Before introducing any of the new dual-frame machinery, we need to spend one post examining a very deep question:
Why should one underlying scalar progression generate two distinct kinds of observable structure?
And equally important:
Why do those structures interact and constrain each other so precisely?
This is the final conceptual bridge between the classical RS foundations (scalar motion, displacement arithmetic, rotational combinations) and the projection-based formalism of DFT.
1. The Paradox at the Heart of the Reciprocal System
Larson often emphasizes that space and time are reciprocal aspects of motion, not separate substances. Yet he also treats certain operations—such as inward 2-D rotation versus outward spatial progression—as if they belonged to different categories of behavior. In RS this is not an inconsistency; it is a consequence of the fact that the NRS has no geometry until a reference system is chosen. But this poses a subtle conceptual problem:
- In the NRS, motion has no assigned direction or geometry.
- In a reference frame, motion must take on directional and geometric form.
- But the same scalar progression might appear as outward expansion in space or inward rotation in time, depending on which aspect is being projected.
DFT-9 is where we unpack that implicit element and prepare for the formalism that will follow in later posts.
2. Why Interpretation Is Unavoidable: The RS “Text” Problem
In Nothing But Motion, Larson repeatedly notes that mathematics alone is insufficient without the “text”—the interpretive rules that tell us how to read a mathematical expression inside a physical frame. Bridgman’s point, which Larson quotes frequently, is decisive here: two identical equations can describe radically different physical processes depending on how the variables are interpreted.
For example:
- A linear displacement of
in space produces an outward spatial effect.
- A linear displacement of
- A rotational displacement of
in time produces the inward gravitation-like behavior of atomic structure.
- A rotational displacement of
Thus the question is unavoidable: How do we consistently decide whether a displacement is being interpreted as a spatial effect or a temporal effect?
RS answers this case-by-case. DFT will attempt to answer it systematically. DFT does not override RS interpretations; it systematizes the interpretive rules that RS uses implicitly.
3. The Hidden Symmetry: Space and Time as Homomorphic Carriers of Scalar Motion
Larson postulates that space and time have precisely the same dimensionality, and the same algebraic structure, differing only in reciprocal relation. That means each can carry:
- progression,
- vibration,
- rotation,
- vectorial motion.
But structural symmetry alone does not explain the empirical asymmetry of observed phenomena. The observed universe has far more spatial structure than temporal structure. Every atom has spatial extension, angular momentum, a magnetic pattern; all of these are rotational expressions “in space.” By contrast, rotational expressions “in time” are visible mostly as gravitation and the hidden inward structure of the atom.
So if space and time are symmetric carriers, why do we observe their contributions so unevenly?
What breaks the symmetry?
This is the exact point where projection enters the story. Not as an invention, but as a logical necessity.
The observed asymmetry is not ontological but instrumental. Our measuring apparatus couples primarily to spatial quantities because our operational reference frame is spatially indexed. The T-projection (phase, internal rotation, quantized harmonic structure) is equally present, but it appears indirectly through spectra, invariants, stability patterns, and discrete energy relations. DFT does not posit asymmetry in the underlying motion; it derives the observational asymmetry from coupling to a spatially biased representational frame.
4. Why Two Projections Exist: The Scalar Trajectory Must Be Read Through a Frame
The reason there are exactly two projections is not an arbitrary modeling choice: the scalar progression enters the observable domain only through the s/t ratio. The reciprocal relation does not permit a decomposition into more than two complementary representational aspects. If we had a ternary structure (e.g., s/t/u), three projections would be required. But RS tells us explicitly that the fundamental observable distinction is binary. Thus the S-projection and T-projection are not merely convenient; they are the only possible distinct readings of the scalar content.
The key idea, which now follows directly from RS logic, is this:
A scalar progression has no geometry; geometry exists only after a projection into a chosen frame.
Once we choose a reference frame—Larson’s stationary spatial frame—the scalar progression must be interpreted through spatial coordinates. Everything that appears “in space” comes from reading the scalar progression through this projection.
But the scalar progression also has a temporal aspect. If we instead read the scalar progression through the temporal coordinate system, the same underlying motion produces a different kind of structure: inward motion, coordinate-time accumulation, and the rotational content responsible for atomic structure.
The scalar progression is not two motions; it is one motion with two representational aspects.
It has one motion, but two ways to read that motion.
The distinction is not ontological; it is interpretive.
RS treats these readings as separate phenomena. DFT treats them as two projections of the same underlying scalar trajectory.
5. The Consequences for Physical Structure
Once you recognize the necessity of two projections, several previously mysterious RS features fall into a coherent pattern:
- The outward space progression of galaxies is the spatial reading of scalar motion.
- Gravitation is the temporal reading of the same scalar motion.
- 2-D inward rotation in atoms is the temporal projection of a compound displacement.
- The magnetic 2-D pattern of atoms is the spatial projection of the same compound displacement.
- The emergence of mass when rotation spans three dimensions is a projection effect: in the spatial frame, 3-D rotation appears as resistance to acceleration.
Each observed structure is a mixture determined by how much of the scalar content is expressed in the S-projection and how much is expressed in the T-projection.
Which projection dominates in a given case determines what we observe.
This is exactly what DFT will formalize as the motion budget.
6. Preparing for DFT-10: The S-Frame and T-Frame Defined
The next post will finally introduce the S-frame and T-frame with explicit definitions:
- The S-frame is the spatial projection of scalar progression.
- The T-frame is the temporal (phase-rotational) projection of scalar progression.
- Both result from applying different coordinate representations of the same scalar trajectory.
- RS phenomena such as electric displacement, magnetic displacement, mass, charge, isotopic stability, and nonlocality can all be reinterpreted as behaviors arising from these two projection maps.