Perception-Time Scaling (PTS)

• Perception-Time Scaling is a framework that defines subjective time through the integration of sensory, cognitive, and environmental factors.
• It employs methodologies combining psychophysics, neural decay models, and Bayesian estimation to quantify internal time dynamics.
• Applications range from AI and VR systems to mental health monitoring, leveraging wearable biosensors and adaptive control devices.

Perception-Time Scaling (PTS) is a framework encompassing the mechanisms, mathematical models, and empirical evidence describing how subjective perception of temporal intervals dynamically scales with sensory, cognitive, affective, and environmental factors. PTS unifies research from psychophysical experimentation, computational neuroscience, artificial intelligence, machine learning, and real-world assessments, addressing both the origins and modulations of perceived time across contexts and timescales.

1. Conceptual Foundations of Perception-Time Scaling

PTS refers to the non-constant relationship between externally measured time and its subjective counterpart. Classical models recognize that interval estimation variability follows the scalar property—standard deviation scaling linearly with mean duration, formalized as $\frac{\sigma}{\mu} = k$ (Basgol et al., 2020). Mechanistically, PTS is driven by two factors: (a) internal @@@@1@@@@ (e.g., oscillators, decay of memory traces); and (b) sensory, cognitive, or affective modulation, which dynamically alters the rate of an organism’s or system’s “internal clock.”

The distinction between “external time” (chronological) and “internal time” (subjective/neuronal) is critical. Recent mathematical frameworks formalize decoupling of these, showing that internal time may diverge (stretch) relative to external duration under pathological and end-of-life conditions (Kareva et al., 12 May 2025).

2. Psychophysical and Neurobiological Grounding

Empirical studies, including the Length-Duration Relation (LDR) method (Soyfer, 2011), reveal that human observers construct an amodal, modular mental scale for correlating spatial and temporal intervals—even in the absence of explicit numerical cues. This scale leverages two measuring systems: innate biological metrics (e.g., endogenous rhythmicity) and learned social metrics (e.g., seconds, centimeters). The transitional process involves:

Stage	Mental Process	Behavioral Outcome
Adaptation	Calibration of modulus and limits; golden section division	Systematic biases, lower accuracy
Activation	Rapid readout of scale points	Doubling of correct response rate, reduced latency

The organization of the mental scale under high uncertainty approximates division by the golden section: if interval limits are $m$ (minimum) and $M$ (maximum), the internal division $I$ satisfies $\frac{M - I}{I - m} \approx \phi$, with $\phi \approx 1.618$ (golden ratio). Correct recognition and systematic distribution of errors increase markedly from first to second presentation, demonstrating a two-stage activation model.

Neurobiologically, models combine microstimuli-based representations (e.g., decaying traces, Gaussian basis functions) and Bayesian estimation from environmental dynamics, reproducing animal and robotic discrimination performance (Lourenço et al., 2023). Internal parameters (number of microstimuli, decay rates) directly modulate perceived timescale.

3. Mathematical Models: Subjective Passage and Scaling Laws

Several formulations capture PTS quantitatively:

Scalar Property and Internal Clock Models

• Pacemaker-accumulator: $T_p = \sum_{i=1}^N \Delta t_i$, with $N$ modulated by sensory features.
• Oscillator models: $S(t) = \sum_j A_j \cos(2\pi f_j t + \phi_j)$.
• Memory decay: $m(t) = m_0 e^{-\lambda t}$.

Subjective Passage of Time

• Life-course model: For subjective unit $U_s$ and objective unit $U_o$,

$U_{s1} = \frac{1}{T-T_1} U_o$

and subjective speed increases as $V_{s1} = T-T_1$ (Galam, 8 Jan 2024).

• Extension via social rituals (clock stacking):

$U_{sl} = \frac{1}{\prod_{i=1}^l (T-T_i)} U_o$

with horizons defined via summations, and damping via a power law $U_{sa} = 1/(T-T_1)^a$.

Aging Model

• Transition from exponential to logarithmic sensitivity as age $I$ increases:

$S(I) = w(I)\, a e^{bI} + (1-w(I))\, k \log(I/I_0)$

with logistic weight $w(I)$ yielding an inversion point at mental maturity (Sanchez, 24 Oct 2024).

Neural Decay and Brain Death

• Neural extinction: $dN/dt = -k N^p$, internal time variable $q(t)$ diverges as population vanishes:

$$q(t) = p N(0)^{1-p} \left[(1 - k N(0)^{1-p}(1-p)t)^{-1/p} - 1\right]$$

Extinction time: $T = N(0)^{1-p}/(k(1-p))$, with optimal $p_{opt} = 1 - 1/\ln N(0)$ (Kareva et al., 12 May 2025).

4. Measurement and Real-Time Monitoring

Recent approaches integrate wearable biosensors and artificial intelligence to classify passage of time perception (POTP). Features from respiration, ECG, EDA, and skin temperature contribute to classification accuracy as high as 79% for fast vs. slow time perception (Orlandic et al., 2021, Aust et al., 28 Mar 2024). EDA emerges as the most descriptive biomarker, and closed-loop control devices (e.g., ChronoPilot) aim to modulate users’ perception of time to optimize performance and reduce stress.

In high-pressure professions, machine learning pipelines leverage signal feature engineering (min–max normalization, bandpass filtering, SHAP for feature importance) and robust cross-validation to automate classification, forming foundations for future adaptive systems.

5. Perception-Time Scaling in Artificial and Virtual Environments

Computational models apply PTS principles in both AI agents and human-centered VR systems. In AI, models such as LSTM agents and RL-based frameworks can encode dynamic timing behavior by scaling internal clocks as functions of sensory salience: $r = r_0 + \alpha S$ (Basgol et al., 2020). Reinforcement learning with verifiable rewards further refines perception steps for large vision-LLMs (LVLMs), as demonstrated by the PTS paradigm, which decomposes perception into token-rich intermediate steps and achieves substantial accuracy gains (from 8.0% to 64.7% on the DisTANCE benchmark) (Li et al., 10 Oct 2025).

In VR, EEG spectral analysis provides objective measurement: delta/theta power increases for time overestimation, alpha/beta for accurate estimation, and high-beta/gamma for underestimation (Niknam et al., 10 Apr 2025). Emotional valence and attentional load dynamically modulate perceived intervals via internal clock (ICM) and attentional gate (AGM) models; the number of counted pulses $N$ is determined by pacemaker rate $r$ and gate width $g$: $N_{eff} = g \times r \times T$ (Syrigou et al., 12 May 2025).

Visualization research addresses human temporal judgments in timeline charts. EventLines implements piecewise constant display allocation for event intervals, embedding visual cues (coils, stippling, thickness changes) into the time axis to facilitate accurate perception of compressed time regions, empirically validated by graphical perception studies (Wong et al., 23 Jul 2025).

6. Practical Applications and Implications

PTS underpins methodologies across fields:

• Mental health: Continuous, unobtrusive measurement of POTP reflects stress and can trigger interventions (Orlandic et al., 2021, Aust et al., 28 Mar 2024).
• High-stakes professions: Feedback devices modulate perceived time to support operators under cognitive load.
• Human-computer interaction: Visual timeline axis distortions require explicit encoding of time scaling to guide user interpretation (Wong et al., 23 Jul 2025).
• AI multimodal reasoning: Explicit perception decomposition improves both algebraic reasoning and perceptual estimation, with RL-driven reward shaping fostering improved generalization (Li et al., 10 Oct 2025).
• VR immersion: EEG-based PTS tracking enables real-time adaptation for enhanced user experience and therapeutic applications (Niknam et al., 10 Apr 2025, Syrigou et al., 12 May 2025).

7. Controversies and Future Research Directions

PTS models are evolving, with debates over the precise role of baseline stress, the dominant mechanism (internal clock vs attention gate), and best practices for encoding non-linear time scaling in data visualizations. Empirical findings indicate that emotional valence and momentary attentional load frequently outweigh trait-level stress in influencing time judgments (Syrigou et al., 12 May 2025). The decoupling of internal and external time, especially in end-of-life neural dynamics, raises foundational questions for neuroscientific theory and consciousness studies (Kareva et al., 12 May 2025).

Open research pathways include integration of multi-scale timing mechanisms (combining interval, circadian, and motor timing); empirical validation of PTS models in robotics and embodied agents; development of neurocomputational models linking state-dependent network dynamics to subjective timing; and extension of reinforcement learning paradigms for richer perception-action loops.

In summary, Perception-Time Scaling is a multifaceted framework unifying experimental, computational, and applied research on the dynamic modulation of subjective temporal experience. It guides the design of both human-facing monitoring systems and artificial agents capable of robust, context-sensitive timing, while continuing to inform theoretical advances in neuroscience and psychophysics.