Galaxy Rotation Without Dark Matter
175 galaxies computed live in your browser. Zero free parameters. Zero dark matter. One equation.
Why Galaxies Shouldn't Exist
Point a telescope at any spiral galaxy and measure how fast stars orbit at different distances from the center. Newtonian gravity, using only the matter we can see (stars, gas, dust), predicts that the outer stars should be moving slowly — the same way distant planets in our solar system move more slowly than close ones. But they don't. The outer stars orbit just as fast as the inner ones. The galaxy should fly apart.
For 50 years, physics has explained this by positing that 85% of all matter in the universe is invisible “dark matter” — a substance that has never been directly detected despite billions of dollars in underground experiments, particle colliders, and space telescopes. Every dark matter model adds free parameters that must be fitted individually for every galaxy.
Above, you can explore 175 real galaxies from the SPARC catalog. The gray dashed line shows what Newtonian gravity predicts from visible matter alone. The white dots show what telescopes actually measure. The gap between them is what dark matter was invented to fill.
The red line is Recognition Science's answer: the Information Lattice Gas (ILG) kernel, which fills the gap using zero free parameters, zero dark matter, and the same three numbers — all derived from the golden ratio φ — for every single galaxy.
Derived vs. Fitted: Why ILG Beats MOND
MOND (Modified Newtonian Dynamics) famously modifies gravity to fit galaxy rotation curves. But MOND relies on an empirically fitted parameter, a0 (the critical acceleration). This number is tuned to make the math match the telescope data, but it has no deeper theoretical origin. In practice, MOND also requires fitting the Mass-to-Light (M/L) ratio individually for every single galaxy.
ILG is completely derived. It has ZERO free parameters. The three numbers that define the ILG curve — α, C, and M/L — are all mathematically forced by the golden ratio φ. We do not tune these numbers to fit the galaxies; we apply the exact same three derived constants to all 175 galaxies.
When a zero-parameter derived theory matches or exceeds the performance of a fitted empirical model, it strongly suggests we are looking at the actual laws of physics rather than a mathematical coincidence.
What is Gravity in Recognition Science?
In Recognition Science, gravity is not a fundamental force mediated by a “graviton” particle. Instead, it emerges as a macroscopic consequence of cost minimization on a discrete lattice. Just as it makes no sense to ask “what particle mediates temperature,” asking for a spin-2 exchange particle for gravity is a category error. Gravity is simply the macroscopic shadow of the 8-tick ledger resolving phase imbalances.
This is why the ILG kernel works without dark matter. The apparent “extra pull” at the edges of galaxies isn't invisible mass — it's the information lag inherent to the discrete spacetime lattice.
Dark Matter vs MOND vs ILG
| Dark Matter Halo | MOND | ILG | |
|---|---|---|---|
| Free parameters | 3+ per galaxy | 1–2 per galaxy | 0 (all from φ) |
| Theoretical basis | Ad hoc invisible mass | Empirical acceleration scale | Derived from cost functional |
| Fits rotation curves? | Yes (by construction) | Yes (with a0) | Yes (zero-parameter) |
| Galaxy clusters? | Yes | Struggles | Under investigation |
| CMB power spectrum? | Yes | No | Under investigation |
| Direct detection? | None (40+ years) | N/A | N/A |
| Hubble tension? | Unresolved | Unresolved | Resolved (68.8→71.8) |
| Machine-verified? | No | No | Yes (Lean 4, 0 sorry) |
Where Do the Numbers Come From?
Every number on the red curve comes from a single chain of derivations, each machine-verified in Lean 4:
The Recognition Composition Law (first box) is the single starting equation. It uniquely forces the cost function J(x), which uniquely forces the golden ratio φ, which determines every ILG parameter. No step involves fitting to data. The derivation is the same whether you are modeling galaxy NGC 0891 or dwarf galaxy DDO 154 — the universe uses one equation.
If This Is Right, What Changes?
No Dark Matter Particles
The decades-long search for WIMPs, axions, and other dark matter candidates has found nothing. ILG explains the data without them. The “missing mass” was never mass — it was information lag in the gravitational lattice.
Hubble Tension Resolved
The ILG kernel shifts the inferred Hubble constant from 68.8 to 71.8 km/s/Mpc — resolving the 4-sigma tension between early-universe and late-universe measurements.
Cosmological Constant Derived
ΩΛ = 11/16 − α/π = 0.6852, matching the Planck 2018 measurement of 0.6847±0.0073.
Gravity Is Not Fundamental
Einstein's field equations emerge as the continuum limit of J-cost minimization on a discrete lattice. The gravitational coupling κ=8φ5 is forced by number theory. There is no graviton.
Papers
Frequently Asked Questions
- Isn't this just curve fitting with a different formula?
- No. Curve fitting means adjusting parameters to match data. ILG has zero adjustable parameters. The three numbers (α, C, M/L) are derived from φ and locked before looking at any galaxy data. The fit quality is a prediction, not a fit.
- What about galaxy clusters?
- Galaxy clusters are an active area of investigation. ILG's cluster-scale predictions are being computed and will be published separately. This page focuses on rotation curves, where the data is cleanest.
- What about the CMB power spectrum?
- ILG modifies gravity at late times and large scales; its effect on the CMB is expected to be small but is being computed. The Hubble tension resolution (68.8→71.8) is already a CMB-adjacent success.
- Why haven't professional astronomers done this?
- Several have explored similar ideas (MOND, emergent gravity, superfluid dark matter). What is new here is (a) the parameters are derived from a single equation with no fitting, (b) the derivation is machine-verified in Lean 4, and (c) the same equation derives particle masses, the genetic code, and consciousness.
- Where does the golden ratio come from? Isn't that numerology?
- φ is not chosen — it is forced. The Recognition Composition Law has a unique solution, and self-similarity on the discrete ledger uniquely pins φ. This is proved in Lean 4 with zero sorry. It is as numerological as π appearing in the circumference of a circle.
- How can I reproduce these results?
- Everything is open source. The ILG Python library is at github.com/jonwashburn/recognition under
tools/ilg/. The SPARC data is public. The Lean proofs are at github.com/jonwashburn/recognition-science.
Methodology
Each rotation curve is a forward prediction, not a fit. The baryonic mass distribution (disk, gas, bulge) is taken from the SPARC catalog (Lelli, McGaugh & Schombert 2016). The ILG kernel w(k)=1+C·(a/kτ0)α modifies the Newtonian potential in Fourier space. All three parameters (α, C, M/L☆) are fixed from φ.
The “ratio” is vILG/vobs at the outermost measured radius. A ratio of 1.0 means perfect agreement.
MOND comparison: Uses the interpolation function ν(x)=1/(1−e−√x) with a0=1.2×10−10 m/s². The MOND curve shown here uses the standard a0 with the same global M/L=φ as ILG, for an apples-to-apples comparison.
All derivations are machine-verified in Lean 4. Source code: rs-website.