The Foundational Tables of Multiplication

I wanted to share with you some of the foundational basics of arithmetic I have uncovered through my research. Incredibly, it seems that numbers have been widely misunderstood throughout time. I have found evidence that certain ancient people knew of the true nature of numbers, but by and large the information has been kept shrouded in secrecy or otherwise concealed and/or forgotten.

The time has come to clarify this information and its implications, as the lack of this clear understanding has for too long contributed to the hindrance of  humanities continued development as a truly advanced technological civilization.

One of the first “truths” children are taught about mathematics is that all numbers exist on a construct called the number line.

the number line

the number line

The idea of a number line easily supports the apparent reality that adding and subtracting  numbers is an exercise in traversing distances to the right and left along the line. If you want to involve higher dimensions (multiplication, exponents, division and square roots) then you turn 90 degrees for each dimension, create some more distance between points  and begin measuring areas and volumes and the unit integers contained by these spaces.

All of this geometry works out just fine when dealing with life within the normal range of our ordinary human experience, however there are layers of important meaning lost by not taking into account the underlying information which the numbers themselves indicate to us about how they are actually positioned in relation to one another.

The reality is that numbers position themselves on a circle divided into nine parts, and so we live in a MOD9 universe. To be even more precise,  numbers are positioned on the circle along the lines of a spiral whose growth is governed by the Golden Ratio, Phi. This spiral gives form to the vortex which has shown itself to be so fundamental in the physical creation. It is at this very place that the “abstract” counting numbers can first be seen as what they really are – the fundamental granularity of the “physical” Creation.

numeric spiral

numeric spiral

Let’s take a careful look at what it means to multiply numbers together.

Here are the multiplication tables which have been typically taught to students.

tables of multiplication

tables of multiplication

Although the above table is a clear expression of the geometric growth of numbers in two dimensions, it fails to offer a true representation of how the numbers relate to each other in the two dimensional geometry. When one accounts for the reality of the circle of nine, one sees that the tables of multiplication are in reality as given below.

foundational tables of multiplication

foundational tables of multiplication

We can derive universal structure from the table above.

table of the universal structures underlying geometric growth

table of the universal structures underlying geometric growth

Each multiplication table for the foundational numbers 1 through 9 posses a specific geometric signature. The one’s table chart is given below in the diagram below.

the one's table foundational chart

the one's table foundational chart

The two’s table chart is given below in the diagram below.

the two's table foundational chart

the two's table foundational chart

The three’s table chart is given below in the diagram below.

the three's table foundational chart

the three's table foundational chart

The path of the Three Chart traces the enclosed equilateral triangle 3 times.

The four’s table chart is given below in the diagram below.

the four's table foundational chart

the four's table foundational chart

The five’s table chart is given below in the diagram below. Note that between 4 and 5 lies the path through the singularity (the zero point). Once crossed the direction of the flow is reversed.

the five's table foundational chart

the five's table foundational chart

The six’s table chart is given below in the diagram below. Here again, the triangle is lapped three times.

the six's table foundational chart

the six's table foundational chart

The seven’s table chart is given below in the diagram below.

the seven's table foundational chart

the seven's table foundational chart

The eight’s table chart is given below in the diagram below.

the eight's table foundational chart

the eight's table foundational chart

The path of nine has no component and is therefore always zero. It is a perfect unperturbed circle.

the nine's table foundational chart

the nine's table foundational chart

Again, the shapes formed in the charts above are derived directly from the foundational multiplication tables

color coded table showing geometric growth structures

color coded table showing geometric growth structures

The sequences that arise from the foundational multiplication tables are perfectly summarized by the vortex glyph

vortex glyph

vortex glyph

Simply by organizing the numbers 1 through 9 and 0, we can see the doubling pattern, it gives rise to a polarity driven system which provides the framework for the expansion and contraction of systems within Creation.

I think it was said best by Fibonacci himself in 1202 AD:

“These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.”

This statement, although seemingly straight forward, is actually quite significant and layered with meaning.

For those interested, I would like to announce that I will be releasing my first book on the subject of Foundational Mathematics.

The Nature of Numbers
Mapping the Terrains of Conciousness

by Alexander S. Petty

(to be released in Summer of 2010 – target release date: 08/15/2010)

8 Responses to “The Foundational Tables of Multiplication”

  1. Mike Hedge says:

    great work Alex. love it!

  2. mAt says:

    I’ve discovered your blog only recently, and it’s now a must-read.
    Thanks for spending so much time sharing all this. This is great. And well explained.
    I’ll keep reading you.

  3. Adam says:

    Im starting to understand this now.

  4. Joseph says:

    Your site is helpful to understanding the deeper side of math as related to energy. Please email me when your book is published. I have a Sony eReader. Publish to the e-reader formats if you can. Otherwise, I will happily by a pdf version from you.

  5. Derrick says:

    I really like your work! It is keeping me up at nights though…

  6. Gert Kramer says:

    Dear Alexander,

    Could you please send me your e-mail address as I think I have a piece of the Universal Puzzle for you. You can find some presentations about it on my YouTube channel TheSharingSociety.

    Best regards,

    Gert Kramer
    The Netherlands

  7. Matthew Beasley says:

    Thank you for posting the foundational multiplication tables in your blog I’ve always struggled with relating to “basic” math the way it’s taught in schools the more complex theories always made more sense to me in the abstract, then the practical basics. But the way you presented it some “things” started clicking in my head when I started thinking in the terms you presented. Could you maybe point me in a direction of study for this problem I have… Basic math makes no sense to me yet as long all terms are presented in the abstract I’ve no difficulty grasping concepts and frameworks… I’d like to correct this crippling problem or at least understand it better if I can.

    Matthew Beasley
    U.S.A.

  8. Julie Almeida says:

    I was looking for a multiplication table for my cousin on Google and came across this. Let’s just say I was pleasantly suprised; this is definitely the most interesting thing I’ve stumbled upon in many months. Thank you!

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