Eeek! The “*m*” word! Oh no! Mumbling and grumbling resound across the abyss between words and numbers!

It is true that one of the many ways Quadernity is modeled is mathematically. Quadernity’s chalkboard not only taught a deeper way to understand what numbers represent; the lessons led to marveling at elegant mathematical truths.

Although this part of the story is important to the whole understanding, even a few amazing mathematical formulae might be fearsome to some readers. Rest assured that 98% of Quadernity’s math is contained in the grouping of chapters here, under the heading, Mathematical Models — fair warning for those of you who think you are “allergic to math”.

Side-step these chapters if you must and we will reconnect in the conclusive Part Four, Philosophic and Scientific Models. Before making your final decision, though, please allow me the opportunity to allay anxieties that might prevent you from following our compelling exploration of Creation through numerical revelations.

Remember these two points:

- When my visions began in 1999, whatever introduction I had been given in high school to basic algebra and geometry had expired from lack of use during the intervening three decades. Many of you are far more competent mathematicians than I am.
- Every delicious bit of math encountered here will be presented in bite-size chunks and explained in straight-forward, simplified steps that carry their part of the story to a delightful wrap-up. My intention is to illuminate, not intimidate.

What follows could be the inoculation that desensitizes you sufficiently to stick with me. If your eyes do not start bleeding when you see the formula below, you can rest assured that this is as bad as it gets!

**( ia +1b) (ia -1b)**

See? No nasty little Greek letter symbols that confound us non-mathematicians!

When this formula appeared, crystal clear, upon the chalkboard in my mind one morning, I was actually shocked right out of my meditation. Why would something so foreign to me arise in blaring insistence?

Were it not for the plus and negative signs, I would not have recognized it as a mathematical formula. Even so, I did not know what to do with it, other than write it down in my notebook.

Some time later, my husband was providing chiropractic services to a man who was a math teacher in a local private school. I asked him if he would help me understand what the letters of the mysterious formula meant, and how it could be interpreted.

In his brief tutorial, he explained three math facts relevant to the formula:

- The letter ‘
*i’*stood for the word, imaginary. One can only imagine the √-1, he explained. Squaring either positive or negative numbers will always produce positive numbers. There is no number that, when squared, equals -1. - The FOIL method provided the correct sequence of operations, (First, Outer, Inside, Last) when multiplying the terms inside the parentheses. The solution to the formula turned out to be: -1(a² + b²).
- The letters ‘a’ and ‘b’ are called variables. As the formula stood alone, no numbers were assigned to, or represented by, these variables, so the mystery continued. (Answered in the first chapter of Math Models,
**Discovering Portals between Dual Dimensions**.)

Only years later did this strange looking formula prove to be integral to the whole of Quadernity and suggestive of the answer to the original question that launched my quest to discover how two tales of Creation, told so differently, could both be pointing to a singular event. In the final chapter of the Mathematical Models, we will wrap back to this formula for its full reveal. You have a treasure in store when you receive what this equation means to Creation!

Throughout the math chapters are slide presentations, some animated and many personally narrated (so be sure to turn on sound). Please grant me your forbearance of my admittedly primitive animations, achingly behind the exponential growth curve of computer graphics professionals. My sincere desire to share content with you keeps me from being dissuaded or embarrassed to just do what I can with my self-taught capabilities.

Even without snazzy special effects, the visuals and vocal intonation should still aid comprehension, making this chapter more stimulating and easier to digest than expected.

For example, here is the first narrated video, a little over two minutes long, which shows how the formula above was solved, for those of you who care to know. It is totally optional viewing.

(Keep your cursor off the video screen for unobstructed viewing.)

Although I have yet to learn the symbology of more advanced maths, my mind does easily recognize and appreciate patterns, including mathematical patterns. Yours does too, quite naturally, even if you have never thought of it this way before.

Reaching into the right spot to catch a ball and estimating how long it will take to cross the street ahead of oncoming traffic are common problem-solving skills, without necessarily knowing how to calculate the answers on paper.

Even dogs in the park thrill to successfully act on what calculus can merely represent: intuitively chomping slobbery Frisbees.

**Bees also do math.** **And ants can count**.

Here is a little fish demonstrating super-human geometrical precision. This astonishing short video is well-worth the few minutes invested! Math intuition is a gift from Nature that is shared among Her creatures.

Inanimate planets perform perfectly symmetrical patterns in their celestial movements. As seen from earth, the **path of Venus** delineates a five petaled flower every eight years.

Sometimes we *do know* that we *do not know* something. I knew I did not know what to do with the algebraic formula from my dream.

Conversely, other times we *do not know* what it is that we *do know*, as the critters in the examples above demonstrated.

The animals knew exactly what to do without having a formula; I had a formula and knew not what to do with it.

Mathematics is, for all intents and purposes, a language for formulaically expressing the generalities of natural patterns.

Profound patterns are found throughout nature, in the cosmos, in tiny life-forms and even in our own bodies. For both the math-o-phobic and math-o-philic, “ah ha!” moments are scattered throughout the chapters here.

If the videos above left you cold, then just skip to the next mast-head title; Nature did her best to entice you. No worries!

For readers who are experiencing an (unexpected?) appreciation for the beauty of patterns and the extraordinary ways they show up in the natural world, Quadernity promises fun figuring out just how our fabulous world is finessed.

For readers with expert skills in mathematics, the fun lies in Quadernity’s novelty of approach. Numbers are numinous and visions are venerated in the beginner’s mind of the author. Intriguing intuitions arise and are confirmed by calculations, rather than the other way around.

Here we begin modeling Quadernity from a mathematical vantage point. This time, its dynamic relationships will reveal uniquely powerful proportions, rarely taught in schools, yet held sacred by secret societies.

#### Chapters Forthcoming Under this Heading

**Discovering Portals between Dimensions**

Golden Ratio (that which is hidden is most revealed)

- Historical, Artistic, Architectural, Biological, Geometrical
- Pyramid, Earth and Moon
- Auspicious 108

- Meditating Man
- Chakra System
- Mandelbrot

- Fibonacci and Lucas Series
- Triplets, Cone Spiral
- Relationships between the series

Mathematical Visions:

- Full Spectrum Number Line
- Geometrical Vision, May 2017
- Sacred Algebra Vision from 2004, Grand Finale