Waves Do Math

In the paper's words

Stand at the edge of the ocean. One is at the boundary between two worlds: the solid, seemingly definite world underfoot, and the fluid, ever-changing world of the sea. Intuition tells us these are fundamentally different kinds of existence.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. 6.2.1 The “Thing” as a High-Fidelity Resonant State: A Wave Pattern of Statistically Overwhelming Stability Synthesizing the conclusion of this Part—that a thing is a persistent resonant wave pattern—with the statistical principles of this section, we arrive at a deeper definition.

   from 6.0 Statistical Origin of the

How it is done

1. 1.1 The Universal Law of Superposition The Principle of Compounded Motion is formally understood as the Universal Law of Superposition , which describes how distinct wave patterns integrate their effects.

   from 1.0 The Principle of

2. In a typical interference pattern, such as alternating light and dark fringes from a double-slit experiment, the energy missing from dark fringes is exactly accounted for by the excess energy found in bright fringes.

   from 2.0

3. Under this framework, apparent randomness and uncertainty in physics—particularly quantum mechanics—arises not from reality’s intrinsic indeterminacy, but from epistemological limitations inherent in our method of acquiring knowledge from an inherently infinite and continuous system.

   from 4.0

4. However, by performing an experiment repeatedly—that is, by drawing a large number of samples from the same population—we can calculate stable statistical measures such as the mean, median, and variance.

   from 5.0 Probability as a

What would falsify it

1. This inherent gap between total reality (the population) and our observable knowledge (the sample) necessitates the use of statistics and probability .

   from One Reality, Many Scales

2. I: A Tangible Wave - Principles of a Fractal Reality In this first part, we ground our inquiry in direct, observable phenomena from the macroscopic world.

   from Part

3. This fundamental arithmetic of nature is ceaselessly at play, from the molecular realm to gravitational phenomena, offering an elegant framework for understanding all observable complexities.

   from 1.0 The Principle of

Where the claim stops

1. It reveals that the contours of ignorance , the boundaries of what we do not know, are often shaped by our observational methods and conceptual frameworks, rather than by an inherent fuzziness of reality itself.

   from One Reality, Many Scales

2. Compounded Motion This section establishes the most fundamental characteristic of a wave-based reality: influences do not clash or obstruct, but rather merge and combine.

   from 1.0 The Principle of

3. This capacity for additive interaction is a defining feature of a continuous wave field, contrasting sharply with the exclusive nature of solid objects, which cannot interpenetrate.

   from 1.0 The Principle of

Where to read

1. One Reality, Many Scales442 words · 2 min
2. Part5,779 words · 25 min
3. Part II:4,670 words · 20 min
4. Part III:4,469 words · 19 min
5. 10 Discussion: The Ocean of1,578 words · 7 min
6. 11.0 Future Directions and1,260 words · 5 min