Chapter 3 The Cost of Switching: Task Switching, Attention Residue and Interruptions of a Few Seconds

In everyday speech “multitasking” is often treated as a skill. What laboratory research mostly finds is a cost: moving from one task to another takes time and adds errors, and the cost cannot be removed entirely by “preparing better”.

Switch costs and residual costs

Evidence

The alternating-runs paradigm. Rogers and Monsell had participants alternate between two simple classification tasks in a predictable order (for example AABB) and compared reaction times on switch and repeat trials. Switch trials were clearly slower and more error-prone; as the interval between responses lengthened from very short to about 600 ms the switch cost fell substantially, but a sizeable residual cost remained even beyond a second. They argued that part of the reconfiguration of the task set can be completed in advance by endogenous control, and part only once the stimulus arrives (Rogers and Monsell 1995). Review. Monsell’s 2003 review summarised the main findings of task-switching research: the switch cost, the preparation effect, the residual cost that survives ample preparation, and the “mixing cost” whereby even repeat trials in mixed-task blocks are slower than in single-task blocks (Monsell 2003).

Calculation

A toy model of this structure: the activations $a_1$ , $a_2$ of two task sets each decay and inhibit each other:

$\tau \frac{da_1}{dt} = -a_1 + c_1 – w\,a_2, \qquad \tau \frac{da_2}{dt} = -a_2 + c_2 – w\,a_1$

$c$ is the control input: the cued task gets $c = 1$ , the other 0. Following Rogers and Monsell, before the stimulus the new task’s input can reach at most 0.65; the rest arrives only with the stimulus. A response is made when the difference between new and old activation exceeds a criterion; the higher the old task’s leftover activation at stimulus onset, the likelier an error. All parameters are illustrative.

# Competing task sets with decay and mutual inhibition (toy model, units ms, values illustrative):
#   tau da1/dt = -a1 + c1 - w*a2,   tau da2/dt = -a2 + c2 - w*a1
# Before the stimulus the new set's input is capped at PREP (after Rogers & Monsell 1995);
# RT = base + time until a_new - a_old > CRIT; errors rise with a_old at stimulus onset.
import math
TAU, W, PREP, CRIT, BASE, DT = 150.0, 0.6, 0.65, 0.80, 450.0, 1.0

def trial(switch, rsi):
    a_new, a_old = (0.0, 1.0) if switch else (1.0, 0.0)   # state left by the previous trial
    t, c_new = 0.0, PREP if switch else 1.0
    def step(a, b, ca, cb):
        da = (-a + ca - W * b) / TAU; db = (-b + cb - W * a) / TAU
        return max(0.0, a + da * DT), max(0.0, b + db * DT)
    while t < rsi:                                         # preparation interval
        a_new, a_old = step(a_new, a_old, c_new, 0.0); t += DT
    old_at_onset = a_old
    rt = 0.0
    while a_new - a_old < CRIT:                            # stimulus: full input to the new set
        a_new, a_old = step(a_new, a_old, 1.0, 0.0); rt += DT
    p_err = 0.02 + 0.25 / (1 + math.exp(-(old_at_onset - 0.30) / 0.08))
    return BASE + rt, p_err

print("preparation (RSI ms) | repeat RT | switch RT | switch cost | switch error rate")
for rsi in (50, 150, 300, 600, 1200, 2400):
    r, _ = trial(False, rsi); s, e = trial(True, rsi)
    print(f"{rsi:20d} | {r:9.0f} | {s:9.0f} | {s - r:11.0f} | {e:10.1%}")
r, _ = trial(False, 5000); s, _ = trial(True, 5000)
print(f"residual cost with unlimited preparation: about {s - r:.0f} ms (cannot be prepared away)")
# preparation (RSI ms) | repeat RT | switch RT | switch cost | switch error rate
#                   50 |       450 |       738 |         288 |      26.9%
#                  150 |       450 |       677 |         227 |      16.8%
#                  300 |       450 |       605 |         155 |       2.6%
#                  600 |       450 |       546 |          96 |       2.6%
#                 1200 |       450 |       534 |          84 |       2.6%
#                 2400 |       450 |       534 |          84 |       2.6%
# residual cost with unlimited preparation: about 84 ms (cannot be prepared away)

Left: in the toy model, the switch cost falls with preparation time, but only down to a residual cost. Right: sequence-error rates after interruptions of about 2.8 and 4.4 seconds in two experiments (dots) and their own baselines (squares); the solid line is a descriptive fit, the dotted line extrapolation beyond the data.

The model reproduces the qualitative shape of the experiments: with 50 ms of preparation the switch cost is about 288 ms and the error rate about 27 %; with 600 ms of preparation the cost falls to about 96 ms; beyond a second it stays at about 84 ms, the part preparation cannot remove. The exact values depend on illustrative parameters and should not be compared point by point with any experiment.

Attention residue

Evidence

Leroy 2009. In two experiments Leroy had participants first do a word task (which could or could not be finished, with or without time pressure) and then move to evaluating job candidates’ CVs. In a lexical-decision task inserted between the two, responses to words related to the first task were faster, indicating that attention was still on it. The first experiment (84 undergraduates) found the least residue in those who had finished the first task under time pressure; the second (78 undergraduates) found that they also did best on the CV evaluation. Leroy called the phenomenon attention residue, and suggested that finishing under time pressure brings a sense of cognitive closure that lets people turn fully to the next task (Leroy 2009).

Attention residue shows that the cost of switching is not just a few hundred milliseconds of reconfiguration: something left unfinished keeps occupying part of attention and working memory. But note the scope of Leroy’s experiments: the tasks were short laboratory tasks and residue was measured within minutes, so they cannot tell us directly “how long residue lasts”.

Interruptions at the office: what were the “23 minutes”?

Evidence

An observational study. Mark, Gonzalez and Harris observed 24 information workers (managers, analysts and software developers) at an outsourcing firm providing IT and accounting services to financial companies in detail, for more than 700 hours in all, grouping related activities into “working spheres”. People stayed in a working sphere for an average of 11 min 4 s before turning to another; 57.1 % of working-sphere segments were interrupted; 77.2 % of interrupted work was resumed the same day, and that same-day work was picked up again after 25 min 26 s on average, with an average of 2.26 other working spheres in between; externally interrupted work was resumed sooner (22 min 37 s on average) than work people interrupted themselves (29 min 1 s), though this difference was only a trend ( $p < .055$ ) (Mark et al. 2005). An experiment. Mark, Gudith and Klocke had 48 participants process email with interruptions inserted. When interrupted, people actually finished faster, with no significant loss of quality, but reported more stress, frustration, time pressure and mental workload (Mark et al. 2008).

The widely repeated “after an interruption it takes 23 minutes to regain focus” is roughly a retelling of these numbers, but its meaning has shifted: the original study measured how long before people returned to the interrupted work, mostly doing other things in between; it did not measure focus.

Interruptions of a few seconds and errors at the next step

Evidence

Altmann, Trafton and Hambrick 2014. Three hundred students performed a procedure whose steps had to be carried out in a fixed order, and were occasionally interrupted by having to type a string of characters. In Experiment 1 interruptions averaged about 4.4 seconds; the sequence-error rate at the first step after an interruption was 5.8 % against a baseline (the error rate at steps 2 to 5 of the same procedure) of 1.8 %, more than three times as high. In Experiment 2 interruptions averaged about 2.8 seconds; the error rate was 4.3 % against a baseline of 2.0 %, more than twice as high. Errors unrelated to sequence were unaffected (Altmann et al. 2014). The authors explain this with the activation-based theory of memory for goals: the mental marker of “which step I’m on” decays during the interruption (Altmann and Trafton 2002).

Calculation

What can two data points tell us? The program below writes the excess error rate over baseline in the descriptive form $b \cdot D^k$ (our choice, not the authors’ model) and checks whether it already shows saturation.

# Altmann, Trafton & Hambrick (2014): sequence errors after interruptions of about 2.8 s (4.3 %,
# baseline 2.0 %) and 4.4 s (5.8 %, baseline 1.8 %), from two separate experiments.
# Descriptive fit (our choice, not the authors' model): excess error = b * D**k.
import math
DATA = [(2.76, 0.043, 0.020), (4.36, 0.058, 0.018)]      # duration (s), error rate, baseline

(d1, p1, b1), (d2, p2, b2) = DATA
e1, e2 = p1 - b1, p2 - b2
k = math.log(e2 / e1) / math.log(d2 / d1)
b = e1 / d1 ** k
print(f"excess sequence errors: {e1:.1%} after {d1} s, {e2:.1%} after {d2} s")
print(f"ratio to own baseline: {p1 / b1:.1f} x and {p2 / b2:.1f} x  ('doubled', 'tripled')")
print(f"power fit: excess = {b * 100:.2f} % * D^{k:.2f}, a little steeper than linear")
print(f"  (about {e1 / d1 * 100:.1f} percentage points per second of interruption)")
lin_ratio = d2 / d1
print(f"a saturating curve through the origin can rise at most {lin_ratio:.2f}-fold"
      f" from {d1} to {d2} s;")
print(f"the data rise {e2 / e1:.2f}-fold, so within this range they show no sign of levelling off")
print("extrapolation (shape assumed, NOT supported by the data):")
for d in (10.0, 30.0):
    print(f"  {d:4.0f} s: power law {min(1.0, b1 + b * d ** k):.0%}; but the next-step error rate"
          f" must level off somewhere")
print("these are errors at the NEXT step of an interrupted procedure, not minutes of lost focus")
# excess sequence errors: 2.3% after 2.76 s, 4.0% after 4.36 s
# ratio to own baseline: 2.1 x and 3.2 x  ('doubled', 'tripled')
# power fit: excess = 0.67 % * D^1.21, a little steeper than linear
#   (about 0.8 percentage points per second of interruption)
# a saturating curve through the origin can rise at most 1.58-fold from 2.76 to 4.36 s;
# the data rise 1.74-fold, so within this range they show no sign of levelling off
# extrapolation (shape assumed, NOT supported by the data):
#     10 s: power law 13%; but the next-step error rate must level off somewhere
#     30 s: power law 43%; but the next-step error rate must level off somewhere
# these are errors at the NEXT step of an interrupted procedure, not minutes of lost focus

Each second of interruption adds roughly 0.8 percentage points to the next-step sequence-error rate, and between 2.8 and 4.4 seconds there is no sign of levelling off. But the two points come from different experiments and participants: they are two points, not a curve, and extrapolating to 10 or 30 seconds has no support in the data. More importantly, the errors are at the next step of the interrupted procedure, not “unable to focus for minutes afterwards”.

“A glance at a message wrecks 15 minutes”?

The author’s framework contains the sentence “a 10-second glance at WeChat wrecks the next 15 minutes”. This book found no study that directly supports it: no experiment has measured the effect of a 10-second look on the following 15 minutes of work. The evidence above shows that interruptions have costs, but it cannot supply a specific figure such as “15 minutes”.

Calculation

A toy “one-hour budget” shows how heavily a conclusion like “15 minutes” depends on assumptions. Each switch costs about 0.3 seconds of reconfiguration, 30 seconds of finding one’s place, and attention residue: efficiency drops by 30 % after the switch and recovers with time constant $\tau_{res}$ . $\tau_{res}$ is not a quantity any study has measured.

# One-hour budget for switching: reconfiguration (s), resumption (s) and attention residue,
# efficiency 1 - R*exp(-t/TAU_RES) after each switch. R and TAU_RES are NOT measured quantities;
# the program shows how strongly the answer depends on TAU_RES.
import math
HOUR = 3600.0
RECONF, RESUME, R = 0.3, 30.0, 0.30          # seconds, seconds, initial efficiency loss

def effective_minutes(switches, tau_res):
    if switches == 0:
        return 60.0
    gap = HOUR / switches                     # evenly spaced switches
    lost = switches * (RECONF + RESUME)
    work = max(0.0, gap - RECONF - RESUME)
    # integral of R*exp(-t/tau) over one working stretch
    residue = R * tau_res * (1 - math.exp(-work / tau_res)) if tau_res > 0 else 0.0
    lost += switches * residue
    return max(0.0, (HOUR - lost) / 60)

print("effective working minutes in one hour (60 = no loss)")
print("switches/hour | residue tau = 0 s | 60 s | 5 min | 15 min")
for n in (0, 2, 6, 12, 30, 60):
    row = [effective_minutes(n, t) for t in (0, 60, 300, 900)]
    print(f"{n:13d} | {row[0]:17.1f} | {row[1]:4.1f} | {row[2]:5.1f} | {row[3]:6.1f}")
print("claim to test: 'a 10-second glance at a message ruins the next 15 minutes'")
one = 60 - effective_minutes(1, 900)
print(f"  with tau = 15 min this toy model loses {one:.1f} min per glance; with tau = 60 s, "
      f"{60 - effective_minutes(1, 60):.1f} min.")
print("  the answer is set by an assumed parameter, so the model cannot confirm the claim")
# effective working minutes in one hour (60 = no loss)
# switches/hour | residue tau = 0 s | 60 s | 5 min | 15 min
#             0 |              60.0 | 60.0 |  60.0 |   60.0
#             2 |              59.0 | 58.4 |  56.0 |   51.2
#             6 |              57.0 | 55.2 |  49.3 |   44.3
#            12 |              53.9 | 50.4 |  43.3 |   40.0
#            30 |              44.9 | 37.9 |  33.2 |   32.0
#            60 |              29.7 | 22.7 |  21.2 |   20.9
# claim to test: 'a 10-second glance at a message ruins the next 15 minutes'
#   with tau = 15 min this toy model loses 4.9 min per glance; with tau = 60 s, 0.8 min.
#   the answer is set by an assumed parameter, so the model cannot confirm the claim

In this model, with 12 switches an hour, effective working time falls from 60 minutes to anywhere between 54 minutes (no residue) and 40 minutes (residue time constant 15 minutes); the cost of one “glance” ranges from 0.8 to 4.9 minutes, depending entirely on the assumed $\tau_{res}$ . That is exactly the point: a model can help organise the question, but it cannot replace measurement.

Hypothesis · not established

Residue time-constant hypothesis (not yet established). After a brief look at a phone, the loss of efficiency on the main task recovers exponentially with a time constant between 1 and 5 minutes, not 15. Testable prediction: in an experiment with a continuous proofreading task and one randomly timed 10-second message check, compare the error rate in each minute after the check with control stretches without a check; the excess should fall below a third of its initial value within 5 minutes. If a clear excess remains after 15 minutes, the hypothesis is wrong, and the “15 minutes” claim gains support.

Chapter summary

Task switching has reliable costs: switch trials are slower and more error-prone; preparation reduces the cost, but a residual part cannot be prepared away. Unfinished tasks leave attention residue, and finishing under time pressure reduces it. Interruptions of a few seconds roughly double to triple the next-step sequence-error rate; the “23 minutes” is the average interval before interrupted work was resumed, not the time to regain focus; and “a glance at a message wrecks 15 minutes” has no direct evidence. The next chapter turns to motivation: when do rewards crowd out a person’s interest in the activity itself?

References

Altmann, Erik M., and J. Gregory Trafton. 2002. “Memory for Goals: An Activation-Based Model.” Cognitive Science 26 (1): 39–83. https://doi.org/10.1207/s15516709cog2601_2.

Altmann, Erik M., J. Gregory Trafton, and David Z. Hambrick. 2014. “Momentary Interruptions Can Derail the Train of Thought.” Journal of Experimental Psychology: General 143 (1): 215–26. https://doi.org/10.1037/a0030986.

Leroy, Sophie. 2009. “Why Is It so Hard to Do My Work? The Challenge of Attention Residue When Switching Between Work Tasks.” Organizational Behavior and Human Decision Processes 109 (2): 168–81. https://doi.org/10.1016/j.obhdp.2009.04.002.

Mark, Gloria, Victor M. Gonzalez, and Justin Harris. 2005. “No Task Left Behind? Examining the Nature of Fragmented Work.” Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’05) (New York), 321–30. https://doi.org/10.1145/1054972.1055017.

Mark, Gloria, Daniela Gudith, and Ulrich Klocke. 2008. “The Cost of Interrupted Work: More Speed and Stress.” Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’08) (New York), 107–10. https://doi.org/10.1145/1357054.1357072.

Monsell, Stephen. 2003. “Task Switching.” Trends in Cognitive Sciences 7 (3): 134–40. https://doi.org/10.1016/S1364-6613(03)00028-7.

Rogers, Robert D., and Stephen Monsell. 1995. “Costs of a Predictable Switch Between Simple Cognitive Tasks.” Journal of Experimental Psychology: General 124 (2): 207–31. https://doi.org/10.1037/0096-3445.124.2.207.

Fan, Y. (2026). Attention Networks, the Working-Memory Bottleneck and Self-Determination Theory: From Posner's Tripartite Network and Motivation Crowding-Out to the Information Theory of Flow, Read Beside Neo-Confucian Reverence (Jìng) [注意力网络、工作记忆瓶颈与内在动机的自决定理论] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23761341 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).