I Am a Strange Loop (33 page)

It is all too easy to forget that moths, flies, dogs, cats, neonates, television cameras, and other small-souled beings do not perceive a television screen as we do. Although it’s hard for us to imagine, they see the pixels in a raw, uninterpreted fashion, and thus to them a TV screen is as drained of long-ago-and-far-away meanings as is, to you or me, a pile of fall leaves, a Jackson Pollock painting, or a newspaper article in Malagasy (my apologies to you if you speak Malagasy; in that case, please replace it by Icelandic — and don’t tell me that you speak that language, too!). “Reading” a TV screen at the representational level is intellectually far beyond such creatures, even if for most humans it is essentially second nature already by age two or so.

A dog gazing vacantly at a television screen, unable to make out any imagery, unaware even that any imagery is intended, is thus not unlike Lord Russell staring blankly at a formula of his beloved system
PM
and seeing only its “easy” (arithmetical) meaning, while the other meaning, the mapping-mediated meaning due to Gödel, lies intellectually beyond him, utterly inaccessible, utterly undreamt-of. Or perhaps you think this comparison is unfair to Sir Bertrand, and in a way I agree, so let me try to make it a little more realistic and more generous.

Instead of a dog that, when placed in front of a TV screen, sees only pixels rather than people, imagine little three-year-old Chantal Duplessix, who is watching
La Femme du boulanger
with her parents. All three are native speakers of French, so there’s no language barrier. Just like her
maman
and
papa,
Chantal sees right through the pixels to the events in the village, and when that wonderful final scene arrives and Aimable rakes the cat over the coals, Chantal laughs and laughs at Aimable’s fury — but she doesn’t suspect for a moment that there is
another
reading of his words. She’s too young to get the analogy between Aurélie and Pomponnette, and so for her there is only one meaning there. Filmmaker Pagnol’s analogy-mediated meaning, which takes for granted the “simple” (although dog-eluding) mapping of pixels to remote events and thus piggybacks on it, is effortlessly perceived by her parents, but for the time being, it lies intellectually beyond Chantal, and is utterly inaccessible to her. In a few years, of course, things will be different — Chantal will have learned how to pick up on analogies between all sorts of complex situations — but that’s how things are now.

With this situation, we can make a more realistic and more generous comparison to Bertrand Russell (yet another analogy!). Chantal, unlike a dog, does not merely see meaningless patterns of light on the screen; she effortlessly sees people and events — the “easy” meaning of the patterns. But there is a second level of meaning that takes the people and events for granted, a meaning transmitted by an analogy between events, and it’s that
higher
level of meaning that eludes Chantal. In much the same way, Gödel’s higher level of meaning, mediated by his mapping, his marvelous analogy, eluded Bertrand Russell. From what I have read about Russell, he never saw the second level of meaning of formulas of
PM.
In a certain sad sense, the good Lord never learned to read his own holy books.

Pickets at the Posh Shop

As I suggested above, your recently returned roving sweetheart might well hear an extra level of meaning while listening to Aimable chastise Pomponnette. Thus a play or film can carry levels of meaning that the author never dreamt of. Let’s consider, for example, the little-known 1931 play
The Posh Shop Picketeers,
written by social activist playwright Rosalyn Wadhead (ever hear of her?). This play is about a wildcat strike called by the workers at Alf and Bertie’s Posh Shop (I admit, I never did figure out what they sold there). In this play, there is a scene where shoppers approaching the store’s entrance are exhorted not to cross the picket line and not to buy anything in the store (“Alf and Bertie are filthy dirty! Please don’t cross our Posh Shop pickets! Please cross over to the mom-and-pop shop!”). In the skilled hands of our playwright, this simple situation led to a drama of great tension. But for some reason, just before the play was to open, the ushers in the theater and the actors in the play got embroiled in a bitter dispute, as a result of which the ushers’ union staged a wildcat strike on opening night, put up picket lines, and beseeched potential playgoers not to cross their lines to see
The Posh Shop Picketeers
.

Obviously, given this unanticipated political context, the lines uttered by the actors inside the play assumed a powerful second meaning for viewers in the audience, an extra level of meaning that Rosalyn Wadhead never intended. In fact, the picketing Posh Shop worker named “Cagey”, who disgustedly proclaims, after a brash matron pushes her aside and arrogantly strides into Alf and Bertie’s upscale showroom, “Anyone who crosses the picket line in front of Alf and Bertie’s Posh Shop is scum”, was inevitably heard by everyone in the audience (which by definition consisted solely of people who had crossed the picket line outside the theater) as saying, “Anyone who crossed the picket line in front of this theater is scum”, and of course this amounted to saying, “Anyone who is now sitting in this audience is scum”, which could also be heard as “You should not be listening to these lines”, which was the diametric opposite of what all the actors, including the one playing the part of Cagey, wanted to tell their audience, whose entry into the theater they so much appreciated, given the ushers’ hostile picket line.

But what could the actors do about the fact that they were unmistakably calling their deeply appreciated audience “scum” and insinuating that no one should even have been there to hear these lines? Nothing. They
had
to recite the play’s lines, and the analogy was there, it was blatant and strong, and therefore the ironic, twisting-back, self-referential meaning of Cagey’s line, as well as of many others in the play, was unavoidable. Admittedly, the self-reference was
indirect
— mediated by an analogy — but that did not make it any less real or strong than would “direct” reference. Indeed, what we might be tempted to call “direct” reference is mediated by a code, too — the code between words and things given to us by our native language (Malagasy, Icelandic, etc.). It’s just that
that
code is a simpler one (or at least a more familiar one). In sum, the seemingly sharp distinction between “direct” reference and “indirect” reference is only a matter of degree, not a black-and-white distinction. To repeat, analogy has force in proportion to its precision and visibility.

Prince Hyppia: Math Dramatica

Well, so much for Rosalyn Wadhead and the surprise double-edgedness of the lines in
The Posh Shop Picketeers,
admittedly a rather obscure work. Let’s move on to something completely different. We’ll talk instead about the world-famous play
Prince Hyppia: Math Dramatica,
penned in the years 1910–1913 by the celebrated British playwright Y. Ted Enrustle (surely you’ve heard of
him
!). Fed up with all the too-clevah-by-hahf playsabout-plays that were all the rage in those days, he set out to write a play that would have nothing whatsoever to do with playwriting or acting or the stage. And thus, in this renowned piece, as you doubtless recall, all the characters are strictly limited to speaking about various properties, from very simple to quite arcane, of whole numbers. How could anyone possibly get any further from writing a play about a play? For example, early on in Act I, the beautiful Princess Bloppia famously exclaims, “7 times 11 times 13 equals 1001!”, to which the handsome Prince Hyppia excitedly retorts, “Wherefore the number 1001 is composite and not prime!” Theirs would seem to be a math made in heaven. (You may now groan.)

But it’s in Act III that things really heat up. The climax comes when Princess Bloppia mentions an arithmetical fact about a certain very large integer
g,
and Prince Hyppia replies, “Wherefore the number
g
is saucy and not prim!” (It’s a rare audience that fails to gasp in unison when they hear Hyppia’s most math-dramatical outburst.) The curious thing is that the proud Prince seems to have no idea of the import of what he is saying, and even more ironically, apparently the playwright, Y. Ted Enrustle, didn’t either. However, as everyone today knows, this remark of Prince Hyppia asserts — via the intermediary link of a tight analogy — that a certain long line of typographical symbols is “unpennable” using a standard set of conventions of dramaturgy that held, way back in those bygone days. And the funny thing is that the allegedly unpennable line is none other than the proclamation that the actor playing Prince Hyppia has just pronounced!

As you can well imagine, although Y. Ted Enrustle was constantly penning long lines of symbols that adhered to popular dramaturgical conventions (after all, that was his livelihood!), he’d never dreamt of a connection between the natural numbers (whose peculiar properties his curious characters accurately articulated) and the humble lines of symbols that he penned for his actors to read and memorize. Nonetheless, when, nearly two decades later, this droll coincidence was revealed to the playgoing public in a wickedly witty review entitled “On Formerly Unpennable Proclamations in
Prince Hyppia: Math Dramatica
and Related Stageplays (I)”, authored by the acerbic young Turko-Viennese drama critic Gerd Külot (I’ll skip the details here, as the story is so well known), its piercing cogency was immediately appreciated by many, and as a result, playgoers who had read Külot’s irreverent review became able to rehear many of the famous lines uttered in
Prince Hyppia: Math Dramatica
as if they were not about numbers at all, despite what Y. Ted Enrustle had intended, but were direct (and often quite biting) comments about Y. Ted Enrustle’s play itself!

And thus it wasn’t long before savvy audiences were reinterpreting the droll remarks by the oddball numerologist Qéé Dzhii (a character in
Prince Hyppia: Math Dramatica
who had gained notoriety for her nearly nonstop jabbering about why she preferred saucy numbers to prim numbers) as revealing, via allusions that now seemed hilariously obvious, why she preferred dramatic lines that were unpennable (using the dramaturgical conventions of the day) to lines that were pennable. Drama lovers considered this new way of understanding the play too delicious for words, for it revealed
Prince Hyppia
to be a play-about-a-play (with a vengeance!), although most of the credit for this insight was given to the brash young foreign critic rather than to the venerable elder playwright.

Y. Ted Enrustle, poor fellow, was simply gobsmacked — there’s no other word for it. How could anyone in their right mind take Qéé Dzhii’s lines in this preposterous fashion? They were only about
numbers
! After all, to write a drama that was about numbers and
only
about numbers had been his sole ambition, and he had slaved away for years to accomplish that noble goal!

Y. Ted Enrustle lashed out vehemently in print, maintaining that his play was decidedly
not
about a play, let alone about itself! Indeed, he went so far as to insist that Gerd Külot’s review could not conceivably be about
Prince Hyppia: Math Dramatica
but had to be about
another
play, possibly a
related
play, perhaps an
analogous
play, perchance even a perfectly
parallel
play, peradventure a play with a similar-sounding title penned by a pair of paranoiac paradoxophobes, but in any case it was not about
his
play.

And yet, protest though he might, there was nothing at all that Y. Ted Enrustle could do about how audiences were now interpreting his beloved play’s lines, because the two notions — the sauciness of certain integers and the unpennability of certain lines of theatrical dialogue — were now seen by enlightened playgoers as precisely isomorphic phenomena (every bit as isomorphic as the parallel escapades of Aurélie and Pomponnette). The subtle mapping discovered by the impish Külot and gleefully revealed in his review made both meanings apply equally well (at least to anyone who had read and understood the review). The height of the irony was that, in the case of a few choice arithmetical remarks such as Prince Hyppia’s famous outburst, it was
easier
and
more natural
to hear them as referring to unpennable lines in plays than to hear them as referring to non-prim numbers! But Y. Ted Enrustle, despite reading Külot’s review many times, apparently never quite caught on to what it was really saying.

Analogy, Once Again, Does its Cagey Thing

Okay, okay, enough’s enough. The jig’s up! Let me confess. For the last several pages, I’ve been playing a game, talking about strangely named plays by strangely named playwrights as well as a strangely titled review by a strangely named reviewer, but the truth is (and you knew it all along, dear reader), I’ve
really
been talking about something totally different — to wit, the strange loop that Austrian logician Kurt Gödel (Gerd Külot) discovered and revealed inside Russell and Whitehead’s
Principia Mathematica.

“Now, now,” I hear some voice protesting (but of course it’s not
your
voice), “how on earth could you have
really
been talking about Whitehead and Russell and
Principia Mathematica
if the lines you wrote were not about them but about Y. Ted Enrustle and
Prince Hyppia: Math Dramatica
and such things?” Well, once again, it’s all thanks to the power of analogy; it’s the same game as in a
roman à clef,
where a novelist speaks, not so secretly, about people in real life by ostensibly speaking solely about fictional characters, but where savvy readers know precisely who stands for whom, thanks to analogies so compelling and so glaring that, taken in their cultural context, they cannot be missed by anyone sufficiently sophisticated.