Learning “The Hard Way”: Negative Thinking in Context Spaces
Robert Burke, March 2000
David and Helen are going to the Symphony on a Friday night. David has never been to the Symphony before and isn’t sure what he should wear. He decides to dress only somewhat formally. When he arrives at the performance, he feels comfortable. But when he meets Helen, he finds she is much more formally dressed than he is, and this makes him feel uncomfortable.
On countless occasions, David has searched through his wardrobe for something to wear. But this evening, the context in which he made his decision was unique. To help make the decision, David remembered past experiences that took place in similar contexts. In the future, when he finds himself facing a similar decision, he should also draw upon what he learned tonight at the Symphony.
As Dr Minsky points out in section 2-1 of The Emotion Machine, this process of learning and re-membering is rather complex. David will need to “file” information about his experience -- both positive and negative -- in such a way that it can be readily recalled the next time he makes a similar decision. Retrieving this information will require David to partition and search through the set of all possible contexts in which a question like “what should I wear?” can be posed.
In The Dimensions of Context-Space, Doug Lenat proposes classifying contexts along twelve dimensions: time, type of time, geographic location, type of place, culture, sophistication, topic, granularity, modality/disposition, argument-preference, justification, and domain assumptions. Lenat is considering context as a building block needed to construct a knowledge base, which is precisely what David’s mind is doing: building an efficient, but adaptive and thorough, compilation of knowledge.
When we begin thinking about a twelve-dimensional context space, it becomes immediately (and perhaps painfully!) clear why David’s mind faces such hard problems. In this paper, we’ll discuss some of those problems -- like hypothesis forming, generalizing and searching in a context space. What we’ll find, once again, is the power of negative thinking. By maintaining both negative and positive hypotheses, and taking advantage of the Corrector, Suppressor, and Censor mechanisms Dr Minsky describes in section 3-4 of The Emotion Machine, we can avoid brute-force searches through context space and turn it into a manageable habitat for ideas.
Generalization and Learning
Years ago, David went to a highschool semi-formal in jeans and a T-shirt and was teased by his peers. At the time, some of these peers were among David’s imprimers, and their mockery was a formative experience. His mind formed hypotheses about what he should learn from the experience. One student he respected told him he should wear a tie in the future. Another told him he shouldn’t wear jeans. But David didn’t interpret this to mean he should always wear a tie or never wear jeans. Instead, David subconsciously (or, perhaps consciously) solved the so-called credit assignment problem in his mind, figuring out which aspects of the context were most salient.
In terms of Lenat’s context space dimensions, David might have considered the type of place, type of time and culture dimensions to be particularly salient. Then, around a particular point in context space, he generalized by carving out a subspace that contained all the contexts he thought this new information might apply to. For example, “type of place” might have been generalized to include all semi-formal public gatherings, and not just high-school dances.
As David grows up, he assembles an increasingly intricate map of the context space, which serves as a sort of address book for the kinds of decisions he should -- and shouldn’t -- make in various contexts.
Decision Making: Searching the Context Space
In making his decision to wear formal clothes to the Symphony, David first decided which elements of the context were most salient. It’s probably not important that it’s the 23rd of March as opposed to the 22nd, but it is likely important that David will be attending a cultural event, with someone he respects and wants to impress, on a Friday evening in a New England climate. This brings him to a much narrower locale in context space.
The fact that the Symphony is a cultural event seems to be the most salient of these parameters, for reasons which could fill another paper in and of themselves. Quickly, one might hypothesize that the fact it is a cultural event is the most salient information for David because, for him, it is the aspect of the event that is most out of the ordinary. Indeed, it is so far out of the ordinary that David has never been to the Symphony before. He won’t find a perfect, specific event from his past to draw knowledge from; instead, he will have to generalize from past knowledge and form a new hypothesis.
Decision Making: Hypothesis Forming
Even before David begins to think and form a hypothesis, we see how Censors, as postulated by Freud, can help cull off a vast array of absurd possibilities. It simply won’t occur to David to wear a bathing suit, or attend the Symphony in the nude. It might be possible that our mind, in order to save time, discards these silly possibilities as a first step before really considering the context space.
The context space has been filling up with two types of knowledge. The first consists of positive examples of things that can potentially form hypotheses:
“In another semi-formal situation on a Friday night, I impressed someone by dressing formally.”
“Someone I respect told me to wear a tie to formal gatherings.”
“I have heard that educated people are comfortable wearing dressy clothes to the Symphony.”
The others are negative examples that are woven into Suppressors and Correctors:
“I once intimidated someone by being too formally dressed.”
“I once embarrassed myself by wearing jeans and a T-shirt to a semi-formal occasion.”
“A mentor once told me never to wear poorly creased pants at a public gathering.”
All of these thoughts need not be stored in explicit detail; rather, the relation of each thought to other knowledge in the context space provides us with implicit information. Perhaps even more importantly, these relationships provide us with a built-in mechanism that facilitates arbitrary levels of generalization. After this trip to the Symphony, for example, David will still be careful not to intimidate people by overdressing. However, he might build in a new, more specific suppressor that suggests, “Helen can be very well dressed, and not matching her level of formality can be embarrassing.” That way, David might dress the same way the next time he attends the Symphony, unless he’s planning on meeting Helen there.
Sometimes, our search through context space will reveal a perfect or near-perfect match to a past situation which serves as a positive example of how we might proceed. How far should we stray from a positive example of something that worked in the past? We certainly don’t always make the same decisions, although some people are more adventurous than others. If we never tried new options in old contexts, we wouldn’t learn very much. We each strike a unique balance between experimentation with new options, and exploitation of knowledge gained from old successes (and, indirectly, failures). Maintaining this experimentation-versus-exploitation balance allows us to refine our notions of how we partition context space, while at the same time taking advantage of knowledge that we’ve acquired.
More on Learning the Hard Way
What would happen if we ignored negative thinking, and didn’t maintain negative as well as positive hypotheses in our context spaces? We would still tend to reinforce positive experience. However, during experimentation, we would be more likely to stumble back on old mistakes. If David hadn’t maintained a suppressor that reminded him not to wear jeans at a formal occasion, his mind might have decided this Symphony trip was a good chance to experiment with jeans as potential formal attire.
Perhaps the strongest argument for negative thinking arises from the complexity of the context space. Each of the twelve dimensions Lenat mentions, like “type of place” and “culture,” are themselves highly intricate and multidimensional spaces. In the paper, Lenat suggests that there were originally over 100 dimensions considered for their system. If we consider the many sub-dimensions of the dozen “uber-dimensions” Lenat arrived at, we will likely be back to at least 100 dimensions again.
If we are rewarded for an action (our expectations are met or exceeded, we are praised by an imprimer, etc.) we will want to form hypotheses which suggest potential contexts in which a similar action might also be rewarded. (In essence, this is exactly what David did once when he dressed formally for a semi-formal situation and impressed the people he respected. He hypothesized that wearing formal attire again in a similar situation would result in a similar positive reaction.) There are a near-infinite number of such potential hypotheses, varying both in terms of generality, and in which dimensionalities of the context are considered most salient. It is likely that these hypotheses will accumulate quickly. In any case, hypotheses will “fade” or “be culled” if they aren’t confirmed or tested within a reasonable timeframe. Instead of creating a vast number of positive hypotheses -- most of which will eventually be discarded as false -- the mind can keep track of salient negative hypotheses as well.
Thus, in addition to preventing us from revisiting negative experience, negative hypotheses let us effectively probe a high-dimensional context space. Very few people want to subject themselves to suffering. But there’s much to be said about the importance of learning things “the hard way.”