Changes

===Taking Aim at Higher Dimensional Targets===

===Taking Aim at Higher Dimensional Targets===

<p>The past and present wilt . . . . I have filled them and<br>

The past and present wilt . . . . I have filled them and<br>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;emptied them,<br>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;emptied them,<br>

And proceed to fill my next fold of the future.</p>

And proceed to fill my next fold of the future.

 

<p>Walt Whitman, ''Leaves of Grass'', [Whi, 87]</p>

| align="right" | &mdash; Walt Whitman, ''Leaves of Grass'', [Whi, 87]

In the next Subdivision I consider a logical transformation ''F'' that has the concrete type ''F''&nbsp;:&nbsp;[''u'',&nbsp;''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;''y''] and the abstract type ''F''&nbsp;:&nbsp;['''B'''²]&nbsp;&rarr;&nbsp;['''B'''²].  From the standpoint of propositional calculus, the task of understanding such a transformation is naturally approached by parsing it into component maps with 1-dimensional ranges, as follows:

In the next Subdivision I consider a logical transformation ''F'' that has the concrete type ''F''&nbsp;:&nbsp;[''u'',&nbsp;''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;''y''] and the abstract type ''F''&nbsp;:&nbsp;['''B'''²]&nbsp;&rarr;&nbsp;['''B'''²].  From the standpoint of propositional calculus, the task of understanding such a transformation is naturally approached by parsing it into component maps with 1-dimensional ranges, as follows: