Kevin Wacknov's Insights Notes

The BodyMind can seem Discontinuous

The human body-mind field is not continuous in the mathematical sense. Suppose I hold a posture and make smaller and smaller movements (muscular or intentions) around a point (pick a dantian). If I choose a response I want to be a maximum, but then reduce the movement that gave rise to it, I often get a larger response.

Let F be the held posture. The body-mind response R is a function of a small change in intention during the held posture. So F(0) is a perfectly held posture.

R = F(0) - F(delta I)

if
R1 = F(0) - F(dI1), and
R2 = F(0) - F(dI2), dI2 < dI1,
then, often, R2 > R1.

Definition of Limit (Wikipedia)

The $(\varepsilon, \delta)$ definition of the limit of a function is as follows:

Let $f(x)$ be a function defined on an open interval containing $c$ (except possibly at $c$ ) and let $L$ be a real number. Then we may make the statement

$\lim_{x \to c} f(x) = L \,$

if and only if

the value of $x$ is within a specified $\delta$ units from $c$ , and this implies that $f(x)$ is within a specified $\varepsilon$ units from $L$ .

Definition of Continuity (Wikipedia)

A function f is said to be continuous at c if it is both defined at c and its value at c equals the limit of f as x approaches c:

$\lim_{x\to c} f(x) = f(c).$

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