Gödel, Escher, Bach: An Eternal Golden Braid (116 page)

Sloth: Bah! You might as well transport this game to the Moon.

Crab: No sooner said than done! Just a twiddle here, a twiddle there ...

(On the screen there appears a desolate crater-pitted field, with two teams in space
suits facing each other, immobile. All at once, the two teams fly into motion, and the
players are making great bounds into the air, sometimes over the heads of other
players. The ball is thrown into the air, and sails so high that it almost disappears,
and then slowly comes floating down into the arms of one space-suited player, roughly
a quarter-mile from where it was released.)

Announcer: And there, friends, you have the subjunctive instant replay as it would have happened on the Moon. We'll be right back after this important commercial message from the friendly folks who brew Glumpf Beer-my favorite kind of beer!

Sloth: If I weren't so lazy, I would take that broken TV back to the dealer myself! But alas, it's my fate to be a lazy Sloth ... (
Helps himself to a large gob of French fries
.) Tortoise: That's a marvelous invention, Mr. Crab. May I suggest a hypothetical?

Crab: Of course!

Tortoise: What would that last play have looked like if space were four-dimensional?

Crab: Oh, that's a complicated one, Mr. T, but I believe I can code it into the dials. Just a moment.

(He steps up, and, for the first time, appears to be using the full power of the control
panel of his Subjunc-TV, turning almost every knob two or three times, and carefully
checking various meters. Then he steps back with a satisfied expression on his face.)
I think this should do it.

Announcer: And now let's watch the subjunctive instant replay.

(A confusing array of twisted pipes appears on the screen. It grows larger, then
smaller, and for a moment seems to do something akin to rotation. Then it turns into a
strange mushroom-shaped object, and back to a bunch of pipes. As it metamorphoses
from this into other bizarre shapes, the announcer gives his commentary.)
Tedzilliger's fading back to pass. He spots Palindromi ten yards outfield, and passes it to the right and outwards-it looks good! Palindromi's at the 35-yard plane, the 40, and he's tackled on his own

43-yard plane. And there you nave it, 3-L tans, as it would have looked if football were played in four spatial dimensions.

Achilles: What is it you are doing, Mr. Crab, when you twirl these various dials on the control panel?

Crab: I am selecting the proper subjunctive channel. You see, there are all sorts of subjunctive channels broadcasting simultaneously, and I want to tune in precisely that one which represents the kind of hypothetical which has been suggested.

Achilles: Can you do this on any TV?

Crab: No, most TV's can't receive subjunctive channels. They require a special kind of circuit which is quite difficult to make.

Sloth: How do you know which channel is broadcasting what? Do you look it up in the newspaper?

Crab: I don't need to know the channel's call letters. Instead, I tune it in by coding, in these dials, the hypothetical situation which I want to be represented. Technically, this is called "addressing a channel by its counterfactual parameters". There are always a large number of channels broadcasting every conceivable world. All the channels which carry worlds that are "near" to each other have call letters that are near to each other, too.

Tortoise: Why did you not have to turn the dials at all, the first time we saw a subjunctive instant replay?

Crab: Oh, that was because I was tuned in to a channel which is very near to the Reality Channel, but ever so slightly off. So every once in a while, it deviates from reality. It's nearly impossible to tune EXACTLY into the Reality Channel. But that's all right, because it's so dull. All their instant replays are straight! Can you imagine? What a bore!

Sloth: I find the whole idea of Subjunc-TV's one giant bore. But perhaps I could change my mind, if I had some evidence that your machine here could handle an INTERESTING counterfactual. For example, how would that last play have looked if addition were not commutative?

Crab: Oh me, oh my! That change is a little too radical, I'm afraid, for this model. I unfortunately don't have a Superjunc-TV, which is the top of the line. Superjunc-TV's can handle ANYTHING you throw at them.

Sloth: Bah!

Crab: But look-I can do ALMOST as well. Wouldn't you like to see how the last play would have happened if 13 were not a prime number? Sloth: No thanks! THAT

doesn't make any sense! Anyway, if I were the last play, I'd be getting pretty tired of being trotted out time and again in new garb for the likes of you fuzzy-headed concept-slippers. Let's get on with the game!

Achilles: Where did you get this Subjunc-TV, Mr. Crab?

Crab: Believe it or not, Mr. Sloth and I went to a country fair the other evening, and it was offered as the first prize in a lottery. Normally I don't indulge in such frivolity, but some crazy impulse grabbed me, and I bought one ticket.

Achilles: What about you Mr. Sloth?

Sloth: I admit, I bought one, just to humor old Crab.

Crab: And when the winning number was announced, I found, to my amazement, that I'd won the lottery!

Achilles: Fantastic! I've never known anyone who won anything in a lottery before!

Crab: I was flabbergasted at my good fortune.

Sloth: Don't you have something else to tell us about that lottery, Crab?

Crab: Oh, nothing much. It's just that my ticket number was 129. Now when they announced the winning number, it was 128 just one off. Sloth: So you see, he actually didn't win it at all. Achilles: He ALMOST won, though ...

Crab: I prefer to say that I won it, you see. For I came so terribly close . . If my number had been only one smaller, I would have won. Sloth: But unfortunately, Crab, a miss is as good as a mile.

Tortoise: Or as bad. What about you, Mr. Sloth? What was your number: Sloth: Mine was 256-the next power of 2 above 128. Surely, that counts as a hit, if anything does! I can't understand why, however, those fair officials-those UNfair officials-were so thickheaded about it. They refused to award me my fully deserved prize. Some other joker claimed HE deserved it, because his number was 128. 1 think my number was far closer than His, but you can't fight City Hall.

Achilles: I'm all confused. If you didn't win the Subjunc-TV after all, Mr. Crab, then how can we have been sitting here all afternoon watching it? It seems as if we ourselves have been living in some sort of hypothetical world that would have been, had circumstances just been ever so slightly different ...

Announcer: And that, folks, was how the afternoon at Mr. Crab's would have been spent, had he won the Subjunc-TV. But since he didn't, the four friends simply spent a pleasant afternoon watching Home Team get creamed, 128-0. Or was it 256-0? Oh well, it hardly matters, in five-dimensional Plutonian steam hockey.

Prospects

"Almost" Situations and Subjunctives

AFTER READING
Contrafactus
, a friend said to me, "My uncle was almost President of the U.S.!" "Really?" I said. "Sure," he replied, "he was skipper of the PT 108." (John F.

Kennedy was skipper of the PT 109.)

That is what
Contrafactus
is all about. In everyday thought, we are constantly manufacturing mental variants on situations we face, ideas we have, or events that happen, and we let some features stay exactly the same while others "slip". What features do we let slip? What ones do we not even consider letting slip? What events are perceived on some deep intuitive level as being close relatives of ones which really happened? What do we think "almost" happened or "could have" happened, even though it unambiguously did not? What alternative versions of events pop without any conscious thought into our minds when we hear a story? Why do some counterfactuals strike us as

"less counterfactual" than other counterfactuals? After all, it is obvious that anything that didn't happen didn't happen. There aren't degrees of "didn't-happen-ness". And the same goes for "almost" situations. There are times when one plaintively says, "It almost happened", and other times when one says the same thing, full of relief. But the "almost"

lies in the mind, not in the external facts.

Driving down a country road, you run into a swarm of bees. You don't just duly take note of it; the whole situation is immediately placed in perspective by a swarm of

"replays" that crowd into your mind. Typically, you think, "Sure am lucky my window wasn't open!"-or worse, the reverse: "Too bad my window wasn't closed!" "Lucky I wasn't on my bike!" "Too bad I didn't come along five seconds earlier." Strange but-possible replays: "If that had been a deer, I could have been killed!" "I bet those bees would have rather had a collision with a rosebush." Even stranger replays: "Too bad those bees weren't dollar bills!" "Lucky those bees weren't made of cement!" "Too bad it wasn't just one bee instead of a swarm." "Lucky I wasn't the swarm instead of being me."

What slips naturally and what doesn't-and why?

In a recent issue of
The New Yorker
magazine, the following excerpt from the

"Philadelphia Welcomat" was reprinted:'

If Leonardo da Vinci had been born a female the ceiling of the Sistine Chapel might never have been painted.1

The
New The New Yorker
commented:

And if Michelangelo had been Siamese twins, the work would have been completed in half the time.

The point of
The New Yorker's
comment is not that such counterfactuals are false; it is more that anyone who would entertain such an idea-anyone who would "slip" the sex or number of a given human being-would have to be a little loony. Ironically, though, in the same issue, the following sentence, concluding a book review, was printed without blushing:

I think he [Professor Philipp Frank would have enjoyed both of these books enormously.2

Now poor Professor Frank is dead; and clearly it is nonsense to suggest that someone could read books written after his death. So why wasn't this serious sentence also scoffed at? Somehow, in some difficult-to-pin-down sense, the parameters slipped in this sentence do not violate our sense of "possibility" as much as in the earlier examples.

Something allows us to imagine "all other things being equal" better in this one than in the others. But why? What is it about the way we classify events and people that makes us know deep down what is "sensible" to slip, and what is "silly": Consider how natural it feels to slip from the valueless declarative "I don't know Russian" to the more charged conditional "I would like to know Russian" to the emotional subjunctive "I wish I knew Russian" and finally to the rich counterfactual "If I knew Russian, I would read Chekhov and Lermontov in the original". How flat and dead would be a mind that saw nothing in a negation but an opaque barrier! A live mind can see a window onto a world of possibilities.

I believe that "almost" situations and unconsciously manufactured subjunctives represent some of the richest potential sources of insight into how human beings organize and categorize their perceptions of the world.

An eloquent co-proponent of this view is the linguist and translator George Steiner, who, in his book
After Babel
, has written:

Hypotheticals, 'imaginaries', conditionals, the syntax of counter-factuality and contingency may well be the generative centres of human speech.... [They] do more than occasion philosophical and grammatical perplexity. No less than future tenses to which they are, one feels, related, and with which they ought probably to be classed in the larger set of 'suppositionals' or àlternates', these ìf' propositions are fundamental to the dynamics of human feeling... .

Ours is the ability, the need, to gainsay or 'un-say' the world, to image and speak it otherwise.... We need a word which will designate the power, the compulsion of language to posit 'otherness'. . . . Perhaps 'alternity' will do: to define the òther than the case', the counter-factual propositions, images, shapes of will and evasion with which we charge our mental being and by means of which we build the changing, largely fictive milieu of our somatic and our social existence... .

Finally, Steiner sings a counterfactual hymn to counterfactuality: It is unlikely that man, as we know him, would have survived without the fictive, counter-factual, anti-determinist means of language, without the semantic capacity, generated and stored in thèsuperfluous, zones of the cortex, to conceive of, to articulate possibilities beyond the treadmill of organic decay and death .3

The manufacture of "subjunctive worlds" happens so casually, -so naturally, that we hardly notice what we are doing. We select from our fantasy a world which is close, in some internal mental sense, to the real world. We compare what is real with what we perceive as almost real. In so doing, what we gain is some intangible kind of perspective on reality. The Sloth is a droll example of a variation on reality-a thinking being without the ability to slip into subjunctives (or at least, who claims to be without the ability-but you may have noticed that what he says is full of counterfactuals'.). Think how immeasurably poorer our mental lives would be if we didn't have this creative capacity for slipping out of the midst of reality into soft "what if'-s! And from the point of view of studying human thought processes, this slippage is very interesting, for most of the time it happens completely without conscious direction, which means that observation of what kinds of things slip, versus what kinds don't, affords a good window on the unconscious mind.