An Explanation of Digit Span and the Stroop effect using the Model Human Processor Framework

Problem Solving and Reasoning Section

Herb Simon, Jill Larkin, & Jonathan Cohen
David Crow


Chase and Ericsson (1982 as cited in Anderson, 1995) have suggested that experts have a advantage in long-term memory over novices. Experts have been shown an increased capacity to store domain specific information (Anderson, 1995).

Digit Span

The strongest evidence that experts are able to recall more patterns as well as larger patterns comes from the work of Chase and Ericsson (1982 as cited in Anderson, 1995). They studied a subject, SF, increase his digit span to 81 random digits presented at a rate of 1 digit per second. The explanation for this feat of human memory is that SF was learning to chunk the digits into meaningful patterns and he was using what Chase and Ericsson called a retrieval structure which enabled him to recall 22 chunked patterns. SF was a long distance runner and part of his technique was to convert the digits into running times. The chunking of digits into meaningful patterns such as birthdays, ages, and years is a common strategy used. The retrieval structure described by Chase and Ericsson was very specific, it did not generalize to the recall of letters, only digits. Chase and Ericsson hypothesize that part of what underlies development of expertise is the development of retrieval structures which allow for the superior retrieval of past patterns.

Model: MHP

The Model Human Processor is capable of providing an account of the development of these retrieval structures and the increased performance of long-term memory. The model human processor (MHP) is an engineering model of human behavior (Card, Moran, & Newell, 1983). The MHP is designed to make approximate predictions of gross human behavior. The model can be described by a set of memories and processors with a set of principles. The model can be divided into three interacting subsystems:


  1. the perceptual system;
  2. the cognitive system;
  3. the motor system, each with its own set of memories and processors (Card et al., 1983, pp. 24).


The memories and processors are described by a few parameters:

the storage capacity in items

the decay time of an item

the main code type (physical, acoustic, visual, semantic)

the cycle time.

Working memory

Working memory consists of a subset of elements from Long-Term memory that have been activated. Working memory has the following adjustable parameters: WM= 3 [2.5-4.1] chunks; WM* = 7 [5-9] chunks; WM = 7 [5-226] sec; WM(1 chunk) = 73 [73-226] sec; WM(3 chunks) = 7 [5-34] sec; WM = Acoustic or Visual. Access to each item in working memory is provided by the cognitive processor which the time parameter C = 70 [25-170] msec.

Long-term memory (chunks)

In the MHP the activated elements of Long-Term Memory consist of symbols called chunks. The chunks can be organized into larger units. What constitutes a chunk is a function combining the characteristics of the user and of the task.


The increase in digit span can be accounted for in the cognitive processor, the working memory and the long-term memory of the MHP. Working memory holds the intermediate products of thinking and the representations by the perceptual system of the MHP (Card et al., 1983, pp. 36).

Major connection between model and data

If the user performs a recoding of the presented symbols rapidly enough then long lists of random lists can be mapped into prepared chunks. An example of a recoding is the mapping of binary digits into hexadecimal digits (Card, Moran, & Newell, 1983). A list of zeros and ones, e.g., 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0, can be grouped into 0100 0010 0001 0110 0110 1000 which can be recoded into hexadecimal digits that represent the same information, 4 2 1 3 6 6 8. This recoding must be done in both directions, i.e., from binary to hexadecimal and from hexadecimal back to binary. With extended effort this can increase the WM* (the effective capacity of working memory) of the user beyond the 5-9 chunks usually stored.

Chase and Ericsson (1982 as cited in Anderson, 1995) have explained that this recoding and storage would have allowed SF to increase his digit span to approximately 20 digits.

Practice Effects in the MHP

The MHP is capable of modeling this increase in working memory.

Sufficient time for recoding

In the MHP the cognitive cycle time decrease with practice allowing the user to have more than enough time use a complex recoding process before the presentation of the next digit (P6. The Power Law of Practice states that amount of time to perform a task on a trial is power function in the form of Tn = T1n-, where = .4 [.2-.6]).

Retrieval structure

Chase and Ericsson describe the process that SF used to increase his digit span to 81 digits involved a retrieval structure. The MHP explains this retrieval structure in P2. The Encoding Specificity Principle. Basically this principle states

The MHP would account for these retrieval structures as a gross application of the Encoding Specificity principle. The retrieval structure in MHP could be described as the user having developed a specific encoding operation whose recall cues are specific to the presentation of digits in the laboratory setting are strong enough to facilitate effective access to the stored digits (Card et al., 1983).

The MHP is an engineering model of human performance and may not adequately explain how the retrieval structures are built or represented in Long-Term Memory. The retrieval structures are better described using a more detailed model of the cognitive processor. Soar is generally consistent with the MHP and describes cognition and memory in the fashion of a programmed computer with memory accessing organization and the full details of the operation of the processors (John, Vera, & Newell, 1993). Soar formulates all tasks in problem spaces in which operators are selectively applied to the current state to attain the desired state (John et al., 1993, pp. 1214). In Soar the retrieval structure are defined in long-term memory as productions. A Soar model of the digit span task determine that the accumulated coded knowledge in working memory is insufficient to repeat the digits and an impasse occurs. Soar then responds by creating a subgoal in which a new problem space can be used to acquire the need knowledge (the retrieval structure). Once the model has the necessary knowledge, obtained through problem solving, the chunking mechanism of Soar adds the new productions to the recognition memory that encode the results of the problem solving. The nature of the productions in Soar is that the rule applied applies to a class of situations due to the abstractness of each production (Anderson, 1995). Thus in Soar the retrieval structures are represented as abstract productions for the storage of digits in long-term memory. Thus as Soar creates new problem spaces to solve the storage and recall of digits new productions regarding the storage of digits are created using problem solving operators. These productions increase the number of digits that can be stored with practice.

The Stroop Effect


Reading is an automatic process that requires little or no attention to execute but it is a very difficult process to stop from executing. Word recognition in well practiced readers is virtually impossible to stop. The strong tendency to words to control processing is known as the Stroop effect (Anderson, 1995).

The Stroop task consists of two subtasks, word reading and color naming (Anderson, 1995; Cohen, Dunbar, & McClelland, 1988). Subjects are required to either name the color of the ink in which a word is printed (color naming task) or to read the word aloud ignoring the color of the ink (word reading task) (Cohen et al., 1988). There are typically three types of stimuli used: conflict stimuli where the word and the ink color are different; congruent stimuli where the word and the ink are the same; and a control stimuli. Table 1 provides an example of the stimulus in each condition.

Table 1. Example stimuli in the Stroop Task (from Cohen et al., 1988, pp. 5).
Condition Example Stimulus

(where "red" is the response")
Color naming task:
Control XXX in red ink
Conflict GREEN in red ink
Congruent RED in red ink
Word reading task:
Control RED in black ink
Conflict RED in green ink
Congruent RED in red ink

The results of performance on the Stroop task has demonstrated that:

  1. Word reading is faster than color naming
  2. In word reading, ink color has no effect on the time it takes to read the word.
  3. In color naming, in the conflict condition performance is slower than the control or the congruent conditions.


The Model Human Processor can be used to model the control condition of the Stroop effect. A MHP model of reading a single syllable word and identifying the word is provided in Figure 1. The MHP predicts that this model would require 547 msec to correctly read the word in the word reading task. This model consists of the following steps:

  1. the model must attend to the word, C = 50 msec (from John, Vera & Newell, 1993; Gray, John & Atwood, 1993)
  2. the model then initiates an eye-movement to the word, C = 50 msec
  3. the eye-movement occurs, M = 30 msec (John & Gray, 1995)
  4. the model must perceive the word to get it into working memory, P = 100 msec (John & Gray, 1995)
  5. the word is placed into working memory, C = 50 msec
  6. the word is matched to a word in Long-Term Memory, C = 50 msec
  7. the speech is initiated, C = 50 msec
  8. the word is spoken, M = 170 msec for unfamiliar words (John & Gray, 1995)

This model totals 547 msec to read the word this is constant regardless of the stimuli presented to the MHP. A similar model (Figure 2) demonstrates how the MHP would predict the control condition in the color naming task. This task has an added operator at step 6, because naming the color is not as well learned there is an additional operator requiring the model to make a decision about what word to use. The model of color naming predicts a time of 630 msec. The MHP accurately predicts that word reading for the control condition is faster than the color naming control condition.

Extensions to the MHP

The MHP does not adequately describe the observed results from the conflict or the congruent conditions in the color naming task. The granularity of the operators in the MHP does not allow the distinction in processing between the stimuli in the color naming task. These results can be explained using a production system like Soar. Soar can be used to describe each of the cognitive operators in greater detail than what is provided in the MHP. Using Soar an explanation of the classify color operator and the match color operator (Figure 2) could account for the differences in reaction time for the color naming task. It can be assumed that because word reading can be very well learned and in MHP and Soar it is likely the first cognitive operation that happens after the word is in working memory.

Conflict stimuli

In MHP this is an assumption in Soar this would be because after the first decision cycle and all productions matching the goal would be firing that because word recognition has a preference for the word recognition. This does not solve the goal of identifying the color in the conflict condition and the model creates a new subgoal to identify the ink color however the word is present in working memory and the system and the decision cycle for the goal of identifying the color is influenced by the contents of working memory (Anderson, 1993). Because word recognition occurs automatically and places the word into working memory there is a conflict in the color recognition operator. Because of this conflict it is possible the because of the strength of the word reading production that it is selected even in the color naming goal and that a number of new goals are created in order to overcome this conflict. The operator required to classify the color in the MHP becomes longer as the number of subgoals and conflicts grow. A similar process occurs in the match color operator and the number of subgoals could increase because of the conflict between working memory and the productions.

Congruent Stimuli

The congruent stimuli follows a similar process to above except that the after the word has been recognized the goal of classifying the color does not have a conflict in the productions because the working memory contents (the word) and the color are in agreement. Because there is no conflict the operator changes the problem state and the model move on. The word name is already in working memory and the conflict resolution of the productions prefers items that have entered working memory recently. This would cause the model to return and move to the next goal. Because there is very little conflict resolution between productions with congruent stimuli the cognitive operations in the model would be faster and it would produce a faster reaction time.


The Model Human Processor provides an engineering model of human performance. However much of the processing in the is not well explained or covered by general principles that are not computationally described (John et al., 1993). The MHP is far from a complete cognitive theory however it has been conceptually rich enough to support the extension made with CPM (Critical Path Method; Cognitive, Perceptual, Motor) - GOMS, including continuous interaction tasks such as typing, and talking-while-keying tasks (John et al., 1993).

The MHP can be used to explain the results from a number of psychological observations. The model however requires additional assumptions and inadequate description of the processes to describe much of the cognitve processes. A production system model like Soar, or ACT-R, can provide a better description of the cognitive processes to extend the MHP to be applicable to psychological data. The computational nature of production systems provide an explicit representation of the process that occurs in each cognitive operator. Soar basically subsumes the Model Human Processor and provides a better basis to build models of cognition however the Model Human Process is robust enough to account for expert, error-free performance on routine task.


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Anderson, J. R. (1995). Cognitive Psychology and its Implications (4th Ed.). New York: W. H. Freeman and Company.

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Cohen, J. D., Dunbar, K., & McClelland, J. L. (1988). On the Control of Automatic Processes: A Parallel Distributed Processing Model of the Stroop Effect. CMU Technical Report AIP-40 (3).

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