The Formula - Artistic Output = f ( t 0 + Δ t ) - A work in Progress

 

Peter Davidson - Two sake bottles and cups
Pastel pencil on coloured pastel paper -A4

The t₀ Paradox: A Temporal Theory of Perceptual Delay in Artistic Practice

 Discipline: Art Theory, Perception Studies, Temporal Philosophy Status: Ongoing Research

Abstract

This paper introduces the t₀ Paradox, a conceptual framework that describes the inherent delay between perception and artistic execution. Drawing from cognitive science and temporal theory, it proposes that all acts of representation—particularly in painting—are temporally displaced echoes of reality. The formula $\text{Artistic Output}=f(t_0+\mathrm{\Delta }t)\backslash text\{Artistic\; Output\}\; =\; f(t₀\; +\; \Delta t)$ captures this delay, where $t_{0}t₀$ is the moment of perception, $\mathrm{\Delta }t\Delta t$ is the cognitive and motor latency, and $ff$ represents the artist’s interpretive process. The t₀ Paradox reframes painting as a philosophical act: not a mirror of the present, but a textured record of its passing.

I. Introduction: The Problem of Presence

Can we ever truly capture the present moment? In painting, the artist attempts to record what is seen—but the moment the eye perceives, the brain begins to process, and the hand begins to move, the present has already slipped into the past. This delay is not a flaw—it is a fundamental condition of human perception. The t₀ Paradox offers a way to understand this phenomenon through a simple temporal formula.

II. The Formula

$$$$Artistic Output=f(t0+Δt)\text{Artistic Output} = f(t₀ + Δt)

• $t_{0}t₀$: The moment of raw perception—the instant visual data enters the eye.

• $\mathrm{\Delta }t\Delta t$: The delay introduced by cognition, memory, motor response, and material execution.

• $ff$: The artist’s interpretive function—style, emotion, technique, and medium.

This formula suggests that every artwork is a processed, delayed transformation of reality. The artist never paints the present—they paint a remembered version of it.

III. The Hand-to-Eye Paradox

Artists often speak of “capturing the moment,” yet the coordination between eye and hand is always subject to delay. In figure painting, for example, the curve of a shoulder or the glint of light on skin is perceived in $t_{0}t₀$, but rendered in $t_0+\mathrm{\Delta }tt₀\; +\; \Delta t$. The painting becomes a surface of accumulated delay—a visual record of time passing.

IV. Micro and Macro Focus

• Micro Focus ("I'm Here") Each brushstroke attempts to record a fragment of visual truth—light, hue, texture. Techniques like impasto and surface rupture resist the brain’s smoothing tendencies.

• Macro Focus ("I'm Not Here") The brain assembles fragments into a coherent image—a reclining figure, a landscape. This whole is an illusion: a cognitive reconstruction, not a direct capture.

V. Painting as a Temporal Loop

The act of painting becomes a loop:

1. Perception occurs at $t_{0}t₀$.

2. Delay is introduced ($\mathrm{\Delta }t\Delta t$).

3. The artwork records $t_0+\mathrm{\Delta }tt₀\; +\; \Delta t$—a past moment.

This loop is not a failure—it is the truth of artistic practice. Each layer of paint is a sediment of delay, a physical trace of the artist’s temporal struggle.

VI. Conclusion: Honoring the Delay

The t₀ Paradox reframes painting as a philosophical gesture. It is not about immediacy—it is about honoring the impossibility of immediacy. Every brushstroke is a reach toward a moment that can never be held. In embracing this delay, the artist does not diminish reality—they deepen it.

Acknowledgments

This work represents an ongoing exploration, developed through active painting and drawing practice paired with deep, sustained reflection. The research originated and took its initial shape at the 2 Dogs Art Space in Akashi, Japan, made possible by the generous support of family and friends, and inspired by the two dogs who lend the space their spirit.

Over the years, I owe special thanks to all my former academic professors, whose enduring guidance provided the necessary foundation for this inquiry. Furthermore, I acknowledge the valuable contributions of modern tools, specifically my AI collaborators—Google Gemini and Microsoft Copilot—for their assistance in refining the structure and language of this theoretical framework.