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| ==Note 8== | | ==Note 8== |
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− | <pre>
| + | 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. | |
| | | |
| + | <pre> |
| 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: |