To Mazur’s consternation, the simple test of conceptual understanding showed that his students had not grasped the basic ideas of his physics course: two-thirds of them were modern Aristotelians. “The students did well on textbook-style problems,” he explains. “They had a bag of tricks, formulas to apply. But that was solving problems by rote. They floundered on the simple word problems, which demanded a real understanding of the concepts behind the formulas.”...Serendipity provided the breakthrough he needed. Reviewing the test of conceptual understanding, Mazur twice tried to explain one of its questions to the class, but the students remained obstinately confused. “Then I did something I had never done in my teaching career,” he recalls. “I said, ‘Why don’t you discuss it with each other?’” Immediately, the lecture hall was abuzz as 150 students started talking to each other in one-on-one conversations about the puzzling question. “It was complete chaos,” says Mazur. “But within three minutes, they had figured it out. That was very surprising to me—I had just spent 10 minutes trying to explain this. But the class said, ‘OK, We’ve got it, let’s move on.’ “Here’s what happened,” he continues. “First, when one student has the right answer and the other doesn’t, the first one is more likely to convince the second—it’s hard to talk someone into the wrong answer when they have the right one. More important, a fellow student is more likely to reach them than Professor Mazur—and this is the crux of the method.
...There’s also better retention of knowledge. “In a traditional physics course, two months after taking the final exam, people are back to where they were before taking the course,” Mazur notes. “It’s shocking.” (Concentrators are an exception to this, as subsequent courses reinforce their knowledge base.) Peer-instructed students who’ve actively argued for and explained their understanding of scientific concepts hold onto their knowledge longer. Another benefit is cultivating more scientists. A comparison of intended and actual concentrators in STEM (science, technology, engineering, mathematics) fields indicates that those taught interactively are only half as likely to change to a non-STEM discipline as students in traditional courses.
A classic paper by Drew McDermott, “Artificial Intelligence Meets Natural Stupidity,” criticized AI programs that would try to represent notions like happiness is a state of mind using a semantic network:
And of course there’s nothing inside the HAPPINESS node; it’s just a naked LISP token with a suggestive English name.
So, McDermott says, “A good test for the disciplined programmer is to try using gensyms in key places and see if he still admires his system. For example, if STATE-OF-MIND is renamed G1073. . .” then we would have IS-A(HAPPINESS, G1073) “which looks much more dubious.”
Or as I would slightly rephrase the idea: If you substituted randomized symbols for all the suggestive English names, you would be completely unable to figure out what G1071(G1072, G1073) meant. Was the AI program meant to represent hamburgers? Apples? Happiness? Who knows? If you delete the suggestive English names, they don’t grow back.
Suppose a physicist tells you that “Light is waves,” and you believe the physicist. You now have a little network in your head that says:
IS-A(LIGHT, WAVES)
As McDermott says, “The whole problem is getting the hearer to notice what it has been told. Not ‘understand,’ but ‘notice.’ ” Suppose that instead the physicist told you, “Light is made of little curvy things.”1 Would you notice any difference of anticipated experience?
How can you realize that you shouldn’t trust your seeming knowledge that “light is waves”? One test you could apply is asking, “Could I regenerate his knowledge if it were somehow deleted from my mind?”
This is similar in spirit to scrambling the names of suggestively named lisp tokens in your AI program, and seeing if someone else can figure out what they allegedly “refer” to. It’s also similar in spirit to observing that an Artificial Arithmetician programmed to record and play back
Plus-Of(Seven, Six) = Thirteen
can’t regenerate the knowledge if you delete it from memory, until another human re-enters it in the database. Just as if you forgot that “light is waves,” you couldn’t get back the knowledge except the same way you got the knowledge to begin with—by asking a physicist. You couldn’t generate the knowledge for yourself, the way that physicists originally generated it.
The same experiences that lead us to formulate a belief, connect that belief to other knowledge and sensory input and motor output. If you see a beaver chewing a log, then you know what this thing-that-chews-through-logs looks like, and you will be able to recognize it on future occasions whether it is called a “beaver” or not. But if you acquire your beliefs about beavers by someone else telling you facts about “beavers,” you may not be able to recognize a beaver when you see one.
This is the terrible danger of trying to tell an artificial intelligence facts that it could not learn for itself. It is also the terrible danger of trying to tell someone about physics that they cannot verify for themselves. For what physicists mean by “wave” is not “little squiggly thing” but a purely mathematical concept.
As Donald Davidson observes, if you believe that “beavers” live in deserts, are pure white in color, and weigh 300 pounds when adult, then you do not have any beliefs about beavers, true or false. Your belief about “beavers” is not right enough to be wrong.2 If you don’t have enough experience to regenerate beliefs when they are deleted, then do you have enough experience to connect that belief to anything at all? Wittgenstein: “A wheel that can be turned though nothing else moves with it, is not part of the mechanism.”
Almost as soon as I started reading about AI—even before I read McDermott—I realized it would be a really good idea to always ask myself: “How would I regenerate this knowledge if it were deleted from my mind?”
The deeper the deletion, the stricter the test. If all proofs of the Pythagorean Theorem were deleted from my mind, could I re-prove it? I think so. If all knowledge of the Pythagorean Theorem were deleted from my mind, would I notice the Pythagorean Theorem to re-prove? That’s harder to boast, without putting it to the test; but if you handed me a right triangle with sides of length 3 and 4, and told me that the length of the hypotenuse was calculable, I think I would be able to calculate it, if I still knew all the rest of my math.
What about the notion of mathematical proof? If no one had ever told it to me, would I be able to reinvent that on the basis of other beliefs I possess? There was a time when humanity did not have such a concept. Someone must have invented it. What was it that they noticed? Would I notice if I saw something equally novel and equally important? Would I be able to think that far outside the box?
How much of your knowledge could you regenerate? From how deep a deletion? It’s not just a test to cast out insufficiently connected beliefs. It’s a way of absorbing a fountain of knowledge, not just one fact.
A shepherd builds a counting system that works by throwing a pebble into a bucket whenever a sheep leaves the fold, and taking a pebble out whenever a sheep returns. If you, the apprentice, do not understand this system—if it is magic that works for no apparent reason—then you will not know what to do if you accidentally drop an extra pebble into the bucket. That which you cannot make yourself, you cannot remake when the situation calls for it. You cannot go back to the source, tweak one of the parameter settings, and regenerate the output, without the source. If “two plus four equals six” is a brute fact unto you, and then one of the elements changes to “five,” how are you to know that “two plus five equals seven” when you were simply told that “two plus four equals six”?
If you see a small plant that drops a seed whenever a bird passes it, it will not occur to you that you can use this plant to partially automate the sheep-counter. Though you learned something that the original maker would use to improve on their invention, you can’t go back to the source and re-create it.
When you contain the source of a thought, that thought can change along with you as you acquire new knowledge and new skills. When you contain the source of a thought, it becomes truly a part of you and grows along with you.
Strive to make yourself the source of every thought worth thinking. If the thought originally came from outside, make sure it comes from inside as well. Continually ask yourself: “How would I regenerate the thought if it were deleted?” When you have an answer, imagine that knowledge being deleted as well. And when you find a fountain, see what else it can pour.
1 Not true, by the way.
2 Richard Rorty, “Out of the Matrix: How the Late Philosopher Donald Davidson Showed That Reality Can’t Be an Illusion,” The Boston Globe, 2003, http://archive.boston.com/news/globe/ideas/articles/2003/10/05/out_ of_ the_ matrix/.