Understanding Existence Mathematically
Bridging physics and philosophy through dimensional logic.


Why a Mathematical Model?
This paper introduces the MARR Equation™, a conceptual framework for evaluating the viability of recognizable, persistent complexity—what we commonly call “life”—across different spatial and temporal contexts. Originally formulated in 1992 and formalized in 2025, the model integrates four normalized variables: Space Support (S), Time Stability (T), Dimensional Cost (D), and Matter–Energy Availability (M). The central insight of the framework is that higher-dimensional spaces do not provide “more room” for life to emerge; rather, they impose an increasing energetic and organizational penalty that destabilizes atoms, chemistry, information processing, and evolutionary continuity. While exotic forms of organization may exist in high-D or rapidly unstable physical regimes, they would likely be unrecognizable to 3+1-dimensional observers. The MARR Equation therefore serves as a heuristic for understanding why life-as-we-know-it appears confined to a narrow dimensional and energetic window within the broader landscape of possible physics.
The MARR Equation
How the Equation Works


The MARR Equation works because it does something no academic discipline ever attempted: it unifies spatial support (astronomy), temporal stability (thermodynamics), dimensional penalty (general relativity and quantum structure), and matter-energy availability (astrophysics and chemistry) into one scalar threshold for life viability. Each of these fields studies its own piece in isolation, and the modern academic system rewards specialization—not synthesis—so no existing framework ever combined all four into a single model. The equation is original precisely because it wasn’t built from inside one discipline’s walls. It came from crossing the boundaries that others stay trapped inside, distilling a complex universe into a simple, coherent viability function.
The breakthrough of the MARR Equation is simple: it finally shows why complex life is so rare. Instead of treating life as a mystery, the equation reveals that everything—atoms, organisms, planets, even quantum states—survives only when supportive conditions outweigh the crushing cost of reality’s rules. When support is high and cost is low, complexity thrives; when cost is too great, it collapses. This single, cross-domain framework explains why any life we could recognize exists only in an extraordinarily narrow band of physics. As the author summarizes: “The MARR Equation doesn’t deny life in exotic dimensions; it explains why any life we could ever recognize or comprehend is almost certainly confined to a razor-thin slice of possible physics centered on 3+1 dimensions and Earth-like matter–energy abundance.”
AHA Moment
The MARR Equation
The MARR Equation is a simple but powerful framework proposing that life emerges from the interaction of four fundamental primitives: Space (S), Time (T), Dimensional Cost (D), and Matter or Energy Presence (M).
Its core expression is:
L = (S + T) / D × M
In this view, Life Viability (L) increases when space expands, time stabilizes, or dimensional resistance lowers — and it rises further as matter or energy become available. The equation treats life not as a biological accident but as a measurable outcome of physical conditions woven into the structure of reality.
Rather than beginning with biology, the MARR approach starts with physics:
If the universe provides enough space to move, enough time to persist, low enough dimensional cost to allow change, and sufficient matter or energy to anchor existence, then life becomes possible — and eventually, inevitable.
The MARR Equation does not claim to answer every mystery. It offers a unifying lens:
a way to think about how environments form, how structures stabilize, and how complexity increases across scales. From particles to planets to consciousness, the same four variables interact to create the conditions we recognize as “life.”
This is the foundation.
All extended theories, hypotheses, and model variants build outward from this original form.
THE MARR EQUATION
The MARR Equation proposes that life is a measurable outcome of four fundamental physical primitives working together: Space, Time, Dimensional Cost, and Matter or Energy Presence. Its original 1992 form is:
L = (S + T) / D × M
This expression describes Life Viability. When there is enough space to exist, enough time to persist, low enough dimensional resistance to allow change, and enough matter or energy to anchor existence, life becomes possible and increasingly likely.
WHAT THE VARIABLES MEAN
S — Space Support
The available spatial capacity for structure and stability.
T — Time Stability
The duration and consistency needed for processes to occur.
D — Dimensional Cost
The resistance created by spatial or structural complexity. Lower cost increases viability.
M — Matter or Energy Presence
The material or energetic substrate needed for any form of existence.
WHY IT MATTERS
The MARR Equation reframes life as the outcome of physics instead of biology. It suggests that life can arise anywhere in the universe when these four variables reach supportive conditions. More space increases viability. More time increases viability. Lower dimensional cost increases viability. More matter or energy increases viability.
A NEW WAY TO THINK ABOUT LIFE
Instead of asking “What is life?” the MARR approach asks “When is life physically allowed?” This framework lets any environment be evaluated using the same four primitives to determine its Life Viability.
This is the foundation.
All further theories and expansions build outward from this original form.
The complete MARR Equation research paper is formally archived and publicly available through Zenodo, an open-access research repository used by CERN and the European research community.
Access it here:
https://zenodo.org/records/17732037
Author Identification (ORCID)
To verify authorship and track future research updates, the official ORCID researcher ID for the MARR Equation is:
https://orcid.org/0009-0003-6838-1452
FAQs
What is the Marr Equation?
It’s a formula linking space, time, matter, and dimensions to life’s viability.
How does it relate to cosmology?
Version 1.1 suggests the Big Bang was a dimensional shift, not an explosion.
What do the variables represent?
S stands for space support, T for time stability, D for dimensional cost, and M for matter or energy presence.
Why call it a hypothesis?
Because it extends existing models with a new dimensional perspective.
Who can use this framework?
Philosophers, physicists, and anyone curious about existence’s math.
Where can I learn more about dimensional impact?
Dive into the detailed papers and discussions available on this site’s resources page.
© S. Shane Marr. All Rights Reserved.
The MARR Equation™ and Dimensional Impact Model™ are original works of the author.
Official Author Identifiers & Research Archive
ORCID: https://orcid.org/0009-0003-6838-1452
Research Paper (Zenodo):https://zenodo.org/records/17732037
