Creative and geometric times in physics, mathematics, logic, and philosophy

The paper distinguishes between "geometric time," which serves as a deterministic parameter for evolution, and "creative time," which represents the emergence of novel information through indeterministic events, exploring how these concepts map onto classical and intuitionistic frameworks in mathematics, logic, and philosophy.

The Gist

Imagine you are watching a movie. There are two ways to think about the "time" in that movie, and this paper argues that our universe actually uses both.

The authors, Flavio Del Santo and Nicolas Gisin, suggest that we have been confusing two very different types of time: Geometric Time and Creative Time.

1. Geometric Time: The "Film Strip"

Think of a movie printed on a physical strip of film. All the frames—the beginning, the middle, and the end—already exist. They are sitting there in a box. If you want to know what happens at minute 40, you don't "wait" for it to happen; you simply move your finger to the 40th minute on the strip.

In physics, this is Geometric Time. It treats time like a map or a coordinate. In a "deterministic" world (like a perfectly predictable machine), if you know where every atom is right now, you can calculate exactly where they will be in a thousand years. In this view, the future is already "written"; we are just traveling through the pages. It’s like a GPS: the road is already there; you’re just driving along it.

2. Creative Time: The "Live Improvisation"

Now, imagine a different kind of movie: a live jazz improvisation. The musicians know the key and the tempo, but they don't know exactly which note will be played next. The music isn't "sitting in a box" waiting to be played; it is being created in the moment. Every note played is "new information" that didn't exist a second ago.

This is Creative Time. The authors argue that the universe isn't just a pre-recorded movie; it is a live performance. Because of things like quantum mechanics, some events in nature are truly unpredictable. They aren't just "unknown" to us; they are "undecided" by nature itself. When a particle finally "chooses" a path, it’s like a musician hitting a new note. That moment of choice is what makes time actually pass. It’s not just a coordinate; it’s a process of creation.

---

How this connects to other worlds

The authors show that this isn't just a physics problem; it’s a pattern that repeats across all human knowledge:

• In Mathematics:
  • Geometric Math is like a completed puzzle. All the pieces are there, and the picture is finished.
  • Creative Math (Intuitionism) is like drawing a line that never ends. You are constantly adding new dots, and the "truth" of the line grows as you draw it.
• In Logic:
  • Geometric Logic assumes everything is either True or False right now (like a light switch that is either ON or OFF).
  • Creative Logic realizes that for things in the future, the switch is currently in a "maybe" state. It only becomes True or False once the "creative time" event actually happens.
• In Philosophy:
  • The authors link Geometric Time to the idea of a "Block Universe" (where the past, present, and future are all equally real and fixed).
  • They link Creative Time to the "Growing Block" theory (where the past is fixed and solid, but the future is a cloud of possibilities that only becomes "real" as it happens).

The Big Idea

The paper’s "punchline" is that we shouldn't try to force the universe into one single definition of time.

If you want to calculate the orbit of a planet, Geometric Time works perfectly—it’s a predictable, mathematical track. But if you want to understand why the universe feels "alive," why the future feels "open," and why the "present" feels so special, you need Creative Time.

The present, according to the authors, is the "edge" of reality: it is the thin line where the "maybe" of the future turns into the "definitely" of the past.

Technical Summary

Technical Summary: Creative and Geometric Times in Physics, Mathematics, Logic, and Philosophy

Authors: Flavio Del Santo and Nicolas Gisin
Date: February 10, 2026

---

1. The Problem: The Bifurcation of Time

The authors address a fundamental tension in modern science: the discrepancy between the "time" used as a mathematical parameter in physical equations and the "time" perceived as a process of actual change and becoming.

Current physical theories, particularly those influenced by General Relativity, tend to treat time as a fourth dimension in a static, four-dimensional "block universe" (Eternalism). This approach, while mathematically successful, struggles to account for the "constructive" role of time—the sense that the future is open and that the present is a unique boundary where novelty is generated. The authors argue that existing philosophical and physical accounts fail to integrate both the deterministic/geometric aspect of time and the indeterministic/creative aspect.

2. Methodology: Ontic Indeterminacy and Information Theory

The paper employs a multidisciplinary approach, bridging physics, mathematics, logic, and metaphysics. The core methodological pillar is the assumption of ontic (fundamental) indeterminacy.

Unlike epistemic uncertainty (lack of knowledge), the authors propose that nature itself possesses "worldly imprecision." They adopt a physicalist interpretation of information, following Landauer’s dictum: information is physical and is instantiated in the degrees of freedom of material systems. They argue that "creative time" is the process of actualization, where a potentiality (an indeterminate state) becomes a determinate property, thereby creating new, objective information in the universe.

3. Key Contributions: The Dual Concept of Time

The authors propose a formal distinction between two types of time:

• Geometric Time:
  • Nature: A parametric coordinate used in deterministic equations of motion.
  • Function: It labels fixed events in a manifold (the "block universe").
  • Information: No new information is created; the evolution is a mere unfolding of pre-existing data.
• Creative Time:
  • Nature: An active "processing" of time triggered by non-necessary events.
  • Function: It marks the transition from the potential (future) to the determinate (past).
  • Information: It is characterized by the creation of novel information through the actualization of ontic indeterminacy.

4. Results: Cross-Disciplinary Parallels

The authors demonstrate that this distinction is not merely a physical hypothesis but finds deep structural parallels across several fields:

• Mathematics:
  • Geometric Time $\leftrightarrow$ Classical Mathematics: Platonistic view where real numbers exist "all at once" (even uncomputable ones).
  • Creative Time $\leftrightarrow$ Intuitionistic Mathematics: A constructive view where mathematical entities (like choice sequences) are generated progressively through time.
• Logic:
  • Geometric Time $\leftrightarrow$ Classical Logic: Compatible with the Law of the Excluded Middle (LEM), where all propositions are pre-determinedly true or false.
  • Creative Time $\leftrightarrow$ Intuitionistic/Tense Logic: Aligns with the rejection of the LEM for future contingents. In an open future, a proposition is neither true nor false until the "creative" event of actualization occurs.
• Philosophy of Time:
  • Geometric Time $\leftrightarrow$ B-Theory (Eternalism): Time is a relational, static dimension.
  • Creative Time $\leftrightarrow$ A-Theory (Temporalism): Time involves a fundamental distinction between past, present, and future. The authors propose a relativistic version of the "Growing-Block" theory, where the "present" is a local edge of determinacy propagating within a light cone.

5. Significance and Implications

The paper provides a unified framework to reconcile the "static" success of relativity with the "dynamic" reality of quantum indeterminacy and thermodynamics.

Key implications include:

• Relativity Compatibility: By defining the "present" as a local boundary of determinacy (the edge of a light cone), the authors attempt to make creative time compatible with the absence of a global absolute present in Special Relativity.
• Resolution of Paradoxes: The framework suggests that the arrow of time and the second law of thermodynamics emerge naturally from the continuous creation of information via creative time.
• Foundational Physics: It offers a way to interpret the "measurement problem" in quantum mechanics not as a mathematical anomaly, but as the fundamental mechanism of creative time.

Conclusion: The authors conclude that "science without time is but ruin of intelligibility." By distinguishing between the time that passes (geometric) and the time that occurs (creative), they provide a more robust naturalistic foundation for understanding a universe that is both structured and evolving.