all times, so the thinking of individuals is shot through and through with creative acts. They are not just on the highest plane; they are everywhere. Most of them are small and have been made a million times before—but they are close cousins to the most highly creative and new acts. Computer programs today do not yet seem to produce many small creations. Most of what they do is quite “mechanical” still. That just testifies to the fact that they are not close to simulating the way we think—but they are getting closer.

Perhaps what differentiates highly creative ideas from ordinary ones is some combined sense of beauty, simplicity, and harmony. In fact, I have a favorite “meta-analogy”, in which I liken analogies to chords. The idea is simple: superficially similar ideas are often not deeply related; and deeply related ideas are often superficially disparate. The analogy to chords is natural: physically close notes are harmonically distant (e.g., E-F-G); and harmonically close notes are physically distant (e.g., G-E-B). Ideas that share a conceptual skeleton resonate in a sort of conceptual analogue to harmony; these harmonious “idea-chords” are often widely separated, as measured on an imaginary “keyboard of concepts”. Of course, it doesn’t suffice to reach wide and plunk down any old way—you may hit a seventh or a ninth! Perhaps the present analogy is like a ninth-chord-wide but dissonant.

With that in mind, it becomes somewhat natural to think of Hofstadter’s project, or at least the bulk of his popular writing, as a kind of futzing around on this “keyboard of concepts”, looking for harmonies, trying to cull disparate ideas that really are deeply related. Along the way, he has no doubt become an expert in letting concepts “slip”, that is, in perceiving apparently unrelated phenomena as being “fundamentally ‘the same’ at a deeper, more abstract level”. [3] And it’s by watching him do this, by reading and engaging him in the act of analogy-making, that we gradually slip into the same slippable state.

Here’s one of my favorite examples from Le Ton Beau so far, on pages 40-41:

Over the years, I suppose largely because of my fanatical obsession with acquiring native-style accents in various languages, I gradually abstracted and generalized the notion of “foreign accent”. My exploration was rooted in languages and so the first abstractions that I made of it were naturally still language-based, but others soon transcended language.

For example, after I had been studying Chinese for a while, I realized with shame that my clumsily-drawn characters must have a very foreign-looking “visual accent” to them. In the course of trying to get rid of this “accent”, I started to wonder if there was such a thing as a “Japanese accent” in Chinese calligraphy, given that both languages revere the same set of characters and have calligraphic traditions stretching back thousands of years. [. . .]

Moving away from the realm of language, consider baseball, which has spread from America to other parts of the world, where it is played with equal enthusiasm. Do Cubans and Japanese, for instance, have “foreign accents” when they play baseball? Does a lifelong chess player have a “chess accent” in playing Go for the first time? Do I have an “Algol accent” when I write computer programs in Lisp (Algol having been my first computer language)? In the 1950’s and 1960’s, many physicists decided to move over into the exciting new field of molecular biology. Did they all have a recognizable “physics accent” in their various approaches to the problems of this alien discipline? Do Americans have an American accent when they drive in Europe? Do Europeans have European accents when they drive in America? Is it possible to recognize an Italian driver on a German Autobahn, or vice versa (not cheating by using license plates or car makes)?

What is a “French accent” in music? Certainly in the classical genres, Ravel, Debussy, Fauré, Poulenc, and Satie epitomize this notion, but what about someone like Hector Berlioz, who to me sounds more German that French? And what about César Franck, who, although Belgian, can sound just as French as any of them? I even know a piano-trio movement by Russian composer Alexander Scriabin that sound as “French” as anything I can think of. But what is this elusive French musical accent?

The feeling I get after reading stuff like this… that’s the “Hofstadterian mood”. It’s the feeling of having my brain rebooted, or maybe overclocked: I shed my simple-mindedness, I learn how to think analogically again, connectedly, using questions like Hofstadter’s “What is a ‘French accent’ in music?” to slip from one idea into another, stringing concepts together into one of those long-distance harmonic “idea-chords” that blend into the unmistakable euphonious thrum of a fertile mind at work.

Notes

[1] From “Hofstadter’s Quest: A Tale of Cognitive Pursuit“, Ch. 14 of Daniel Dennett’s Brainchildren: Essays on Designing Minds.

[2] Here’s one attempt—look Ma, no “E”s!—using the preceding paragraph as a model:

His writing—all of it—is swarming with accounts of brainy larks, or whimsical dips into rich tracts of thought: translating a Stanislaw story from Polish to Anglo-Saxon, pointing a photo-gizmo at its own TV output to study spiral loops, training to talk backwards, and so on. It’s hard not to act on such findings: what can you do, upon noticing that his last paragraph is missing our script’s most copious symbol—that paragraph was making a point about constraints—but try it too?

[3] From James B. Marshall PhD dissertation, Metacat: A Self-Watching Cognitive Architecture for Analogy-Making and High-Level Perception

When I was planning my first long drive from school in Ann Arbor back home to New Jersey, I remember looking up directions on Google Maps and noticing, as in the results here, that it really doesn’t take a lot of steps — or driving maneuvers — to get what seems to be a pretty long way across the country. In fact it only requires seventeen turns using the route Google gives, and even that number is inflated (those “keep left” and “keep right” steps are helpful, maybe, but not necessary).

Just for fun, I tried comparing that 500+ mile trip to one a fraction of its size, something closer to ten miles. You can see such a route here.

Remarkably, at only 2% of the distance, this short hop from one small town in New Jersey to another requires just fifteen steps, or only two fewer than the hefty road trip to Michigan.

I began to wonder: what’s the relationship between the length of a road trip and the complexity of the route? Do most trips, long or short, require roughly the same number of steps? How many steps are there in the most complex route in the country? What’s the distribution of step counts for every possible route in the contiguous United States?

These questions turn out to be tractable, thanks in large part to Google’s Directions API, which gives lowly developers like me access to their full suite of mapping, geolocation, and pathfinding algorithms, huge stores of data, and fast servers that can deliver tens of thousands of query results to a single client computer in a matter of minutes.

Before we dive into methods and results, though, let’s lay out exactly what we’re looking for:

1. We want a histogram of step counts for some representative sample of routes within the US. This will give us a really good sense of how complex a typical road trip might be.

2. We’d like to find the most complex route in the country, i.e., a pair of points such that the driving directions between them, given by Google, include a larger number of steps than for any other pair in the contiguous US. It’s extremely unlikely that we’ll find the monster route, but at least we’d like a ballpark estimate of its step count — is it 35, 500, 90, 180?

3. We want a plot of route distance against route complexity. What will the plot look like? Is complexity a linear function of distance? Is there a direct or inverse relationship? Will there be any pattern at all?

4. It would be pretty cool to find a “coefficient of friction” for regions in America, that is, a numerical estimate of how hard it is to drive through a particular region based on how many steps there are, on average, in a route passing through it. We could use this information to create a “heat map” of the entire US, with individual counties or zip codes shaded by friction. Such a map would help us figure out which states have the thorniest roads, or where the most straightforward routes are, or which cities are the hardest to get out of.

To get started, then, I went looking for a random sample of points. One way to do that would be to draw a box inscribed within the continental US and simply generate random lat-longs within that box. The trouble with that method, I thought, was that it could easily drop you in barren or ridiculous places like deserts or lakes; I wanted to focus on plausible real-life trips from one population center to another.

So I went looking for a data set, and before long, found one: the “MaxMind World Cities with Population” file, a 33 MB free download with more than enough data to get things rolling: after eliminating non-U.S. cities (a simple grep did the trick, since the text is nicely structured), I was left with 141,989 points covering nearly every corner of the country.

I hacked together a tiny Rails project (RoR being my hammer-that-makes-everything-look-like-a-nail at the moment) to (a) load the cities and lat-longs into some structured form, (b) drop that data into an HTML page hooked up to the JavaScript Google Directions API, and (c) write the results back to a database. All of the relevant code, along with a SQLite3 database with the structured cities data and results, is available at this github project page.

Perhaps the most important snippet, which I’ll excerpt below, is the code that actually samples points and talks to Google:

var map;
var directionDisplay;
var directionsService;
var stepDisplay;
var markerArray = [];
var step_counts = [];
var step_summaries = [];

function initialize() {
  // Instantiate a directions service.
  directionsService = new google.maps.DirectionsService();
}

function calcRoute(start, end) {
  // Retrieve the start and end locations and create
  // a DirectionsRequest using DRIVING directions.
  var city_start = [start[2], start[3]].join(", ");
  var city_end = [end[2], end[3]].join(", ");
  var latlong_start = [start[0], start[1]].join(",");
  var latlong_end = [end[0], end[1]].join(",");
  var request = {
      origin: latlong_start,
      destination: latlong_end,
      travelMode: google.maps.DirectionsTravelMode.DRIVING
  };

  // Route the directions and pass the response to a
  // function to count the number of returned steps.
  directionsService.route(request, function(response, status) {
    if (status == google.maps.DirectionsStatus.OK) {
      var step_ct = countSteps(response);
      step_counts.push(step_ct);
      step_summaries.push([step_ct, city_start, city_end])
    } else {
      console.warn("Couldn't count steps for this route.");
    }
  });
}

function countSteps(directionResult) {
    var myRoute = directionResult.routes[0].legs[0];
    return myRoute.steps.length;
}

function getAndExecutePairs(n) {
    $.get("/directions/get_pairs", {n: n},
        function(ret) {
            pairs = ret;
            console.log(n + " lat/long pairs downloaded successfully.");
            execute(pairs);
        }
    )
}

function execute(pairs) {
    for (i = 0; i < pairs.length; i++) {
        pair = pairs[i];
        start = pair[0];
        end = pair[1];
        calcRoute(start, end);
    }
}

It’s all pretty straightforward. The process is kicked off by the getAndExecutePairs() function, which just hits the Rails server for n pairs of cities. This is the code it calls:

def get_pairs
    n = params[:n].to_i
    cities = City.find(:all, :limit => n * 2, :order => "random()");
    lat_longs = cities.collect {|c| [c.latitude, c.longitude, c.city, c.state]}
    pairs = Hash[*lat_longs].to_a
    render :json => pairs
end

And that’s it. With just ~100 or so lines of code, I was able to get a decent grip on the first three of the four questions posed above. In particular:

1. What’s the distribution of step counts for every possible route in the contiguous United States?

The answer, based on a random sample of some 2,000 points (and confirmed later by 8,000 more trials), is that you have a sort of right-skewed distribution centered at 20-30 steps and tailing out near 60.

2. How many steps are there in the most complex route in the country?

This is a lot less definitive, but the answer I got was 69 steps, in a route from Ponderose Pine, NM to Wildwood, MN. A friend suggested something like the following approach for finding more complicated routes:

Suppose you’re getting “good” (i.e., stepful) routes between points A and B. Draw a box around each of A and B and “wiggle” your start points within that box. If wiggling in one direction removes steps, try wiggling in another direction; or if it’s not direction that matters, but rather something tricky like “being within a development or behind a river,” maybe you could just select points within the box randomly and assign scores to different areas (sort of like a game of Battleship). That way you slowly optimize promising routes until you end up with truly high numbers.

One potential pitfall of this approach is that there could be discontinuities — A to B could take an unremarkable 35 steps, but (A + ε) to B could take 70 steps — in which case you might not choose the right starting points to begin with. But this would probably only happen if there was something like a maze next to a normal neighborhood.

3. What’s the relationship between trip distance and route complexity?

The graph above plots route distance (measured as the surface distance between the two lat-long pairs) against step counts. Aside from a few outliers, you’ll notice that a really wide range of step counts is covered by a relatively narrow range of distances: that is, most of the variation in step counts is accounted for in trips less than a few hundred miles; and at the margin, an extra mile buys you very little in terms of route complexity.

Perhaps the most interesting points are those short routes with a large number of steps. See, for example, the 69-step route called out above (just over 1,000 miles), or the 67-step route from South Lyndeborough, NH to Hartley, GA (875 miles).

(You’ll notice a few routes with more than 70 steps — these can be safely ignored, since they either originate from or end up in Alaska (oops!)).

4. Can you generate a “heat map” that shades regions by their “coefficient of friction,” i.e., a numerical estimate of how hard it is to drive through a particular region based on how many steps there are, on average, in a route passing through it?

This is left as an exercise for the reader, as is the task of finding even longer routes (here’s a 75-stepper) and the more general underlying problem of understanding which features — of cities and roads and geography — are implicated in route complexity.

One way to appreciate good acting is to try to imagine some of your favorite lines written rather than spoken. Try to clear your mind of the actor’s specific performance. Focus on the words themselves, on the way they look on a page. Now do you see the distance between the screenplay and the speech? Isn’t it remarkable, the work that goes into enlivening those lines?

I have a mug here next to my keyboard that’s full of water. But I’ve been drinking it just like people in those Folgers commercials drink coffee: the way I go to pick it up; the way I hold it, with two hands; the way I hold it up to my nose, and close my eyes, and inhale appreciatively before I take a small sip; etc. If you were watching me from across the room you’d be convinced that I was drinking coffee, not water, just based on the way I’m moving.

Now the remarkable thing is that because of those movements, I get some of the pleasure, drinking water, that I would be getting if it really were coffee. That is, the movements themselves — the rituals — are enough to trick my brain into thinking the water is sort of rich and warm and fulfilling. How strange.

Not bothering about those guys at the bar who are being rude and rambunctious, or those cackling girls on the bus, is not just about dissociating to calm your nerves. It’s not just about ignoring them or putting them out of your mind. It’s about actively trying to appreciate their fun on their terms, and being heartened, or cheered up, or at the very least not repulsed by what you discover in their minds.

But imaginative empathy only goes so far, you say. “What about the vociferous leader of a hate group? I can’t understand how someone could get that way.” Can’t you? Work to imagine it! What did you learn?

Think of what “The Big Bang Theory” celebrates. Raj is socially inept, Howard is a little boy who tries too hard, Sheldon is smug, and Leonard is femininely sensitive. They’re all book-smart and street-dumb.

We’re supposed to like these guys, not in spite of their (one-dimensional) distinguishing features, but because of them. We’re supposed to applaud the fact that these are not your typical male leads. So Raj’s ineptitude is meant to be cute; we’re meant to see a bit of ourselves in Howard; we’re meant to take Sheldon down a notch, but to still laugh along with his jokey parade of negativity; we’re meant to appreciate Leonard’s emotional openness.

It’s remarkable that these features don’t actually repulse us. We are so accustomed to good-looking high-status self-confident male protagonists with nice smiles, that you’d think we’d reject a group of awkward nitwits with loser attitudes. How do these guys earn our admiration, or even command our attention, if most of what they do is pine and bicker and trade masturbatory nerdy in-jokes?

Answer: they’re really smart. We are constantly reminded that these are four very talented scientists, former prodigies and possibly future Nobelists, PhDs in physics and engineering at CalTech. And with that, the basic premise of the show instantly transmogrifies from “four self-satisfied dopes failing socially and indulging ComiCon culture” into “the lighter side of genius.” All of those quirks and shortcomings are suddenly framed as the amusing side effects of their brilliance; their social gaffes take place against an implied backdrop of impressive academic achievement; their (irritating) overuse of jargon in everyday situations, their (childish) intellectual one-upsmanship, and their (regrettable) inability to connect with regular minds, are all explained away as the native burden of the brainiac.

All of this is achieved, mind you, not by convincing demonstrations of actual problem-solving ability or quick thinking or wisdom (though God knows what that means), but by mouthful after mouthful of highly technical vocabulary, often ripped from context, that has the veneer of intelligence.

For people who understand it, this kind of dialogue is a cheap enjoyable ego-massage—for what better way is there to feel good about yourself than to swallow whole the very same sentences that are causing so much trouble for the show’s “normal” characters, like Penny and her friends? And those viewers who can’t parse the jargon are, by virtue of the aforementioned buffoonery, encouraged to pat themselves on the back for not being too smart, for being “well-adjusted.” Everybody wins.

Penny, incidentally, is almost the show’s saving grace. She’s friendly, neighborly, warm, and refreshingly open-minded. She manages to both hold her own among these bizarre boys and stay unflinchingly positive in the face of their haughty and patronizing swagger. But I say “almost” the saving grace because she is, alas, reduced to being a babe. That is, much of the show’s action and comedy pivots on her attractiveness, in a way that clouds and crowds out her excellent attitude (among other things). So where her role could be to teach these guys about a life outside their geeky cloister—and granted, she does do this to a significant extent—she operates mainly as The Girl, that enduring staple of nerd fantasy.

But in the end what bothers me most about this show is that these idiots are held up as models, sort of, by the nerd community. I can understand their enthusiasm—the demographic has been shortchanged by just about every sitcom that ever was—but I wish they held out for something less cheap.

Any atheist who’s had the opportunity will tell you that arguing against Christians, especially new-agey ones, is exhausting. Whatever angle you take—pick apart the Bible, attack the standard arguments for God, demonstrate indoctrination, etc.—the debate always seems to end up in the same place, what I call the “faith impasse”:

Listen: I just believe. I have faith. I’m sorry if you can’t understand that—I really am—but faith is not about reason, and God is not the sort of thing that you can explain.

This is the discursive equivalent of a guy in a duel insisting, after he misses his only shot, that it’s not fair for you to have a gun. It seems like a very low tactic, like a last resort. But it works. And if we’re going to defeat it, we’re going to have to figure out how.

Belief in belief

Dan Dennett, in Breaking the Spell: Religion as a Natural Phenomenon, points out that believing that (a) “democracy is good” is different from believing that (b) “belief in democracy is good.” Someone who held a might write a pamphlet espousing the benefits of a democratic society, whereas someone who held b might see to the distribution of that pamphlet: theirs is a “second-order belief” or, as Dennett puts it, a “belief in belief.”

Historically, religious beliefs tended to be of the first order: “you sacrifice an ox if you want it to rain” because “you really believe that the rain god won’t provide rain unless you sacrifice an ox” (Dennett 227). Belief for its own sake—the kind that drives us to the “faith impasse”—appears to be a relatively recent invention. One explanation is that “the meme for faith exhibits frequency-dependent fitness: it flourishes particularly in the company of rationalistic memes”; since “rationalistic memes” have proliferated in recent centuries, so have calls for “blind faith” and belief in belief (231).

That is, because we have so drastically increased our stock of hard facts over the years—stuff like “rain clouds are formed by colliding air fronts at different temperatures,” or “a baby’s sex doesn’t depend on phases of the moon”—religions that once made all sorts of empirical claims have had to slowly untie themselves from the actual world, in order not to be disproved.

And what happens when a religion no longer has purchase on the real? It retreats into the minds of its believers. All that is solid melts into air: God becomes less a coherent entity than a kind of indescribable omnipresence, an Emersonian oversoul that hears our prayers and “acts in mysterious ways.” He becomes, more and more throughout the years, like a beetle in a box.

Wittgenstein’s beetles

After discussing the Druze—a peculiar religious community based in Beirut where residents insist on lying to outsiders about their beliefs—Dennett goes on, in Breaking the Spell, to quote the following passage at length from Wittgenstein’s Philosophical Investigations:

Suppose everyone had a box with something in it: we call it a “beetle.” No one can look into anyone else’s box, and everyone says he knows what a beetle is only by looking at his beetle.—Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing. —But suppose the word “beetle” had a use in these people’s language?—If so it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty. —No, one can “divide through” by the thing in the box; it cancels out, whatever it is. (§293, as quoted on Dennett 235)

Dennett remarks that

much has been written on Wittgenstein’s beetle box, but I don’t know if anybody has ever proposed an application to religious belief. In any case, it seems fantastic at first that the Druze might be an actual example of the phenomenon.

Indeed, the idea of a religion with beliefs that cannot be observed and that (possibly) change constantly sounds a lot like Wittgenstein’s hypothetical box. But the connection seems just as valid for any other religion, or any other belief at all. Every concept, from God to I to chair, is like a beetle in a box: we all use the same word “chair” and say we know what it means based only on our own personal, internal mental contents (the brain state we’re in when we think of chairs), contents which constantly change.

There is a way in which some concepts seem more like beetles in a box than others, though. My concept of two, for instance, is probably very much like everyone else’s; we all have (roughly) the same beetle in our boxes. Thus our word “two” is not pulling any tricks—it is not, as Wittgenstein puts it, that “the thing in the box has no place in the language-game,” for the internal mental contents referred to by “two” are (presumably) not arbitrary. Of all concepts, in fact, two would probably be one of the least like a beetle in a box.

The word “I,” on the other hand, and its corresponding concept of me or my self, is probably much closer to what Wittgenstein had in mind (and to the Druze’s religion). Each person understands “I” based only on his or her own self, obviously, and every self is (just as obviously) different. But still, “I” has a place in the language-game, because everyone who says it is referring to the same type of object, even if the actual constitution of that object is unique. So it goes for any “relative reference”: that chair, the telephone closest to X, etc. Example: “n is the biggest number I can think of” depends on who says it (and is thus just as relative as “I”), but since whoever says it is doing the same sort of thing (mentally) when he “processes” the phrase, it is not useless in the way that Wittgenstein’s “beetle” is useless.

You’ll notice that as we move from one concept to another, we seem to be playing with or turning two critical “knobs,” which together define what I’ll call “the beetle-box metric”: the concept’s articulability, or the degree to which a person can examine and describe his X, and its sharedness, or the degree to which my X is the same as your X.

It should be no surprise that religions—and in particular, their various conceptions of “God”—also admit to degrees of beetle-in-a-box-resemblance. As it happens, these are often distributed across time, with those most like a beetle in a box appearing latest. Dennett gives a run-through, though he doesn’t realize he’s taking steps up the beetle-box ladder: from rain gods and Greek gods to Yahweh of The Old Testament, through to the original New Testament Lord, “that “genderless Person without a body who nevertheless answers prayers in real time (Stark’s conscious supernatural being),” etc., all the way up to “a Higher Power (Stark’s essence).”

What a beetle-box does to your brain

Imagine that in your religion the idea of God is neither shared nor articulable—imagine, in other words, that your most deeply held convictions are about something that’s isomorphic to Wittgenstein’s beetle in a box. What would that mean?

On its own, probably not much. It would probably be harmless. But consider what happens when such a bizarrely vague God-concept is combined with an imperative toward faith, as it is in some forms of Christianity:

I am the way, the truth, and the life: no man cometh unto the Father but by me. – (John 14: 6)

If your particular brand of Christianity takes this to mean that the only path to eternal bliss is to simply have faith in Christ, then you implicitly have a pretty serious stake in that belief. Dennett warns us what can happen:

Once people start committing themselves (in public, or just in their “hearts”) to particular ideas, a strange dynamic process is brought into being, in which the original commitment gets buried in pearly layers of defensive reaction and meta-reaction.

His point is especially apt when the “particular ideas” to which one is committed are formless and private, like a beetle in a box, because those ideas act like wildcards. That is, ideas that have not been articulated (much) are not yet committed to (m)any facts, and so are compatible with (m)any arbitrary fact(s); moreover, ideas that are private cannot, in principle, undergo the kind of “compatibility checking” with an expert that would elsewise be possible.

The trouble, then, is that it is easy to maintain one’s commitment to these “wildcard” ideas, because there is no inconsistency—logically, cognitively, or publicly—in changing their content if the commitment so demands it. What then happens, as Dennett puts it, is that whatever little actual articulable content comprises the idea gets buried under these changes, or attempts to attack and defend it (his “pearly layers”). This is far less likely when an idea is shared—because an expert’s articulation (the “orthodoxy”) is available—or articulable—because there are more committed-to facts to fix an idea in place.

So someone who claims true belief, but who actually only has a particularly powerful belief in belief, could plausibly not know it, because the truth is buried under all these layers of cognitive infighting.

Through the faith impasse

Where does that leave us?

Well, now we have a (provisional) theory for what leads people to declare their unequivocal faith in a concept they can’t describe. The two critical components are (1) a commitment to belief itself and (2) a sufficiently “slippery” halo of religious concepts to be the object of that belief.

And although it’s a long shot, I’m hoping that we can parlay this theory into a successful attack. The idea is that if we can explicitly articulate the psychological mechanisms at work in a person’s most intimate pernicious religious beliefs, maybe we can help to dismantle them—to at last purge that nasty beetle from its box.