Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 89

Fig. 10. The four types of extrema.

8 The Method to Be Used

The purpose of the Process Grammar is to yield additional information concern-
ing the past history of the shape.
Our procedure for finding this information will be as follows: Let us imagine
that we have two stages in the history of the shape. For example, imagine being
a doctor looking at two X-rays of a tumor taken a month apart. Observe that
any doctor examines two such X-rays (e.g., on a screen), in order to assess what
has happened in the intervening month. If one considers the way the doctor's
thinking proceeds, one realizes that there is a basic inference rule that is being
used: The doctor will try, as much as possible, to explain a process seen in the
later shape as an extrapolation of a process seen in the earlier shape. That is,
the doctor tries to maximize the description of history as extrapolations . We will
show how to discover these extrapolations.
Recall that the processes we have been examining are those that move along
symmetry axes, creating extrema. As a simple first cut, we can say that extrap-
olations have one of two forms:

(1) Continuation: The process simply continues along the symmetry
axis, maintaining that single axis.

(2) Bifurcation: The process branches into two axes, i.e., creating two
processes out of one.

+ ,and
M − . These were discussed at the end of section 7. It is necessary therefore to
look at what happens when one continues the process at each of the four types,
and at what happens when one branches (bifurcates) the process at each of the
four types. This means that there are eight alternative events that can occur:
four continuations and four bifurcations.

+ ,

m − , Now recall, from Fig 10 that there are four types of extrema M m

M + and m −

9Con inu on t

Let us start by considering continuations, and then move on to bifurcations. It
turns out that, when one continues a process at either of the first two extrema,
M

+ or

m − , nothing significant happens, as follows: