First, allow me to rename theses numbers during the remainder of this post to *lateral numbers*, in accordance to the naming convention as was **recommended by Gauss**. I have a special reason for using this naming convention. It will later become apparent why I’ve done this.

If we examine lateral numbers *algebraically*, a pattern emerges:

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$i^0 = 1$

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$i^1 = i$

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$i^2 = -1$

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$i^3 = -i$

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$i^4 = (i^2)^2 = (-1)^2 = 1$

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$i^5 = i \cdot i^4 = i$

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$i^6 = i^2 \cdot i^4 = (-1)(1) = -1$

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$i^7 = i^2 \cdot i^5 = (-1)i = -i$

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$i^8 = i^4 \cdot i^4 = (1)(1) = 1$

When we raise lateral numbers to higher powers, the answers do not get higher and higher in value like other numbers do. Instead, **a pattern emerges after every 4th multiplication.** This pattern never ceases.

**All other numbers, besides laterals, have a place on what currently is called the ‘Real number line’.**

I qualify the naming of the Real Numbers, because even their conceptualisation has come into question by some very incisive modern mathematicians. That is a very ‘volatile’ subject for conventional mathematicians and would take us off on a different tangent, so I’ll leave that idea for a different post.

If we look for laterals on any conventional Real number line, we will never ‘locate’ them.** ***They are found there,** but we need to look at numbers differently in order to ‘see’ them.*

**Lateral numbers solve one problem in particular: ***to find a number, which when multiplied by itself, yields another negative number.*

Lateral numbers* *‘*unify*’* the number line with the algebraic pattern shown above.*

2 is positive and, when multiplied by itself, yields a positive number. It maintains direction on the number line.
When one of the numbers (leaving squaring briefly) being multiplied is negative, the multiplication yields a negative number. The direction ‘flips’ 180° into the opposite direction.

Multiplying -2 by -2 brings us back to the positive direction, because of the change resulting in multiplying by a negative number, which always flips our direction on the number line.

So, it appears as if there’s no way of landing on a negative number, right? We need a number that only rotates 90°, instead of the 180° when using negative numbers. **This is where lateral numbers come into play.**

If we place another lateral axis perpendicular to our ‘Real’ number line, we obtain the desired fit of geometry with our algebra.

When we multiply our ‘Real’ number 1 by *i*, we get *i* *algebraically*, which *geometrically* corresponds to a 90° rotation from 1 to *i*.

Now, multiplying by i again results in i squared, which is -1. This additional 90° rotation equals the customary 180° rotation when multiplying by -1 (above).

We may even look at this point as if we were viewing it down a perpendicular axis of the origin itself (moving in towards the origin from our vantage point, through the origin, and then out the back of our screen).

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[If we allow this interpretation, we can identify the 'spin' of a point around the axis of its own origin! The amount of spin is determined by how much the point moves laterally in terms of *i*.

We may even determine in which direction the rotation is made. I'll add how this is done to this post soon.]

Each time we increase our rotation by multiplying by a factor of* i*, we increase our rotation another 90°, as seen here:

and,

The cycle repeats itself on every 4th power of *i*.

**We could even add additional lateral numbers to any arbitrary point. This is what I do in my knowledge representations of holons. **For example a point at say 5 may be expressed as any number of laterals *i, j, k,… *simply by adding or subtracting some amount of* i, j, k,...:*

*5 + i + j +k +…*

Or better as:

[*5, i, j, k,…*]

**Seeing numbers in this fashion makes a point*** n***-dimensional.**