The Dot (dt) and Cross (nhh) — Kemetic Correspondence
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| Pi-Phi |⟨π|φ⟩|²: Projection Operator Dt (Djet): eternally emerging from primordial substance. Nhh (Neheh): the cyclical, spiral movement of time. Both comprise the two fundamental Kemetic concepts of Time and Eternity and both share a striking resemblance to the Dot (Scalar) and Cross (Vector) product of vector calculus. Within the OSCI Framework, the structural relationships of Pi ($\pi$) and Phi ($\varphi$) map isomorphically onto the eternal concepts of dt (Djet) and nhh (Neheh), clarifying the geometry of physical laws. |
Kemetic Term | ||
dt | nhh | |
Greek Symbol* | ||
Π (Pi) | φ (Phi) | |
Vector Algebra/Calculus | ||
· (Dot Product) | × (Cross Product) | |
Calculus Operations | ||
∇ · F (Divergence) | ∇ x F (Curl) | |
Output Type | ||
Scalar (Size) | Vector (Direction) | |
Geometric Algebra | ||
Inner Product | Outer/Wedge Product | |
Spacetime Geometry | ||
gᵤᵥ (Metric Tensor) | Λ*(M) (Exterior algebra) | |
Raising the Djed
Dot, and Dt (Djet): Pi ($\pi$) functions as the structural multiplier that defines the linear-scalar relationship between the singular point-source center of a circle (the absolute point of emanation) and its geometric sphere of influence (the circumference). This static, perfect ratio perfectly corresponds to the Dot product and dt (Djet), which represents unyielding, changeless eternity, spatial architecture, and a pre-existing field.
Cross, and Nhh (Neheh): Phi ($\varphi$) acts as the dynamic growth factor governing the iterative, non-linear unfolding of log-spiral trajectories observed throughout the natural world. This generative, spiral geometry corresponds directly to the Cross product and nhh (Neheh), which embodies the principles of cyclical time, perpetual movement, and the active unfolding of nature.
Note: In standard mathematics, (Ф) and (π) do not represent these operations.They operate here as a philosophical shorthand—mapping the pairing of Djet (linear/static eternity) and Neheh (cyclical/moving time) from Kemetic philosophy onto the dual structures of modern space-time mathematics.
The Four Constants: QED
In quantum electrodynamics four constants merge to produce the fine structure constant - the coupling constant of quantum electrodynamics.
(e) (Elementary Charge): The magnitude of electric charge carried by a single electron or proton. It defines the standard unit of charge and is central to the electromagnetic force.
(ϵ0) (Vacuum Permittivity): Also called the "electric constant," it represents the ability of a vacuum to permit electric field lines. It relates the units of electric charge to mechanical units like force and distance.
(ℏ) (Reduced Planck Constant): Defined as (h/2π), it sets the scale for quantum phenomena. It is the fundamental unit of action and angular momentum in quantum mechanics.
(c) (Speed of Light): The maximum speed at which all energy, matter, and information can travel in the universe. It serves as a conversion factor between mass and energy (E=mc2) and between space and time.
Four become one: The (φ)Fine-Structure Constant (α) ≈ 1/[C(16,2) + 16+1 = 137]
When these four constants are combined as shown below, their units cancel out to create a dimensionless value:
Coupling Strength: (α) quantifies the strength of the electromagnetic interaction between elementary particles.
Universal Importance: Because it is dimensionless, its value (1/137) is the same regardless of what unit system (metric, imperial, etc.) is used. It is considered a "raw fact" about our universe's structure.
Atomic Physics: It was originally named the "fine-structure" constant because it explains the small energy splits (fine structure) in the spectral lines of atoms.
In other words — 137 is the number of ways to choose 0, 1, or 2 elements from a set of 16.
The Four Constants — Bantu Cosmology
The quoted text below is taken from Solutions for Postmodern Living, (2025, August 16). A note on Bantu philosophy. https://www.solutionsforpostmodernliving.org/world-building-blog/bantu-philosophy.
In it the author references Alexis Kagame's work: Kagame, A. (1970). The Bantu concept of space-time (J.-P. Martinon, Trans.). In The development of philosophy in the contemporary world: Time and history in world cultures. UNESCO. https://jeanpaulmartinon.net/wp-content/uploads/2018/07/Kagame-on-Time.pdf
“Alexis Kagame — effectively abstracted a philosophical cosmology from Bantu languages”...“According to Kagame, the philosophy that can be abstracted from Bantu languages assumes (i) a cosmos that is constituted by a play of forces, termed “ntu” and (ii) that four different kinds of forces are at play in the constitution of the cosmos, these being “muntu”, “kintu”, “hantu” and “kuntu”.”
“Muntu”(e) refers to forces that give rise to mental phenomena (i.e., affected/affecting phenomena) — I have taken to calling such phenomena “complexes” [Hilbert Spaces] in my theoretical framework.
“Kuntu” (c) refers to forces that give rise to modal phenomena [language itself being one such modal phenomena] — I have taken to calling such phenomena “systems” [Lambda] in my theoretical framework.
“Kintu” (ϵ0) refers to forces responsible for material phenomena (i.e., effected/effecting phenomena) — I have taken to calling such phenomena “mechanisms”[Metric Tensor] in my theoretical framework.
“Hantu” (ℏ) refers to forces responsible for spatiotemporal phenomena — I have taken to calling such phenomena “constructs” [scalar, vectors, particles] in my theoretical framework.
Four become one: ntu – root of Bantu (i.e. human)
“according to the languages of the Bantu peoples, light has no nature of its own to reveal to us. Light’s existence (“ntu”) at any given moment is nothing other than an index of an ever changing play of mental forces (muntu), modal forces (kuntu), material forces (kintu), and spatiotemporal forces (hantu).”
The Fine Structure Constant (α ≈ 1/137) emerges from four fundamental constants of electrodynamics — and finds structural resonance in Bantu cosmological categories, where Muntu, Kuntu, Kintu, and Hantu map isomorphically onto the electromagnetic constants of QED.