Surfaces and Essences

by Douglas Hofstadter

  (9)Sometimes it looks as if eating a ghost will pay off big, but at the last moment the ghost catches you off guard and turns into a predator, devouring its former pursuer. Everything flips in a split second. T. learned that taking too big a risk can turn your world upside down.

  (10)T. had experiences in Pac-Man in which hesitating just a tenth of a second cost him everything. It’s not enough to make good decisions; you’ve got to be able to make them on a dime. T. concluded that life doesn’t give you second chances.

  (11)T. retained a bitter memory of games that were extremely promising but where just a moment of distraction made him slip into the clutches of defeat in just a few seconds. He saw that one moment of carelessness, and all your hard work can go up in smoke.

  (12)Sometimes a delicious fruit would appear when the ghosts were edible as well, but when T. tried to eat them all, he usually wound up with nothing instead of a grand feast. Thus he was led to the credo that you shouldn’t try for too much.

  (13)Sometimes T. took extreme risks and perished when, had he been more restrained, he would have won fewer points but would have survived. In this manner, he learned that a bird in the hand is worth two in the bush.

  (14)Whether madly pursuing prey or rapidly fleeing from a predator, T. chose his direction by paying close attention to the distances involved. But sometimes much better results came when he headed off in precisely the wrong direction. In this way, Pac-Man taught T. that the shortest path is not necessarily the best path.

  (15)There were times when the ghosts’ movements were such that no matter what he did, T. simply was done for. He learned that although one is alive now, death may be only moments away.

  These fifteen “life principles” came out of a video game lacking all metaphysical pretension, a game whose sole raison d’être is to entertain. This shows how analogy pervades one’s thinking when one is driven by an obsession. The maxims to which T. was led by his Pac-Man addiction would not have been formulated by someone who was a relative newcomer to the domain; people with just a few minutes or hours of experience with Pac-Man would say, “The only purpose in this game is to get as high a score you can while killing the ghosts — that’s obvious!” It’s most unlikely that their reflections would go any further than that.

  T.’s maxims may seem, like the other obsession-based analogies cited above, to be exaggerated and artificial, in the sense that they seem unrelated to Pac-Man. But on the other hand, his analogies are as legitimate as can be. The connections between the maxims and specific phenomena in the game are always clear as a bell; the analogies are spot-on and also they teach lessons — lessons that someone could learn from real-life experiences. The difference is that in Pac-Man these lessons are learned in a highly compressed time frame and are intensified, since even the strangest circumstances will reappear fairly regularly when one is a Pac-Man addict. During his period of Pac-Man addiction, T. lived tens of thousands of different “lives”.

  It is striking that a simple video game contains enough richness to lead a player to insights about life that are essentially philosophical, all based on analogies that link the trivial “lives” of a Pac-Man entity, involving little more than eating or getting eaten, with the full complexity of human life. In this respect, the Pac-Man microworld is similar to the Copycat microworld, as we will see in the next chapter.

  Irresistible Analogies: Are They Meaningless or Meaningful?

  We now direct our attention towards another frequent type of analogy — specifically, analogies suggested by extremely salient resemblances, which perhaps are superficial and perhaps are not. That’s the key question. Although such analogies are irresistible, do they deserve to be given the time of day or not? We tackle this issue with the help of an example.

  Shortly after giving a lecture, Professor F. was contacted by a reporter who worked for his university’s public relations bureau. She wanted to interview him for a university publication. They met, and as the interview progressed, F., who was not married, found her more and more attractive. He also discovered, to his chagrin, that she was married, but against his better judgment, he invited her to lunch, and she, against her better judgment, accepted. For the next two months, they met frequently for intimate conversations at lunch, always completely platonic but always sparkling. At last F. decided to see if there was any chance of passing from platonism to hedonism, but his hopes were turned down in an unambiguous though compassionate manner.

  Five years later, F., still unmarried, accepted an offer from another university. No sooner had he arrived on campus than a reporter who worked for a magazine published by the university contacted him in the hopes of conducting an interview by telephone. Rather than replying to her, “Great idea — we can both save some precious time that way!”, F. suggested that they meet in person instead. As is obvious, the analogy between the two situations, although it was based on resemblances that were quite superficial, exerted a nearly irresistible pressure on F.

  We are all constantly prone to listen to inner voices that whisper to us, “This situation is extremely reminiscent of a situation that you were in before and that you remember clearly, and so you’re very lucky! Just make your decision on the basis of your prior experience!” Let’s consider another case of this sort.

  G. once wrote a column for a well-known magazine. When he was hired, he was unaware that every issue was eventually published, in translation, in many countries around the world. One day, out of the blue, G. received a package containing various international editions of the magazine, featuring his columns in many different languages. At first he was delighted to see his ideas being spread around the world, but on carefully examining some of the European translations (he had studied a few European languages and was fascinated by them), he was deeply disappointed, as he saw that his very careful writing style had not been faithfully reproduced at all and had been replaced by a style that he found boring and flat. He felt betrayed.

  Some thirty columns later, the magazine’s publisher contacted G. by phone and told him that he had just learned that the directors of the Korean counterpart of the magazine were hoping to publish a volume specially devoted to all of G.’s columns. What an honor for G.! So would G. give the go-ahead to publish this anthology? G., however, just hemmed and hawed. The publisher pressed on: “What’s the problem? This is a great opportunity!” G. then admitted that he hadn’t been pleased with the European translations of his columns, and that although he didn’t speak a word of Korean, he was worried that the same thing might… The publisher cut him off and said, “Now, now, old boy, not to worry! The Korean edition of our magazine uses only the very best translators that can be found — super-experts, extremely sophisticated. That’s a guarantee. So it’s a deal?”

  What would the reader do in G.’s shoes? On the one hand, there was strong pressure coming from the magazine’s upper echelons to publish a book in Korea, which would have been good for G.’s reputation. On the other hand, there was an analogy whose relevance was not in the least clear. What possible link could the disappointing performance of a few European translators have with the performance of unknown translators in a country that was so distant geographically, linguistically, and culturally?

  In the end, G. turned his publisher down. The latter had assured him that the Korean translators were as good as they come, but what did he know about it? It’s inconceivable that he would have said to G., “I know how painful it is for an author to be mangled by a translator. Since you didn’t like any of the European translations, your doubts about the quality of translation into Korean are highly merited.”

  It’s far easier to imagine the publisher saying something like this: “Few things in the world are more different than Korean and European translators! To be sure, some European translations of our magazine have now and then left a bit to be desired, but that problem is completely localized. Korea is another ball of wax. A completely different mentality reigns over there — a far more serious one. Of cour
se I understand your temptation to make an analogy, but believe me, there’s simply no connection. It’s as if you were telling me you would never drive a Korean car after having test-driven only cars built in Eastern Europe. Trust in us, old boy; if we assure you that these are faithful and reliable translators, you can count on us and on them.” But G. didn’t buy this line — after all, “Once burned, twice shy”! And a week later, he received a letter telling him that his column would be terminated. His analogy had cost him dearly.

  What, then, was the bedrock set of beliefs on which G. thought it reasonable to ground his analogy? Was it sensible to leap from the quality of a German translator to the quality of a translator in an extremely distant language? And what about the fact that it wasn’t a question of just one low-quality European translation, but four? And how to take into account the differing levels of G.’s knowledge of those four tongues?

  At what point is it sensible to extrapolate to an unknown world an event that took place in a known world, and on the basis of what kinds of knowledge and what kinds of prior experiences? If a translation into a given language is of low quality, why should a translation into another language, done by another person, also be of low quality? Does one earn the right to make such an extrapolation if there have already been twenty abject translation failures in twenty different languages spread out over all the different continents? Or does one earn the right to make such a leap long before that moment? What does it all depend on, in the end? On the distance between the countries involved? On their cultural distance? On the relatedness of the languages? Does one need to have a deep knowledge of all the languages concerned? Or is it enough to have seen problematic translations into just one or two languages, whatever they might be?

  Bagels Belonging to a Single Batch

  In each of the two foregoing anecdotes, someone presumes that what once took place in one situation has a good chance of taking place again in a new situation that brought the older one to mind. Thus the professor who, five years earlier, fell head over heels for a university public-relations writer who called him up for an interview cannot suppress the tingling feeling, when he’s contacted by a public-relations writer at his brand-new university, that there is a pretty decent chance that he’ll find her to be just his type as well. And the magazine columnist who was disappointed by the translations of his columns into a few languages that he can read can’t help but suspect that the translations into languages of which he can’t read a word will be just as flawed.

  These anecdotes are cases of induction, a form of thought in which one extrapolates to new situations certain observations that one made in one or more prior situations. Such an extrapolation can extend to a sizable category (for example, presuming that all Dutch people are smart after having met a few who are smart, or guessing that Paul is always late on the basis of a couple of late arrivals), or it can be limited to just one other case, or a handful of other cases (for example, presuming that the almond flan, soon to be wheeled in, will of course be delicious — after all, the chiles rellenos were terrifically tasty! — or leaping to the conclusion that Jack and Susan must be just as blond as is their strikingly blond brother). Induction has no claim to logical validity, in the sense that no rigorous rule of reasoning allows a person to arrive at an inductive conclusion with absolute certainty. No known law compels all female university public-relations writers to be heart-throbs for a certain male professor, nor is there any universal principle entailing that all the translators employed by a certain magazine must share an identical level of mediocrity. To be sure, there are powerful, compelling analogies that link the situations in these scenarios, but that doesn’t make the conclusions that these analogies suggest anything close to certain.

  Of course, the fact that a given conclusion is not derivable through watertight logical reasoning doesn’t mean that the conclusion has to be false; far from it! It’s perfectly possible that the Korean translation will be miserable, and that the professor will be smitten beyond belief when he meets the public-relations writer in his new university. In short, the likelihood of a conclusion should not be confused with its logical validity. And indeed, what usually matters in everyday life is how likely something is rather than how logically deducible it is. The professor isn’t looking for an ironclad proof that he will fall in love with a woman he hasn’t yet met; he merely wants to know if the chances are decent that she will appeal to him. And what matters for the columnist is the high probability that the Korean translations will leave much to be desired. Neither of these people cares a hoot about whether their conclusions can be reached by following strict logical reasoning. What matters overwhelmingly to them is simply the question of likelihoods. Moreover, the conclusions reached by these two individuals have very different levels of probability. Whereas the romantic hopes of the starry-eyed professor can strike one as pretty unlikely, the fears of the skeptical columnist may seem somewhat more realistic. And perhaps each of these individuals, in making an “illogical” analogical extrapolation, accurately intuited its likelihood of being right.

  To live one’s life in this world, one has to trust one’s own judgments about what is and what isn’t likely, far more than worrying about fine points of logical validity. If, on some grade-A gray day, you suddenly decided to reject every inductive conclusion you reached simply because it wasn’t the result of an ironclad form of reasoning, then your thinking would have to grind to a halt, because every thought that anyone has, no matter how tiny it is, no matter how spontaneous or mindless it might seem, is an outcome of this kind of mental activity that has no logical validity.

  If A. were to ask Z. a question as innocuous as “How are your fries?”, then Z., in order to be strictly logical, would have to reply, “Well, the six I’ve partaken of so far were most savory, but since I haven’t tasted any of the others on my plate, I have no basis for commenting on how they are.” In some theoretical sense, Z.’s answer may be defensible, but anyone sane would find it grotesquely pedantic. A sensible person would reply, without even thinking twice, “They’re delicious!”, because such a person would unhesitatingly extrapolate outwards — from the titillating twinges of their taste buds triggered by their initial nibblings all the way to the whole plateful. The analogy between the already-savored fries and their yet-to-be-ingested cousins would seem too compelling to allow any other answer even the slightest chance of coming to mind.

  Numerous psychology experiments have identified various factors that contribute to the apparent validity of such generalizations, which is to say, to the feeling that such analogy-based extrapolations are credible. For example, the greater the number of previously observed cases is, the more secure people tend to feel in concluding that the same outcome will take place in a fresh new case. Thus, the more fries one has tasted from one’s plate, the more secure one will feel in guessing that the entire plateful of fries is good.

  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.