always the case, because no two situations are ever the same—and this means that we’re always making analogies. For example, if the problem that you are facing now reminds you have one that you solved in the past, then you may be able to use this to solve your problem by using use a procedure like this:

The problem that I am working on reminds me of a similar one that I solved in the past—but the method that was successful then does not quite work on the problem that I am facing now. However, if I can describe the differences between that old problem and this new one, those differences might help me to change that old method so that it will work for me now.

We call this ‘reasoning by analogy’ and I’ll argue that this is our most usual way to deal with problems. We do this because, in general, old methods will never work perfectly, as new situations are never quite the same. So, instead, we use analogies. But, why do analogies work so well? Here is the best way I’ve seen to explain why this is:

Douglas Lenat: “Analogy works because there is a lot of common causality in the world, common causes which lead to an overlap between two systems, between two phenomena or whatever. We, as human beings, can only observe a tiny bit of that overlap; a tiny bit of what is going on at this level of the world. … [So] whenever we find an overlap at this level, it is worth seeing if in fact there are additional overlap features, even though we do not understand the cause or causality behind it.[126]

So, now let’s inspect an example of this.

A Geometric Analogy Program

Everyone has heard about great improvements in computer speed and capacity. It is not so widely known that, in other respects, computers changed very little from their inception until the late 1970’s. Designed originally for doing high-speed arithmetic, it was usually assumed that this was all computers would ever accomplish—which is why they were misnamed “computers.”

However, people soon began to write programs to deal with non-numerical things such as linguistic expressions, graphical pictures, and various forms of reasoning. Also, instead of following rigid procedures, some of those programs were designed to search through wide ranges of different attempts — so that they could solve some problems by “trial and error”—instead of by using pre-programmed steps. Some of these early non- numerical programs became masters at solving some puzzles and games, and some were quite proficient at designing new kinds of devices and circuits.[127]

Yet despite those impressive performances, it was clear that each of these early “expert” problem-solving programs could operate only in some narrow domain. Many observers concluded that this came from some limitation of the computer itself. They said that computers could solve only “well-defined problems” and would never be able to cope with ambiguities, or to use the kinds of analogies that make human thinking so versatile.

To make an analogy between two things is to find ways in which they are similar—but when and how do we see two things as similar? Let’s assume that they share some common features, but also have some differences. Then how similar they may seem to be will depend upon which differences one decides to ignore. But the importance of each difference depends upon one’s current intentions and goals. For example, one’s concern with the shape, size, weight, or cost of a thing depends on what one plans to use it for—so, the kinds of analogies that people will use must depend upon their current purposes. But then, the prevailing view was that no machine could ever have goals or purposes.

Citizen: But, if your theory of how people think depends on using analogies, how could any machine do such things? People have always told me that machines can only do logical things, or solve problems that are precisely defined—so they cannot deal with hazy analogies.

In 1963, to refute such beliefs, Thomas G. Evans, a graduate student at MIT, wrote a program that performed surprisingly well in what many people would agree to be ambiguous, ill-defined situations. Specifically, it answered the kinds of questions in a widely used “intelligence test” that asked about “Geometric Analogies.”[128] For example, a person was shown a picture like this and asked to choose an answer to: “A is to B as C is to which of the other five figures?” Most older persons choose figure 3—and so did Evans’s program, whose score on such tests was about the same as that of a typical 16 year old.

In those days, many thinkers found it hard to imagine how any computer could solve such problems, because they felt that choosing an answer must come from some “intuitive” sense that could not be embodied in logical rules. Nevertheless, Evans found a way to convert this to a far less mysterious kind of problem. We cannot describe here all the details of his program, so we will only show how its methods resemble what people do in such situations. For if you ask someone why they chose Figure 3, they usually give an answer like this.

“You go from A to B by moving the big circle down, and

You go from C to 3 by moving the big triangle.”

This statement expects the listener to understand that both clauses describe something in common—even though there is no big circle in Figure 3. However, a more articulate person might say:

“You go from A to B by moving the largest figure down, and

You go from C to 3 by moving the largest figure down.”

Now those two clauses are identical—and this suggests that both a person and a computer could use a 3- step process involved these similar kinds of descriptions.

Step 1. Invent descriptions for each of top row of figures. For example, these might be:

A: high large thing, high small thing, low small thing.

B: low large thing, high small thing, low small thing,

C: high large thing, high small thing, low small thing.

Step 2. Invent an explanation for how A might have been changed to B. For example, this might simply be:

Change “high large” to “low large.”

Step 3. Now use this to change the description of figure C. The result will be:

Low large thing, high small thing, and low small thing.

The result is a prediction of how Figure C might also be changed. If this matches one of the possible answers more closely than any other, then we’ll choose that as our answer! In fact it only matches Figure 3, which is the one most people select. (If more than one possible answer is matched, then the program starts out again by

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