The constants the rules rest on: human limits and the laws of interaction

The design rules a taught module carries arrive as instructions. Keep the menu short. Do not spend the user's attention on the interface itself. Each instruction usually arrives with a number, and that number sounds like evidence. This unit argues that the numbers are real measurements but conditional ones. The rule and the measurement are not the same claim. The rule is a decision someone made. The measurement is a result obtained under conditions the rule usually drops.

The constants come in two families. Capacity is how much a person holds at once. Timing is how long a physical or a decisional act takes. Each constant was obtained inside a narrow range of conditions. Quote the number, and the rule looks universal. State the conditions, and the rule becomes a prediction. The next unit asks not how much a person holds but what they hold.

Capacity: one number is quoted, and several were measured

The most quoted constant is the seven. Miller (1956) reviewed experiments on absolute judgement and immediate memory and concluded that performance is limited by a channel capacity of about seven chunks. He offered it as a rough bound, and introduced recoding, the grouping of items into larger units, as how people work within the limit.

The evidence for recoding is a small experiment he reports. A sequence of eighteen binary digits is far beyond the span of immediate memory, but regrouped in threes and named, it becomes six octal digits, which is not. The study he cites had twenty participants, who spanned about nine binary digits and about seven octal ones, and those who learned a recoding scheme raised their binary span. The limit counts chunks, not digits, and the person can change the size of a chunk. A rule that says a person holds seven things quotes a summary of tasks, not a reading from one instrument.

Forty-five years later Cowan (2001) argued that the figure had hardened into something Miller did not claim. He held that the empirical limit averages about four chunks, and that it is observable only under stated conditions, the clearest being the prevention of recoding. A number visible only when rehearsal is blocked describes what happens without support, not what a user does with a familiar screen. Cowan (2010) put the central store at three to five meaningful items. Baddeley and Hitch (1974) used a concurrent task to show that a short-term store is needed for reasoning, comprehension and learning. They also showed that its capacity is separable from long-term memory. The number can be replicated while the mechanism stays contested.

Two laws of movement predict a time only once a convention is fixed

The timing constants are fitted to data and have survived several task versions, but they still depend on how the experimenter defined the task. Fitts (1954) had participants move a stylus between two targets. He found that movement time varied with the logarithm of the ratio of distance to target width, giving a roughly constant throughput. Hick (1952) measured choice reaction time across up to ten equally likely alternatives. He found it rose with the logarithm of the number of choices. Neither relation is linear, and both describe the samples they were fitted to: doubling the alternatives does not double the decision time, and Ketcham and colleagues (2002) found that enlarging a target did not raise older adults' relative distance in the primary submovement as it did the young.

The conventions are not incidental. MacKenzie (1992) reviewed the competing formulations of Fitts' law. He proposed a more theoretically sound index of task difficulty, and across six studies, from the mouse to the eye tracker, found inconsistencies that made comparison between studies difficult. The law predicts a time only once the analyst fixes the difficulty measure, the target width convention and the treatment of errors. The constant is real. The number a designer writes into a spreadsheet is a choice.

Load became a design variable rather than a fixed budget

The capacity constant becomes actionable through load. Sweller (1988) showed that learners solving conventional problems spent limited working memory on means-ends search rather than on building schemas. Instruction that reduced that search improved learning, which turns the limit into a variable the designer controls.

Sweller and Cooper (1985) ran five experiments with Year 9, Year 11 and university mathematics students. Worked examples took considerably less time to study than the same problems solved conventionally. Students who studied them went on to solve problems of the same structure more quickly and with fewer mathematical errors. The authors state the boundary themselves: the advantage held for problems identical in structure to the examples, and this experiment did not test transfer.

Sweller, van Merrienboer and Paas (1998) gathered the account into design principles drawn from the same architecture. The principles come as a bundle, so testing one has not tested the others.

The resources are not one pool, so interference follows what two tasks share

If load were one pool, the total would be what mattered. Wickens (2002) argued that it is not. His four-dimensional multiple-resources model predicts more interference between two tasks the more they share processing stages, sensory modalities, codes and visual channels. The experiments behind it used equipment the authors were proposing for aircraft. A memory search suffered more from competition for visual encoding, while a tracking task suffered more from shared manual responding. A simulated flight task was disturbed least when a spatial task was seen and answered by hand and a verbal task was heard and spoken (Wickens, Sandry and Vidulich, 1983). Two demanding tasks can coexist when they use different resources. Two modest ones can collide when they share one.

The limit also sits inside a wider family of control functions. Diamond (2013) reported that inhibitory control, working memory and cognitive flexibility are separable but correlated, and trainable only within narrow limits.

The limits do not describe the work

Some of the work the field designs for is not a capacity. Endsley (1995) defined situation awareness as the perception of elements, their comprehension and the projection of future states. She identified attention and working memory as limits on its formation, and she introduced a taxonomy of errors based on the model. She argues that much decision failure is an awareness failure rather than a decision failure. A capacity constant says how much a person holds, not whether what is held is the right model of a changing situation.

Endsley (1995b) reviewed the available methods and tested one. The method interrupts a simulation for a moment to ask the operator what is happening at that instant. In two studies the interruption did not disturb performance, and the answers were not limited by memory for the queries. The technique works by stopping the task and asking the person, which is why the state has to be defined before it can be scored. Simon (1956) argued that organisms satisfy rather than optimise. He held that the appearance of rationality comes from the structure of the environment rather than from unlimited computation. A short menu and a stable interface give the environment that structure.

Contested question: is a capacity limit a constant or a convention?

The literature disagrees about what kind of thing a capacity limit is. On one side is the measured number, taught as a fact about people. Cowan (2001, 2010) holds that the central limit is about four items, and he treats the figure of seven as inherited rhetoric. Against that stands the claim it revises. Miller (1956) presented seven as a bound across tasks and made recoding central, so for him the number was never a fixed property of the store. The rule that says seven is Cowan's target, not Miller's claim.

The second disagreement is about the shape of the limit rather than its size. The cognitive-load tradition from Sweller (1988) to Sweller and colleagues (1998) treats load as drawn from one limited resource, so total load predicts failure. Wickens (2002) treats resources as plural, and he predicts interference from what two tasks share. Diamond (2013) supplies a third reading, in which the relevant functions are separable. The single-pool account says a heavy task degrades everything beside it. The multiple-resource account says a task in another modality is left largely intact.

The disagreements need different evidence. A capacity dispute is settled by a task that blocks recoding and measures the boundary directly, the condition Cowan specifies. A load dispute is settled by dual-task studies that manipulate sharing and demand independently. Neither test has been reported for most of the design rules this unit reviews. That is why the rules keep their numbers and lose their conditions. The evidence on the two sides is unequal. Cowan's four rests on a review of many experiments and is published with peer commentary disputing it, while Miller's seven is a review offering a bound rather than a reading. The single-pool account is an assumption of an instructional tradition, and Wickens's plural resources were fitted to dual-task data from aircraft tasks, so the model's reach beyond that setting is untested.

While the dispute is open, design for what both accounts forbid. Cut total demand, and keep two demanding tasks out of one modality, because overloading a single channel is a fault under either reading. When a rule quotes a number, state the conditions it was measured under.

Where the argument is heading

The direction is re-measurement and disaggregation. Brysbaert (2019) meta-analysed 190 studies with 18,573 participants and put adult silent reading of English well below the figures the field repeats. Diamond (2013) moves from one number to a profile of separable functions. Endsley (1995) moves from a capacity a person has to a state a person must maintain.

The sources this unit rests on

• Miller, G. A. (1956). The magical number seven, plus or minus two. Psychological Review 63(2), 81-97. doi:10.1037/h0043158 Offered seven as a rough bound across tasks and introduced recoding, quoting a twenty-participant study in which a binary span rose when the digits were grouped and named.
• Cowan, N. (2001). The magical number 4 in short-term memory. Behav. Brain Sci. 24(1), 87-114. doi:10.1017/S0140525X01003922 Argued that the seven was rhetorical, that the limit averages about four chunks, and that it is observable only under stated conditions such as the prevention of recoding.
• Cowan, N. (2010). The magical mystery four. Current Directions in Psychological Science 19(1), 51-57. doi:10.1177/0963721409359277 Put the central store at three to five meaningful items.
• Baddeley, A. D. and Hitch, G. (1974). Working memory. Psychology of Learning and Motivation, 47-89. doi:10.1016/S0079-7421(08)60452-1 Used a concurrent task to show that a short-term store is needed for reasoning, comprehension and learning.
• Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology 47(6), 381-391. doi:10.1037/h0055392 Found that movement time between two targets varied with the logarithm of the ratio of distance to target width. The founding measurement of pointing.
• Hick, W. E. (1952). On the rate of gain of information. Quarterly Journal of Experimental Psychology 4(1), 11-26. doi:10.1080/17470215208416600 Found that choice reaction time rose with the logarithm of the number of alternatives.
• MacKenzie, I. S. (1992). Fitts' law as a research and design tool in human-computer interaction. Human-Computer Interaction 7(1), 91-139. doi:10.1207/s15327051hci0701_3 Reviewed competing formulations, proposed a more theoretically sound index of task difficulty, and reviewed six studies, finding inconsistencies that made comparison difficult.
• Ketcham, C. J., Seidler, R. D., Van Gemmert, A. W. A. and Stelmach, G. E. (2002). Age-related kinematic differences as influenced by task difficulty, target size, and movement amplitude. Journals of Gerontology Series B 57(1), P54-P64. doi:10.1093/geronb/57.1.p54 Fifteen older adults (mean age 68) and fifteen young adults aimed at targets on a digitising tablet; enlarging the target did not raise older adults' relative distance in the primary submovement, so the fitted constants describe the sample they came from.
• Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognitive Science 12(2), 257-285. doi:10.1207/s15516709cog1202_4 Showed that learners solving conventional problems spent working memory on means-ends search rather than on building schemas, and that instruction reducing that search improved learning.
• Sweller, J. and Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction 2(1), 59-89. doi:10.1207/s1532690xci0201_3 Five experiments: worked examples took less study time and raised later performance on problems of the same structure, with no evidence of transfer to other structures.
• Sweller, J., van Merrienboer, J. J. G. and Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review 10(3), 251-296. doi:10.1023/A:1022193728205 Assembled the account into design principles derived from working memory, and proposed the worked-example and split-attention effects as consequences.
• Wickens, C. D. (2002). Multiple resources and performance prediction. Theoretical Issues in Ergonomics Science 3(2), 159-177. doi:10.1080/14639220210123806 His four-dimensional multiple-resources model predicts greater interference when two tasks share stages, modalities, codes or visual channels.
• Wickens, C. D., Sandry, D. L. and Vidulich, M. (1983). Compatibility and resource competition between modalities of input, central processing, and output. Human Factors 25(2), 227-248. doi:10.1177/001872088302500209 Two aircraft experiments in which interference followed the shared modality.
• Endsley, M. R. (1995). Toward a theory of situation awareness in dynamic systems. Human Factors 37(1), 32-64. doi:10.1518/001872095779049543 Defined situation awareness as perception, comprehension and projection, and attention and working memory as limits on it.
• Endsley, M. R. (1995b). Measurement of situation awareness in dynamic systems. Human Factors 37(1), 65-84. doi:10.1518/001872095779049499 Reviews measures of situation awareness and tests a query technique that interrupts a simulation to ask the operator what is happening, finding it not intrusive.
• Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review 63(2), 129-138. doi:10.1037/h0042769 Argued that organisms satisfy rather than optimise, and that the appearance of rationality comes from the structure of the environment.
• Diamond, A. (2013). Executive functions. Annual Review of Psychology 64(1), 135-168. doi:10.1146/annurev-psych-113011-143750 Reported that inhibitory control, working memory and cognitive flexibility are separable but correlated and trainable only within narrow limits.
• Brysbaert, M. (2019). How many words do we read per minute? A review and meta-analysis of reading rate. Journal of Memory and Language 109, 104047. doi:10.1016/j.jml.2019.104047 Meta-analysed 190 studies with 18,573 participants: adult English silent reading at 238 words per minute for non-fiction and 260 for fiction.