The holofractal universe implies patterns of scale, but how do we understand those patterns without indulging in "numerology?" Nassim Haramein was the first to point out the geometric connection between the Planck mass, Planck length, proton mass, and proton radius, which led to the inference of the Planck sphere medium. I've taken that definition of the Planck sphere as a starting point and [developed a model that makes real predictions](https://medium.com/the-planck-sphere/the-planck-sphere-solution-to-gravity-dark-energy-and-dark-matter-88675c8434c1) about the true value of the Hubble constant (74.3 km/s/Mpc) and the maximum photon energy (2.5 PeV). But anytime I present this model, I'm met with the same response: "that's numerology."

[In the latest article](https://medium.com/the-planck-sphere/when-numerology-reveals-patterns-of-scale-in-physics-eee44139260e), I point out that Kepler was an unabashed numerologist, and discovered the laws of planetary motion by just trying out different ratios until he found one that fit. Newton was not into numerology in the same way as Kepler, but his model of universal gravitation between distant bodies explicitly leaves out a causal mechanism. Mass is defined as a "quantity of matter" (a number of *something*) but he never addresses exactly what that thing is, and in practice, mass is determined relative to the resistance to a given force, which creates a circular definition between mass and force. The mathematics surely works, but at least in its original formulation, it's all just numbers.

Newton's framework implies the gravitational constant G, which Einstein later adopts into his field equation for general relativity. Then as now, it's just taken for granted that when you plug this number into the equation, it returns the correct answer. *But what is this number?*

That's why the Planck sphere approach is so powerful. It doesn't take for granted that G is a magic number but uncovers what it actually represents: The term G/c\^4 that is *required* for real world calculations using general relativity is simply the ratio of Planck length to Planck mass-energy, subject to the simultaneous constraint imposed by hc/2π.

G/c\^4 = l\_P/(m\_P c\^2)

hc/2π = l\_P \* m\_P c\^2

  
The Planck sphere model is the only model that can make sense of these intrinsic limits of length, mass, and energy within general relativity. The scale of proton and electron masses. The fundamental scale of electrostatic to photon energy that defines the fine-structure constant. The scale of the CMB relative to the electron rest mass energy. The scale of the maximum photon energy relative to the proton rest mass energy. The scale of the universe relative to the proton, and the scale of the proton relative to the Planck sphere.

If it's numerology, then it's in good company alongside Kepler's ratios, and I have no idea how else one would go about understanding scale without exploring, organizing, and interpreting ratios of fundamental physical limits.

Are the patterns of scale in the holofractal framework just NUMER0L0GY?