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into two episodes or vice versa, from transformations that trans-
form episodes one for one, and then in the latter category,
transformations that lengthen an episode's representation in
effective time from transformations that shorten it. Thus, we
extend the property of being a mathematical partitioning down
to the third level of this taxonomy. And again, as with the {create}
and {erase} transformations, there are similar variations.
Next, for both the {lengthen} and {shorten} transformations, it
is possible to do so at the beginning or at the end of the episode.
And so we complete this taxonomy with the assurance that no
instance of any parent node can fail to be an instance of a child
node of that parent, and also that every instance of any parent
node exists as no more than one instance across the set of its
child nodes.
Another way to reassure ourselves of the completeness of this
taxonomy is to note its bilateral symmetry. If the diagram were
folded along a vertical line running between the {merge} and
{split} nodes, and also between the {lengthen forwards} and
{shorten backwards} nodes, each transformation would overlay
the transformation that is its inverse.
A third way to assure ourselves of completeness is to analyze
the taxonomy in terms of its topology. On a line representing a
timeline, we can place a line segment representing an episode.
We can also remove a line segment from that line. Given a line
segment, we can either lengthen it forwards or backwards,
shorten it forwards or backwards, or split it. Given two line
segments with no other segments between them, we can merge
them (by lengthening one forwards towards the other and/or
lengthening the other backwards towards the first, until they
[meet]). There is nothing that can be done with the placement
of segments on a line that cannot be done by means of com-
binations and iterations of these basic operations.
Finally, we need to be aware of the different scenarios possi-
ble under each of these nodes. As we have already pointed out,
any of these transformations can result in changes to past, pres-
ent or future effective time. Additional variations come into play
when we distinguish between transformations that are applied
to closed or to open episodes, and between transactions which
leave an episode in a closed or open state.
With eight possible topological transformations, nine possi-
ble combinations of past, present and future effective time
(three for the target and three for the transaction), and four pos-
sible open/closed combinations (two for the target and two for
the transaction), we have a grand total of 288 scenarios. And this
doesn't even take into consideration deferred assertions, which
