The Natural Order of Maths
A Manifesto from Basic Addition to the Reality of Negative Volume
By Chris Young
Introduction
This journey that you are about to take is not focused on solving problems or offering a typical understanding of how concepts function. It is about revealing the fundamental nature of basic mathematics and the reality of how these concepts truly work. Although many years have been spent researching these terms, the findings and outcomes presented here are the result of deep insight and a commitment to how mathematics was intended to function—not merely how it was invented.
The following information is a demonstration of what is actually occurring within the numbers. I am not concocting a new perspective or forcing a concept to work just to fit a presentation; I am not reaching for answers where they do not exist. Every theory included in this book has been weighed, proven right, and then rigorously tested until it could be proven wrong. If a sub-concept benefited a major idea but contained even a small part that did not work, the entire concept was deemed flawed. This meant discarding the approach completely and starting again from scratch to uncover the correct and intended way the mathematics was supposed to function. What remains in these pages is only that which I have found impossible to prove wrong, no matter how much effort was applied.
A successful foundation in basic mathematics ensures that each chapter leads so naturally to the next that the content becomes predictable before the page is even turned. In this book, no concept is forced to work through clever wording or hidden steps. Mathematics is not a matter of opinion, and it should never be written in a way that tries to convince a reader of something that is not naturally visible. The logic here is plain, direct, and self-evident.
Preface: How to Use the Natural Order
This book is designed to be read in sequence. Because mathematics is a language built on foundations, each chapter provides the ‘DNA’ for the next.
To the parents sitting at the kitchen table: You do not need a background in advanced mathematics to understand these pages. All you need is a willing mind and, occasionally, a pencil to sketch the physical reality we are discussing.
To the teachers in the classroom: These chapters are provocations. They are designed to spark a “Wait, that actually makes sense” moment in your students. Use the diagram provided for negative integers to illustrate the structural truth of the operation. Use the physical examples of the hole and the shovel. Consider the physical relationship between a hole (the negative) and the shovel (the operation); the ground level represents the zero boundary.
The goal is not the memorisation of rules; the goal is the observation of the universe.
Contents
- Subtraction, Minus or Negative, What is the Difference?
- The Very Basic Workings of Addition and Subtraction
- Commutation and What This Means for Subtraction
- Fractions vs Division
- Subtraction of Multiple Numbers
- The Addition/Subtraction Column Algorithm
- Is the Square Root of a Negative Number a Real Possibility?
- Negative Division with Remainders: The Last Hurdle
- A Product of Two Negatives: Misconceptions and Reality
- Multiplication and its Concepts Explained
- Collatz Conjecture a Negative Conundrum
- How Base Ten Works and Why it is Perfect
- New Possibilities
- Negative Volume, Displacement and Shapes in General
- More New Possibilities: The Real-World Impact