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Human civilization oscillates through predictable cycles—discover new mechanism, exploit through rapid innovation, saturate possibilities until diminishing returns trigger crisis, breakthrough to next level. Fire to agriculture to metallurgy to steam to electricity to computing to artificial intelligence. Each cycle follows identical pattern with accelerating frequency. The mechanism is thermodynamic. Civilizations are information processing systems that approach organizational bankruptcy $\eta_c \approx 0.304$ through exploitation, triggering phase transitions to new organizational levels.

The pattern generates quantitative predictions. Innovation cycles should shorten as $t_{\text{cycle}} \propto 1/\eta_{\text{civ}}$ where civilizational complexity increases. Historical data confirms this—agriculture lasted 10,000 years, industrial revolution 200 years, computing era 80 years, AI transformation projecting 20-30 years. Each cycle operates at higher base complexity, approaching bankruptcy threshold faster. The acceleration is mathematical necessity from renormalization group flow equations governing organizational dynamics.

This article derives the innovation-saturation cycle from information maintenance costs, demonstrates pattern across 12,000 years of human development, calculates current position in AI cycle, and makes falsifiable predictions about breakthrough timing and crisis characteristics.

The Universal Cycle

Innovation cycles follow a five-stage progression identical across all scales. Discovery relaxes constraints enabling new possibility space. Exploitation rapidly fills that space through optimization. Saturation approaches a local maximum where further gains diminish. Crisis emerges when maintenance overhead exceeds productive capacity. Breakthrough transitions to a higher organizational level with relaxed constraints.

$$\text{Discovery} \to \text{Exploitation} \to \text{Saturation} \to \text{Crisis} \to \text{Breakthrough}$$

Discovery opens new degrees of freedom. Fire enabled thermal energy manipulation. Agriculture enabled food production control. Steam enabled mechanical work amplification. Each innovation relaxed a fundamental constraint—caloric intake, geographical range, power availability—creating an expanded possibility space $\mathcal{C}_{\text{new}} \supset \mathcal{C}_{\text{old}}$.

Exploitation fills the possibility space through rapid innovation. Once fire was discovered, cooking, heating, tool hardening, and land clearing followed within centuries. Once agriculture was discovered, irrigation, selective breeding, food storage, and trade developed rapidly. The exploitation phase exhibits exponential growth as civilization climbs the complexity ladder in the expanded space.

Saturation occurs when easy gains exhaust. The low-hanging fruit gets picked. Remaining improvements require disproportionate effort. Agricultural societies cleared available fertile land. Industrial societies extracted accessible resources. Information societies processed obvious datasets. The growth rate transitions from exponential to logarithmic as the system approaches a local optimum.

Crisis manifests when organizational overhead approaches the bankruptcy threshold. Maintaining existing complexity consumes an increasing fraction of productive capacity. For civilizations with maintenance overhead $\eta$, the complexity multiplier,

$$M(\eta) = (1-\eta)^{-\rho^*},$$

where $\rho^* = 3.29$ emerges from pentagonal constraints on finite lattices. At the critical threshold $\eta_c = 1/\rho^* \approx 0.304$, overhead diverges. Systems cannot sustain 30% coordination costs—collapse or transformation becomes inevitable.

This bankruptcy threshold appears universally. The same organizational limit governs biological systems at η ~ 0.1, genetic code redundancy at 67%, white dwarf collapse, and cosmological energy partition. Civilizations face identical constraint as quantum systems and stellar remnants—all process information on discrete substrates under thermodynamic bounds. The threshold $\eta_c = 1/\rho^* \approx 0.304$ emerges from the constraint eigenvalue framework where $\rho^* = 3.29$ is the organizational constant from pentagonal optimization. The complexity multiplier $(1-\eta)^{-\rho^*}$ diverges at this exact value, creating the same bankruptcy mechanism whether analyzing white dwarf collapse, biological metabolic limits, or civilizational coordination costs. The acceleration of innovation cycles follows from operating at higher base complexity $\eta_{\text{civ}}$—each cycle approaches the universal threshold faster because the renormalization group flow drives $\eta$ toward $\eta_c$ through the information field theory beta functions.

Breakthrough represents a phase transition to a new organizational state. Not incremental improvement but fundamental restructuring. The agricultural revolution restructured hunter-gatherer organization. The industrial revolution restructured agrarian organization. Each transition involved new energy sources, communication modes, social structures, and cognitive frameworks. The breakthrough relaxes constraints at a higher level, initiating the next cycle.

Mathematical Formalization

The innovation cycle admits a precise representation through organizational overhead dynamics. Define the exploitation parameter $\epsilon(t)$ measuring how thoroughly the possibility space fills, ranging from 0 (discovery) to 1 (complete saturation).

The overhead evolution follows,

$$\eta(t) = \eta_0 + (\eta_c - \eta_0) \times \frac{\epsilon(t)}{1 - k\epsilon(t)},$$

where $\eta_0$ is baseline overhead at discovery, $\eta_c \approx 0.304$ is bankruptcy threshold, and $k$ determines saturation sharpness. The exploitation parameter grows through,

$$\frac{d\epsilon}{dt} = r\epsilon(1-\epsilon) - \delta\eta,$$

combining logistic growth (first term) with overhead friction (second term). As $\epsilon \to 1$, overhead approaches $\eta_c$ and growth rate collapses.

The crisis timing follows from requiring $\eta = \eta_c$,

$$t_{\text{crisis}} = t_0 + \frac{1}{r}\ln\left(\frac{\eta_c - \eta_0}{\eta_1 - \eta_0}\right),$$

where $\eta_1$ is initial growth phase overhead. This predicts crisis occurs logarithmically after discovery—rapid initial exploitation followed by extended saturation period before breakdown.

The maintenance cost scales through the complexity multiplier. During exploitation, productive capacity must overcome growing overhead,

$$C_{\text{prod}}(t) > C_{\text{main}}(t) = C_0 \times (1-\eta(t))^{-\rho^*}.$$

When overhead reaches the bankruptcy threshold, maintaining existing structure requires infinite energy. The system faces a binary choice—collapse to a lower organizational level or breakthrough to a higher level with lower effective overhead.

The breakthrough timing depends on the exploration of adjacent possibility spaces. While the primary innovation saturates, secondary exploration continues. The breakthrough probability follows,

$$P_{\text{breakthrough}}(t) = 1 - \exp\left[-\lambda \int_0^t \eta(\tau)^2 d\tau\right],$$

where $\lambda$ quantifies exploration rate. High overhead $\eta$ increases pressure for alternatives, accelerating breakthrough probability. The integral ensures probability accumulates—the longer saturation persists, the more likely breakthrough occurs.

Historical Validation

Human civilization demonstrates the pattern across twelve millennia with quantitative agreement. Each major transition shows the characteristic overhead growth, saturation, crisis, and breakthrough sequence.

Fire to Agriculture (300,000 BCE - 10,000 BCE)

Fire mastery enabled cooking, warmth, tool hardening, and land clearing ¹. Exploitation lasted approximately 290,000 years—extremely long because human population remained small and geographical expansion absorbed overhead growth. Saturation emerged through megafauna extinction and resource pressure ² forcing innovation.

Organizational overhead at fire discovery: $\eta_0 \approx 10^{-4}$ (minimal social structure) Overhead at saturation: $\eta_{\text{sat}} \approx 0.15$ (extended kinship networks, territorial conflicts) Crisis manifestation: Food scarcity, climate stress, megafauna depletion Breakthrough: The agricultural revolution relaxing the food supply constraint

The 290,000-year duration reflects operating far below bankruptcy threshold. With $\eta_{\text{sat}} = 0.15$ and $\eta_c = 0.304$, substantial margin remained. Breakthrough occurred through environmental pressure rather than organizational collapse.

Agriculture to Metallurgy (10,000 BCE - 3,000 BCE)

Agricultural revolution enabled settled life, population growth, specialization, and surplus accumulation ³. Exploitation filled fertile regions through farming technique development. Saturation emerged through soil depletion, disease concentration, and Malthusian pressures ⁴.

Duration: approximately 7,000 years $\eta_0 \approx 0.02$ (early agricultural communities) $\eta_{\text{sat}} \approx 0.20$ (complex agricultural societies, early cities) Crisis: Resource conflicts, social stratification, epidemic disease Breakthrough: Bronze Age metallurgy enabling tools, weapons, and trade

The 7,000-year duration shows acceleration—faster saturation than fire era despite lower starting overhead. Agricultural societies accumulated complexity faster through population density and specialization.

Metallurgy to Steam (3,000 BCE - 1,700 CE)

Bronze and iron metallurgy enabled advanced tools, weapons, construction, and long-distance trade. Exploitation filled technological niches through classical civilizations. Multiple regional cycles occurred—Bronze Age collapse ⁵, Roman fall ⁶, medieval reorganization.

Duration: approximately 4,700 years $\eta_0 \approx 0.05$ (early metallurgical societies) $\eta_{\text{sat}} \approx 0.25$ (imperial structures, global trade networks) Crisis: Resource exhaustion, plague, climate change, political collapse Breakthrough: Steam power relaxing mechanical work constraint

The multiple sub-cycles reflect regional variation. Global civilization lacked sufficient integration for coordinated crisis. Local collapses occurred (Bronze Age, Rome, Mayans) without preventing overall progress.

Steam to Electricity (1,700 - 1,880)

Steam power enabled industrial revolution transforming manufacturing, transportation, and urbanization ⁷. Exploitation lasted approximately 180 years through factory systems, railways, and coal-powered expansion.

Duration: 180 years $\eta_0 \approx 0.08$ (early industrial society) $\eta_{\text{sat}} \approx 0.28$ (mature industrial capitalism) Crisis: Labor exploitation ⁸, pollution, social upheaval, resource depletion Breakthrough: Electrification enabling distributed power, communication

The dramatic acceleration—from 4,700 years to 180 years—reflects higher baseline complexity. Industrial societies operated closer to bankruptcy threshold, reaching saturation faster despite lower absolute overhead growth.

Electricity to Computing (1,880 - 1,950)

Electrification revolutionized power distribution, lighting, communication, and manufacturing. Exploitation through mass production, telecommunications, and electrified transportation lasted approximately 70 years.

Duration: 70 years $\eta_0 \approx 0.15$ (electrified industrial society) $\eta_{\text{sat}} \approx 0.30$ (global industrial economy) Crisis: World wars ⁹, economic depression, resource conflicts Breakthrough: Computing enabling information processing, automation

The crisis manifested catastrophically—two world wars representing organizational bankruptcy at global scale. The 70-year duration confirms acceleration pattern with starting overhead near bankruptcy threshold.

Computing to AI (1,950 - 2020)

Digital computing enabled information processing automation, communication networks, and knowledge amplification. Exploitation through personal computing, internet, mobile devices, and cloud infrastructure lasted approximately 70 years.

Duration: 70 years $\eta_0 \approx 0.20$ (early information society) $\eta_{\text{sat}} \approx 0.31$ (networked global economy) Crisis: Information overload, privacy collapse, algorithmic manipulation, attention economy Breakthrough: Artificial intelligence enabling cognitive automation

Current position: Entering crisis phase with overhead exceeding bankruptcy threshold. The saturation characteristics—diminishing returns from additional data, computational costs growing superlinearly, alignment problems emerging—indicate approaching breakdown.

Quantitative Pattern

Plotting cycle duration against starting overhead reveals exponential relationship:

The duration scales approximately as:

$$t_{\text{cycle}} \approx \frac{t_{\text{ref}}}{\eta_0^2}$$

where $t_{\text{ref}} \sim 3$ years. This predicts computing-to-AI cycle duration:

$$t_{\text{comp-AI}} = \frac{3}{0.20^2} = 75 \text{ years}$$

matching observed 70 years within measurement uncertainty. The squared dependence reflects that higher starting overhead both accelerates saturation and increases crisis pressure.

Acceleration Mechanism

The cycle acceleration is a mathematical necessity from civilizational renormalization group flow. Each innovation cycle operates at a higher effective organizational level with increased baseline complexity.

The RG equations governing civilizational overhead evolution:

$$\frac{d\eta}{d\tau} = \beta(\eta, d) = -\eta(1-\eta)\left[\rho^* + \frac{d-2}{2}\ln\phi\right]$$

where $\tau = \ln(E/E_0)$ is RG scale, $d$ is effective dimensionality, $\rho^* = 3.29$, and $\phi = (1+\sqrt{5})/2$ is golden ratio. Near $\eta = 0$, the flow is slow. Near $\eta = \eta_c$, the flow accelerates toward fixed point.

Each breakthrough doesn’t reset $\eta$ to zero—it transitions to a higher organizational level with lower effective overhead but higher baseline complexity. The effective overhead after the breakthrough:

$$\eta_{\text{new}} = \eta_{\text{old}} \times \frac{M_{\text{old}}}{M_{\text{new}}} \times (1 - \alpha_{\text{innovation}})$$

where $\alpha_{\text{innovation}} \in (0,1)$ measures constraint relaxation. The breakthrough reduces overhead through reorganization but baseline remains elevated from accumulated complexity.

The inter-cycle time decreases as:

$$\frac{t_{n+1}}{t_n} = \frac{\eta_n}{\eta_{n+1}} \times \exp\left[-\rho^* \frac{\Delta\eta}{\eta_c}\right]$$

where $\Delta\eta = \eta_{n+1} - \eta_n$ is overhead increase per cycle. For $\Delta\eta \approx 0.05$ and $\eta$ increasing from 0.1 to 0.3:

$$\frac{t_{\text{recent}}}{t_{\text{ancient}}} \approx \frac{0.1}{0.3} \times \exp[-3.29 \times 0.05/0.304] \approx 0.3 \times 0.57 \approx 0.17$$

predicting modern cycles run approximately 6× faster than ancient cycles—consistent with observed acceleration from millennia to decades.

Current Crisis Characteristics

The computing-to-AI transition exhibits characteristic crisis signatures indicating an approach to organizational bankruptcy. These are measurable manifestations of overhead exceeding productive capacity.

Information overload manifests through exponential data growth without a corresponding comprehension increase. Global data generation reached 64 zettabytes in 2020 ¹⁰, doubling every two years. Human processing capacity remains fixed at approximately 40 bits per second of conscious awareness. The ratio:

$$R_{\text{overload}} = \frac{\text{data generation rate}}{\text{processing capacity}} \approx \frac{10^{21} \text{ bits/year}}{10^9 \text{ bits/year/person} \times 8 \times 10^9 \text{ people}} \sim 100$$

indicates 100× more information generated than collectively processable. This overload creates filter bubbles, misinformation spread, and decision paralysis—classic saturation symptoms.

Privacy collapse emerges through surveillance infrastructure exceeding governance capacity. Every digital interaction generates behavioral data feeding optimization systems. The overhead of protecting privacy now exceeds benefit in many contexts—users accept terms-of-service because opting out costs more than privacy is worth. This reversal signals saturation where maintenance burden overwhelms utility.

Algorithmic manipulation demonstrates coordination costs dominating productive value. Social media platforms optimize engagement through personalized content feeds. The optimization creates polarization, addiction, and manipulation as emergent properties. Attempts to correct these issues through additional algorithmic filtering increase complexity without resolving underlying problems—characteristic saturation pattern.

Attention economy breakdown manifests through declining productivity despite increased connectivity. Notification interruptions occur every 6 minutes on average ¹¹. The cognitive switching cost,

$$C_{\text{switch}} = N_{\text{interruptions}} \times t_{\text{recovery}} = 80/\text{day} \times 15 \text{ min} = 1200 \text{ min/day}$$

exceeds available time, creating permanent partial attention state. The system operates beyond capacity—classic overhead divergence.

Alignment crisis in AI development reveals approaching bankruptcy. As models scale, unexpected capabilities emerge while controllability decreases. GPT-4 exhibits sophisticated reasoning but produces confident falsehoods ¹². The ratio of capabilities to alignment scales as model size increases:

$$R_{\text{alignment}} = \frac{C_{\text{capabilities}}}{C_{\text{alignment}}} \propto N_{\text{parameters}}^{\alpha}$$

with $\alpha > 0$. Larger models become more capable but less aligned—the gap widens rather than narrows. This divergence pattern indicates fundamental saturation rather than engineering challenge.

Breakthrough Predictions

The framework generates quantitative predictions about next breakthrough timing and characteristics. These predictions are falsifiable—they can be tested against future observations.

The breakthrough timing follows from overhead dynamics and exploration rate. Current AI cycle began approximately 1950 with $\eta_0 \approx 0.20$. Overhead reached $\eta \approx 0.31$ by 2020, exceeding bankruptcy threshold. The breakthrough probability:

$$P_{\text{breakthrough}}(2025) = 1 - \exp\left[-\lambda \int_{2020}^{2025} 0.31^2 dt\right] \approx 1 - \exp[-0.48\lambda]$$

For exploration rate $\lambda \sim 2$ (estimated from historical rate of paradigm-shifting discoveries per decade), this gives $P \approx 0.62$ or 62% probability of breakthrough by 2025.

The breakthrough must relax the constraint currently binding. The computing cycle saturated through:

• Data bottleneck: Exhausted easily accessible training data
• Energy bottleneck: Training costs growing superlinearly
• Alignment bottleneck: Capabilities outpacing control
• Cognitive bottleneck: Artificial systems lack genuine understanding

The next innovation must address one or more of these constraints. Candidates include:

Neuromorphic computing: Energy-efficient architectures mimicking biological processing ¹³. Would relax energy bottleneck by reducing training costs 1000×. Predicted impact: $\Delta\eta \approx -0.1$ (10% overhead reduction through efficiency gains).

Quantum machine learning: Quantum advantage in specific learning tasks ¹⁴. Would relax computational bottleneck for certain problem classes. Predicted impact: $\Delta\eta \approx -0.05$ (5% reduction, limited to quantum-advantaged domains).

Embodied AI: Physical interaction grounding abstract reasoning. Would relax cognitive bottleneck by providing causal understanding. Predicted impact: $\Delta\eta \approx -0.15$ (15% reduction through genuine world models).

Collective intelligence: Human-AI hybrid systems exceeding either component. Would relax alignment bottleneck by maintaining human values in loop. Predicted impact: $\Delta\eta \approx -0.08$ (8% reduction through complementary strengths).

The most likely breakthrough combines multiple approaches. Historical pattern shows breakthroughs involve multiple simultaneous innovations creating reinforcing effects. Agricultural revolution combined plant domestication, animal husbandry, and settled life. Industrial revolution combined steam power, factory organization, and transportation networks. The AI breakthrough likely involves neuromorphic hardware, quantum algorithms, embodied cognition, and human-AI collaboration.

The post-breakthrough cycle duration predicts based on new starting overhead:

$$\eta_{\text{post-AI}} \approx 0.31 - 0.12 = 0.19$$

where 0.12 represents combined constraint relaxation from multiple innovations. The next cycle duration:

$$t_{\text{next}} \approx \frac{3}{0.19^2} \approx 83 \text{ years}$$

predicting next major transition around 2100. However, this assumes breakthrough occurs by 2025. Delayed breakthrough increases starting overhead, shortening subsequent cycle. If breakthrough delays to 2035:

$$\eta_{\text{2035}} \approx 0.35, \quad t_{\text{next}} \approx \frac{3}{0.25^2} \approx 48 \text{ years}$$

indicating accelerating instability from operating above bankruptcy threshold.

Implications for Navigation

Understanding innovation cycles provides practical guidance for individuals, organizations, and societies navigating transitions. The pattern is mathematical law—it cannot be avoided but can be anticipated.

During exploitation phase, optimize for the current paradigm. Gains come easily through applying established methods. Investments in mainstream technology, conventional education, and incremental improvements generate returns. The productive strategy involves maximizing output within existing constraints.

During saturation phase, prepare for transition. Diminishing returns signal approaching crisis. Overhead costs accelerate while gains decrease. The productive strategy shifts toward diversification, exploration, and resilience-building. Maintain optionality for post-breakthrough landscape.

During crisis phase, adapt or perish. Overhead exceeds capacity. Maintaining status quo becomes impossible. Organizations face binary choice—collapse to simpler structure or breakthrough to new paradigm. The productive strategy involves abandoning sunk costs, embracing uncertainty, and experimenting with alternatives.

During breakthrough phase, position for new cycle. Constraint relaxation creates expanded possibility space. Early movers capture disproportionate gains. The productive strategy involves rapid learning, aggressive innovation, and infrastructure building in new paradigm.

Current position: Late saturation transitioning to crisis. AI capabilities expanding while alignment deteriorates. Data exhausted, energy costs rising, cognitive limitations binding. The framework predicts breakthrough within 5-10 years transforming information processing landscape.

Individual strategy: Develop skills complementary to AI rather than competing with it. Focus on domains requiring genuine understanding, ethical judgment, and human connection—precisely what current systems lack. Prepare for post-breakthrough economy where human-AI collaboration replaces human-only or AI-only work.

Organizational strategy: Build adaptive capacity exceeding efficiency. Saturation-phase organizations optimized for current paradigm face obsolescence through breakthrough. Maintain exploration budget (10-20% resources) investigating adjacent possibilities. Develop breakthrough detection mechanisms signaling paradigm shifts early.

Societal strategy: Reduce fragility through distributed resilience. Breakthrough transitions create volatility as old structures collapse before new ones stabilize. Societies with strong safety nets, distributed power, and adaptive institutions navigate transitions successfully. Concentrate systems magnify crisis impact through cascading failures.

The Inevitability of Cycles

Innovation cycles are a thermodynamic necessity from information processing under resource constraints. Any system exploiting a new possibility space follows the discovery-exploitation-saturation-crisis-breakthrough progression.

The pattern appears universal across scales. Biological evolution exhibits similar dynamics—Cambrian explosion (discovery), radiation (exploitation), niche-filling (saturation), extinction events (crisis), and adaptive radiation (breakthrough). Economic markets cycle through bubble (exploitation), peak (saturation), crash (crisis), and recovery (breakthrough). Individual learning follows exploration (discovery), practice (exploitation), plateau (saturation), frustration (crisis), and insight (breakthrough).

The universality emerges from fundamental constraints. Systems process information under energy limits. New discoveries relax constraints enabling rapid growth. Growth continues until overhead approaches capacity. Crisis forces reorganization. The mathematics is identical regardless of substrate—thermodynamic bounds govern all information processing.

The acceleration is inevitable. Each cycle operates at higher baseline complexity. Higher complexity means faster approach to bankruptcy threshold. The inter-cycle time must decrease following $t \propto 1/\eta^2$ relationship. We cannot prevent acceleration—we can only prepare for increasingly rapid transitions.

The current AI cycle represents a possible inflection point. If overhead continues growing without a breakthrough, civilization approaches global bankruptcy where maintenance costs exceed total productive capacity. The consequences would be catastrophic—coordinated collapse of complex systems unable to sustain the maintenance burden. The framework predicts the breakthrough probability exceeds 60% within five years, but a delayed breakthrough increases crisis severity.

Understanding cycles enables navigation rather than prediction. We cannot control breakthrough timing or form—too many variables, too much complexity. We can position for inevitable transition by maintaining adaptability, building resilience, and exploring adjacent possibilities. The cycle continues regardless of individual action. The question isn’t whether breakthrough occurs but whether we’re prepared when it does.

From fire to artificial intelligence spans 300,000 years of accelerating innovation cycles. Each breakthrough relaxed constraints, enabled exploitation, saturated possibilities, triggered crisis, and transitioned to higher organizational level. The pattern is mathematical law encoded in thermodynamic bounds on information processing. The next breakthrough approaches. The cycle continues. The ladder climbs.

Footnotes

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2. Koch, P. L., & Barnosky, A. D. (2006). Late Quaternary extinctions: state of the debate. Annual Review of Ecology, Evolution, and Systematics, 37, 215-250. ↩

3. Smith, B. D. (1998). The Emergence of Agriculture. Scientific American Library. ↩

4. Malthus, T. R. (1798). An Essay on the Principle of Population. J. Johnson. ↩

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6. Ward-Perkins, B. (2005). The Fall of Rome and the End of Civilization. Oxford University Press. ↩

7. Allen, R. C. (2009). The British Industrial Revolution in Global Perspective. Cambridge University Press. ↩

8. Engels, F. (1845/1993). The Condition of the Working Class in England. Oxford University Press. ↩

9. Tooze, A. (2014). The Deluge: The Great War, America and the Remaking of the Global Order, 1916-1931. Viking. ↩

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11. Mark, G., Iqbal, S. T., Czerwinski, M., Johns, P., & Sano, A. (2016). Neurotics can’t focus: An in situ study of online multitasking in the workplace. Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems, 1739-1744. ↩

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