Better Call Saul: Memory Scanning

Let's start with a little warm-up exercise. Memorize the following list of numbers: 

   5, 9, 3, 7, 2

Once you can recite those numbers without error, answer the following question: Does your list contain the following number?

   7 

How long did it take you to answer? What if you were given the same list, but without the last digit? Would it have taken you the same amount of time? What if you were given a much longer list? Would it have taken the same amount of time?  

Reaction Times & Mental Events

Cognitive Science is a relatively new discipline. According to whom you ask, it got its start in the mid-1960s. Behavioralism was all the rage thanks to psychologists like B.F. Skinner, Edward C. Tolman, and Clark L. Hull. By the 1960s though, the theory was wearing a little thin. Psychologists began to realize they needed more than drives, stimulus-response pairs, and reinforcement schedules to explain the complexity of human behavior. Thus, experimental psychologist began to investigate how the mind encoded, stored, and manipulated symbols. In other words, scientists began to talk about the mind as a computer. It's not much of a coincidence that the rise of cognitive science coincided with the computer revolution [1].

One of the early studies of cognition that deviated from the behaviorist tradition was conducted by a scientist named Saul Sternberg. He was interested in understanding how immediate memory (a distant relative of short-term memory) worked. Specifically, he was interested in measuring how long it takes to scan immediate memory for a specific item.

Here's how he set up an experiment to measure how long it takes to scan immediate memory. First, he defined a set of items that he wanted his volunteers to memorize. Saul chose the domain of whole numbers between 1 and 9. Then, within the set of all possible items, he selected a subset of numbers for his participants to memorize. He also varied how many items were in the set (that is, the set size). For example, suppose Saul selected a set size of five, and the items in our set are: 3, 8, 9, 2, 6. Once his participant had memorized those five items, he would present a probe (e.g., 9) and ask the participant if the probe was part of the original set. In this case, the proper response is "yes" (i.e., a positive item). Saul was interested in measuring the duration between the probe and the response, or the reaction time.

When is memory scanning finished?

Saul repeated the above procedure for set sizes between one and six. Each time he measured the reaction time and plotted it against the set size (see Fig. 1). In addition, he also included probes that were not in the original set of items (e.g., for the set: 5, 9, 3, 7, 2 the probe is 6 is not in the list). We will call these negative items.

Figure 1. Mean reaction time (RT) as a function of set size
for positive and negative items.

What can we conclude from the evidence collected so far? The simple conclusion is a linear relationship between set size and the mean reaction time. For each item that you add to the set, you need an extra ~40 milliseconds to verify that the probe is in the list (or not).

A follow-up question is: Why is there a linear relationship between set size and reaction time? First, it helps to discriminate between two types of memory scanning. The first type, which we will call self-terminating serial search, compares the probe to the first item in the set. If it matches, then the search immediately stops or terminates. If it doesn't match, then the probe is compared to the second item, and so on for all the items in the set. If memory scanning is a self-terminating serial process, then there should be a linear relationship between set size and reaction time. 

The second type of memory scanning is called exhaustive serial search. In this case, the probe is simultaneously compared to all the items in the set. Only after testing all of the items can the participant give a response. 

On average the exhaustive serial search will require more comparisons than the self-terminating serial search. To discriminate between the two types of search, we need to introduce another concept called serial position, which is equivalent to the ordinal number (e.g., 1st, 2nd, 3rd, etc.) of each item. In the example above, the probe, 9, matched the 3rd item. If we use a self-terminating search, then it would be faster because it would stop after comparing only three items. In addition, negative items will take longer, on average, because you need to compare all of the items in a set to know that the probe is not among them. 

An exhaustive search would take longer than the self-terminating search because it would have to test all five items. Negative items would take the same amount of time because all items need to be tested. If we use an exhaustive search, then there should be no discernible difference between positive and negative items.

If you introspect into your own process of completing this task, what would conclude? Do you use a self-terminating or an exhaustive search? According to Sternberg's paper, we use what he calls high-speed exhaustive search. In other words, he didn't find an effect of serial position on reaction time, nor did he find a difference between positive and negative items (the orange and yellow data points in Fig. 1 are very similar). This finding is surprising because even his participants who were tested using sets that they memorized extremely well reported that they thought they used a self-terminating serial search.

The STEM Connection

How does this connect to education? First, it is an interesting, real-world demonstration of a linear function. According to the original study [2], the mean reaction time is given by the following linear equation: RT = 37.9s + 397.2; where s is equal to the set size. You can talk to your class about what it means to have a y-intercept of approximately 400 milliseconds, and does that value have meaning with a set size of zero. You can also talk about the limits of extrapolating past the given information. For instance, what would it mean to have a set size of 79, and is that even realistic? 

Another discussion point around this topic is its generality. Saul Sternberg kept referring to immediate memory in his original study. Since then, cognitive science has introduced refinements to this concept in the form of short-term memory and working memory. In addition, there is also a distinction between short-term and long-term memory. Do the findings from the original memory scanning experiment generalize to different types of memory? For example, do we use a serial exhaustive search when scanning long-term memory? Do the results generalize to other types of items, such as images, sounds, and words? Science advances when we start to question the boundary conditions of the original findings. 

Memory scanning studies, which made extensive use of reaction times as a dependent measure, helped to usher in a new branch of experimental psychology. They helped move us away from training animals to investigating unseen mental processes. And for that, we are very lucky for Saul Sternberg.


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Dr. Bob

For More Information

[1] Isaacson, W. (2014) The Innovators: How a Group of Hackers, Geniuses, and Geeks Created the Digital Revolution. New York: Simon & Schuster.

[2] Sternberg, S. (1969). Memory-scanning: Mental processes revealed by reaction-time experiments. American Scientist, 421-457.