III Grow Math

Imposed Identity

Wholeness

Remember Jane, observing the flower? Imagine Jane, in this case, at two years old, observing the flower. Within the model, there is nothing unusual about this:

Jane is the observer. (Oᴿ)

Looking is the process of observing. (Oᴳ)

The flower is observed. (Oᴰ)

Then another person introduces a statement:

Jane is a rock.

The statement alone does not physically transform Jane into a rock, but it has at the very least entered the field of experience. The problem of imposed identity begins there.

Details

The ordinary observation can be represented conceptually as:

C(Jane, age 2) = [Oᴿ(Jane), Oᴳ(observing), Oᴰ(flower)]

Now introduce an external or social observer, represented by:

u

In the present notation, u refers to an external observer whose characterization has not been affirmed, (unaffirmed) by Jane. The imposed observation is:

Oᴰ(Jane = rock; u)

Jane's experience may now include both:

Oᴰ(flower)

and:

Oᴰ(Jane = rock; u)

A fuller working expression becomes:

C₂ = (Oᴿ(Jane), Oᴳ, {Oᴰ(flower), Oᴰ(Jane = rock; u)})

The important distinction is:

Oᴿ(Jane) ≠ Oᴰ(Jane = rock; u)

Jane-as-observer is not identical to the external observer's description of Jane. The description may nevertheless become integrated within Jane's lived experience. If the statement happens once, it can be represented as an event.

If it happens repeatedly, another index becomes useful:

Rₖ = Oᴰ(Jane = rock; u, k)

Here:

Rₖ = the kth recurrence of this particular imposed observation
k = recurrence number

This is different from n.

n tracks the broad succession of experience.

k tracks repeated occurrences of the same specific experience or singular, particular proposition.

Jane will theoretically have millions of experiences between age 2 and age 22, while “Jane is a rock” occurs at some subset of those times. That distinction prevents the model from confusing an entire life with both a singular instance, as well as one successively repeated message within it.

The cumulative recurrence can be represented as:

L₂→₂₂ = Σₖ₌₁ᴷ Rₖ

where each recurrence has its own time:

tₖ ∈ [2, 22]

This immediately exposes another problem; ten repetitions are not necessarily equivalent to ten other repetitions.

One statement may be fleeting, another may be shouted, and another may last for years. A statement may occur during a developmentally sensitive period, happen during important social or cultural events, or become upheld as truth by influential or authoritative figures in Jane’s life. Simple recurrence does not describe the whole experience.

Refraction

Counting tells us how often something happened. It does not necessarily tell us how much it mattered. Two experiences with the same frequency can differ enormously in force, duration, context, physiological response, developmental timing, and subsequent integration. Once that becomes apparent, recurrence needs another dimension.

The question changes from:

How many times did this happen?

to:

What was the magnitude of the experience?