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REVIEW 3 major objections 6 minor 50 references

Thermodynamic Human-Computer Interaction

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Fitts' law is derived from equilibrium thermodynamics, not merely fit to data, in this paper's central claim.

desk verdict A useful target-prediction heuristic with a real empirical deployment, wrapped in an overclaimed thermodynamic derivation that does not hold as stated. read the letter →

arxiv 2608.07123 v1 pith:UUJFAG6K submitted 2026-08-07 cs.HC cs.PFphysics.data-an

Uzafir Ahmad Rafaq , Muaz Hassan , Ali Muzaffar This is my paper · ORCID
classification cs.HCcs.PFphysics.data-an
keywords targetpredictionintentprobabilisticmodelingspatialinteractionFitts'lawstatisticalmechanicsthermodynamicsprefetching
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes that human interaction with digital targets is a thermodynamic process and that during smooth pointing it sits in thermal equilibrium. Starting from a Gibbs distribution over cursor-target microstates, it derives Fitts' law rather than fitting it: a harmonic potential centered on the target makes the agent perform damped harmonic motion, and the time until oscillations stay inside the target width gives the logarithmic movement-time law. The same derivation produces a Gaussian distribution of click endpoints and a target-prediction score that needs no training data, runs in constant time, and transfers between mouse and touch interfaces. The authors present this as the equilibrium half of a two-phase picture: large targets and ballistic motions are non-equilibrium phases where the Gaussian and logarithmic laws break down.

What carries the argument

The load-bearing object is the Gibbs distribution $P = Z^{-1} e^{-\mathcal{H}/k_B T}$ over an agent-target microstate whose Hamiltonian is $\mathcal{H} = \frac12 m_a v_a^2 + \frac12 m_i v_i^2 + V_{ai}(d_{ai})$. A Taylor expansion of $V_{ai}(d_{ai})$ about $d=0$ yields the harmonic potential $\frac12 k d^2$, which converts the distance exponent into a Gaussian kernel $\exp(-d^2/2\sigma_{\mathrm{spatial}}^2)$; combining this with a damped harmonic oscillator equation for approach gives the logarithmic time law. The partition function includes a null state (agent alone), and a Bayesian expected-utility rule decides when to act on the predicted probability.

What would settle it

A controlled pointing task with a small fixed target where the recorded endpoint distribution is clearly bimodal or skewed rather than Gaussian, or where movement time as a function of $D$ and $W$ departs from $\log_2(2D/W)$ at constant damping, would contradict the core derivation.

Watch

Extended reading notes

Core claim

The central claim is that a digital target behaves as a harmonic potential well in a thermal bath: assign the cursor and target kinetic energies and a potential that grows with squared distance to the target center, put the system in the Gibbs distribution, and every major empirical law of pointing follows as a theorem. The Gaussian endpoint distribution emerges from the quadratic potential, the damped-oscillator solution of the movement equation yields $MT = \tau_e + (\ln 2/\zeta\omega_n)\log_2(2D/W)$, i.e., Fitts' law, and the per-microstate probability $\psi_i = \mathcal{K}_a \mathcal{K}_i \mathcal{V}_{ai}$ becomes a ready-made predictor. The paper further claims that button properties such as color contrast and label clarity enter as additive, independent parameters that reshape the potential field, so the interaction probability is a joint product of separate Gaussians. Limitations are reinterpreted as phase transitions: for large targets the system leaves equilibrium, detected when the mean Lagrangian $\langle T\rangle - \langle V\rangle$ is nonzero.

Load-bearing premise

The argument assumes the cursor-target pair is a closed system in thermal equilibrium with a smooth potential that is quadratic in distance from the target's geometric center; if the potential is not harmonic, or the interaction is not equilibrated, the Gaussian endpoints and logarithmic time law do not follow.

Editorial extensions

If this is right

  • Fitts' law becomes a special case of equilibrium statistical mechanics, so its known failures for ballistic movements or very large targets are explained as non-equilibrium phases rather than as unexplained anomalies.
  • A uniform target predictor can be built that requires no training data, evaluates in constant time, and works across desktop cursors and mobile touch scrolling without retuning.
  • Button design properties like color contrast and label clarity can be encoded as independent, additive potential-field parameters, with endpoint dispersion shrinking as clarity increases.
  • A diagnostic criterion emerges for detecting when the interaction has left equilibrium: a nonzero mean Lagrangian $\langle T\rangle-\langle V\rangle$.
  • Web prefetching can be driven by the model's probability output through an expected-utility rule, reducing wasted bandwidth compared with trajectory heuristics while preserving high click-accuracy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If Fitts' law is an equilibrium-phase result, then other information-theoretic laws of HCI may likewise be equilibrium-phase results, and each would come with its own non-equilibrium correction terms.
  • The harmonic-potential picture suggests a concrete test for the 'temperature' of an interface: the measured endpoint variance of a user could serve as an operational $k_B T$, letting the model be personalized from a single calibration trial.
  • The additive-parameter assumption was only tested for contrast and label clarity; the same experimental design could be run on other paired parameters (size and spacing, or color and border radius) to see where the zero-coupling approximation starts to fail.
  • A natural extension is to let the potential well be non-quadratic or time-dependent during UI changes, which would predict systematic shifts in endpoint distributions that the current model cannot capture.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a thermodynamic framework for human-computer interaction, modeling each agent-target pair as a microstate with kinetic and potential energies under a Gibbs distribution. It claims to derive Fitts' law, Schmidt's law, and a Gaussian endpoint distribution from equilibrium statistical mechanics, and introduces a non-equilibrium criterion based on the average Lagrangian. The framework is implemented in a prefetching system and evaluated on desktop and mobile with 30 participants, reporting a desktop fetch:click ratio of 1.37 at 98.1% accuracy, alongside a controlled 2x2 experiment showing that label clarity and color contrast independently reduce endpoint variance.

Significance. If the central derivation were sound, this would be a genuinely unifying theoretical result with practical implications: a parameter-free, training-free, O(1) target predictor derived from energy principles. The empirical evaluation is a real strength: the prefetching system is deployed on a production-like e-commerce testbed, the within-subject ANOVA for endpoint variance is competently reported, and the implementation is publicly released. The endpoint Gaussian distribution is a direct mathematical consequence of the chosen quadratic potential plus the Gibbs measure, and the prediction model is not circular, since sigma_v is estimated from a Kalman filter and W_ei comes from target geometry rather than being fitted to click outcomes. However, the paper's central claim overreaches: the Fitts' law step is not a consequence of equilibrium thermodynamics alone, because equilibrium statistical mechanics contains no dynamics. The logarithmic time law is obtained by postulating an underdamped harmonic oscillator with free parameters.

major comments (3)
  1. [§3.4, Eqs. (22)–(27)] The derivation of Fitts' law is not a derivation from equilibrium thermodynamics. Equations (22)–(25) introduce an underdamped harmonic oscillator with damping ratio ζ, natural frequency ω_n, and additive delay τ_e, none of which are determined by the Gibbs measure in Eqs. (1)–(21) or measured independently. Equilibrium statistical mechanics provides a stationary distribution, not a time-to-target. The logarithmic law in Eq. (27) is therefore a consequence of the additional dynamical postulate, not of the equilibrium model. The abstract's claim that 'we derive Fitts' law ... from equilibrium thermodynamics' is unsupported. Please either derive the dynamics from the model, measure the constants independently, or revise the claim to state that Fitts' law is reproduced under a separate damped-oscillator assumption.
  2. [§3.3, Eq. (8)] The substitution m/k_BT = 1/σ_v^2 is introduced by fiat. The paper correctly notes that mass is not a property of an information system, but then uses dimensional analysis alone to equate a thermal-energy ratio with a velocity variance. This is a definitional choice, not a derivation, and it is load-bearing because the kinetic factors in Eq. (21) and the Gaussian endpoint distribution rely on it. No empirical or theoretical justification is given for why the Gibbs temperature maps exactly to velocity variance in this way. The paper should either provide an independent justification (e.g., from a fluctuation-dissipation argument) or explicitly label this as an assumption and test the model's sensitivity to it.
  3. [§3.6, Theorem 2, Eqs. (45)–(52)] The proof of Theorem 2 is invalid. Equation (47) states σ_p^2 ∝ ⟨Δq_p^2⟩, and Eq. (49) then yields σ_p^2 ∝ ⟨Δq_p⟩^2 + σ_p^2, which is a tautology, not a derivation. The transition from Eq. (51) to Eq. (52) asserts proportionality between the variances of two different degrees of freedom (velocity and position) without justification. Since this theorem is used to claim recovery of Schmidt's law and to motivate the non-equilibrium criterion, it needs to be corrected or explicitly presented as a conjecture supported by the empirical literature.
minor comments (6)
  1. [§3.2, Eqs. (3)–(4)] The null probability ψ_null is set to 1 on the argument that a stationary agent with no targets has zero Hamiltonian and hence ψ_null = exp(0) = 1. This is an arbitrary normalization; please clarify whether it is a convention and discuss its effect on the normalized probabilities in Eq. (4).
  2. [§3.5, Eq. (30)] The Taylor expansion of k(0;L) at L = 0 uses ΔL as the deviation from L = 0, but at the expansion point ΔL = 0, making the second-order term vanish. The exposition should be clarified, for example by expanding around a reference value L_0 and defining ΔL = L − L_0.
  3. [§3.9.1, Eq. (58)] The manually placed agent anchor (0.5W_px, 0.55H_px) is justified by 'natural thumb zone analysis' without a citation or empirical validation; this is a free parameter that could affect the mobile prefetching results.
  4. [§5.1.2] The reported accuracy of 98.1% is the fraction of clicked links prefetched; the baselines achieve 100% accuracy at higher fetch:click cost. The paper should either report whether the fetch:click ratio differences are statistically significant or explicitly state that the comparison is descriptive.
  5. [§6.2, Theorem 4] The condition |⟨T⟩ − ⟨V⟩| > 0 is presented as a new diagnostic criterion, but it is simply the negation of the equipartition condition for a harmonic oscillator. The connection to the Lagrangian ⟨L⟩ ≠ 0 is asserted rather than derived from the Hamiltonian formulation used earlier.
  6. [Figure 3] The caption does not specify the simulation parameters used to generate the damped sinusoidal curve, making the figure qualitative. Please add parameter values or state that it is illustrative.

Circularity Check

2 steps flagged · score 6.0 of 10

Fitts-law 'recovery' is the assumed damped-oscillator decay time restated; the Gibbs measure contributes no time-to-target.

  1. self definitional [Section 3.4, 'Damped Harmonic Motion', Eqs. (22)-(28)]
    "After substitution from Equation (25), this yields T = τ_e + (ln(2)/(ζω_n)) log2(2D/W) (27) ... This formulation is consistent with the movement time MT of Fitts' law [12]. MT = a + b log2(2D/W) (28). Consequently, the empirically determined Fitts' law is not just a fit to data, but a consequence of a system in equilibrium."

    The equilibrium Gibbs derivation in Sections 3.2-3.3 ends with the stationary Gaussian distribution (Eqs. 9, 17, 21) and contains no time evolution. The logarithmic law enters only after Eq. 22 postulates an underdamped oscillator, and Eq. 24 defines the interaction time as the moment its amplitude decays inside W. Eq. 27 is therefore algebraically identical to the Fitts-law form Eq. 28 by construction, with a = τ_e and b = ln(2)/(ζω_n) as free parameters that the Gibbs measure does not determine. The claimed recovery of Fitts' law from equilibrium thermodynamics is a restatement of the damped-oscillator ansatz, not a consequence of equilibrium statistical mechanics.

  2. self definitional [Section 6.2, Theorem 4, Eqs. (60)-(67)]
    "Theorem 4. For a harmonic agent-target model, an interaction lies outside the equilibrium phase if |⟨T⟩−⟨V⟩| > 0. Equivalently, ⟨L⟩ = ⟨T⟩−⟨V⟩ ≠ 0. Proof. For the proposed harmonic agent-target model, equilibrium requires the average kinetic and potential energies to be equal: ⟨T⟩ = ⟨V⟩."

    The theorem simply negates the assumption stated in its own proof: 'equilibrium requires ⟨T⟩=⟨V⟩' is the premise, and the theorem's condition |⟨T⟩−⟨V⟩|>0 is that same condition's negation. No independent measurement of ⟨T⟩ and ⟨V⟩ is reported to classify the large-target failures, so the non-equilibrium explanation is the equilibrium definition re-labeled rather than an empirically derived criterion.

full rationale

The prefetching pipeline is not circular: the unnormalized microstate probability uses Kalman-filter velocity variance and target-geometry effective width, and the reported 98.1%/98.0% accuracies are measured against external baselines (ForesightJS, viewport-all) rather than fitted to clicks. Theorem 3's endpoint-variance predictions are also tested against independent 2x2 within-subject data. There are no load-bearing self-citations in the reference list. The circularity is concentrated in the headline theory claims: the derivation of Fitts' law from equilibrium thermodynamics reduces to the containment time of an extra damped-oscillator ansatz with free constants, and Theorem 4's non-equilibrium criterion is its own definition restated. Because the central 'recovered law' claim is forced by construction while the empirical prediction and endpoint contributions remain independent, a partial circularity score of 6 is appropriate.

Assumptions & free parameters 6 free parameters · 6 assumptions · 3 invented entities

The model rests on a chain of assumptions: the Gibbs distribution for a cursor-target pair, a harmonic potential centered on the target, a reparameterization that cancels mass, a unity null-probability constant, and hand-set utility weights. The parameterized potential field adds unmeasured cognitive uncertainty variances. The target's attractive force and the equilibrium versus non-equilibrium phase distinction are new conceptual constructs without direct falsifiable handles outside the reported experiments.

free parameters (6)
  • Velocity variance sigma_v = from Kalman filter covariance (R=300, Q=0.1 in appendix)
    Controls the kinetic factor exp(-v^2/2 sigma_v^2); the filter noise parameters are chosen by the authors, not derived.
  • Effective target width W_ei (or sigma_spatial) = unspecified in the paper; likely the physical link width
    Controls the spatial Gaussian exp(-pi e d^2 / W_ei^2); the paper never states how W_ei is set for the prefetching links, and the relationship between W_ei and endpoint variance is assumed via MacKenzie's formula.
  • Null probability psi_null = 1
    Set by asserting a stationary agent with zero energy has Hamiltonian 0; this constant scales the normalized probability in Equation (4) and affects the prefetch decision threshold.
  • Utility weights omega_gain and omega_cost = 0.5 and 0.1
    Hand-set in Section 4.1 because usage metrics were unavailable; these weights determine the E[U]>0 prefetch trigger and therefore the Fetch:Click ratio.
  • Cognitive uncertainties sigma_L, sigma_C = not measured
    Introduced in Theorem 1 (Eq. 35-36 and Eq. 41) for label clarity and color contrast; no procedure is given to estimate them, and the prefetching evaluation ignores them.
  • Fitts' law constants (tau_e, zeta, omega_n) = not derived
    In Equation (27), the intercept tau_e and the slope ln(2)/(zeta omega_n) are free; the derivation of Fitts' law does not predict their values.
assumptions (6)
  • domain assumption The agent-target system is in thermal equilibrium and described by the Gibbs distribution (Eq. 1).
    Section 3.2 maps the cursor and a button to a thermodynamic system; the paper later concedes large targets are non-equilibrium, so this holds only for a subset of interactions.
  • ad hoc to paper The target exerts a harmonic potential V approx 1/2 k d^2 with minimum at its geometric center.
    Section 3.3, Eq. 12: Taylor expansion around d=0 with V(0)=0 and V'(0)=0; this quadratic form is assumed, not measured, and it forces the Gaussian endpoint distribution.
  • ad hoc to paper Mass m is not a property of an information system and can be eliminated via m/kBT = 1/sigma_v^2.
    Section 3.3, Eq. 8: dimensional analysis is used to replace mass with a velocity variance; this is a reparameterization rather than a physical derivation.
  • domain assumption Equipartition theorem applies to the agent-target degrees of freedom (average energy = 1/2 kBT per degree).
    Used in Theorem 2 and Theorem 3 (Eqs. 44, 54); equipartition is a property of thermal equilibrium and inherits the equilibrium assumption.
  • domain assumption Parameters such as label clarity and color contrast are independent, so cross terms in the Taylor expansion vanish.
    Eq. 39 in Lemma 4 sets coupled derivatives to zero; the ANOVA in Experiment 3 supports independence for these two parameters, but the general claim for all design parameters is untested.
  • ad hoc to paper A stationary agent with no targets has zero Hamiltonian, so psi_null = 1.
    Section 3.3: this fixes the normalization constant of the Gibbs measure without independent evidence.
invented entities (3)
  • Attractive force field of a target (including contributions from color, text, border radius)
    purpose: Explains why users aim at target centers and why design properties influence clicking probability.
    The force is a modeling construct; Experiment 3 shows contrast and label affect endpoint variance, but no direct measurement of force is provided.
  • Cognitive uncertainty parameters sigma_L, sigma_C
    purpose: Quantify the spread in how users perceive label clarity and color contrast in the parameterized potential field.
    These are free latent variables in Theorem 1 with no estimation procedure or direct measurement.
  • Equilibrium and non-equilibrium phases of interaction
    purpose: Partition the interaction lifecycle to explain why Fitts' law and the model fail on large targets.
    The phase distinction is inferred post hoc from the model's failure on large targets (Section 6.2), not independently operationalized.

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Cite this review

Pith. "Pith review of Thermodynamic Human-Computer Interaction." pith.science (2026). https://pith.science/paper/UUJFAG6K

@misc{pith2026260807123,
  author       = {Pith},
  title        = {Pith review of: Thermodynamic Human-Computer Interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UUJFAG6K}},
  note         = {Machine review of arXiv:2608.07123}
}
read the original abstract

Traditional human-computer interaction models rely on domain-specific techniques to model target prediction; models designed for cursor interaction prediction fail to generalize to mobile interfaces and vice versa. We introduce a unifying framework grounded in thermodynamics, proposing that human interaction is composed of phases in thermodynamic equilibrium and non-equilibrium. To demonstrate this, we derive Fitts' law and the proposed target prediction model from equilibrium thermodynamics by assigning kinetic and potential energies to a moving agent and target. Subsequently, we analyze the shortcomings of the prediction model and Fitts' law in edge cases, such as predicting intent for large targets. This analysis demonstrates that large targets cannot be accurately modeled using equilibrium thermodynamics. The proposed model scales across interaction modalities without modification, requires zero training data, and evaluates in constant O(1) time. Furthermore, we show that design properties such as the color of a button act as independent parameters that influence the attractive force exerted on an agent. Applied to live web prefetching tasks, the framework achieved an efficient Fetch:Click ratio of 1.37 and predicted the user's target with an accuracy of 98.1%.

Figures

Figures reproduced from arXiv: 2608.07123 by the authors.

Figure 1
Figure 1. A digital target acts as a harmonic potential well. The cursor follows a noisy path towards the potential minimum [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The probability of a system being in a particular microstate [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 2
Figure 2. The dotted shapes define the system boundaries [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: This figure represents a target with a width of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]
Figure 4
Figure 4. Figure 4: Left: Unnormalized probability rises prior to the click, triggering prefetches with significant lead time. Error bars [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Prefetch strategy trade-off. The Proposed Model captures nearly all intended clicks with 98% accuracy while drastically [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Overall endpoint standard deviation (𝜎𝑠𝑝𝑎𝑡𝑖𝑎𝑙) grouped by button condition. Higher contrast and clearer labels generally resulted in tighter endpoint distributions. 6.1 Experiment Results Discussion At 1.5 seconds prior to the click, mobile interactions exhibited a hig…
Figure 7
Figure 7. Figure 7: Within-subject effects of button parameters on endpoint standard deviation. Left & Center: High contrast and [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 9
Figure 9. Figure 9: The generated code was reviewed, modified, and tested [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 8
Figure 8. Figure 8: The custom e-commerce environment for Experiment 1 and 2. From left to right: The dense homepage, an individual [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: The controlled testing environment for Experiment 3. Top: The testing interface, which enforces a strict 280px target [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

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Works this paper leans on

50 extracted references · 20 canonical work pages

  1. [1]

    GoogleChromeLabs/Quicklink

    2026. GoogleChromeLabs/Quicklink. GoogleChromeLabs. https://github.com/ GoogleChromeLabs/quicklink

    work page 2026

  2. [2]

    Ahmad, Patrick M

    Bashar I. Ahmad, Patrick M. Langdon, Simon J. Godsill, Richard Donkor, Rebecca Wilde, and Lee Skrypchuk. 2016. You Do Not Have to Touch to Select: A Study on Predictive In-car Touchscreen with Mid-air Selection. InProceedings of the 8th International Conference on Automotive User Interfaces and Interactive Vehicular Applications (Automotive’UI 16). Associ...

    arXiv 2016

  3. [3]

    Takeshi Asano, Ehud Sharlin, Yoshifumi Kitamura, Kazuki Takashima, and Fumio Kishino. 2005. Predictive Interaction Using the Delphian Desktop. InProceedings of the 18th Annual ACM Symposium on User Interface Software and Technology (UIST ’05). Association for Computing Machinery, New York, NY, USA, 133–141. doi:10.1145/1095034.1095058

    arXiv 2005

  4. [4]

    Xiaojun Bi, Yang Li, and Shumin Zhai. 2013. FFitts Law: Modeling Finger Touch with Fitts’ Law. InProceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’13). Association for Computing Machinery, New York, NY, USA, 1363–1372. doi:10.1145/2470654.2466180

    arXiv 2013

  5. [5]

    Pradipta Biswas, Gokcen Aslan Aydemir, Pat Langdon, and Simon Godsill. 2013. Intent Recognition Using Neural Networks and Kalman Filters. InHuman- Computer Interaction and Knowledge Discovery in Complex, Unstructured, Big Data, Andreas Holzinger and Gabriella Pasi (Eds.). Springer, Berlin, Heidelberg, 112–123. doi:10.1007/978-3-642-39146-0_11

    work page doi:10.1007/978-3-642-39146-0_11 2013

  6. [6]

    2009.Speed Matters for Google Web Search

    Jake Brutlag. 2009.Speed Matters for Google Web Search. Technical Report. Google. https://services.google.com/fh/files/blogs/google_delayexp.pdf

    work page 2009

  7. [7]

    Olivier Chapuis, Jean-Baptiste Labrune, and Emmanuel Pietriga. 2009. DynaSpot: Speed-Dependent Area Cursor. InProceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’09). Association for Computing Machinery, New York, NY, USA, 1391–1400. doi:10.1145/1518701.1518911

    arXiv 2009

  8. [9]

    Xiuli Chen, Aditya Acharya, Antti Oulasvirta, and Andrew Howes. 2021. An Adaptive Model of Gaze-based Selection. InProceedings of the 2021 CHI Conference on Human Factors in Computing Systems (CHI ’21). Association for Computing Machinery, New York, NY, USA, 1–11. doi:10.1145/3411764.3445177

    arXiv 2021

Show all 50 references
  1. [10]

    Seungwon Do, Minsuk Chang, and Byungjoo Lee. 2021. A Simulation Model of Intermittently Controlled Point-and-Click Behaviour. InProceedings of the 2021 CHI Conference on Human Factors in Computing Systems (CHI ’21). Association for Computing Machinery, New York, NY, USA, 1–17....

    2021

  2. [11]

    Florian Fischer, Arthur Fleig, Markus Klar, and Jörg Müller. 2022. Optimal Feedback Control for Modeling Human–Computer Interaction.ACM Trans. Comput.-Hum. Interact.29, 6 (Nov. 2022), 51:1–51:70. doi:10.1145/3524122

    2022 doi

  3. [12]

    Paul M. Fitts. 1954. The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement.Journal of Experimental Psychology47, 6 (1954), 381–391. doi:10.1037/h0055392

    1954 doi

  4. [13]

    T Flash and N Hogan. 1985. The Coordination of Arm Movements: An Experi- mentally Confirmed Mathematical Model.The Journal of Neuroscience5, 7 (July 1985), 1688–1703. doi:10.1523/JNEUROSCI.05-07-01688.1985

    1985

  5. [14]

    Kwok, Erin You Wu, Hong Va Leong, Grace Ngai, and Stephen C.F

    Eugene Yujun Fu, Tiffany C.K. Kwok, Erin You Wu, Hong Va Leong, Grace Ngai, and Stephen C.F. Chan. 2017. Your Mouse Reveals Your Next Activity: Towards Predicting User Intention from Mouse Interaction. In2017 IEEE 41st Annual Computer Software and Applications Conference (COMP...

    2017 doi

  6. [15]

    Tovi Grossman and Ravin Balakrishnan. 2005. The Bubble Cursor: Enhancing Target Acquisition by Dynamic Resizing of the Cursor’s Activation Area. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’05). Association for Computing Machinery, New Yo...

    2005

  7. [16]

    Yves Guiard, Renaud Blanch, and Michel Beaudouin-Lafon. 2004. Object Pointing: A Complement to Bitmap Pointing in GUIs. InProceedings of Graphics Interface 2004 (GI ’04). Canadian Human-Computer Communications Society, Waterloo, CAN, 9–16. https://dl.acm.org/doi/10.5555/100605...

    2004

  8. [17]

    Harris and Daniel M

    Christopher M. Harris and Daniel M. Wolpert. 1998. Signal-Dependent Noise Determines Motor Planning.Nature394, 6695 (Aug. 1998), 780–784. doi:10.1038/ 29528

    1998

  9. [18]

    Steven Hoober. 2017. Design for Fingers, Touch, and People, Part 1 :: UX- matters. https://www.uxmatters.com/mt/archives/2017/03/design-for-fingers- touch-and-people-part-1.php

    2017

  10. [19]

    Aleksi Ikkala, Florian Fischer, Markus Klar, Miroslav Bachinski, Arthur Fleig, Andrew Howes, Perttu Hämäläinen, Jörg Müller, Roderick Murray-Smith, and Antti Oulasvirta. 2022. Breathing Life Into Biomechanical User Models. In Proceedings of the 35th Annual ACM Symposium on Use...

    2022

  11. [20]

    E. T. Jaynes. 1957. Information Theory and Statistical Mechanics.Physical Review 106, 4 (May 1957), 620–630. doi:10.1103/PhysRev.106.620

    1957 doi

  12. [21]

    R. E. Kalman. 1960. A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering82, 1 (March 1960), 35–45. doi:10.1115/1.3662552

    1960 doi

  13. [22]

    Hyo Chang Kim and Yong Gu Ji. 2019. Natural Thumb Zone on Smartphone with One-Handed Interaction: Effects of Thumb Length and Screen Size. In Proceedings of the 20th Congress of the International Ergonomics Association (IEA 2018), Sebastiano Bagnara, Riccardo Tartaglia, Sara A...

    2019

  14. [23]

    Markus Klar, Florian Fischer, Arthur Fleig, Miroslav Bachinski, and Jörg Müller

  15. [24]

    Williamson, and Roderick Murray-Smith

    Markus Klar, Sebastian Stein, Fraser Paterson, John H. Williamson, and Roderick Murray-Smith. 2025. An Active Inference Model of Mouse Point-and-Click Behaviour. arXiv:2510.14611 [cs.HC] doi:10.48550/arXiv.2510.14611

    2025 doi

  16. [25]

    Ron Kohavi and Roger Longbotham. 2007. Online Experiments: Lessons Learned. Computer40, 9 (Sept. 2007), 103–105. doi:10.1109/MC.2007.328

    2007 doi

  17. [26]

    Edward Lank, Yi-Chun Nikko Cheng, and Jaime Ruiz. 2007. Endpoint Prediction Using Motion Kinematics. InProceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’07). Association for Computing Machinery, New York, NY, USA, 637–646. doi:10.1145/1240624.1240724

    2007

  18. [27]

    Huy Viet Le, Valentin Schwind, Philipp Göttlich, and Niels Henze. 2017. Pre- dicTouch: A System to Reduce Touchscreen Latency Using Neural Networks and Inertial Measurement Units. InProceedings of the 2017 ACM International Conference on Interactive Surfaces and Spaces (ISS ’1...

    2017

  19. [28]

    Scott MacKenzie

    I. Scott MacKenzie. 1992. Fitts’ Law as a Research and Design Tool in Human-Computer Interaction.Human–Computer Interaction7, 1 (1992), 91–139. arXiv:https://doi.org/10.1207/s15327051hci0701_3 doi:10.1207/ s15327051hci0701_3

    1992 doi

  20. [29]

    Alberto Álvarez Martín, Henrik Gollee, Jörg Müller, and Roderick Murray- Smith

    J. Alberto Álvarez Martín, Henrik Gollee, Jörg Müller, and Roderick Murray- Smith. 2021. Intermittent Control as a Model of Mouse Movements.ACM Trans. Comput.-Hum. Interact.28, 5 (Aug. 2021), 35:1–35:46. doi:10.1145/3461836

    2021 doi

  21. [30]

    Michael McGuffin and Ravin Balakrishnan. 2002. Acquisition of Expanding Targets. InProceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’02). Association for Computing Machinery, New York, NY, USA, 57–64. doi:10.1145/503376.503388

    2002

  22. [31]

    McGuffin and Ravin Balakrishnan

    Michael J. McGuffin and Ravin Balakrishnan. 2005. Fitts’ Law and Expanding Targets: Experimental Studies and Designs for User Interfaces.ACM Trans. Comput.-Hum. Interact.12, 4 (Dec. 2005), 388–422. doi:10.1145/1121112.1121115

    2005

  23. [32]

    Michał Patryk Miazga, Hannah Bussmann, Antti Oulasvirta, and Patrick Ebel

  24. [33]

    Robert B. Miller. 1968. Response Time in Man-Computer Conversational Trans- actions. InProceedings of the December 9-11, 1968, Fall Joint Computer Conference, Part I (AFIPS ’68 (Fall, Part I)). Association for Computing Machinery, New York, NY, USA, 267–277. doi:10.1145/147658...

    1968

  25. [34]

    Hee-Seung Moon, Yi-Chi Liao, Chenyu Li, Byungjoo Lee, and Antti Oulasvirta

  26. [35]

    Mott and Jacob O

    Martez E. Mott and Jacob O. Wobbrock. 2014. Beating the Bubble: Using Kine- matic Triggering in the Bubble Lens for Acquiring Small, Dense Targets. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’14). Association for Computing Machinery, New...

    2014

  27. [36]

    Atsuo Murata. 1998. Improvement of Pointing Time by Predicting Targets in Pointing With a PC Mouse.International Journal of Human–Computer Interaction 10, 1 (March 1998), 23–32. doi:10.1207/s15327590ijhc1001_2

    1998 doi

  28. [37]

    Bhawna Nigam and Suresh Jain. 2010. Analysis of Markov Model on Different Web Prefetching and Caching Schemes. In2010 IEEE International Conference on Computational Intelligence and Computing Research. 1–6. doi:10.1109/ICCIC. 2010.5705732

    2010

  29. [38]

    Antti Oulasvirta, Jussi P. P. Jokinen, and Andrew Howes. 2022. Computational Rationality as a Theory of Interaction. InProceedings of the 2022 CHI Conference on Human Factors in Computing Systems (CHI ’22). Association for Computing Machinery, New York, NY, USA, 1–14. doi:10.1...

    2022

  30. [39]

    Eunji Park and Byungjoo Lee. 2020. An Intermittent Click Planning Model. In Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems (CHI ’20). Association for Computing Machinery, New York, NY, USA, 1–13. doi:10.1145/3313831.3376725

    2020

  31. [40]

    Patrick Baudisch, Edward Cutrell, Daniel Robbins, Mary Czerwinski, Peter Tandler, Benjamin Bederson, and Alex Zierlinger. 2003. Drag-and-Pop and Drag-and-Pick: Techniques for Accessing Remote Screen Content on Touch- and Pen-Operated Systems. InHuman-Computer Interaction, INTE...

    2003

  32. [41]

    Schmidt, Howard Zelaznik, Brian Hawkins, James S

    Richard A. Schmidt, Howard Zelaznik, Brian Hawkins, James S. Frank, and John T. Quinn Jr. 1979. Motor-Output Variability: A Theory for the Accuracy of Rapid Motor Acts.Psychological Review86, 5 (1979), 415–451. doi:10.1037/0033- 295X.86.5.415

    1979 doi

  33. [42]

    C. E. Shannon. 1948. A Mathematical Theory of Communication.The Bell System Technical Journal27, 3 (July 1948), 379–423. doi:10.1002/j.1538-7305.1948. tb01338.x

    1948

  34. [43]

    Bart Spaans. 2026. Spaansba/ForesightJS. https://github.com/spaansba/ ForesightJS

    2026

  35. [44]

    Aileen Worden, Nef Walker, Krishna Bharat, and Scott Hudson. 1997. Making Computers Easier for Older Adults to Use: Area Cursors and Sticky Icons. In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems (CHI ’97). Association for Computing Machinery, ...

    1997

  36. [45]

    Shumin Zhai, Jing Kong, and Xiangshi Ren. 2004. Speed–Accuracy Tradeoff in Fitts’ Law Tasks—on the Equivalency of Actual and Nominal Pointing Precision. International Journal of Human-Computer Studies61, 6 (Dec. 2004), 823–856. doi:10.1016/j.ijhcs.2004.09.007

    2004 doi

  37. [46]

    Zhi Li, Maozheng Zhao, Dibyendu Das, Hang Zhao, Yan Ma, Wanyu Liu, Michel Beaudouin-Lafon, Fusheng Wang, I. V. Ramakrishnan, and Xiaojun Bi. 2022. Select or Suggest? Reinforcement Learning-based Method for High-Accuracy Target Selection on Touchscreens. InProceedings of the 20...

    2022

  38. [47]

    Andrew Bagnell

    Brian Ziebart, Anind Dey, and J. Andrew Bagnell. 2012. Probabilistic Pointing Target Prediction via Inverse Optimal Control. InProceedings of the 2012 ACM International Conference on Intelligent User Interfaces (IUI ’12). Association for Computing Machinery, New York, NY, USA,...

    2012

  39. [48]

    2016.Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology

    George Kingsley Zipf. 2016.Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Ravenio Books. 9 Appendix 9.0.1 1D Discrete Kalman Filter.Filter configuration for mobile vertical scrolling that was used in the production website during the evalua...

    2016

  40. [2023]

    Simulating Interaction Movements via Model Predictive Control.ACM Transactions on Computer-Human Interaction30, 3 (June 2023), 44:1–44:50. doi:10. 1145/3577016

    2023

  41. [2024]

    InPro- ceedings of the 2024 CHI Conference on Human Factors in Computing Systems (CHI ’24)

    Real-Time 3D Target Inference via Biomechanical Simulation. InPro- ceedings of the 2024 CHI Conference on Human Factors in Computing Systems (CHI ’24). Association for Computing Machinery, New York, NY, USA, 1–18. doi:10.1145/3613904.3642131

    2024

  42. [2026]

    InPro- ceedings of the 2026 CHI Conference on Human Factors in Computing Systems (CHI ’26)

    Log2Motion: Biomechanical Motion Synthesis from Touch Logs. InPro- ceedings of the 2026 CHI Conference on Human Factors in Computing Systems (CHI ’26). Association for Computing Machinery, New York, NY, USA, 1–22. Uzafir Ahmad Rafaq, Muaz Hassan, and Ali Muzaffar doi:10.1145/3...

    2026

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.