Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (75 page)

The presumed
diversity of members of the category
is another factor: that is, the more diverse one believes the category to be, the more cautious one will be in accepting the analogical extrapolation. Thus, if the first few people one sees in a certain town are all greatly overweight, one is less likely to jump to the conclusion that everyone who lives there is obese than if one knows that one is dealing with a trait that is generally very uniform among samples, such as electrical conductivity. If the first few samples one tests of a new material all conduct electricity well, then one is very likely to conclude that anything made of that material will conduct electricity well.

The greater the
diversity of observed cases
is, the greater will be one’s confidence in an analogical extrapolation to the whole population. Thus, the more different dishes one has ordered in a restaurant, the more justified one will feel in making a claim about the overall quality of that restaurant’s food, whereas if one has always limited one’s orders to just the vegetarian dishes, no matter how many there are and no matter how many times one has ordered each one, one will be less likely to jump to a broad conclusion about the restaurant’s overall quality.

Another factor that is likely to influence one’s tendency to believe in one’s analogical extrapolation to a large population is the degree to which one thinks one has observed
typical members of the category.
In other words, one is more likely to generalize outwards from a case that one takes to be a prototypical member of the category than from a case that one takes to be peripheral. Thus, in estimating the quality of a restaurant, one is going to place more trust in one’s judgment of its baked salmon than in one’s judgment of its olive bread or of its mocha latte.

A modest metaphor that we call “bagels from the same batch” will help us to unify the preceding considerations. All of the bagels that are cooked in a single batch are presumably interchangeable in most ways, in the sense that they should all be equally salty, equally tasty, equally warm, equally soft, etc. The general question of whether one can extrapolate from a given situation to a different situation then becomes the question of how much these situations belong, so to speak, to “the same batch”. Do all the French fries on one’s plate count as “bagels from the same batch”? In all likelihood, yes. And what about all the various translators who are hired by a given magazine? When it comes to their competence in translation, can they all be seen as “bagels from the same batch”? And what about all the public-relations writers hired by different universities — are they all “bagels from the same batch”? When things are cast in this light, we see the key question “Is it analogy-making or is it categorization?” coming back and grabbing center stage, because how one answers the analogical question “Are these two items essentially bagels from a single batch?” will depend on the degree to which one perceives the items as belonging to a single category.

Sometimes the answer is so obvious that one would cringe at someone even posing the question explicitly. For example, all the copies of a novel printed at the same time
by the same printing plant are clearly bagels from the same batch, and it makes no sense to imagine someone wondering whether
one
of those copies of the novel would be a good read if they have already read and enjoyed
another
of those copies. On the other hand, recognizing
sour grapes
situations as such amounts to seeing bagels from the same batch, but on the basis of traits that are far less immediately obvious — and when a scientist makes a great discovery by jumping by analogy from one phenomenon to another within a single domain or even across domains, it’s because that scientist saw bagels from the same batch where all of their colleagues merely saw a pile of highly diverse breakfast edibles. A different way of asking the question “Do these situations share a single essence?” is thus to ask oneself, “Are these essentially bagels from a single batch?” The analogies that invade our minds and channel our thoughts, most often doing so unbeknownst to us, and sometimes doing so helpfully and sometimes misleadingly, are those that strike us intuitively as being bridges built between bagels belonging to a single batch.

Analogy can play an even more coercive role. Sometimes analogies not only arise naturally out of situations, as we’ve just seen, but they can then shut out all other viewpoints. In such cases, we are dealing with, so to speak, “the tyranny of analogies”.

This intergenerational analogy has great power, because the fact that it would instantly spring to everyone’s mind totally blocked K. from doing something that her father would have loved to do and that she herself thought would be a beautiful gesture. And yet there is no causal power linking one trip to the other. There is no reason for a sane person to believe that taking one’s father on a trip to see huge redwood trees will bring about the latter’s death in short order. “The Curse of the Avenue of the Giants” might be a good title for a murder mystery, but it should nonetheless not have inspired great fear in K.’s father or in any other member of the family.

Though not grounded in logic, this analogy constitutes a greater pressure than could emerge from any kind of formal deductive reasoning. Everyone knows that if
A implies B
and
B implies C
, then
A implies C
, and yet such reasoning patterns don’t exert great psychological force on us. We know that there are often hidden traps in what appear to be valid modes of reasoning. The way that the redwood-tree analogy, which has no logical power, takes over our minds willy-nilly forms a stark contrast with the way that we react to formal reasoning.

If one day we were to read that the proof of some famous theorem — say that of Fermat’s Last Theorem, discovered toward the end of the twentieth century — had been shown to have flaws in it, we would not keep on believing in its validity. We have all heard arguments that sound logical and rational but that lead to conclusions that are blatantly false, and so we have learned that sometimes it pays to be prudent when faced with scientific-sounding reasoning, even when it sounds ironclad. In contrast, in the case of K.’s analogy, we are overwhelmed by the stark power of the resemblance; it is so strong that the conclusion is irresistible. In short, it is easier to be suspicious of a logical argument than of an argument by analogy.

The analogy between the two trips to the redwoods, though it lacks any basis in logic, and though its conclusion may well be totally false, is so blatant that it cannot be shrugged off. Without in the least believing in any kind of “paranormal analogical force” that will kill her father, K. feels completely trapped, because she, like any other human being, is incapable of suppressing the heavy pall that the analogy would cast over such a trip. Even if K. and her whole family had a long talk about it, and everyone, including her father, were in total agreement that it was just an analogy with no meaning, there would still remain in everyone’s mind the salient vision of the sword of Damocles that the analogy would have brought into existence, which would be the thought, “Suggesting this trip to Dad inevitably says to Dad that we all think his days are numbered.” Indeed, a long family conversation about it all would only strengthen and entrench the analogy’s grip on everyone’s mind.

The two trips, so far apart in time and yet so similar in the minds of all involved, cannot psychologically be pulled apart. The mapping is so salient that the human mind concludes that the two stories have to end identically. It’s a classic case of the proverb “One does not speak of rope in the house of someone who was hanged.” No one would believe that taking the trip would actually
bring about
the father’s death; it is simply that the idea of taking the trip would inevitably be contaminated by the image of
that other trip
one generation earlier, and the analogy would impose itself heavily and sadly.

Human thought simply is this way. Certainties do not come from following rigid deductive laws; indeed, conclusions reached through such reasoning strike many people as suspect for that very reason. By contrast, categorizations brought about by analogy-making impose their conclusions in a manner that is hard to resist. If it’s a dog, then it ought to bark. If’s it’s a chair, then one ought to be able to sit on it. If it’s night, it’s hard to see. If I suggest the trip, then Dad will think that we all think he’s at death’s door. This particular case has shown that analogies can make up our minds for us in a very firm fashion. Just as we cannot help thinking “four legs” when we think “table”, or “feathers” when we think “bird”, or “genius” when we think “Einstein”, so K. and her family wouldn’t have been able to resist thinking “imminent death of Dad” if they were to think “a trip for Dad so that he can savor, one last time, the Avenue of the Giants”.

At this juncture in our book, another analogy in the same vein imposes itself on us. It begins when Chilean physicist Francisco Claro, accompanied by his wife Isabel and their three children, set out from their native land for Indiana University in Bloomington, where they were going to spend Francisco’s first sabbatical year ever. This couple was among the best friends of the American couple, Doug and Carol.

Many similarities linked these two couples. Doug and Francisco were just a couple of years apart in age, and both had gotten their doctorates in physics working under the same professor at the same university; both adored Bach and Chopin and played piano frequently for each other. As for Carol and Isabel, they were good friends, both had gotten degrees in librarianship and had worked as librarians, and each of them had a kind of soft Latin beauty.

Several months after Francisco’s arrival at Indiana University, Isabel started having a series of agonizing headaches. After being taken to Bloomington Hospital, she was diagnosed as having a brain tumor, and was instantly transferred to a much more sophisticated hospital in Indianapolis, about sixty miles to the north, for further tests and procedures. The tumor was found to be very large, and indeed, before operating, the surgeon described it to Francisco and Isabel as “the size of a lemon”. Never in their lives had they known such a terrible fear as at that moment. And yet, in the course of the operation on Isabel, which was necessary to forestall her death, it was discovered that the tumor was benign, and not only that: it was encapsulated and was thus able to be removed very naturally. Isabel recovered quickly from the surgery, and there were no lasting consequences.

Seventeen years after this event, Doug left his native land with his wife Carol and their two children to spend their first-ever sabbatical year in the university town of Trento, Italy. After a few marvelous months there, Carol started having a series of excruciating headaches. Doug took her to the hospital in Trento, where they did tests and discovered a brain tumor. She was instantly transferred by ambulance to the much more fully equipped hospital of Verona, some sixty miles to the south, for more extensive testing and procedures. The tumor was found to be very large, and indeed,
before operating, the surgeon described it to Doug and Carol as “the size of a lemon”. Never in their lives had they known such a terrible fear as at that moment.

The analogy between these two situations is incredibly strong, so strong that readers might think it is all just an invention, but it is all true down to the finest detail. In each case, we are in the presence of a young family during their first sabbatical year ever, undertaken in a foreign country; these families are analogous for the reasons given above, and the strength of their friendship lends great strength to the analogy. In both situations, a tumor is detected in the brain of the wife after a series of terrible headaches; in both cases, the patient is instantly transferred from the local hospital to a much better equipped hospital in the nearest large city, roughly sixty miles away; in both cases, the tumor, once measured, is described as being “lemon-sized”.

Now given the strength of this analogy so far, no one could hear it and not be at least tempted to conclude that “history was inevitably going to repeat itself” in the case of the two couples — that is to say, that Carol’s tumor, like Isabel’s, would be found to be benign and encapsulated and would be removed perfectly, with no consequences, and that everything would be fine afterwards. Indeed, for Doug and Carol, this belief was more than just tempting — it was enormously powerful, and it allowed them to face this horrifying situation and even to feel optimistic, as if this whole story was simply one part of the parallel unfolding of the two couples’ lives, and thus was inevitably bound to have a similar ending. And although all this turned out to be wrong, Doug and Carol were sustained until nearly the very end by this compelling analogy.