[Inquiry] Re: Differential Logic

[Jon Awbrey]

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DLOG.  Note D76

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Transformations of Type B^2 -> B^2 (cont.)

Figure 63 give a more complete picture of the transformation F,
showing how the points of U% are transformed into points of X%.
The lines that cross from one universe to the other trace the
action that F induces on points, in other words, they depict
the aspect of the transformation that acts as a mapping from
points to points, and chart its effects on the elements that
are variously called cells, points, positions, or singular
propositions.

             o-----------------------------------------------------o
             |`U` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
             |` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `|
             |` ` ` ` ` ` o-----------o ` o-----------o ` ` ` ` ` `|
             |` ` ` ` ` `/' ' ' ' ' ' '\`/' ' ' ' ' ' '\` ` ` ` ` `|
             |` ` ` ` ` / ' ' ' ' ' ' ' o ' ' ' ' ' ' ' \ ` ` ` ` `|
             |` ` ` ` `/' ' ' ' ' ' ' '/^\' ' ' ' ' ' ' '\` ` ` ` `|
             |` ` ` ` / ' ' ' ' ' ' ' /^^^\ ' ' ' ' ' ' ' \ ` ` ` `|
             |` ` ` `o' ' ' ' ' ' ' 'o^^^^^o' ' ' ' ' ' ' 'o` ` ` `|
             |` ` ` `|' ' ' ' ' ' ' '|^^^^^|' ' ' ' ' ' ' '|` ` ` `|
             |` ` ` `|' ' ' ' u ' ' '|^^^^^|' ' ' v ' ' ' '|` ` ` `|
             |` ` ` `|' ' ' ' ' ' ' '|^^^^^|' ' ' ' ' ' ' '|` ` ` `|
             |` `@` `o' ' ' ' @ ' ' 'o^^@^^o' ' ' @ ' ' ' 'o` ` ` `|
             |` ` \ ` \ ' ' ' | ' ' ' \^|^/ ' ' ' | ' ' ' / ` ` ` `|
             |` ` `\` `\' ' ' | ' ' ' '\|/' ' ' ' | ' ' '/` ` ` ` `|
             |` ` ` \ ` \ ' ' | ' ' ' ' | ' ' ' ' | ' ' / ` ` ` ` `|
             |` ` ` `\` `\' ' | ' ' ' '/|\' ' ' ' | ' '/` ` ` ` ` `|
             |` ` ` ` \ ` o---|-------o | o-------|---o ` ` ` ` ` `|
             |` ` ` ` `\` ` ` | ` ` ` ` | ` ` ` ` | ` ` ` ` ` ` ` `|
             |` ` ` ` ` \ ` ` | ` ` ` ` | ` ` ` ` | ` ` ` ` ` ` ` `|
             o-----------\----|---------|---------|----------------o
            " "           \   |         |         |               " "
         "       "         \  |         |         |            "       "
      "             "       \ |         |         |         "             "
   "                   "     \|         |         |      "                   "
o-------------------------o   \         |         |   o-------------------------o
| U                       |   |\        |         |   |`U```````````````````````|
|      o---o   o---o      |   | \       |         |   |``````o---o```o---o``````|
|     /'''''\ /'''''\     |   |  \      |         |   |`````/     \`/     \`````|
|    /'''''''o'''''''\    |   |   \     |         |   |````/       o       \````|
|   /'''''''/'\'''''''\   |   |    \    |         |   |```/       /`\       \```|
|  o'''''''o'''o'''''''o  |   |     \   |         |   |``o       o```o       o``|
|  |'''u'''|'''|'''v'''|  |   |      \  |         |   |``|   u   |```|   v   |``|
|  o'''''''o'''o'''''''o  |   |       \ |         |   |``o       o```o       o``|
|   \'''''''\'/'''''''/   |   |        \|         |   |```\       \`/       /```|
|    \'''''''o'''''''/    |   |         \         |   |````\       o       /````|
|     \'''''/ \'''''/     |   |         |\        |   |`````\     /`\     /`````|
|      o---o   o---o      |   |         | \       |   |``````o---o```o---o``````|
|                         |   |         |  \      *   |`````````````````````````|
o-------------------------o   |         |   \    /    o-------------------------o
 \                        |   |         |    \  /     |                        /
   \      ((u)(v))        |   |         |     \/      |        ((u, v))      /
     \                    |   |         |     /\      |                    /
       \                  |   |         |    /  \     |                  /
         \                |   |         |   /    \    |                /
           \              |   |         |  /      *   |              /
             \            |   |         | /       |   |            /
               \          |   |         |/        |   |          /
                 \        |   |         /         |   |        /
                   \      |   |        /|         |   |      /
             o-------\----|---|-------/-|---------|---|----/-------o
             | X       \  |   |      /  |         |   |  /         |
             |           \|   |     /   |         |   |/           |
             |            o---|----/--o | o-------|---o            |
             |           /' ' | ' / ' '\|/` ` ` ` | ` `\           |
             |          / ' ' | '/' ' ' | ` ` ` ` | ` ` \          |
             |         /' ' ' | / ' ' '/|\` ` ` ` | ` ` `\         |
             |        / ' ' ' |/' ' ' /^|^\ ` ` ` | ` ` ` \        |
             |   @   o' ' ' ' @ ' ' 'o^^@^^o` ` ` @ ` ` ` `o       |
             |       |' ' ' ' ' ' ' '|^^^^^|` ` ` ` ` ` ` `|       |
             |       |' ' ' ' f ' ' '|^^^^^|` ` ` g ` ` ` `|       |
             |       |' ' ' ' ' ' ' '|^^^^^|` ` ` ` ` ` ` `|       |
             |       o' ' ' ' ' ' ' 'o^^^^^o` ` ` ` ` ` ` `o       |
             |        \ ' ' ' ' ' ' ' \^^^/ ` ` ` ` ` ` ` /        |
             |         \' ' ' ' ' ' ' '\^/` ` ` ` ` ` ` `/         |
             |          \ ' ' ' ' ' ' ' o ` ` ` ` ` ` ` /          |
             |           \' ' ' ' ' ' '/ \` ` ` ` ` ` `/           |
             |            o-----------o   o-----------o            |
             |                                                     |
             |                                                     |
             o-----------------------------------------------------o
Figure 63.  A Transformation of Positions

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