Changes

Because the initial space ''X'' = 〈''A''〉 is one-dimensional, we can easily fit the second order extension E²''X'' = 〈''A'', d''A'', d²''A''〉 within the compass of a single venn diagram, charting the couple of converging trajectories as shown in Figure 12.

Because the initial space ''X'' = 〈''A''〉 is one-dimensional, we can easily fit the second order extension E²''X'' = 〈''A'', d''A'', d²''A''〉 within the compass of a single venn diagram, charting the couple of converging trajectories as shown in Figure 12.

<pre>

<br>

o-------------------------------------------------o

[[Image:Diff Log Dyn Sys -- Figure 12 -- The Anchor.gif|center]]

| E^2.X                                          |

<center>'''Figure 12.  The Anchor'''</center>

<br>

|            /        ->-        \            |

Figure 12.  The Anchor

</pre>

If we eliminate from view the regions of E²''X'' that are ruled out by the dynamic law d²''A''&nbsp;=&nbsp;(''A''), then what remains is the quotient structure that is shown in Figure 13.  This picture makes it easy to see that the dynamically allowable portion of the universe is partitioned between the properties ''A'' and d²''A''.  As it happens, this fact might have been expressed "right off the bat" by an equivalent formulation of the differential law, one that uses the exclusive disjunction to state the law as (''A'',&nbsp;d²''A'').

If we eliminate from view the regions of E²''X'' that are ruled out by the dynamic law d²''A''&nbsp;=&nbsp;(''A''), then what remains is the quotient structure that is shown in Figure 13.  This picture makes it easy to see that the dynamically allowable portion of the universe is partitioned between the properties ''A'' and d²''A''.  As it happens, this fact might have been expressed "right off the bat" by an equivalent formulation of the differential law, one that uses the exclusive disjunction to state the law as (''A'',&nbsp;d²''A'').