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not considered all possibilities yet. Notice that
becomes true and is
among the current eects after having applied the rst one of the causal
relationships (2.15), and it stays true until the last one is applied. Therefore
we may insert causal relationship
light
causes
detect
if
>
somewhere
in between. This additionally causes
detect
to become true, that is, the
following state-eect pair can also be generated:
light
(
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
;
relay
; :
light
;
detect
g ;
f
(
s
1
)
;
;
; :
(
s
2
)
; :
g
)
up
detect
relay
up
light
Its rst component is acceptable and dierent from the causal successor
above. No further causal successor states can be obtained.
Now, the rst one of the two successors, i.e.,
T
1
=
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
;
relay
; :
light
; :
detect
g
is strictly closer to initial state
S
than the second one, i.e.,
T
2
=
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
;
relay
; :
light
;
detect
g
This indicates that the latter cannot be a causal minimizing-change successor.
Indeed, while
T
1
is xpoint of
T: f`
:((
S \ T
)
[ E;E
)
R
`g
(with
E
=
f
up
(
s
1
)
g
), state
T
2
is not because
((
S \ T
2
)
[ E;E
)=(
f
up
(
s
3
)
; :
light
;
up
(
s
1
)
g; f
up
(
s
1
)
g
1
R
detect
This domain proves that minimization is not always a concept adequate for
distinguishing between possible indirect eects on the one hand, and un-
founded changes on the other hand. This observation challenges the common
belief that minimizing change is essential for solving the Ramication Prob-
lem. In fact, the aim of generating ramications is not to minimize change
but to avoid changes that are not caused, which, as we have seen, need not
be identical goals.
2.7 Triggered vs. Coupled Eects
The instructive example concluding the preceding section shows how causal
relationships often literally run a race. A dierent nish sometimes means
a dierent successor state, thus giving rise to uncertainty in form of non-
determinism. This raises the question whether it might be overly credulous
to consider possible any order in which these relationships are applied. Not
all computed chains of indirect eects may be equally likely to happen in
reality. This would be the case if the causal lag between some particular
indirect eect and its triggering cause is generally shorter than the causal lag
between another particular eect and its cause. Suppose, for instance, our
