this page, Bootstrapping a Metaphor

We see natural numbers as representing real, distinct, objects. Negative numbers, which may be taken to represent absense or lack, are chosen to be the subjective, interior, invisble, internal representation of the external objects. This leaves zero as a boundary and point of reflection, the real reflected within the mind.

Next: PowerCircles

Bootstrapping a Metaphor

Counting Numbers as Concrete Objects

In the beginning of the numbers there was ONE. It meant I held one object. Numbers were inseperable from objects. Always N objects. For the purposes of this metaphor and interpretation, lets consider each counting number to BE a discrete entity in Communal CONsensual UNI-VERSE-ALL Reality.

Let there be an ordering relation, a sort of Absolute Value, arraying discrete objects in the historical, evolutionary, physical universe, so they are in a standard order, each identified by successive counting numbers. Notice that we have left the realm of "9 apples" to a realm of "9 unique fruits."

Negative Numbers as Mental Experience of Concrete Objects

Zero is initially seen in the empty hand, as Absense.

Following a concrete pattern, Negative numbers indicate lack, or missing, or desire. (-2) -> I don't have 2 fruits; I need 2 fruits; I am short 2 fruits.

In constructing this interpretive metaphor I am going to reverse the notion of negative as lack. Instead, if N is an external object, -N is the internal, mental experience of that object. Thus, there is a place for each object in the universe to be held in mind. Following the poetry:

The Friend, the Beloved, your Soul,
is a River with the trees and buds of the world
reflected in it. And it’s no illusion!
The reflections are real, real images, through which
God is made real to you.

-Rumi, We are Three p. 55.

Zero as Relative Origin and Mirror

Apply to zero: mirror, center of self, arbitrary origin. Many Subjectives in one Objective.

First Duality: Two Directions on the Number Line

DUALITY of directions on number line: note 180 degrees, when 90 is considered independant.

Second Duality: Two axis Orthogonally Arranged

DUALITY of number lines, each with two rays, positive and negative, form Real and Imaginary, Complex, right-angled, Plane.

this page, Bootstrapping a Metaphor

We see natural numbers as representing real, distinct, objects. Negative numbers, which may be taken to represent absense or lack, are chosen to be the subjective, interior, invisble, internal representation of the external objects. This leaves zero as a boundary and point of reflection, the real reflected within the mind.

Next: PowerCircles

Notes below the line

The Unit, One

{Checking the Metaphor: Looking at Mathematics

Repeating Addition, Repeating Subtraction, DUALITY of directions on number line.; note 180 degrees, when 90 is considered independant.

• Tangent: Representing Whole numbers by division of wholes and by multiplication of wholes.}

Jump to:

Empowering 1, -1, I

uestion the system: Empowering (repeated multiplication): 1, -1;

meaning of empowering, results on 1, results on negative one

negative one requires complex numbers;

interpret I [SQRT investigation], AREA interaction, investigate I.

• Tangent: avoiding infinite regress
• Tangent: Adding all three
• Tangent: as Sin[x], Cos[x]

Back in metaphor, consider transformations of initial point - mirrors;

then empower them in mathematica

then interpret in metaphor.}