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## The CLSTX Hypothesis: Object Indexes Underpin Infants’ Abilities

Three requirements

• segment objects
• represent objects as persisting (‘permanence’)
• track objects’ interactions

How? Object Indexes!

In adult humans, there is a system of object indexes which enables them to track potentially moving objects in ongoing actions such as visually tracking or reaching for objects, and which influences how their attention is allocated \citep{flombaum:2008_attentional}.
The leading, best defended hypothesis is that their abilities to do so depend on a system of object indexes like that which underpins multiple object tracking or object-specific preview benefits \citep{Leslie:1998zk,Scholl:1999mi,Carey:2001ue,scholl:2007_objecta}.
But what is an object index? Formally, an object index is ‘a mental token that functions as a pointer to an object’ \citep[p.\ 11]{Leslie:1998zk}. If you imagine using your fingers to track moving objects, an object index is the mental counterpart of a finger \citep[p.~68]{pylyshyn:1989_role}.
Leslie et al say an object index is ‘a mental token that functions as a pointer to an object’ \citep[p.\ 11]{Leslie:1998zk}
‘Pylyshyn’s FINST model: you have four or five indexes which can be attached to objects; it’s a bit like having your fingers on an object: you might not know anything about the object, but you can say where it is relative to the other objects you’re fingering. (ms. 19-20)’ \citep{Scholl:1999mi}
The interesting thing about object indexes is that a system of object indexes (at least one, maybe more) appears to underpin cognitive processes which are not strictly perceptual but also do not involve beliefs or knowledge states. While I can’t fully explain the evidence for this claim here, I do want to mention the two basic experimental tools that are used to investigate the existence of, and the principles underpinning, a system of object indexes which operates between perception and thought ...
Object indexes ... \begin{itemize} \item guide ongoing action (e.g.~visual tracking, reaching) \item influence how attention is allocated \citep{flombaum:2008_attentional} \item can be assigned in ways incompatible with beliefs and knowledge \citep[e.g.][]{Mitroff:2004pc, mitroff:2007_space} \item have behavioural and neural markers, in adults and infants \citep{richardson:2004_multimodal,kaufman:2005_oscillatory}. \item are subject to signature limits \citep[pp.~83--87]{carey:2009_origin} \item sometimes survive occlusion \citep{flombaum:2006_temporal} \end{itemize}
Suppose you are shown a display involving eight stationary circles, like this one.

Four of these circles flash, indicating that you should track these circles.
All eight circles now begin to move around rapidly, and keep moving unpredictably for some time.
Then they stop and one of the circles flashes. Your task is to say whether the flashing circle is one you were supposed to track. Adults are good at this task \citep{pylyshyn:1988_tracking}, indicating that they can use at least four object indexes simultaneously.
(\emph{Aside.} That this experiment provides evidence for the existence of a system of object indexes has been challenged. See \citet[p.\ 59]{scholl:2009_what}: \begin{quote} I suggest that what Pylyshyn’s (2004) experiments show is exactly what they intuitively seem to show: We can keep track of the targets in MOT, but not which one is which. [...] all of this seems easily explained [...] by the view that MOT is simply realized by split object-based attention to the MOT targets as a set.' \end{quote} It is surely right that the existence of MOT does not, all by itself, provide support for the existence of a system of object indexes. However, contra what Scholl seems to be suggesting here, the MOT paradigm can be adapated to provide such evidence. Thus, for instance, \citet{horowitz:2010_direction} show that, in a MOT paradigm, observers can report the direction of one or two targets without advance knowledge of which targets' directions they will be asked to report.)

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.)
The objects now start moving.
At the end of the task, a letter appears on one of the objects. Your task is to say whether this letter is one of the letters that appeared at the start or whether it is a new letter. Consider just those cases in which the answer is yes: the letter at the end is one of those which you saw at the start. Of interest is how long this takes you to respond in two cases: when the letter appears on the same object at the start and end, and, in contrast, when the letter appears on one object at the start and a different object at the end. It turns out that most people can answer the question more quickly in the first case. That is, they are faster when a letter appears on the same object twice than when it appears on two different objects \citep{Kahneman:1992xt}. This difference in response times is the % $glossary: object-specific preview benefit \emph{object-specific preview benefit}. Its existence shows that, in this task, you are keeping track of which object is which as they move. This is why the existence of an object-specific preview benefit is taken to be evidence that object indexes exist. Kahneman et al 1992, figure 3 The \emph{object-specific preview benefit} is the reduction in time needed to identify that a letter (or other feature) matches a target presented earlier when the letter and target both appear on the same object rather than on different objects. Three requirements • segment objects • represent objects as persisting (‘permanence’) • track objects’ interactions How? Object Indexes! ok, so now we know what object indexes are ... Why think that they answer the question How? First part of the answer: maintaining object indexes requires all three things! What is required for assigning and maintaining object indexes? To see the need for principles, return to the old-fashioned logistician who is keeping track of supply trucks. In doing this she has only quite limited information to go on. She receives sporadic reports that a supply truck has been sighted at one or another location. But these reports do not specify which supply truck is at that location. She must therefore work out which pin to move to the newly reported location. In doing this she might rely on assumptions about the trucks’ movements being constrained to trace continuous paths, and about the direction and speed of the trucks typically remaining constant. These assumptions allow her to use the sporadic reports that some truck or other is there in forming views about the routes a particular truck has taken. A system of object indexes faces the same problem when the indexed objects are not continuously perceptible. What assumptions or principles are used to determine whether this object at time$t_1$and that object at time$t_2$have the same object index pinned to them? [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. maintaining object indexes involves segmenting objects representing them as perstising tracking their causal interactions knowledge of objects involves segmenting them representing them as perstising tracking their causal interactions object indexes can survive brief occlusion 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.

maintaining object indexes
involves

segmenting objects

representing them as perstising

tracking their causal interactions

knowledge of objects
involves

segmenting them

representing them as perstising

tracking their causal interactions

[object indexes and representing causal interactions]

maintaining object indexes
involves

segmenting objects

representing them as perstising

tracking their causal interactions

knowledge of objects
involves

segmenting them

representing them as perstising

tracking their causal interactions

The Principles of Object Perception are the key to specifying one way of meeting these three requirements.
This suggests that, maybe, The Principles of Object Perception which characterise infants’ abilities to track physical objects also characterise the operations of a system of object indexes.
\emph{The CLSTX conjecture} Five-month-olds’ abilities to track occluded objects are not grounded on belief or knowledge: instead they are consequences of the operations of object indexes. \citep{Leslie:1998zk,Scholl:1999mi,Carey:2001ue,scholl:2007_objecta}.

The CLSTX conjecture:

Five-month-olds’ abilities to track briefly unperceived objects

are not grounded on belief or knowledge:

they are consequences of the operations of

a system of object indexes.

Leslie et al (1989); Scholl and Leslie (1999); Carey and Xu (2001)

(‘CLSTX’ stands for Carey-Leslie-Scholl-Tremoulet-Xu \citep[see][]{Leslie:1998zk,Scholl:1999mi,Carey:2001ue,scholl:2007_objecta})
Their upshot is not knowledge about particular objects and their movements but rather a perceptual representation involving an object index.
One reason the hypothesis seems like a good bet is that object indexes are the kind of thing which could in principle explain infants’ abilities to track unperceived objects because object indexes can, within limits, survive occlusion.
Note that the CLSTX conjecture assumes that the Principles of Object Perception which characterise infants’ abilities to track physical objects also characterise the operations of a system of object indexes.
:treflecting on \citet{mccurry:2009_beyond} in one of the seminars ... distinguishedinitiating action and continuing to perform an action ... object indexes supportguidance of action but not its initiation.
This amazing discovery is going to take us a while to fully digest. As a first step, note its significance for Davidson's challenge about characterising what is going on in the head of the child who has a few words, or even no words.
\footnote{\label{fn:mot_proximity} The findings cited in this paragraph all involve measuring object-specific preview benefits. Some researchers have argued that in multiple object tracking with at least four objects, motion information is not used to update indexes during the occlusion of the corresponding objects \citep{keane:2006_motion,horowitz:2006_how}; rather, MOT through occlusion seems to rely on a simple heuristic based only on the proximity of reappearance locations to the objects’ last known preocclusion locations' (\citealp{franconeri:2012_simple}, p.\ 700). However information about motion is sometimes available \citep{horowitz:2010_direction} and used in tracking multiple objects simultaneously \citep{howe:2012_motion, clair:2012_phd}. One possibility is that, in tracking four objects simultaneously, motion information can be used to distinguish targets from distractors but not to predict the future positions of objects \citep[p.\ 8]{howe:2012_motion}. }

Three Questions

1. How do four-month-old infants model physical objects?

2. What is the relation between the model and the infants?

3. What is the relation between the model and the things modelled (physical objects)?

2. What is the relation between the model and the infants?

the Simple View ... generates incorrect predictions

the Core Knowledge View ... generates no relevant predictions

the CLSTX Conjecture

Why doesn’t the CLSTX generate the same incorrect predictions as the Simple View?

... 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.

Three Questions

1. How do four-month-old infants model physical objects?

2. What is the relation between the model and the infants?

3. What is the relation between the model and the things modelled (physical objects)?

the Simple View ... generates incorrect predictions

the Core Knowledge View ... generates no relevant predictions

the CLSTX Conjecture

evidence?

behavioural and neural indicators

behavioural: OSPB-like-effect (Richardson & Kirkham; note their caveats); neural Kaufmann, Csibra et al
If we consider six-month-olds, we can also find behavioural markers of object indexes in infants \citep{richardson:2004_multimodal} ...
... and there are is also a report of neural markers too \citep{kaufman:2005_oscillatory}.

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?

Signature Limits

The key to doing this is to exploit signature limits.
A \emph{{signature limit} of a system} is a pattern of behaviour the system exhibits which is both defective given what the system is for and peculiar to that system.
\citet{carey:2009_origin} argues that what I am calling the signature limits of object indexes in adults are related to signature limits on infants’ abilities to track briefly occluded objects.

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

\emph{The CLSTX conjecture} Five-month-olds’ abilities to track occluded objects are not grounded on belief or knowledge: instead they are consequences of the operations of object indexes. \citep{Leslie:1998zk,Scholl:1999mi,Carey:2001ue,scholl:2007_objecta}.

The CLSTX conjecture:

Five-month-olds’ abilities to track briefly unperceived objects

are not grounded on belief or knowledge: