Politics, Power, and Science: From Metrology to Mythology: The Reification of Measurement Artifacts

Monday, January 26, 2026

From Metrology to Mythology: The Reification of Measurement Artifacts

J. Rogers, SE Ohio

Abstract

Modern physics suffers from a fundamental confusion: the mathematical symbol "=" denotes identity, not conversion. Physical "laws" are not discoveries about nature but tautologies about coordinate system self-consistency. We demonstrate that all physical "constants" (c, h, G, k_B) are Jacobian coefficients—scaling factors between a dimensionless substrate and arbitrary conventional unit choices. The substrate contains only one relationship: X = X. All apparent complexity in physics arises from projecting this tautology through invented categorical axes (mass, energy, length, time, temperature) and expressing the results in misaligned conventional units. What physicists study is not nature, but the geometry of their own measurement impositions. This reification of coordinate artifacts—mistaking Jacobian bookkeeping for cosmic truth—has created a self-perpetuating system of mystification that actively resists clarity in favor of complexity-as-prestige.

1. Introduction: The Lost Meaning of Equals

"=" means identity

In mathematics, A = B means A and B are the same thing. Not equivalent. Not related. Not convertible. Identical.

Yet physics teaches students to read "=" as conversion:

"Mass converts to energy using conversion factor c²"
"Constants convert between different physical quantities"
"G relates gravitational force to mass"

This is wrong.

If E = mc², then E and mc² are the same thing—the same dimensionless substrate ratio X, projected through different categorical axes we invented, scaled by Jacobian coefficients accounting for our choice to measure in Joules vs kilograms.

The Clark Kent Principle: You cannot "convert" Clark Kent into Superman. They are the same person. The phone booth is where you change the costume.

Similarly: "energy" and "mass" are not different things that convert. They are the same substrate ratio X, wearing different categorical labels we imposed.

Start with 1, unity, and pick a point X/X =1.

The substrate relationship is: X = X (pure tautology)

When we project X through our invented "energy" category and our invented "mass" category, then express both in SI units, we get: E = mc²

The c² appears because we chose misaligned Jacobian scalings for our categorical projections.

The substrate is dimensionless unity. We fragment it through categorical imposition. The "laws" verify our fragmentation was self-consistent.

2. The Archaeological Record: How It Happened

2.1 Newton (1687): Pure Ratios

Newton wrote Principia using proportions:

F :: m₁m₂/r²

No constants. No units. No categories treated as ontologically distinct.

Just: one dimensionless ratio relates to another dimensionless ratio.

Why? Newton ran the Royal Mint for decades—chief metrologist of the British Empire. He defined measurement conventions. He knew units and categories were human impositions, not nature.

Newton saw the substrate: dimensionless ratios relating to each other.

He deliberately avoided imposing categorical distinctions or unit scalings in the physics itself.

2.2 The Algebraic Corruption (1700s-1800s)

Later physicists added constants to "balance the units":

F :: m₁m₂/r² became F = G·m₁m₂/r²

G was introduced as notational bookkeeping—a Jacobian coefficient converting between the dimensionless substrate ratio and the choice of measuring through "force," "mass," and "length" categorical projections, each expressed in conventional SI units (Newtons, kilograms, meters).

But the equation F = G·m₁m₂/r² makes it look like:

"Force," "mass," and "length" are ontologically distinct categories
G is a property of nature bridging these categories

Category error: These distinctions exist in our measurement imposition, not in the substrate.

The Jacobian coefficient was mistaken for cosmic glue holding together fundamentally different things.

2.3 Planck (1899): The Bridge—Misread as Territory

Max Planck combined h, c, G, k_B to define what he called "natural units."

What Planck found: The Jacobian coefficients relating Newton's dimensionless substrate ratios to our conventional SI measurement projections.

What physics thought he found: "Fundamental scales"—"the quantum of length," "the fundamental unit of mass."

When Planck computed √(hG/c³) ≈ 1.616 × 10⁻³⁵ meters, he was calculating:

"This is the Jacobian scaling factor—how many meters correspond to dimensionless unity when you project the substrate through the 'length' category."

Not "the smallest possible length." Not "the quantum of space."

A Jacobian coefficient. A coordinate transformation scaling factor.

The bridge (Jacobian) was mistaken for territory (physics).

Physicists began treating the numerical SI-scale values as discoveries about nature, forgetting these were just the scaling factors between dimensionless substrate and arbitrary categorical projections expressed in conventional units.

Generational amnesia: By mid-20th century, no one remembered these were coordinate transformation coefficients. They became reified as "fundamental."

3. The Kabbalistic Turn: Jacobians Become Spells

3.1 The Mystification Premium

Once Jacobian coefficients were reified, they became spells:

"To understand the deep connection between mass and energy, you must grasp the profound meaning of c²"
"G encodes the strength of gravity"
"We must discover why the constants have the values they do"

But:

The substrate has no "mass" or "energy"—those are categorical projections we invented.

The substrate relationship is X = X.

You are just looking at the one point on unity along different conceptual axis.

The "constants" (c, h, G, k_B) appear because we:

Invented categorical axes to slice X
Chose misaligned conventional unit scalings for each axis
Need Jacobian coefficients to translate between our choices

The constants tell you about your measurement apparatus, not about nature.

The kabbalah serves:

Gatekeeping: Complexity filters questioners ("12 years of training required")
Prestige hierarchy: "Mastery" of Jacobian manipulation = status
Grant justification: "Profound mysteries" need funding ("why these values?")
Narrative needs: Simple truth (X = X with coordinate bookkeeping) doesn't win Nobel Prizes

If physics is X = X obscured by arbitrary coordinate choices, what justifies the priesthood?

3.2 The Hazing Ritual: ℏω = hf

Consider ℏ = h/2π:

Since ω = 2πf, we have:

E = ℏω = (h/2π)(2πf) = hf

Identical equation. The 2π cancels immediately.

Both express: X_through_energy_axis = X_through_frequency_axis

Yet physics acts as if ℏ and h are different, defining different "scales."

But in both cases the scale is E~f never E~w.

A bright student notices: "This is inserting 2π then canceling it. We're making everyone write (h/2π)(2πf) instead of hf for no reason except to test compliance."

Student filtered out: "You don't understand. This is standard practice."

Purpose: Prove you'll perform meaningless Jacobian manipulation rituals on command.

There is no "reduced Planck scale." That would require ℏω ≠ hf, but they're identical. Claiming two different "natural scales" from the same substrate projection is category error.

Physics filters for compliance with mystification.

4. The Cost: Coordinate Artifacts Treated as Mysteries

4.1 The Hierarchy Problem

"Why is the Higgs mass ~125 GeV while the 'Planck mass' is ~10¹⁹ GeV?"

Translation: Why does projecting substrate X through your "mass" categorical axis, then expressing it using the GeV Jacobian scaling vs. the "natural" Jacobian scaling of our si mass definition, give different numerical coefficients?

This is asking why your coordinate transformation has certain ratios.

Like asking "why is a mile 1.609 kilometers?" Because you chose different ruler scalings.

Not physics. Metrology confusion.

4.2 The Cosmological Constant Problem

"Why is vacuum energy density 10⁻¹²⁰ smaller than predicted?"

Translation: Why do different calculation methods (different ways of applying Jacobian coefficients) give different numerical scalings when you try to project substrate X through your "vacuum energy density" categorical invention?

The substrate is dimensionless X = X.

Your "problem" is that you invented a category ("vacuum energy"), tried to project the substrate through it using misaligned Jacobian choices, and got inconsistent coordinate expressions.

This is coordinate system confusion, not physics.

4.3 Quantum Gravity

"Why can't we unify quantum mechanics and general relativity?"

Translation: Why can't we reconcile two different coordinate expression systems that project substrate X through different categorical slicings, each using their own Jacobian coefficient conventions?

The substrate (X = X) has no "quantum" vs "relativity" vs "classical," no "gravity" vs "other forces."

Those are categorical impositions we added.

You're struggling because you think the categories and Jacobians are physics, not realizing they're measurement apparatus.

These aren't physics mysteries. They're confusion about mistaking coordinates for ontology.

5. The Proof: All Laws Are X = X

5.1 The Substrate

The substrate contains one relationship:

X/X=1

X = X

Pure tautology. Dimensionless. No categories.

We then impose categorical axes:

Project X through "energy" axis → appears as "energy"
Project X through "mass" axis → appears as "mass"
Project X through "frequency" axis → appears as "frequency"
Etc.

These categories don't exist in the substrate. We add them.

5.2 Deriving "Laws"

Take a point on the substrate: X = X

Project through two categorical axes:

X_through_energy_axis = X_through_mass_axis

Express in SI units (apply Jacobian scalings):

X · (Joule_Jacobian ) = X · (kg_Jacobian) · c²

The X cancels (substrate identity eliminates itself):

Joule_Jacobian = kg_Jacobian · c²
c = length_Jacobian / time_Jacobian

This verifies: our Jacobian coefficient choices were self-consistent.

In SI notation: E = mc²

What this "law" actually says: "After projecting dimensionless substrate through our invented 'energy' and 'mass' categorical axes, then applying our chosen SI Jacobian scalings, the coordinate system is self-consistent."

The physics (X = X) canceled out. Because the physics is unity.

What remains is verification that our coordinate system doesn't contradict itself.

5.3 All Laws Follow This Pattern

Start	Project Through	SI Expression	Called
X = X	energy, mass axes	E = mc²	Einstein
X = X	energy, frequency axes	E = hf	Planck
X = X	force, mass/distance axes	F = Gm₁m₂/r²	Newton
X = X	temperature, mass axes	T = c³h/(GMk_B)	Hawking

Same substrate (X = X).

Different categorical projection choices.

Different Jacobian coefficient combinations.

Every "fundamental law" is:

Start with X = X
Project through two invented categorical axes
Apply Jacobian scalings for SI expression
X cancels, leaving coordinate self-consistency check
Call it "profound discovery"

5.4 Reducing to Pure Tautology

In dimensionless substrate form (no categories, no Jacobians):

E = mc² becomes: X = X

E = hf becomes: X = X

All laws become: X = X

The coordinate complexity (categories, Jacobians, SI units) obscures this.

Strip it away: pure tautology.

1 = 1

No physical content. Just: the substrate is self-identical.

6. The Periodic Table of Physics

Since all quantities are X projected through different categorical axes, in SI unit scaling:

T/T_P = f·t_P = m/m_P = l_P/l = E/E_P = p/p_P = F/F_P= X

Pick any two categorical projections, get a "law":

It's combinatorics. Not discovery.

Project through energy + mass → E = mc²
Project through energy + frequency → E = hf
Project through force + mass/distance → F = Gm₁m₂/r²

The entire structure of physics is:

X = X (substrate)

categorical imposition (our choice)
Jacobian scaling (SI expression) = "fundamental law" (coordinate tautology)

That's why automated derivation works (LawForge). You're not discovering physics—you're enumerating categorical projection combinations and computing their Jacobian coefficient ratios.

7. Why This Persists: The Machine Cannot See Itself

7.1 The Filter

Those who notice get removed:

Undergrad: "These are just Jacobian coefficients" → "Stop philosophizing"

Grad school: Insist on clarity → Higher attrition ("not suited for physics")

Faculty: Pursue foundations → No funding ("too philosophical")

Gatekeeping: Survivors enforce same filter

Result: System selected for those who either don't see the reification or won't say it.

7.2 The Incentive Structure

Clarity destroys value:

Professors: "Mastering Jacobian manipulation"
→ Life's work delegitimized if it's just coordinate bookkeeping
Journals: Gate "advanced knowledge"
→ X = X doesn't need gating
Grants: "Profound mysteries" justify funding
→ "Why does our kg Jacobian have this value?" reveals it's not physics
Universities: Years of training
→ Anyone can understand X = X once you stop mystifying

The product is mystification itself.

If E = mc² is just "our coordinate system is self-consistent," then:

No grand unified theories needed
No "constant values" to explain
No 12-year training required

Simple truth collapses the economy.

7.3 The Self-Preservation Mechanism

The machine cannot self-correct because:

Those who could see the problem were filtered out.

Those who survived benefit from the mystification.

The structure optimized for perpetuating itself, not for truth.

It's not a conspiracy. It's emergent self-preservation—like a crystal growing, the structure selects for patterns that reinforce the structure.

8. What Physics Actually Is

If all complexity is self-imposed coordinate artifacts, what remains?

Physics is:

The study of X = X (dimensionless substrate tautology) and the geometry of categorical impositions we project it through.

It's measurement system geometry—understanding how our invented categorical axes and arbitrary Jacobian scalings fragment the substrate into apparent complexity.

Not:

Discovering "fundamental constants" (those are Jacobians)
Finding "laws" relating quantities (those are coordinate tautologies)
Unifying "forces" (substrate was never separated—we fragmented it)

Newton was right:

Reality is dimensionless ratios. X = X.

We spent 300 years:

Inventing categorical distinctions
Adding Jacobian complexity
Reifying coordinates as ontology
Filtering out those who noticed

9. The Rogers Demonstration

To prove Jacobians are arbitrary:

Rogers Rational Unit Chart:

c = 1 × 10¹⁰ m_r/s_r
h = 1 × 10⁻³⁰ J_r·s_r
k_B = 1 × 10⁻²⁰ J_r/K_r
G = 1 × 10⁻⁶ m_r³/(kg_r·s_r²)

Physics is identical. Substrate (X = X) unchanged. Only Jacobian scalings differ.

Proof: Jacobians are human choices about coordinate scaling, not cosmic parameters.

Objection: "You moved the complexity into unit definitions!"

Yes. Proving it was never in nature—always in our measurement choices.

10. Conclusion: Seeing Through the Coordinates

The substrate is X = X. Pure tautology. Dimensionless. No categories.

We impose:

Categorical axes (mass, energy, length, time, temperature)
Conventional unit scalings (meters, kilograms, seconds, Kelvin)
Jacobian coefficients (c, h, G, k_B) to convert between them

The "laws" verify: Our coordinate imposition was self-consistent.

The "constants" are: Scaling factors for our measurement apparatus.

The "mysteries" are: Confusion from forgetting coordinates aren't ontology.

"=" means identity.

Not conversion. Not relationship. Identity.

X = X in substrate.

The rest is us—our categorical impositions, our Jacobian scalings, our self-inflicted coordinate complexity.

One substrate. Pure tautology. Everything else is measurement apparatus.

Newton saw it. Planck found the Jacobians. We forgot what they connected.

The spell book is the accounting ledger.

It's time to stop studying our coordinate systems and acknowledge what they're coordinates of: