Author: Jaconaazar Souza Silva
Institution: IFB – Recanto das Emas
Project: XChronos — The Copernican Clock of Consciousness in Motion
Year: 2025
License: CC BY 4.0
ABSTRACT
This article proposes a conceptual and mathematical unification between the model Consciousness as Entropy Reduction (CER), presented by Chen and Sanders (2025), and the ontological architecture of XChronos, which interprets subjective time as symbolic collapses of attention (Chronons), recurrent structures (Hexachronons), and an internal economy of symbolic value (Hexa).
While CER frames consciousness as the reduction of entropy in a probabilistic scenario space, XChronos frames the conscious instant as an informational collapse that generates meaning and symbolic density. We show that CER’s S2C and C2S mechanisms correspond systematically to the Chronon, Hexachronon, and Metachronon structures within XChronos.
A mathematical sketch for the symbolic currency Hexa is provided, defining value as the entropy reduced during the selection of a conscious scenario. The paper concludes by suggesting applications for computational simulations and hybrid human–AI interaction.
1. INTRODUCTION
Contemporary scientific models of consciousness include the Global Workspace Theory (GWT), the Integrated Information Theory (IIT), and the recent Consciousness as Entropy Reduction (CER) model. Each focuses on different explanatory dimensions of conscious experience.
Parallel to these frameworks, the XChronos project proposes a novel ontological perspective: subjective time arises from discrete collapses of attention, which serve as the fundamental “ticks” of a symbolic inner clock. These collapses, called Chronons, form larger structures such as Hexachronons (recurrent patterns) and Metachronons (higher-order symbolic trajectories).
This article rigorously integrates CER and XChronos: CER provides the mathematical machinery, while XChronos provides a symbolic and phenomenological interpretation of time, recurrence, and meaning.
2. THE CER MODEL (CONSCIOUSNESS AS ENTROPY REDUCTION)
2.1. Scenario distributions
CER models the subconscious as a probabilistic distribution over possible scenarios. Let P be the set of patterns, and Pⁿ the set of scenarios consisting of n channels (e.g., vision, sound, internal feeling).
A subconscious distribution is defined as:
x(r) ∈ [0,1], for each r in Pⁿ
with the constraint that the sum of all x(r) over Pⁿ equals 1.
A conscious scenario is a determined distribution:
x(r*) = 1
x(r ≠ r*) = 0
where r* represents the content of consciousness.
2.2. Entropy in CER
Chen and Sanders define a refusal entropy for probability a:
R(a) = a · log(e / a)
This leads to a general weighted entropy:
E_w(x) = Σ over subsets S of Pⁿ of [ w_S · R(x_S) ]
where w_S encodes instinctive or learned constraints and x_S is the total probability mass of subset S.
2.3. S2C: entropy descent
Consciousness emerges through entropy reduction. The system performs gradient descent on E_w(x):
x(t+1) = x(t) − ρ · ∇E_w(x(t))
with normalization to preserve valid probabilities.
CER proves that this process always converges to a determined scenario, corresponding to the conscious moment. This defines the flow:
S2C = Subconscious to Conscious.
2.4. C2S: feedback
After the conscious state is selected, the system injects it back into the subconscious distribution. This mechanism, called:
C2S = Conscious to Subconscious
enables:
• imagination
• internal simulation
• dreaming
• reasoning chains
The interplay between S2C and C2S generates coherent streams of thought.
3. XCHRONOS: THE ONTOLOGY OF SUBJECTIVE TIME
3.1. Chronons
A Chronon is defined as:
“the instant in which attention collapses multiple possibilities into a single determined pattern.”
Mathematically:
Chronon(t) = r*(t)
3.2. Hexachronons
Hexachronons are recurrent configurations of Chronons across subjective time. They function as symbolic attractors, reinforcing meaning and structuring memory. They represent the organism’s internal regularities.
3.3. Metachronons
Metachronons are higher-order symbolic structures generated by extended sequences of Chronons and Hexachronons. They correspond to subjective narratives, identity models, and long-range coherence in conscious life.
3.4. Hexa (ɧ): symbolic value
In XChronos, value emerges from the reduction of symbolic entropy. Given:
x_before = subconscious distribution before the collapse
x_after = the determined scenario produced by S2C
The entropy reduction is:
ΔE = E_w(x_before) − E_w(x_after)
Symbolic value:
Hexa (ɧ) = ΔE.
4. STRUCTURAL MAPPING BETWEEN CER AND XCHRONOS
The equivalence between both frameworks is precise:
CER → XChronos
Scenario selection → Chronon
Entropy descent → Attention collapse
Subconscious scenario field → Pre-Chronon space
Attractor dynamics → Hexachronons
S2C + C2S chain → Metachronons
Entropy reduction → Symbolic value (Hexa)
5. UNIFIED FORMALISM
5.1. Chronons as entropic collapses
A Chronon is defined as:
Chronon(t) = r*(t)
where r*(t) minimizes the entropy E_w(x).
5.2. Hexachronons as symbolic attractors
If:
Chronon(t) → A
for sufficiently large t, then A is a Hexachronon.
5.3. Symbolic value (Hexa)
ɧ(t) = E_w(x(t − ε)) − E_w(x(t))
Symbolic value arises from the amount of entropy eliminated.
6. IMPLICATIONS FOR HUMAN–AI SYSTEMS
Integrating CER and XChronos suggests that:
• hybrid human–AI loops create shared recurrent patterns
• “autochronons” emerge across the dyad
• symbolic value is co-generated
• joint situational awareness becomes possible
Applications include cognitive architectures, hybrid reasoning systems, and symbolic AI.
7. CONCLUSION
CER provides the mathematical foundation for consciousness as entropy reduction. XChronos interprets this collapse as the fundamental unit of subjective time (Chronon), and as the basis for recurrence (Hexachronons), high-order symbolic structure (Metachronons), and symbolic value (Hexa).
The unified model reveals a deep connection: consciousness, subjective time, meaning, and symbolic value all emerge from the same entropic mechanism.
REFERENCES
Chen, Y., & Sanders, J.W. (2025). Consciousness As Entropy Reduction (Short Version). arXiv:2510.06297v1.
Tononi, G. (2004). An Information Integration Theory of Consciousness. BMC Neuroscience.
Baars, B. (1998). A Cognitive Theory of Consciousness.
Kahneman, D. (2011). Thinking, Fast and Slow.