Changes

==Note 8==

==Note 8==

I am going to tip-toe in silence/consilience past many questions of a philosophical nature/nurture that might be asked at this juncture, no doubt to revisit them at some future opportunity/importunity, however the cases happen to align in the course of their inevitable fall.

I am going to tip-toe in silence/consilience past many

questions of a philosophical nature/nurture that might

be asked at this juncture, no doubt to revisit them at

some future opportunity/importunity, however the cases

happen to align in the course of their inevitable fall.

Instead, let's "keep it concrete and simple", taking up the

Instead, let's "keep it concrete and simple", taking up the consideration of an incrementally more complex example, but having a slightly more general character than the orders of sequential transformations that we've been discussing up to this point.

consideration of an incrementally more complex example, but

having a slightly more general character than the orders of

sequential transformations that we've been discussing up to

this point.

The types of logical transformations that I have in mind can

The types of logical transformations that I have in mind can be thought of as ''transformations of discourse'' because they map a universe of discourse into a universe of discourse by way of logical equations between the qualitative features or logical variables in the source and target universes.

be thought of as "transformations of discourse" because they

map a universe of discourse into a universe of discourse by

way of logical equations between the qualitative features

or logical variables in the source and target universes.

The sequential transformations or state transitions that we have

The sequential transformations or state transitions that we have been considering so far are actually special cases of these more general logical transformations, specifically, they are the ones that have a single universe of discourse, as it happens to exist at different moments in time, in the role of both the source and the target universes of the transformation in question.

been considering so far are actually special cases of these more

general logical transformations, specifically, they are the ones

that have a single universe of discourse, as it happens to exist

at different moments in time, in the role of both the source and

the target universes of the transformation in question.

Onward and upward to Flatland, the differential analysis of

Onward and upward to Flatland, the differential analysis of transformations between 2-dimensional universes of discourse.

transformations between 2-dimensional universes of discourse.

Consider the transformation from the universe U% = [u, v] to the

Consider the transformation from the universe U% = [u, v] to the

universe X% = [x, y] that is defined by this system of equations:

universe X% = [x, y] that is defined by this system of equations: