Indeed, if we make the If of a rule too specific, then it will only apply to a few situations. This means that our rules must not specify too many details, but need to express more abstract ideas. So a rule that applies to a physical object will need to represent that object in some non-pictorial way that does not change when that object changes its visual shape. Naively, most of us tend to believe that we ‘envision’ visual scenes by imagining them as like images. However, section §5-8 below will suggest that this must be mostly illusory, because those images do not much behave the ways that pictures do.
Consider that in the physical realm, when you think of grasping and lifting a block, you anticipate the feel of its weight—and predict that if you weaken your grasp, then the block will be likely to fall. In the economic realm, if you pay for a purchase, then you will own the thing you have bought, but otherwise you must give it back. In the realm of communication, when you make a statement, then your listeners may remember it—but this will more likely to happen if you also tell them that this is important.
Every adult knows many such things, and regards them as obvious, commonsense knowledge, but every child takes years to learn how things behave in different realms. For example, if you move an object in the physical realm, then this will change the place that it’s in—but if you tell some information to your friend, that knowledge will then be in two places at once. We’ll discuss such matters more in chapter §6.[76]
By linking two or more If–>Do–>Then rules into a chain, we can imagine what would happen after several actions—and thus look several future steps ahead—if we can match the Then of each rule to the If of the next. For example, if you are in situation P and want to be in situation Q, you might already know a rule for that, such as, If P–>Do A–>Then Q. But what if you do not know such a rule? Then you could search your memory to try to find a chain of two rules that link together like these, where S is some other intermediate situation.
If P–>Do A–>Then S and then If S–>Do B–>Then Q.
Then, if you cannot find any such two-step chain, then you could simply go on to search for some longer chain that goes through several more steps in between. Clearly, much of our thinking is based on finding such ‘chains of reasoning,’ and once you learn to use such processes, you can plan out ways to solve more difficult problems by predicting several steps ahead. For example, you frequently think like this:
If I ask Charles to drive me to the store, then he might reply with “Yes” or “No.” If he says ‘Yes,’ that will be fine, but if he says ‘No,’ then I will offer him some reward, and that probably will change his mind.
However, when you need to look many steps ahead, such a search may quickly become too large because it grows exponentially, like a thickly branching tree. Thus, even if each branch leads to only two alternatives then, if the solution need 20 steps, then you might have to search through a million such paths, because that is that number of branches can come from a sequence of twenty successive choices.
However, here is a trick that might be able to make the search become much smaller. For if there is a 20-step path from A to B, then there must exist some place that is only 10 steps from each end! So, if you start searching from both ends at once, they must meet at some middle place M in between.
The left side of this search has only a thousand forks. If this is also true of the side on the right, then the search will be several hundred times smaller. And then, if you also have some way to guess where that middle place M might be, then you might further reduce that search by dividing each side into two 5-step searches.
If all this works, then your total search will have become several thousand times smaller! However, none of this is certain to work because it assumes that each ‘backward’ search also will have only two branches—and that will not always be the case. Still, even if that guess M were wrong, you still can try other such guesses—and even with 50 such tests before you succeed, you would still end up having done less work!
This demonstrates why it helps to make plans. If you can guess some ‘islands’ or “stepping stones” along the path toward solving a very hard problem, this can replace that problem by several substantially smaller ones! So every attempt to “divide and conquer” can make a difficult problem much simpler. In the early years of Artificial Intelligence, when most programs were based on ‘trial and error,’ many researchers attempted to find technical methods resembling this to reduce the numbers of trials. Today, however, it seems more important to find ways to guess how to find those islands—and that’s where commonsense knowledge comes in. Chapter §6 will argue that our most powerful ways to do such things involve making good analogies with problems that we already know how to deal with.
Whenever we work toward solving a problem, we’re likely to try many different ways to think. Some of these have popular names like planning and logical reasoning, but most have no common names at all. Some of those methods seem formal and neat, while others seem more ‘intuitive.’
For example, we often use chains of predictions in ways that resemble such logical statements as: If A implies B, and B implies C, then with perfect certainty, we conclude that A implies C. And if all our assumptions are correct—as well as our logical reasoning— then all our conclusions will be correct, and we’ll never make a bad mistake.
However, it turns out that, in real life, most assumptions are sometimes wrong, because the ‘rules’ they express usually have some exceptions to them. This means that there is a difference between the rigid methods of Logic and the seemingly similar chainlike forms of everyday commonsense reasoning. We all know that a physical chain is only as strong as its weakest link. But long mental chains are flimsier yet, because they keep growing weaker with every new link!
So using Logic is somewhat like walking a plank; it assumes that each separate step is correct—whereas commonsense thinking demands more support; one must add evidence after every few steps. And those frailties grow exponentially with increasingly longer chains, because every additional inference-step may give the chain more ways to break. This is why, when people present their arguments, they frequently interrupt themselves to add more evidence or analogies; they sense the need to further support the present step before they proceed to the next one.
Envisioning long chains of actions is only one way to deliberate—and chapter §7 will discuss a good many more. I suspect that when we face problems in every day life, we tend to apply several different techniques, understanding that each may have some flaws. But because they each have different faults, we may be able to combine them in ways that still can exploit their remaining strengths.
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More details about construction planning were developed by Scott Fahlman in his 1973 paper at ftp://publications.ai.mit.edu/ai-publications/pdf/AITR-283.pdf