Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (86 page)

We wish now to venture momentarily into yet murkier waters, offering the event
xyz ⇒ dyz
as a potential analogue to our standard old tale
abc ⇒ abd.
What’s going on here? To come up with this analogy, a person would have to exhibit a highly implausible kind of confusion, which we will call “dizziness”. First they would discover the subtle idea of mapping of the
a
onto the
z
, and then they would notice the spatial reversal that this implies, involving the conceptual slippage
right ⇒ left
, which leads to the subtle idea of modifying the
x
instead of the
z
— but then, for some reason, they would drop the ball. Totally forgetting all the subtleties they had just noticed, they would blithely interpret the event
abc ⇒ abd
as nothing more than a replacement of a certain letter by the random letter
d
, without any deeper rhyme or reason, and would
mindlessly apply this recipe to the
x.
This is a bizarre twist, because genuine initial insights are followed up by an act that totally betrays the spirit of finesse of what was done only moments before. If one can use the phrase “in bad taste” in such an austere domain, this would certainly seem an appropriate time to do so.

In a word, this analogy is
dizzy
, in the sense that the hypothetical person who made it seems truly confused, exhibiting an incoherent mixture of smartness and stupidity, of insight and myopia, of brilliance and dullness. First there is a moment of genuine insight (mapping
a
onto
z)
and then, further into the process, the same high level of insight continues (mapping
c
onto
x
), and yet, at the very last moment (“What kind of insight is called for now, to modify the
x?”
), comes an act of myopic, local literality — seeing simply the raw letters
c, d
, and
x
, instead of the roles they play inside their worlds.

Such a dizzy hodgepodge, where high insightfulness is found happily coexisting with mind-boggling literal-mindedness, is implausible, to put it mildly. We have never run into anyone who in all seriousness proposed the answer
dyz.
And yet anyone who carefully explores the subtle angles of this particular analogy problem in the Copycat domain will sooner or later bump into this answer, whatever they may think of it in the end; and if this answer is explained to people, they invariably understand its “logic”, even if they find it strange or uncomfortable. We may not
like
this answer, but we can still understand its strange logic, and when we do so, we can even find it humorous.

In this sense, the
dyz
answer to the
xyz
problem is analogous to a joke that circulated in the 1980’s about Nancy Reagan, then the First Lady. It was stated that, upon hearing that there was a glut of butter, she perkily declared, “Oh, before it goes bad, we should distribute all the extra butter to the poor people of our country, so that they have something to dip their lobster tails in.” The First Lady in the world of the joke understood poverty in a ridiculously implausible manner: while realizing perfectly clearly that poor people have no butter, she totally failed to realize that they
also
don’t have lobster tails a-plenty. This joke is reminiscent of the infamous remark by Marie Antoinette, also about poor people, but in the streets of Paris: “Oh, have they no bread? Poor dears! Then let them eat cake!” This is what we mean by “dizziness”.

During the heyday of the First Lady joke, a similar joke about the United States and the Soviet Union was making the rounds. An American, bragging to a Russian about our land’s great freedom of speech, proudly proclaimed, “We in America are so free that we can march up and down in front of the White House and shout, ‘Down with Reagan!’ ” Unimpressed, the Russian replied, “That’s no big deal. We in Russia can do exactly the same — we too can march up and down in front of the Kremlin and shout, ‘Down with Reagan!’ ” The analogy is almost complete, but the ball is fumbled on the one-yard line (much as in
xyz
⇒
dyz
).

We are approaching the rich and important topic of
frame blends.
Rather than defining that term in an abstract fashion, we will do so through a series of very concrete examples in the Copycat microworld, since the phenomenon emerges with great clarity
there. Once again we trot out our same old story of
abc
changing into abd, and this time (exactly as before) we ask, “Of what event in its past was
iijjkk
reminded?” Here is a set of possible answers:

We’ve listed these answers in an order that echoes the amount of frame-blending involved, starting with a lot and finishing with none. Take the third answer, for instance, where the third letter —
j
— was replaced by a
d.
This answer seems very maladroit, for the concept
d
feels like an intruder in the
iijjkk
world; that is, it belongs to the
abc
world, near the beginning of the alphabet. The presence of a
d
in the midst of the letters
i, j
, and
k
(which constitute their own little world, far away in the alphabet from the
abc
world) seems muddle-headed. But that’s not all; the concept
third letter
also seems like an intruder. Borrowed literally from the
abc
world, it has been bluntly thrust into the
iijjkk
world with no regard at all for the fact that
iijjkk
is twice as long as
abc
is, so that the richly pregnant meaning of
third letter
in the
abc
world is utterly lost when the concept is exported in such a literal fashion to the other world. Thus the third answer is the result of a great deal of blending, and esthetically speaking, it suffers for it.

Each of the other answers shown, except for the last one, involves some type of frame-blending, in the sense that some concept belonging to the
abc
world has been borrowed and thrust into the
iijjkk
world, contaminating it. Even the second answer,
iijjkk
, which on its surface exhibits no contamination from the
abc
world, is in fact infected, because the
logic
behind it (“replace the letter
c
by a
d”)
is based on the concepts
c
and
d
, which are both alien to the
iijjkk
world.

On the other hand, the last answer,
iijjll
, doesn’t borrow any concept from the
abc
world that doesn’t belong just as much to the
iijjkk
world. In that sense, the final line constitutes a “purer” form of analogy than all the lines above it do. All the other lines feature some degree of frame-blending, sometimes very blatant and sometimes less so. And there are plenty of other possible frame-blended answers, such as
iijjkk ⇒ aabbdd
or even
iijjkk ⇒ aabbll
.

Finally, it’s amusing to observe that all the answers in our list, except for the first one, are covered by the single frame-blending recipe “Replace the
c
of
iijjkk
by its successor”. Of course this formula is highly ambiguous and subjective, since inside
iijjkk
there is no more an instance of c than there is a Golden Gate Bridge in Indiana, and yet that wouldn’t in the least keep one from speaking of “the Golden Gate of Indiana”, which is actually a much less wacky idea than our old friends from
Chapter 4
, “the Meryl Streep of spitting” and “the Mussolini of mulligatawny”.

We don’t wish to portray frame-blending as being intrinsically feeble-minded or confused. Some frame blends, in fact, are carefully designed to exhibit creativity and humor. The
xyz ⇒ dyz
story is a fine example of this. In it, the letter
d
was quite intentionally stuffed into a world where it has no business at all, like a bull that has been led into a china shop. This move, deliberately gauche, induces a feeling of complete nonsensicality, and thus of humorousness. One needs quite a sense of fantasy to come up with as off-the-wall an answer as this.

But a frame blend can also be made inadvertently, simply by overlooking something, in which case it is more like a makeshift solution to a real-world dilemma: acceptable but not optimal. Indeed, many people come up with the fairly flat answer
xyd
rather than
wyz
for exactly this reason — they don’t examine the strings deeply enough to let the subtle
a–z
connection, followed by its rapid chain reaction of conceptual reversals, jump out at them.

A frame blend can also be made when one simply doesn’t possess the knowledge required to see certain aspects of a situation, and so one necessarily leaves them out. If, for example, someone knew the alphabet but didn’t know how to count, then the answer
mrrjjj ⇒ mrrjjjj
would simply be unavailable to them. On the other hand, with the set of concepts they possess, they could easily come up with
mrrjjj ⇒ mrrkkk.
To some observers, this answer may seem filled with insight and elegance, while to others it may look like the most glaring of frame blends (what is the concept of
alphabetic successor
doing in a world whose essence is not alphabetic but numerical?).

Or suppose that someone with a strangely defective kind of vision were looking at the string
iijjkk
, and could just barely make out that it contained six letters but had no idea that any of them were repeated. They might say, “Change the rightmost letter to its successor!”, thus defining the event
iijjkk ⇒ iijjkl.
To us this looks awkward, but if we take into account the lack of information that gave rise to it, we can understand the oversight. They performed as well as possible, given that their information was partial and incomplete. This is an echo of the earlier idea that people make the deepest analogies that they can, as constrained by their conceptual repertoires.

Although these examples may seem artificial, scientific analogies are often made in just this way — as brave leaps way out into the thickest of fogs. Decades or centuries later, some of those leaps may look silly, because, having been based on precedents well known at their time, they incorporated various naïve assumptions that in the end turned out to be utterly inappropriate to the new situation — but such
ex post facto
judgments of naïveté are a luxury. They are the wisdom that one acquires when one is blessed with, as the phrase goes, “20–20 hindsight”.

To be concrete, let’s recall the way that, in the seventeenth century, light waves were hypothesized to be very similar to sound waves: they were presumed to be longitudinal compression waves carried by some all-pervasive elastic substance very much like air but even more pervasive and even more tenuous than air. (A sufficiently bold spirit might even dare to describe that elusive substance as “ethereal”!) This conceptual leap was an audacious one and contained far more than a grain of truth, as was revealed centuries later, but in those early days, people’s perception of the nature of light was contaminated by incorrect analogical importations from the world of sound — in other words, by a frame blend in which concepts that were to some degree inappropriate were imported from the
sound
side of the bridge.

To be specific, both the idea that light had to be a longitudinal compression wave and the idea that it would need an elastic medium to propagate it were practically perfect carbon copies of what was known to be the case for sound — but in the case of light, both presumptions were eventually discovered to be wrong. Nonetheless, these guesses about light, even if they were later realized to have been slightly off, constituted a great and bold leap in the dark, affording humanity its first inklings of light’s true nature. It would be unjustified to criticize such boldness simply because
some
of it eventually turned out to be wrong. Why would anyone have postulated a
transverse
wave propagating through
vacuum
when such a thing was unheard of, and indeed, virtually inconceivable to people at that time? To criticize the natural even if somewhat cautious leap (as seen from today’s viewpoint) that
was
made would be nonsensical. After all, even the greatest thinkers of the 1600s couldn’t possibly have leapt so far ahead as to anticipate Maxwell’s equations and Einstein’s theory of special relativity, which are indispensable ingredients in today’s understanding of light as a wave.