Suppose you are shown a display involving eight stationary circles, like
this one.
Pylyshyn 2001, figure 6
There is a behavioural marker of object-indexes called the object-specific preview benefit.
Suppose that you are shown an array of two objects, as depicted here.
At the start a letter appears briefly on each object.
(It is not important that letters are used; in theory, any readily
distinguishable features should work.)
Kahneman et al 1992, figure 3
The \emph{object-specific preview benefit} is the reduction in time needed to identify that a
letter (or other feature) matches a target presented earlier when the letter and target both
appear on the same object rather than on different objects.
[object indexes and segmentation: ducks picture]
Is one object index assigned or two?
Assigning object indexes requires segmentation.
[object indexes and segmentation: partially occluded stick]
Spelke, 1990 figure 2a
Consider a stick moving behind a screen, so that the middle part of it is occluded.
Assigning one index even though there is no information about continuity of surfaces
may depend on analysis of motion.
modified from Scholl 2007, figure 4
[object indexes and representing occluded objects]
principle of continuity---
an object traces exactly one connected path over space and time
Franconeri et at, 2012 figure 2a (part)
[Here we’re interested in the issue rather than the details: the point is just that
continuity of motion is important for assigning and maintaining object indexes.]
Suppose object indexes are being used in tracking four or more objects simultaneously and one of these objects—call it the \emph{first object}—disappears behind a barrier.
Later two objects appear from behind the barrier, one on the far side of the barrier (call this the \emph{far object}) and one close to the point where the object disappeared (call this the \emph{near object}).
If the system of object indexes relies on assumptions about speed and direction of movement, then the first object and the far object should be assigned the same object index.
But this is not what typically happens.
Instead it is likely that the first object and the near object are assigned the same object index.%
\footnote{
See \citet{franconeri:2012_simple}. Note that this corrects an earlier argument for a contrary view \citep{scholl:1999_tracking}.
}
If this were what always happened, then we could not fully explain how infants represent objects as persisting by appeal to object indexes because, at least in some cases, infants do use assumptions about speed and direction in interpolating the locations of briefly unperceived objects.
There would be a discrepancy between the Principles of Object Perception which characterise how infants represent objects as persisting and the principles that describe how object indexes work.
But this is not the whole story about object indexes.
It turns out that object indexes behave differently when just one object is being tracked and the object-specific preview benefit is used to detect them.
In this case it seems that assumptions about continuity and constancy in speed and direction do play a role in determining whether an object at $t_1$ and an object at $t_2$ are assigned the same object indexes \citep{flombaum:2006_temporal,mitroff:2007_space}.
In the terms introduced in the previous paragraph, in this case where just one object is being tracked, the first object and the far object are assigned the same object index.
This suggests that the principles which govern object indexes may match the principles which characterise how infants represent objects as persisting.
[object indexes and representing causal interactions]
... Because object index assignments can conflict with knowledge states!
Scholl 2007, figure 4
Consider this scenario
in which a patterned square disappears behind the barrier; later a
plain black ring emerges. You probably don't believe that they are
the same object, but they probably do get assigned the same object index.
Your beliefs and assignments of object indexes are inconsistent in this
sense: the world cannot be such that both are correct.
The CLSTX Conjecture has an advantage which I don’t think is widely recognised.
This is that object indexes are independent of beliefs and knowledge
states.
Having an object index pointing to a location is not the same thing
as believing that an object is there.
And nor is having an object index pointing to a series of locations over time
is the same thing as believing or knowing that these locations
are points on the path of a single object.
Further, the assignments of object indexes do not invariably give rise
to beliefs and need not match your beliefs.
Mitroff, Scholl and Wynn 2005, figure 2
Mitroff, Scholl and Wynn 2005, figure 3
So this is a virtue of the hypothesis that four- and five-month-old
infants’ abilities
to track briefly occluded objects depend on a system of
object indexes.
Since assignments of object indexes do not entail the existence of
corresponding beliefs,
the fact that infants of this age systematically
fail to search for briefly occluded objects is not an objection to the
hypothesis.
Kaufmann et al, 2015 figure 1
(\citet{kaufman:2005_oscillatory} measured brain activity in
six-month-olds infants as they observed a display typical of an object
disappearing behind a barrier.
(EEG gama oscillation over right temporal cortex)
They found the pattern of brain activity characteristic of maintaining
an object index.
This suggests that in infants, as in adults, object indexes can attach
to objects that are briefly unperceived.)
Kaufmann et al, 2015 figure 2 (part)
The evidence we have so far gets us as far as saying, in effect, that someone capable of
committing a murder was in the right place at the right time.
Can we go beyond such circumstantial evidence?
Scholl 2007, figure 4
To illustrate, a moment ago I mentioned that one signature limit of
object indexes is that featural information sometimes fails to influence how objects are assigned in ways that seem quite dramatic.
Carey and Xu 2001, figure 3
There is evidence that, similarly, even 10-month-olds will sometimes
ignore featural information in tracking occluded objects
\citep{xu:1996_infants}.%
\footnote{
This argument is complicated by evidence that infants around 10 months of age do not always fail
to use featural information appropriately in representing objects as persisting
\citep{wilcox:2002_infants}.
In fact \citet{mccurry:2009_beyond} report evidence that even five-month-olds can make use of
featural information in representing objects as persisting \citep[see also][]{wilcox:1999_object}.
%they use a fringe and a reaching paradigm. NB the reaching is a problem for the simple interpretation of looking vs reaching!
% NB: I think they are tapping into motor representations of affordances.
Likewise, object indexes are not always updated in ways that amount to ignoring featural
information \citep{hollingworth:2009_object,moore:2010_features}.
It remains to be seen whether there is really an exact match between the signature limit on
object indexes and the signature limit on four-month-olds’ abilities to represent objects as
persisting.
The hypothesis under consideration---that infants’ abilities
to track briefly occluded objects depend on a system of
object indexes like that which underpins multiple object tracking or
object-specific preview benefits---is a bet on the match being exact.
}
Xu and Carey 1996, figure 4