This is a continuation of this.

#### Definitions

Zeroth waveform configuration space: atomic nucleus = {proton, neutron}

First waveform configuration space: atomic radius = {proton, electron}

#### Introduction

Many people are having a hard time understanding the Periodic Table. It took me several months as well, and I only connected the shape to microcanonical “space” & “time” after much contemplation: there was simply nothing else they could be.

There are only so many unknown variables.

The challenge is in perceiving the totality of the nested structure and also the particular reactions taking place within it. The trick is to recall that no matter how much we “zoom in” on reality, there are 3 space and 1 time dimensions. It’s true on the scale of the universe right down to the scale of a single atom. Thus we can conclude that: Spacetime cardinality (number of independent dimensions (=4)) is preserved under [the] fractal [operator] (zooming in arbitrarily).

A single atom thus represents a particular quantum number within the microcanonical set or: “Periodic Table” (below). A particular atom’s reactions are consequent wholly to its positioning relative this greater fractal shape: the set of all sets of possible waveform stable states (this will be explored in my book).

This is the geometric shape of the Periodic Table: consequent to the {electron, proton} duality. The stable states are the Noble Gases, equal to a full electron complement for a particular heptant (above). (heptant = any of the seven rows of the Periodic Table).

#### Fractal Spiral Geometry

On the finest scale, each micro-canonical “dimension” is nested within subsequent dimensions. As micro-space and micro-time are *entangled*, the Periodic Table has a structure which is *not independent of itself*.

#### Chemical and Nuclear Reactivity

We will see in my book that the microcanonical spacetime cardinality (4) also explains nuclear reactivity. The microcanonical harmonics (heptants delineated by the black oscillating wave) are illlustrated below. The vertical axis represents the number of neutrons and horizontal is protons.

An isotope’s proximity to the (zeroth configuration space) stable states predicts its (nuclear) reactivity (a.k.a.: radioactivity). Specifically, the further a species is from the central (darker) line, the more radioactive it is. By contrast, an element’s proximity to a (first configuration space) stable state (“Noble Gases”) predicts its (chemical) reactivity. The closer a species is to a Noble Gas, the more reactive it is.

We postulate that this inverse relationship stems from the canonical conjugation (CC) of the attributes of the {proton, electron} and {proton, neutron} waveform pairs. Namely, the waveforms possess the qualities of

Ψ Neutron: {dense, uncharged, heavy}

Ψ Proton: {dense, charged, heavy}

Ψ Electron: {diffuse, charged, light}

We can explicitly see that while individual waveform pairs share certain attributes, several are polar opposites. These connections will be further explored in my book.

Since both contain the proton, the pair sets of the zeroth ({Ψn, Ψp}) and first ({Ψe, Ψp}) waveform configuration spaces cannot be 100% independent. But they are also maximally independent. For an example of independence: trends in reactivity are perpendicular and complementary. For an example of dependence, nuclear properties of elements are predicted *both* by their zeroth and first configuration space waveform numbers. This will also be explored in my book: I present a model of universal energetic exchange free of any singularity.

#### The Microcanonical Spacetime Event (if you’ve made it this far, you’re math-core)

Consider a single atom as a spacetime event. The event (Δs^{2}) is defined by the relation:

Δs^{2}=−(cΔt)^{2}+Δx^{2}+Δy^{2}+Δz^{2}

Special Relativity indicates that on the macrocanonical scale (our scale), a single event makes the link between the size of the displacement vector (Δx^{2}+Δy^{2}+Δz^{2}) and the corresponding time interval (Δt) (vis-à-vis the speed of light). When we shrink to the level of an atom (fractal operator), we are additionally bound by the Heisenberg Uncertainty Principle, which states that such (Δx^{2}+Δy^{2}+Δz^{2}) are not independent of their time varying measurements. However, Special Relativity also imposes that these observables are not independent of the time variable (since measurements of state variables *must* take place over a nonzero interval) over which they are measured!

It’s enough to make your head spin.