It's a Jungle in There: How Competition and Cooperation in the Brain Shape the Mind (13 page)

In the mid-1800s a Dutch scientist named Friedrich Donders asked a clever question.
¹
What would happen, he wondered, if he measured the time to respond to stimuli when people were in different mental states? Suppose, for example, that in one condition participants were told to press a key as quickly as possible when a light came on. Simple enough, Donders thought, and he called this the “simple RT” task.

In another condition, Donders presented participants with
two
lights and
two
buttons. If one light turned on, the subject was supposed to press the button assigned to it. If the other light turned on, the subject was supposed to press the other button. A choice was required here, so Donders called this the “choice RT” task.

Donders thought the choice task might take longer than the simple task. When he recorded RTs, he found that this was the case. Simple RTs were about 200 milliseconds (200 ms, or .2 s). Choice RTs were about 500 ms, or .5 s.

Donders’ approach was compelling because it was comparative. Simple RTs and choice RTs could be compared for the same stimuli and responses. Donders could look at the RT to make the very same response to the very same stimulus but in different contexts. This let him say something like the following: “The RT to respond with the left key to a left light is short if the left light is the only possible light and the left key is the only possible key. But the RT is longer if the left light is one of two possible lights and the left key is one of two possible keys.”
²
Donders subtracted the simple RT from the choice RT and concluded that it takes about 300 ms (500 ms minus 200 ms) to make a choice.

Pursuing this line of reasoning leads to interesting predictions. If it takes 300 ms to make
one
choice, it might take 300 more milliseconds to make
two
choices, it might take an additional 300 ms to make
three
choices, and so on. It’s easy enough to add choices to an RT task. If you’re an experimenter, you can give your participants more stimulus-response (S-R) alternatives. For example, you can add more possible lights and keys.

When this experiment has been done, the data have not supported the prediction that choice RTs get longer by a constant amount with each additional S-R alternative. Instead, choice RTs increase by roughly the same amount with each
doubling
of the number of S-R choices. When the number of S-R alternatives climbs from 2 to 4, the RT increases by about 300 ms, when the number of S-R alternatives climbs from 4 to 8, the RT increases by another 300 ms, and so on. This relation was discovered in the early 1950s and is called the Hick-Hyman Law, in honor of the two researchers who discovered it, Edmund Hick and Ray Hyman.
³

Why do choice RTs increase at a roughly constant rate with each doubling of the number of S-R alternatives? Is this outcome consistent with the jungle principle?

To begin with, consider a theory that was supposed to explain the result. The theory is one you’ve encountered in your daily life, though you may not know you have. It’s called
information theory
.
⁴
You’ve encountered it when you thought about the size of your computer’s hard drive. Does it hold 10 gigabytes? 100 gigabytes? A terabyte (1024 gigabytes)?

Bytes are strings of eight consecutive 1s and 0s. Each of those 1s and 0s is a “bit”—short for “binary digit” (either a 1 or a 0). For digital computers, all information is stored as strings of 1s and 0s. What makes computers “digital”
is that they use just these two values, corresponding to two logic states: 1 for “true” and 0 for “false.” Ultimately, the values map onto electrical switches that are either opened or closed when a computer’s power is on.

According to information theory, knowledge can be usefully represented as sets of true-false values. If you’re male, for example, you could be assigned a value of 1 for the proposition “You’re male,” or you could be assigned a value of 0 if you’re not male. If you’re over age 20, you could be assigned a value of 1 for the proposition “You’re at least 20 years old” or 0 if you’re not that old. Considering these two features—gender first and age second—you could be coded as 11, 10, 01, or 00.

For better or worse, this is how computers code everything. The digital era is all about representing information as strings of 1s and 0s. Representing information this way makes it possible to define information of any kind in digital form, whether it’s text or sound or pictures. No matter how the information is formatted at the time of presentation—as words on a page, as sounds on a speaker, or as pictures on a screen—inside the computer, the information is just 1s and 0s (or their analogous switch settings).

How does information theory relate to choice RTs, and how do both topics relate to the jungle principle? Information theory predicts that choice RTs should increase by a constant amount with each doubling of the number of S-R alternatives. The reason is that information theory says that unique S-R alternatives are found by successively splitting the S-R set down the middle until just one S-R alternative remains. A person in an RT experiment trying to identify one of four people who are distinguished by gender and age might therefore ask, “Is the person male?” and then “Is the person at least 20 years old?” Those two questions are all that’s needed to find the one person in four, provided there’s just one person in each of the gender and age categories.

The scenario I’ve just described may remind you of the game “20 questions.” Playing 20 questions is analogous to what might underlie the Hick-Hyman Law of choice RTs. If you’re facing an array of eight lights laid out from left to right with a button beneath each one (a standard setup in cognitive psychology laboratories), the way you could identify the particular S-R alternative in a given trial is to “divide and conquer,” as in 20 questions. In effect, you could ask the following three questions: (1) Is the illuminated light on the left? (2) Is the illuminated light on the left within the side selected in the first step? (3) Is the illuminated light on the left within the quadrant selected in the second step? By the time you’ve answered the third question, you’ve isolated the one required S-R alternative from the original set of eight, whereupon you can press the necessary key. You narrowed the options by splitting them successively down the middle.

As this example shows, it’s possible to explain the relation between choice RT and number of S-R alternatives in terms of series of binary choices. If participants rule out half the S-R alternatives over and over again until they find the one required S-R alternative, choice RTs should increase by roughly a fixed amount with each doubling of the number of S-R pairs.
⁵

This sounds lovely, doesn’t it? So tidy, so mechanical! Indeed, when this theory was advanced in the early 1950s, psychologists were jubilant.
⁶
They had a way of measuring information, and they had evidence that the time to make decisions was lawfully related to the amount of information to be considered. Psychology was beginning to look more like a true science in that its data were orderly and it had a unit of measurement, the bit. Every self-respecting science needs well-defined units of measurement. Physics has its ergs, economics has its GDP (gross domestic product), and so on.

However jubilant psychologists were with information theory, something happened that dampened their enthusiasm for it. The theory proved to be less useful than psychologists first expected, at least when it came to predicting how much information people could remember. It turned out that the number of items people could recall after being exposed to material they were supposed to report immediately thereafter depended on how
meaningful
the items were, not on how many bits the items had. The relevant studies showed that people could remember just a few nonsense syllables such as “blig,” “tuz,” and “frip,” but they could remember many more syllables if those syllables comprised meaningful sentences like this one: “The research I’m telling you about was introduced by a psychologist at Princeton University named George Miller, who showed that the number of meaningful elements, not the number of bits, predicted the amount people could remember.” You could probably recall much of the foregoing sentence, though it has many more syllables than the number of syllables in the nonsense list given before.

George Miller presented this work in one of the most widely cited articles in the history of psychology, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information.” The number seven was the number of meaningful clusters of information, or “chunks,” that people could hold in short-term memory. There was some variability in that number for different people, but for most people it was somewhere between 5 and 9.
⁷

Miller showed that information theory fails when it comes to predicting immediate recall. What accounts for this apparent breakdown? Why does the number of chunks predict memory span, whereas the number of bits, as used in the Hick-Hyman Law and information theory more generally, seem to predict choice RTs?

A way to approach this question is to ask whether the 20-questions explanation of the Hick-Hyman Law is the best one. Do people in fact play 20 questions when they identify one S-R alternative from a set of possibilities? A psychologist at the University of Michigan, Sylvan Kornblum, realized that there was a confound in the experiments showing that choice RT depends on the number of S-R alternatives. Whenever the number of S-R alternatives grew, Kornblum realized, each S-R alternative was tested less often. Kornblum carefully analyzed data from choice RT experiments and found that the data were better predicted by the
history
of choices than by the sheer
number
of choices. The more often and the more recently an S-R alternative was tested, the shorter was its choice RT.
⁸

It’s possible to express this outcome in terms of the jungle principle: The stimulus-response pairs that were tested the most had the most aggressive representatives in the brain. When those S-R alternatives were called for, their internal representatives shouted more loudly than the representatives of the other S-R alternatives. Those other alternatives, in effect, became meeker the bleaker their chances of being tested. Kornblum showed that a mathematically expressed theory, for which the jungle account is just an informal metaphor, could explain the Hick-Hyman Law.
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How does the foregoing discussion relate to Miller’s argument that chunks, and not just bits, determine memory span? Miller’s chunks are meaningful elements, but figuring out what “meaningful” means is a daunting task.

Consider another choice RT task—one where people try to indicate as quickly and as accurately as possible whether a letter string shown on a computer screen is a real word. Is “blig” a real word? What about “tuz” or “frip”? This is a
lexical decision
task. People performing the task must check their mental lexicons (their mental “dictionaries”) to see whether test items are represented there.

People can perform lexical decision tasks quite well. Considering how many words are known by typical participants in lexical decision tasks—40,000 words or so among college students—it’s remarkable how well they do. They manage to answer the is-this-a-word question in a second or less. How can they do this?

To address this question, it’s useful to ask a simple question about the lexical decision task: What is a word, anyway?

A word is an often-encountered letter string (or sound pattern) that’s marked by culture as a valid or “legal.” If you’ve often encountered a non-word
and have had to say it’s a non-word, that can be difficult. College professors (of which I’m one) have many non-words in their heads—letter strings they know are non-words, given though they encounter the misspellings in their students’ writing. When professors write their own prose, they have to suppress those lexical aliens. Suppression isn’t unusual. All of us have to suppress words we know when we find ourselves in polite company and want to say things we know we shouldn’t. Being able to suppress unwanted words, like being able to suppress unwanted actions, reflects inhibition.

Letter strings that are frequent enjoy relative freedom from suppression, as do legal letter strings. If you think of the number of chunks that can be retained in working memory as the number of alliances that can be strongly activated at a given time, you have the beginnings of an explanation of Miller’s discovery. Strength may account for memorability and for choice RTs. (More will be said about lexical decisions later in this chapter.)

When you indicate whether a letter string is a word, you do so without regard to how long ago you first learned it. It would be useful to have a way of studying how well people can recognize items soon after they’ve learned them.

In 1966 a young scientist named Saul Sternberg published a brief but highly influential paper in which he described such a task.
¹⁰
He asked college students to memorize a small set of items, such as one to six letters. He used small set sizes of items because he wanted to see how quickly the items could be recognized, not
whether
they could be, as in traditional studies of memory.

Once Sternberg was satisfied that his participants knew the letters, he showed the letters one at a time and asked his participants to indicate as quickly as they could whether each letter was in the memorized list. If it was, the subject was supposed to press one of two keys. If it wasn’t, the subject was supposed to press the other key.

The data from this task are presented in many textbooks in cognitive psychology because, besides being remarkably orderly, they distinguish among several hypotheses that Sternberg considered. Each hypothesis made a different prediction about the way the data could appear when RT was plotted as a function of the number of items in the memory set (
Figure 5
). It’s instructive to consider these hypotheses because they bring to light several issues that argue for the jungle principle.