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| ==Note 20== | | ==Note 20== |
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| + | In my work on "[[Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0|Differential Logic and Dynamic Systems]]", I found it useful to develop several different ways of visualizing logical transformations, indeed, I devised four distinct styles of picture for the job. Thus far in our work on the mapping <math>F : [u, v] \to [u, v],\!</math> we've been making use of what I call the ''areal view'' of the extended universe of discourse, <math>[u, v, du, dv],\!</math> but as the number of dimensions climbs beyond four, it's time to bid this genre adieu, and look for a style that can scale a little better. At any rate, before we proceed any further, let's first assemble the information that we have gathered about <math>F\!</math> from several different angles, and see if it can be fitted into a coherent picture of the transformation <math>F : (u, v) \mapsto ( ~\texttt{((u)(v))}~, ~\texttt{((u, v))}~ ).</math> |
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| <pre> | | <pre> |
− | In my work on "Differential Logic and Dynamic Systems",
| |
− | I found it useful to develop several different ways of
| |
− | visualizing logical transformations, indeed, I devised
| |
− | four distinct styles of picture for the job. Thus far
| |
− | in our work on the mapping F : [u, v] -> [u, v], we've
| |
− | been making use of what I call the "areal view" of the
| |
− | extended universe of discourse, [u, v, du, dv], but as
| |
− | the number of dimensions climbs beyond four, it's time
| |
− | to bid this genre adieu, and look for a style that can
| |
− | scale a little better. At any rate, before we proceed
| |
− | any further, let's first assemble the information that
| |
− | we have gathered about F from several different angles,
| |
− | and see if it can be fitted into a coherent picture of
| |
− | the transformation F : <u, v> ~> <((u)(v)), ((u, v))>.
| |
− |
| |
| In our first crack at the transformation F, we simply | | In our first crack at the transformation F, we simply |
| plotted the state transitions and applied the utterly | | plotted the state transitions and applied the utterly |