🔢 Mathematical Structures
A Page in Similarity Theory
By Simon Raphael
🌀 Philosophical Framework
🔣 Numbers as Concepts, Not Things
Numbers are not objects in the universe; they are concepts — elegant tools we use to describe and order reality. To say “two apples” is not a cosmic truth but a practical way of quantifying presence. Numbers are the grammar of quantity, not reality itself.
🔟 0 to 9: A Symbolic Ladder
When Similarity Theory speaks of the soul evolving from 0 to 9, this should not be taken as literal counting. The sequence is a symbolic map, a way of describing stages of growth that consciousness passes through.
Here, “soul” does not mean the religious soul, but persistent consciousness — awareness that endures across many frames of time. Each moment of life leaves behind a conscious trace, but the thread that continues through multiple realities is what we call the soul.
This persisting consciousness moves in and out of material form. Each time it incarnates, it gathers more awareness, like a traveller who collects wisdom with every journey.
The numbers 0 to 9 symbolise the stages of experience needed before persistent consciousness can take the next leap. At “10,” it enters not just another stage but a new dimension, with new laws of reality.
🧱 The Difficulty of Beginnings
The greatest difficulty always lies at the foundation:
0 is not nothingness but potential.
The step into 1 is the most challenging leap of all.
From 1 to 2, the progression becomes easier.
Each step smooths until 9 is reached, where the soul is fully matured within a dimension.
At 9, the next leap — to 10 — represents dimensional transition, not just growth but transformation.
Analogy: A stone arch requires immense effort to build. Each block depends on the others, but the entire structure is unstable until the keystone — the central stone at the top — is placed. That final act is the hardest, yet once the keystone is set, the arch locks together and supports itself. In the same way, the leap from nothingness (0) into being (1) is the hardest of all. Once existence is established, further progress flows with increasing stability, until maturity (9) is reached. The move into 10 is not simply another stone but the beginning of a new structure — a new dimension of reality.
🌉 Beyond Nine: Entering Higher Dimensions
The shift from 9 to 10 symbolises entry into higher realms of existence. Each new dimension contains more layers of development than the one before.
Rocks in the first dimension move through a short arc of 0 to 9 — persistence of being.
Plants in the second dimension unfold across broader layers, 10 to 99, with growth, adaptation, and cycles of life.
Animals and humans in the third dimension span an even richer arc, 100 to 999.
Within this third dimension, animals tend to dwell in the earlier layers, where awareness is limited to survival: food, danger, mating, and social bonds.
Humans, by contrast, rise into later layers of the arc, where imagination, creativity, invention, and symbolic thought expand awareness. Humans reshape the landscape, cultivate food, build structures, and explore beyond the planet — a leap in complexity compared to animals, even though both share the same dimension.
Thus, the difference between animals and humans is not dimensional but layered within the same dimension. Each higher dimension multiplies the number of layers available, accelerating complexity and broadening awareness until the soul is ready to step into a new order of reality.
🔭 Shared Laws, Different Layers
Animals and humans share the same third dimension and its physical laws — gravity, chemistry, biology — but they occupy different layers of awareness within that dimension. The leap to a higher dimension, however, is not just another step. It brings different operative laws entirely, just as plants differ from rocks, and humans from plants.
(For a fuller explanation of how movement, physics, and awareness distinguish dimensions, see the Dimensions page.)
⏳ Glimpses Beyond: Time and Imagination
Animals and humans share three spatial dimensions, yet humans perceive more:
Time (fourth dimension): humans consciously grasp it, while animals mostly experience it passively.
Imagination (a glimpse of the fifth dimension): humans use symbolic and counterfactual thinking, opening doors to realities not yet lived.
Dimensional advancement is not about “bigger numbers” but deeper awareness.
⚖️ Symmetry, Asymmetry, and Echoes
Numbers themselves echo the universe’s structure:
Symmetry (11, 22, 333) suggests resonance and stability.
Asymmetry (prime numbers) symbolises creative disruption — preventing stagnation.
Constants such as π or the golden ratio were not invented but discovered, revealing architecture built into reality.
Analogy: Just as shells, flowers, and galaxies display spirals shaped by the golden ratio, so too do numbers mirror the hidden design of existence.
🔬 Scientific Grounding
Mathematics as Language: Galileo described mathematics as the language of the universe. Cognitive science affirms that numbers are abstractions humans use to order perception.
Philosophy of Number: From Pythagoras to Whitehead, numbers have been treated as structural principles rather than objects.
Threshold Difficulty: In physics and biology, foundations demand the greatest energy (e.g., nucleation in crystals, ignition in stars). Once structure forms, evolution accelerates.
Human vs Animal Cognition: Research in cognitive science shows humans possess advanced symbolic reasoning and future projection, making imagination a form of higher-dimensional awareness.
Mathematical Constants: The golden ratio and π recur in natural forms (spirals, waves, growth patterns), suggesting number reflects — not merely describes — universal order.
📖 References
Galileo, G. (1623). The Assayer.
Lakoff, G., & Núñez, R. (2000). Where Mathematics Comes From. Basic Books.
Whitehead, A. N. (1911). An Introduction to Mathematics. Williams & Norgate.
Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics. Oxford University Press.
Livio, M. (2002). The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books.
Raphael, S. (2025). Similarity Theory.
