Kurtis Kemple

Information Physics in Mathematics

July 24th, 2025

Mathematics has always sought truth independent of the observer. Equations described universal laws that worked the same whether calculated by a CEO or a janitor, in New York or New Delhi. Even a janitor at MIT solving millennium problems on hallway chalkboards gets the same answer as the Fields Medal winner. Information Physics changes this fundamental assumption, introducing mathematics where the observer’s position doesn’t just matter—it’s essential to the calculation itself. Where anyone can walk up to the chalkboard and solve the equation through their own lived experience and it’ll still be right.

This isn’t adding complexity to existing mathematics. It’s extending established mathematical foundations (Shannon entropy, vector calculus, information theory) into conscious systems where position, intent, and lived experience become computational primitives. The formulas that emerge are simultaneously simple enough to calculate by hand and profound enough to explain phenomena that traditional mathematics cannot touch.

Entropic Mathematics: A mathematical framework where observer position, conscious intent, and lived experience are treated as fundamental variables. Calculations reflect the agent’s location within a system, their directional intent, and the entropy constraints of their reality.

Observer as Physical Entity

The E variable in Information Physics equations represents actual thermodynamic entropy from actual physical position in reality. This isn’t “difficulty” or “resistance” as abstract concepts—it’s the mathematical encoding of lived physical constraints:

  • Heat affecting cognitive processing speed and accuracy
  • Fatigue constraining available mental operations and decision quality
  • Stress limiting information processing bandwidth and perspective
  • Resource constraints determining possibility space through physical limitations

Different observers calculating the same system change get different results not through measurement error, but through mathematical reality. The same equation produces different outcomes because the observers exist under different entropy conditions. This makes Information Physics the first mathematics designed for conscious beings as physical entities subject to actual thermodynamic constraints.

The Core Innovation: Observer-Dependent Variables

Traditional mathematics treats all observers as equivalent. The speed of light is the same for everyone. Gravity pulls with equal force regardless of who measures it. Even in relativity, while observations might differ, the underlying laws remain observer-independent.

Information Physics mathematics breaks this assumption. The variable E in our equations isn’t just “difficulty” or “resistance”—it’s the mathematical encoding of an observer’s lived reality within a system. A CEO calculating system change from E = 0.2 gets fundamentally different results than a worker calculating from E = 0.9, even with identical operations and intent.

System Entropy Change (SEC): The measurable impact a conscious agent can have on system entropy from their specific position, calculated through observer-dependent mathematics where position, intent, and operations determine possibility.

SEC = O × V / (1 + E)

Where:

  • O = Operations performed (MOVE, JOIN, SEPARATE)
  • V = Vector of actor-group conscious intent (positive for entropy reduction, negative for entropy increase)
  • E = Entropy as measured from individual actor’s position (lived reality/informational constraints/entropy from the system)

This isn’t a bug to be eliminated through better measurement. It’s the core feature that makes the mathematics match reality in human systems.

The Mathematical Revolution

These equations represent several mathematical firsts.

First Observer-Dependent Mathematics

Never before has observer position been a fundamental variable in equations. Even quantum mechanics, which includes observation effects, doesn’t make the observer’s position in a system mathematically essential.

First Conscious Intent as Vector

The V variable mathematically encodes conscious choice. Traditional physics has vectors for force, velocity, acceleration—all describing unconscious phenomena. V represents conscious intent to build or destroy, optimize or sabotage.

First Recursive Optimization Mathematics

The equations can be used to optimize one’s ability to use the equations. This creates a new class of self-improving mathematics where understanding improves application capacity.

First Consensus-Collapse Mathematics

When groups align around shared V vectors, they function as collective measurement apparatus that collapses organizational superposition into definite mathematical reality, paralleling quantum measurement dynamics.

First Position-Specific Reality Mathematics

Different observers calculating the same system change get different results based on their position. This isn’t measurement error—it’s mathematical reality that matches lived experience.

Connecting to Established Mathematics

Information Physics mathematics doesn’t violate traditional mathematics—it extends it into new domains.

Information Theory Connection

Shannon entropy appears in organizational communication. Entropic Gap measurements use established similarity metrics. The innovation is applying these to conscious systems with observer dependence.

Vector Mathematics Connection

Using vectors and cosine similarity connects to established linear algebra. The innovation is using vectors to represent system states and conscious intent.

Calculus Connection

Derivatives and limits work normally within the framework. The innovation is what we’re taking derivatives of—observer-dependent system changes.

Statistical Validation

The equations produce distributions that follow recognizable patterns. The innovation is that different observers sampling the same system get predictably different distributions.

Implications for Mathematical Science

This mathematics opens entirely new fields of study ranging from organizational calculus to quantum organization theory.

Organizational Calculus

Calculating optimal paths through organizational structures by minimizing integral of E over trajectory:

Optimal path = min ∫E(position) dt

Entropy Field Theory

Mapping entropy as a field over organizational space, with gradients showing paths of least resistance for system change.

Multi-Scale Analysis

Using wavelet transforms to analyze entropy patterns across organizational scales, from individual to team to division to company.

Civilizational Mathematics

The same observer-dependent equations governing individual decisions may also explain civilizational development patterns. Human development from hunter-gatherers to global systems potentially follows predictable entropic exhaustion cycles, not random cultural evolution.

At each scale—individual, group, civilization—similar mathematical constraints may apply:

  • Individual: SEC = O × V / (1 + E_personal)
  • Civilizational: SEC = O × V / (1 + E_coordination)

Independent civilizations may have developed identical solutions (writing, hierarchy, currency, law) because they faced identical mathematical constraints. Modern organizational scaling problems potentially mirror ancient city-state transitions because the underlying entropy mathematics may remain constant across scales and centuries.

Planetary Entropy Mathematics

The observer-dependent mathematics potentially extends to planetary systems. If consciousness operates under thermodynamic constraints, then planetary conditions should mathematically affect entropy (E) values for conscious beings.

Theoretical Planetary SEC Formula:

SEC_planetary = O × V / (1 + E_planetary)

Where E_planetary incorporates:

  • Gravitational effects on operation energy requirements
  • Atmospheric constraints on cognitive processing capacity
  • Resource availability determining possibility space
  • Energy distance from stellar sources affecting baseline entropy
  • Communication delays creating information lag entropy

Potential Applications (Requiring Validation):

  • Calculate resource requirements for civilizational migration between worlds
  • Assess exoplanets based on entropy constraints for consciousness rather than just habitability
  • Frame terraforming as mathematical entropy reduction operations
  • Predict how planetary conditions might affect conscious system development

These remain theoretical extensions until empirical measurement validates the mathematical relationships at planetary scales.

Quantum Organization Theory

Exploring whether superposition states exist in human systems—can an actor occupy multiple positions simultaneously before “collapsing” into specific role?

Conclusion

Information Physics mathematics isn’t just new notation for old concepts. It’s genuinely new mathematics for conscious systems where observers can understand and apply the theory to change their own outcomes.

The equations are simple enough that practitioners can use them immediately, yet rich enough to spawn entire fields of mathematical investigation. They bridge the gap between pure mathematics and lived human experience, creating computational tools for phenomena previously thought unmeasurable.

Most remarkably, this mathematics is self-validating. The more you understand it, the better you can apply it. The better you apply it, the more you can achieve. The more you achieve, the more the mathematics is validated. It’s mathematics that improves with use—a property that might be unique in mathematical history.

We’re not just calculating system changes. We’re creating mathematics for the age of conscious systems.

  • Information Physics Field Guide: The field guide to Information Physics.
  • Information Physics LLM Friendly Study Guide: Drop this in your context and ask AI to explain Information Physics objectively.
  • Information Physics: A general theory describing how conscious beings reduce or increase entropy through three operations on information, coordination, and system boundaries.
  • Conservation of Boundaries: A proposed foundational law that system boundaries may not be created or destroyed, only transformed through three operations—move, join, separate.
  • Entropic Mathematics: A proposed applied field of mathematics extending established tools (Shannon entropy, vector calculus, information theory) to conscious systems where observer position and lived experience may be fundamental calculation variables.
  • Entropic Gap: A framework that may help detect system decay before it becomes catastrophic by calculating the distance between intended and current states.
  • Entropic Equilibrium: A theory exploring why systems may stabilize where they do through observer-dependent optimization.
  • Information Physics Throughout History: How Sun Tzu, Machiavelli, and Napoleon may have intuitively applied IP principles centuries before the mathematics existed.
  • Information Physics In Science: How IP may reveal the underlying principle that unites quantum mechanics, biology, and cosmology across all scales.
  • Renaissance Florence vs Silicon Valley: The Innovation Entropy Crisis: Comparing how Silicon Valley may produce 12x fewer innovators per capita than Renaissance Florence despite vastly superior resources—suggesting technology cannot overcome high entropy.
  • Constraint by Design: Entropy Limits in the Gig Economy: Mathematical analysis suggesting that gig economy architecture may make worker advancement impossible regardless of individual effort, potentially demonstrating how structural position determines capability.
  • Survival Trends Across Mass Extinctions: The fossil record suggests a pattern: during mass extinction events, specialists died while generalists thrived. This pattern may represent Information Physics playing out at planetary scale.
  • The Peasant: A playbook for creating positive-sum outcomes in high-entropy (negative-sum) environments.
  • The “Just How It Is” Test: Test Information Physics against traditional frameworks on any stubborn “unchangeable” problem to see which approach may work better from your position.