Structure in the Mind

[This is post 6 in the "Structure and Cognition" series; links to all the posts can be found here]

I’ve been arguing that although human cognition seems very complicated, much of it can be better understood as the result of simple processes. This story is not new in psychology, but the standard telling focuses on heuristics and human irrationality. In this standard account, we frequently use simple cognitive mechanisms, but this is a huge problem and leads to predictable irrationality. Our only hope is to effortfully engage deliberative, System 2 thinking to help us.

The alternative view is based on two important points. First, real world problems are so complicated that no amount of processing can arrive at optimal solutions. No matter how impressive System 2 might be, the real world is orders of magnitude more complicated. Second, simple processes like heuristics can work well not despite their simplicity, but because they are able to exploit structure in the environment. Simple processing is thus necessary and sufficient when it operates in an appropriate situation. (Note that this isn’t quite the same as arguing that heuristics are amazing and that simple mechanisms are all we need. The claim is that the much of the complexity comes from sources other than the cognitive mechanisms themselves).

The previous post in this series noted that structure in the world is not the only kind that matters – we frame structure in particular ways that can either help or hinder us in solving problems. That the framing of problems influences our decisions is often “framed” as further evidence of irrationality, but this is just another example of an impossible problem. An omniscient being could see every possible framing and choose the best one, but given the endless variety of framings any problem or situation can take, a human mind faces strong limits in selecting a frame. Failing to recognize this (despite my intention to write about it) led me to waste weeks trying to figure out the optimal framing for the introductory post to this blog. In other words, I failed to frame the problem of writing the first blog post as a framing problem, because I didn’t immediately recognize the similarity, which in hindsight, is obvious.

So the claim is that structure in the world and its framing guide much of our behavior and allow us to actually solve problems without devoting millennia to considering all of our options. Apparent complexity is (often) the result of interactions of complex structure and simple cognitive processes. But this may seem insufficient to explain the diversity of human thought and behavior.

People behave in strikingly different ways when faced with the same situation. How likely is it that this behavioral heterogeneity is due to differences in framing? Even if it is, that seems to beg the question: if you and I are presented with the exact same situation but frame it entirely differently, how can there be anything other than a complicated mechanism behind our different representations?

And what about more mysterious cognitive abilities like moments of insight where difficult problems suddenly fall away? Can these be explained without positing some unconscious neural networks churning away while our conscious minds focus on other things. Is it possible that these are also just apparent complexity?

I think these examples can also be accounted for with simple processes, but we need to introduce a new source of complexity/structure. If it isn’t in the processing, it must be somewhere else. We saw that complicated looking behavior can result from simple rules that conform to the shape of a complex environment, like Simon’s ant walking on a beach. Other times, problem representations can hold useful information and relieve the burden on working memory, allowing us to easily solve problems we would find difficult if we had to hang on to all their disparate parts simultaneously. The last source of complexity is structure in the mind: memory.

Our memories store vast quantities of information and experience. Arguably more impressive than the memory system’s storage capacity is its ability to retrieve information that is relevant and useful to whatever situation we find ourselves in. Think about searching for something on Google. Specifying the right search terms to elicit information we’re looking for often takes multiple tries despite Google’s huge improvements over earlier search engines. Our memories instantly sort through their contents and provide us with exactly the right knowledge we need (though obviously they aren’t perfect and sometimes require deliberate searching questions and even then, may fail).

This may seem like some pretty involved processing itself but note that simple search procedures can yield excellent results even over a massive database. For example, the game of 20 Questions can narrow down the space of all possible objects in the world to a single likely candidate in only 20 binary (yes/no) tests. The strength of memory may be due more to a rich system of indexing than to a complicated search algorithm. In other words, the algorithm isn’t what’s complicated – it can be a simple search algorithm operating over a large, complex set of data.

Theories of memory prominent in the 1970s* argued that the memory system can be viewed as analogous to an encyclopedia with an index. When we recall experiences or facts, this is akin to reading the “text” of the book. But information is memory is also stored with indices that point to the stored information. In addition to recalling the text, we can also retrieve information by using the index – this is recognition memory.

If an index is recognized, the “text” can be accessed. Of course, the text might contain other indexed terms, meaning you can be reminded of other memories while recalling and can choose to access those texts as well. On these theories, much of encoding new information in memory is elaborating the index so that it is more easily accessed later. For example, if the text for “cat” has many indices pointing to it, e.g., “pet,” “likes milk,” “mammal,” “cute,” etc., you are more likely to be reminded of cats when thinking about those topics.

There’s a paragraph written by Robert Burton (2008) that nicely illustrates both how memory can fail to retrieve what we want if the cues don’t match our indices very well and how recognition of the right cue can instantly enable understanding:

"A newspaper is better than a magazine. A seashore is a better place than the street. At first it is better to run than to walk. You may have to try several times. It takes some skill, but it is easy to learn. Even young children can enjoy it. Once successful, complications are minimal. Birds seldom get too close. Rain, however, soaks in very fast. Too many people doing the same thing can also cause problems. One needs lots of room. If there are no complications, it can be very peaceful. A rock will serve as an anchor. If things break loose from it, however, you will not get a second chance." (p. 5-6)

The problem here is that the paragraph is referencing something only obliquely. Some of the sentences are too vague to point at any one thing and others aren’t facts we tend to index things with, like “whether you may have to try several times.” But once you know that the paragraph refers to a kite, the confusion disappears.

Just like finding a term in a book can be easy if it appears in the index, past experiences can be easily recalled if they are indexed in useful ways and if the system is queried in a way that matches the index.** Again, the argument is that the search procedure is simple, it’s the information contained in the memory system/encyclopedia that is complicated. We have a deep well of knowledge and experiences organized by a complex system of indexing. However, this allows easy search of this knowledge and instant recognition of useful information that we’ve encountered in the past.

A few paragraphs ago, I wrote “we frame structure in particular ways,” but this is entirely unclear – in which ways do we frame structure?

When faced with a problem, we recognize the structure of problems we have experienced and encoded in memory. If a problem is familiar, we don’t need any processing to solve it; we can just use whatever worked last time.

We do this so naturally, it’s almost difficult to even think of recognition as a part of problem solving:

“If one is asked “What is the value of pi?” and immediately answers “3.1416,” it is probable that the answer to the question was recognized: i.e., was already in memory and was simply evoked by the act of understanding the question. One might object that this is hardly an example of a problem. In terms of difficulty, of course, the objection is correct. But the situation fits strictly the set-predicate definition of problem (given the set of real numbers, find the one that equals pi). Thus, the triviality of the problem must owe something to the problem solver’s repertoire of methods. The problem is not easy for all solvers. If a problem solver knows only the definition of pi as the ratio of the circumference to the diameter of a circle, he might have to solve the problem by circumscribing a polygon about the circle-not at all a recognition process.” (Newell & Simon, 1972; pp. 94-95)

Newell and Simon note that much of problem solving comes down to recognition. If we don’t immediately recognize a solution, we break problems down into smaller chunks. One of these smaller pieces must eventually be solved, but it is usually solved by recognition.

This is why high-level chess players can play speed chess – they are operating on recognition of board configurations they’ve seen in the past. As you speed up play, performance goes down compared to normally paced games, but not by much. Exhaustive search just isn’t that helpful in chess and humans aren’t very good at it anyway. Part of why it was so difficult to build computer chess programs was that they tended to rely on exhaustive search and couldn’t recognize patterns.

Recognition of previously encountered structure also explains expert performance more generally. Experts build up lots of categories and experiences in memory and can often instantly recognize important information that laymen miss. This is repeatedly portrayed as a mysterious ability that even the experts themselves can’t explain, but this is just because we don’t have conscious access to our memories’ indices.

This brings us to experiences of “insight,” where solutions to problems suddenly become clear. Here too, the claim is that most of these sparks of intuition are just recognition. Because framing can vary, there are lots of different ways to view information. When our perspective (framing) on one piece of information shifts, it can suddenly look similar to (match the index of) another structure that we’ve encountered before. The earlier experience and/or the connection between the two ideas is recognized, but again, because we don’t have conscious access to this process, it feels mysterious.

But insight and experts are just special cases of how each of us deals with problems. This is (part of) why different people can have very different reactions to the same problem. One may even succeed or fail because of differences in prior experience. This is obvious if we imagine someone who doesn’t know the value of pi. It’s harder to view speed chess in the same light, possibly because we are so inclined to attribute intuition (and advanced chess play) to ineffable wonders of human achievement.

If recognizing previously encountered structure is important, then framing influences how likely you are to realize a problem is one you’ve seen before. If you have to play tic-tac-toe, that’s probably easy – but the isomorphic number scrabble game (discussed in the previous post) seems totally novel because its framing is unfamiliar. The same stimulus may trigger different recognitions and thus different behavior.

This can occasionally backfire, as in the Einstellung effect, where a previous problem-solving method continues to be used in new problems even though a simpler method is available. Probably, this afflicts me every time I copy-paste (and then inevitably have to tweak) old code, but I don’t even realize it most of the time. Generally, this method should be useful to the extent that recognized problems are similar enough to those encountered in the past that they will yield to previous methods. Because the recognition process is conditioning on similarity already, what it comes up with is likely to be useful. (Even in Einstellung effects, using an inefficient but proven method might be better than attempting to start from scratch to develop a new method).

This paragraph is total speculation, but I wonder if one of the benefits of talk therapy might be changing the way people frame their problems. If we tend to recognize and frame similar problems in light of our experiences, those framings might be pathological. There are likely infinite possible framings available, most of which are unhelpful and many of which will be rejected, but talking to another person might be a useful way to explore the space of possible framings and find one that can be useful. It wouldn’t be a coincidence that moments of insight are anecdotally attached to successful therapy if insights are just recognition of a new framing that is consistent with memories other than those usually used to process one’s problems.

In sum, structure, framing, and recognition explain a lot of our abilities. They also explain why we can achieve so much and still struggle with novel problems. When I first read about heuristics and biases, I wondered how to square the view of human irrationality with progress in science and technology. It seemed like we had to either grant that biases weren't so common/problematic in daily life or claim that we could be living on Mars by now if not for our myriad flaws. I now think we often succeed despite using simple heuristics because of our ability to use the complex structures that exist in the environment. We are assisted by framing that structure in ways that help us reduce our need for complex processing. Our memory allows the selection of frame using experience as a guide to the future. These processes allow complex and disparate behavior to emerge from simple mechanisms and might also explain why, when people are presented with novel laboratory tasks divorced from the environment, they often look irrational.

Simon opens The Sciences of the Artificial with a description of a drawing by Dutch physicist Simon Stevin demonstrating that the law of the inclined plane follows from the impossibility of perpetual motion.

We can tell that the chain is at rest in the figure, because if it were not, it would rotate indefinitely. Because the parts of the chain hanging off the ramp on each side are symmetrical, we can imagine cutting hanging section in the middle, leaving four balls dangling on each side, and the chain should remain at rest. This means the balls on the short end of the ramp are balanced by those on the long end, with their ratio reciprocal to the sines of the slope’s angles. This is the mechanical advantage achieved by an incline plane.

Stevin wrote an inscription above the figure, which reads “Wonder, en is gheen wonder,” or, “Wonderful, but not incomprehensible.”  

Simon adds: “This is the task of natural science: to show that the wonderful is not incomprehensible, to show how it can be comprehended – but not to destroy wonder. For when we have explained the wonderful, unmasked the hidden pattern, a new wonder arises at how complexity was woven out of simplicity.”

 

 

Burton, R. A. (2008). On Being Certain: Believing you are right even when you're not. Macmillan.

Newell, A., & Simon, H. A. (1972). Human Problem Solving. Englewood Cliffs, NJ: Prentice-hall.

Simon, H. A. (1996). The Sciences of the Artificial. MIT press.

 

* These theories seem to have abruptly died and I’m not sure why. It may have to do with shifts in popular computational frameworks implementing the models away from the production systems advocated by Simon and Newell. I don’t think the story I’m telling here needs to be tied to these particular models, as long as the general observations about recognition are sound.

** The importance of indexing to information retrieval can be seen in search engine optimization (SEO), which tries to optimize websites to be ranked higher on Google’s search results page. One of the major contributions to Google’s success was its use of the “PageRank,” which uses how many other (good quality) sites link to a site as a measure of its value. For more on indexing in memory, I recommend (the first half of) Dynamic Memory by Roger Schank.