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Abstract

The exogenous attention and endogenous attention results include the outcomes that the time-2 target’s perceived location and perceived features become more accurate.   Because the time-1 nontarget’s perceived location approximates the time-2 target’s physical location (exogenous attention) and because time-1 information indicates the time-2 target’s physical location (endogenous attention), the time-1 perceived location approximates the time-2 target’s physical location.  The time-2 target’s perceived location is less accurate than the time-1 perceived location.  Because of this, the time-2 target’s perceived location assimilates (becomes similar) to the time-1 target’s perceived location.  Hence the time-2 target’s perceived location also becomes similar to its physical location, that is, becomes more accurate.  Because the time-2 target’s perceived location becomes more accurate, so do its perceived features.  Thus these attention results are accounted for.

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The exogenous attention result tends to occur when the location of a time-1 (initial) nontarget object approximates the location of a time-2 (subsequent) target object by chance (e.g. Jonides, 1981).  The endogenous attention result tends to occur when a time-1 nontarget object (cue) predicts the location of a time-2 target object (e.g. Posner, Nissen, & Ogden, 1978).  The endogenous result also tends to occur when a time-1 instruction informs about the physical location of a time-2 target (e.g. Butler, 1980).  The endogenous result also tends to occur in additional ways that presumably also involve cognition (e.g. LaBerge, 1983). 

Both the exogenous attention and endogenous attention results include the outcome that the accuracy of the time-2 target’s perceived location increases, for example, per a more accurate reproduction of its location.  Both the exogenous attention and endogenous attention results also include the outcome that the accuracy of the time-2 target’s perceived features increases, for example, per an improvement in the time-2 target’s detection. 

Evidence of the perceived location outcome is indicated in section 2.0.  Evidence of the perceived features outcome will not be indicated.  The primary reason is that this result is presumably relatively familiar. 

This paper elaborates and supports a theory of both the exogenous and endogenous attention results.  The theory is called assimilation-location theory. 

Assimilation is basically defined as occurring when a perception becomes similar to including the same as another perception.  Illustrative evidence of assimilation between perceived locations (not perceived features) is the result that when a vertical line and an adjacent rectangle were relatively close (near) to each other, the perceived location of the line became similar (assimilated) to the location of the rectangle per a judgment of the line’s location (Ganz, 1964).  An object will also be said to assimilate toward the perceived location of another object.  Simply assimilation will also be referred to.  Assimilation between perceived locations is also called “attraction” (e.g. Smith, 1954) and “spatial compression” (e.g. Born, Kruger, Zimmermann, & Cavanagh, 2016).

Locations of objects involved in assimilation between perceived locations may not be consciously perceived.  For instance, the assimilation may occur so quickly that these locations may not be consciously perceived.  Nevertheless, encodings for (neural information of) these locations presumably exist.

Assimilation-location theory maintains that assimilation between perceived locations enables the exogenous attention and endogenous attention results.  Enables means essential to bringing about but that other factors can also contribute to the bringing about. 

A tendency is for research on exogenous attention and endogenous attention to maintain that attention to a location and the like increases the accuracy of a perception but without indicating or referring to a mechanism for how this increase occurs (e.g. Jonides, 1981; Kowler, 2011; Posner, 1980; Theeuwes, 1992).  For example, a “higher sensitivity at the target position” was indicated to stem from an “attention shift to the target position” (Posner, 1980, p. 16).  Not indicating a mechanism for how the increase in accuracy occurs is a hint that attention does not enable the exogenous attention and endogenous attention results.  Accordingly, assimilation-location theory does not involve attention.  Similarly, from now on only the exogenous and endogenous results will be referred to and “attention” will not be mentioned. 

Assimilation-location theory’s account of the exogenous and endogenous results follows.  For both these results, a premise of the theory is that the time-1 perceived location approximates the time-2 target’s physical location.  (At least the encoding for a time-1 perceived location stands for the time-2 target’s physical location.)  For the exogenous result, this time-1 perceived location is assumed to stem from the physical location of the time-1 nontarget.  This assumption seems sound because, recollecting, the time-1 nontarget’s physical location approximates the time-2 target’s physical location.   For the endogenous result, this time-1 perceived location is assumed to stem from cognition.  This assumption seems reasonable because, for example, when a time-1 nontarget predicts the time-2 target’s physical location, it is believable that cognition can result in a time-1 perceived location that approximates the time-2 target’s physical location.  A statement that is similar is, for example, that “There is considerable evidence that covert visual attention precedes voluntary eye movements to an intended location” (Peterson, Kramer, & Irwin, 2004, p. 398).

Another premise of the theory is that for both the exogenous and endogenous results, the time-1 perceived location is more accurate than the time-2 perceived location (this is prior to the moment that the accuracy of the time-2 target’s perceived location increases).  This premise is called the time-1 perceived location is more accurate premise.  Another premise of the theory is that because the time-1 nontarget’s perceived location is more accurate than the time-2 target’s perceived location, the time-2 target’s perceived location assimilates (becomes similar) to the time-1 nontarget’s perceived location:  the time-2 target assimilates to the time-1 more accurate perceived location premise.  Because, per the initial premise, a time-1 perceived location approximates the time-2 target’s physical location, according to this last premise, the time-2 target’s assimilation to the more accurate time-1 perceived location means that the time-2 target assimilates to a perceived location that approximates its physical location.  Hence the time-2 target’s perceived location becomes more accurate.  Thus the exogenous and endogenous results’ perceived location outcome is accounted for. 

A final premise of the theory is that the accuracy of a perceived location enables the accuracy of perceived features at this location:  the location-accuracy-enables-features-accuracy premise.  Because the accuracy of the time-2 target’s perceived location increases per the preceding paragraph, it follows from this final premise that the accuracy of the time-2 target’s perceived features also increases, which is the exogenous and endogenous results’ perceived features outcome to be accounted for.  Hence the theory accounts for both the exogenous and endogenous results’ perceived location and perceived features outcomes.  

The following synopsis of the assimilation-location theory account may help to understand it.  Because the time-1 perceived location approximates the time-2 target’s physical location and also because the time-2 target’s perceived location assimilates to the time-1 target’s perceived location, the time-2 target’s perceived location becomes more similar to its physical location, that is, more accurate. 

The contents of the subsequent sections are outlined.  Section 1.0 supports the claim that the aim (landing position) of a saccade that is toward a target indicates the target’s perceived location (along with the target’s perceived three-dimensional distance).  Section 2.0 provides evidence that the exogenous and endogenous results include the occurrence of the perceived location outcome, namely, that the accuracy of the time-2 target’s perceived location is increased.  The previously indicated four premises are then supported.  The support for each premise is in a separate section (3.0-6.0), and these sections are in the order that the premises were previously considered.  Sections and also subsections are numbered to readily refer to them.

1.0. The Claim that a Saccade’s Aim Indicates a Perceived Location

A claim is that a saccade’s aim toward a location (its landing position) indicates a location that is being perceived.  According to this claim, a saccade aim’s can (and accordingly will) be taken to be a measure of the accuracy of a perceived location.  This is because per this claim, when a saccade’s aim toward an object is accurate (inaccurate), the object’s perceived location is also accurate (inaccurate). 

This claim is supported in the current section.  A purpose of this support is to use a saccade’s aim as evidence that a target’s perceived location has changed because it has assimilated to the perceived location of a nontarget.  Another purpose is to use the accuracy of a saccade’s aim to indicate the accuracy of a time-2 target’s perceived location. 

The current section also supports a corollary claim that the speed (latency) of a saccade that aims toward a target indicates the relative accuracy of the target’s perceived location.  One purpose in supporting this corollary claim is that a slower (faster) saccade toward a time-2 target is then evidence that the time-2 target’s perceived location is less (more) accurate. 

An ensuing inference is also covered. 

1.1. The Saccade Aim Claim

Evidence for the claim that a saccade’s aim toward a location indicates the location that is being perceived is that associations between the accuracy of a saccade’s aim and the accuracy of presumably accepted measures of perceived location are frequent.  Evidence follows.  An association between the accuracy of a saccade’s aim and the accuracy of accepted measures of perceived location occurred per results from the same research (Aitsebaomo & Bedell, 1992; Miller, 1980; Vishwanath & Kowler, 2003).  For instance, the perceived location of a target was relatively accurate per both the accuracy of a saccade’s aim toward a target’s location and the accuracy of the reproduction of its location (Miller).  The indicated association also occurs per the results of different studies.  For example, less time to process a target decreased the accuracy of its perceived location per both the accuracy of a saccade’s aim toward the target (Aitsebaomo & Bedell, 1992) and accepted measures of a target’s perceived location (Adam, Paas, Ekering, &  van Loon, 1995; Atkinson & Braddick, 1989; Prinzmetal, 2005), for instance, the accuracy of manual pointing toward a target (Adam et al.).  Another example:  A saccade was to be aimed toward a target but its aim was somewhat similar to a relatively near nontarget’s location (Findlay & Gilchrist, 1997; McSorley, Cruickshank, & Inman, 2009), and a target’s perceived location was somewhat similar to the perceived location of a relatively near nontarget per accepted measures of perceived location (e.g. Born et al., 2016; Ganz 64; Rentschler, Hilz, & Grimm, 1975), for instance, per a judgment of the target’s location (Ganz).  One more example:  A saccade aimed toward the unweighted average of two objects’ physical locations (e.g. Findlay, 1982), and an unweighted average of the physical locations of a target and a nontarget was perceived per a reproduction measure of the target’s perceived location (Hazeltine, Prinzmetal, & Elliott, 1997).

There will also be forthcoming additional evidence of an association between the accuracy of a saccade’s aim and the accuracy of accepted measures of perceived location.  This statement also applies to the saccade speed measure of the accuracy of perceived location that the next subsection (1.2) considers.  This forthcoming additional evidence appears in subsections 2.1, 2.2, 3.2, 5.1, 5.2, and 6.6.

1.2. The Saccade Speed Corollary Claim

Evidence for the corollary claim that the speed (latency) of a saccade that aims toward a target is a measure of the accuracy of the target’s perceived location is indicated.  Evidence is that a, say, faster saccade that still accurately aims toward a target implies that the target’s perceived location is sufficiently accurate for the saccade to be faster.  Another kind of evidence is that associations exist between the speed of a saccade that aims toward a target and presumably accepted measures of the accuracy of perceived location.  Such evidence follows.  An association occurred per results from the same research (Ludwig & Gilchrist, 2002):  A target and a nontarget that differed in color resulted in both a faster saccade toward the target and a more accurate choice of the target’s location than a target and a nontarget that were the same in color.  Evidence of associations also comes from different studies.  The saccade to a target was slower when a nontarget was closer (nearer) to the target than less close to the target (Theeuwes, Kramer, Hahn, Irwin, & Zelinsky, 1999 (a control condition result)).  Also, the perceived location of a target was less accurate when a nontarget was closer to the target than less close per a judgment of location measure (Ganz, 1964) and per a reproduction of location measure (Rentschler et al., 1975).  More evidence is that the accuracy of a saccade’s aim, a saccade’ speed, and an accepted measure were all associated:  A singleton lower contrast target’s perceived location was less accurate than a singleton higher contrast target’s perceived location per the accuracy of a saccade’s aim toward the target (Heeman, Van der Stigchel, Munoz, & Theeuwes, 2019), the speed of a saccade’s aim toward a target (Doma & Hallett, 1988; Heeman et al., 2019), and a judgment of the target’s perceived location (Hadani, Meiri, & Guri, 1984).   More evidence:  A time-2 target’s perceived location was more accurate when it appeared by chance in approximately the same physical location as a time-1 nontarget per a faster saccade that aimed toward the time-2 target (Adler, Bala, & Krauzlis, 2002) and per choice of location measures of the time-2 target’s perceived location (Donk & Soesman, 2010; Joseph & Optican, 1996). 

1.3. An Ensuing Inference

The saccade aim and saccade speed claims were sometimes supported with the instruction to saccade toward a feature or features—not a location.  One such instruction was to saccade toward the “target as a whole” (Vishwanath & Kowler, 2003).  Another was to “saccade to a white square” (Findlay & Gilchrist, 1997).  Another was to “saccade to the gray circle” (Theeuwes et al., 1999).  An inference then is that the perception of (more precisely, encoding for) an object’s features enables its location to be perceived.  This inference is used in section 6.1. 

2.0. The Exogenous and Endogenous Outcome that

the Accuracy of the Time-2 Target’s Perceived Location Increases

The Introduction stated that the exogenous and endogenous results include the outcome that the accuracy of the time-2 target’s perceived location increases and that evidence of this outcome will be indicated.  Accordingly, this evidence comes next. 

2.1. The Exogenous Result

Evidence for the exogenous result follows.  A time-2 target’s perceived location was more accurate when it appeared by chance in the same location as a time-1 nontarget per choices of location measures (Joseph & Optican, 1996; Donk & Soesman, 2010). A time-2 target’s perceived location was also more accurate when it appeared by chance in the same location as a time-1 nontarget per a faster saccade that aimed at it (Adler et al., 2002).  Also, a trial-2 (not time-2) target’s perceived location was more accurate when it appeared by chance in the same location as a trial-1 target per the accuracy of a saccade’s aim toward the target (Talcott & Gaspelin, 2020).  Recollecting, section 1.0 vouched for the validity of both the saccade aim and saccade speed measures of the accuracy of perceived location.

2.2. The Endogenous Result

Evidence for the endogenous outcome follows.  A time-2 target’s perceived location was more accurate when a time-1 object predicted the time-2 target’s location than when the time-1 object did not predict this location per choices of location measures (Bashinski & Bacharach, 1980; Muller & Rabbit, 1989), per a reproduction of location measure (Tsal & Bareket, 1999), and per faster saccades that aimed toward this target (Adler et al., 2002; Crawford & Muller, 1992; Senturk, Greenberg, & Liu, 2016).  A time-2 target’s perceived location was also more accurate when a time-1 instruction informed about the time-2 target’s location per a report of the number of objects that were not at the instructed location (Butler, 1980) and per a judgment of location measure (Egly & Homa, 1994).

3.0. The Premise that the Time-1 Perceived Location

Approximates the Time-2 Target’s Physical Location

Assimilation-location theory’s premise that the time-1 perceived location approximates the time-2 target’s physical location is supported for both the exogenous and endogenous results.

3.1. The Exogenous Result

The exogenous result occurs when the time-1 nontarget appears in a physical location that approximates the time-2 target’s physical location.  Hence when a time-1 nontarget’s perceived location is reasonably accurate, it approximates the time-2 target’s physical location.  Thus evidence that the time-1 nontarget’s perceived location is reasonably accurate supports the premise that the time-1 perceived location approximates the time-2 target’s physical location.  Evidence follows.

The exogenous result occurred when the time-1 nontarget was a singleton object (Adler et al., 2002; Anderson & Druker, 2013; Henderson & Macquistan, 1993; Jonides 81; Posner & Cohen, 1984; Talcott & Gaspelin, 2020).  The perceived location of a singleton object is known to tend to be accurate.  In addition, the singleton time-1 nontarget of the just cited research was not processed for a relatively short time.  Hence the singleton time-1 target’s perceived location would not be expected to be relatively inaccurate per evidence about processing time that is in section 4.0. 

The exogenous result also occurred when the time-2 target appeared by chance in a physical location that approximated the physical location of a time-1 nontarget with an unique feature, that is a feature that was dissimilar to a feature on the same dimension that additional time-1 nontargets had in common (Donk & Soesman, 2010; Joseph & Optican, 1996; Kim & Cave, 1999).   The perceived location of an object with a unique feature is relatively accurate per section 4.2.  Hence there is additional evidence that the time-1 nontarget’s perceived location is reasonably accurate.

3.2. The Endogenous Result

The premise that a time-1 perceived location approximates the time-2 target’s physical location is now supported for the endogenous result.  The endogenous result occurred when a time-1 object predicted the physical location of the time-2 target (Adler et al., 2002; Bashinski & Bacharach, 1980; Crawford & Muller, 1992; Muller & Rabbit, 1989; Posner et al., 1978; Senturk et al., 2016; Tsal & Bareket, 1999).  Thus evidence that a predicted location can be accurately perceived supports the premise.  There is such evidence (He & Kowler, 1989):  The perceived location of a target was more accurate when it was predicted than when it was not per the accuracy of a saccade’s aim toward the target. 

The endogenous result also occurred when a time-1 instruction informed about the physical location at which a time-2 target would appear (Butler, 1980; Egly & Homa, 1984).  Recollecting, the premise to be supported is that a time-1 perceived location approximates the time-2 target’s physical location.  Hence evidence that an instructed location is accurately perceived supports the premise.  This evidence obtains:  An instruction to reproduce a target’s location or to saccade toward a target’s location or toward a target’s features resulted in the accurate perception of the target’s location per the reproduction and saccade aim measures of perceived location according to results of Miller (1980) and Heeman et al. (2019).  Also, section 6.1 indicates that an instruction to perceive a target’s feature resulted in an accurate perception of the target’s location per an implication of results of Hoffman and Nelson (1981) and Tsal and Lavie (1988).

4.0. The Premise that the Time-1 Perceived Location Is More Accurate

The current section supports assimilation-location theory’s premise that when the exogenous and endogenous results occur, the time-1 perceived location is more accurate than the time-2 target’s perceived location (i.e., more accurate up to the moment that the accuracy of the time-2 target’s perceived location increases).  This premise will be relied on in the next section to explain why the time-2 target assimilates to the time-1 nontarget’s perceived location.

The next two subsections support the premise. 

4.1. Time to Process an Object

More time to process an object increases the accuracy of its perceived location per the next paragraph.  When the exogenous and endogenous results occur, the time-2 target is processed for a relatively short time per two paragraphs henceforth.  These two results together amount to evidence that when the exogenous and endogenous results occur, the time-1 perceived location is more accurate than the time-2 perceived location.  Hence  the premise is supported.

More processing time increases the accuracy of perceived location per the following.  Processing a singleton target for more time increased the accuracy of its perceived location per a judgment of location measure (Aitsebaomo & Bedell, 1992), the accuracy of a saccade’s aim toward a target (Aitsebaomo & Bedell, 1992), a choice of location measure (Atkinson & Braddick, 1989), and the accuracy of the aim of manual pointing toward the target (Adam et al., 1995). 

Research shows that when the exogenous and endogenous results occur, the time-2 target is processed for a relatively short time.  Because more processing time increases the accuracy of perceived location per the preceding paragraph, this research advises that the time-1 perceived location is more accurate than the time-2 target’s perceived location.  This research is covered next.  The time-2 target was responded to about as quickly as possible (Adler et al., 2002; Donk & Soesman, 2010; Jonides, 1981; Kim & Cave, 1999; Posner et al., 1978; Senturk et al., 2016; Talcott & Gaspelin, 2020 (the time-2 target occurred on a subsequent trial instead of subsequently on the same trial)).  In addition, rapid responding results in less time to process an object.  Hence the time-2 target was processed for a relatively short time.  Also, the time-2 target’s stimulus duration was noticeably less than the time-1 nontarget’s stimulus duration (Bashinski & Bacharach, 1980).  Additionally, the time-2 target appeared along with eight other nontargets for 100 ms whereas there was sufficient time to understand a time-1 instruction (Butler, 1980).  Further, the duration of the time-2 target was 50 ms and it appeared along with a large number of nontargets (Joseph & Optican, 1996).  In addition, the duration of the time-2 target was reduced sufficiently for errors in perceived location to occur (Muller & Rabbit, 1989).  Lastly, the SOA between a singleton time-1 nontarget and two potential time-2 targets was 120 ms, and the duration of these time-2 targets was 30 ms (Montagna, Pestilli, & Carrasco, 2009).   

4.2. An Unique Feature

Per subsection 3.1, the exogenous result occurred when the location of a time-1 nontarget with a unique feature approximated the location of a time-2 target by chance (Donk & Soesman, 2010; Joseph & Optican, 1996; Kim & Cave, 1999).  The perceived locations of these time-2 targets were relatively inaccurate because they were briefly processed per the preceding subsection (4.1).  Furthermore, the perceived location of an object with an unique feature is relatively accurate per the next paragraph.  Hence the exogenous result occurred when the time-1 nontarget’s perceived location was more accurate than the time-2 target’s perceived location.  Thus the current section’s premise that the time-1 perceived location is more accurate than the time-2 target’s perceived location is supported.

Evidence that the perceived location of an object with an unique feature is more accurate follows.  The perceived location of a target with a feature that was less similar to a feature on the same dimension of a large number of simultaneously appearing nontargets was more accurate than the perceived location of a target with a feature that was more similar to a feature of these simultaneously appearing nontargets per the accuracy and speed of manual pointing toward the target (Zehetleitner, Hegenloh, & Muller, 2011a) and also per a choice of location measure (Zehetleitner, Krummenacher, Geyer, Hegenloh, & Muller, 2011b).  For example, the perceived location of a target that was red was more accurate than the perceived location of a target that was yellowish green when the color of the large number of simultaneously appearing nontargets was green per the indicated measures of perceived location (Zehetleitner et al., 2011a). 

5.0. The Premise that the Time-2 Target Assimilates

to the More Accurate Time-1 Perceived Location

The current section supports assimilation-location theory’s premise that the time-2 target assimilates to the more accurate time-1 perceived location.   Support for this premise consists of evidence that a target is more likely to assimilate to a more accurate perceived location than to a less accurate perceived location under other circumstances.  This is because this evidence means that by generalization it becomes likely that the time-2 target assimilates to the more accurate time-1 perceived location, which is the premise that is to be supported.

The premise that the current section supports and assimilation-location theory’s two previously supported premises account for the exogenous and endogenous results’ outcome that the accuracy of the time-2 target’s perceived location increases.  This account was indicated in the Introduction and it is now retold.  Per the first premise, the time-1 perceived location approximates the physical location of the time-2 target.  Per the second premise, the time-1 perceived location is more accurate than the time-2 target’s perceived location.  Per the current section’s premise, the time-2 target assimilates to the more accurate time-1 perceived location.  Hence the time-2 target’s perceived location also becomes more similar to its physical location, that is, more accurate, which is the increased accuracy in perceived location outcome to be accounted for. 

5.1. Time to Process and Assimilation

As the current section’s introduction indicates, the support for the premise that the time-2 target assimilates to the more accurate time-1 perceived location consists of evidence that a target is more likely to assimilate to a more accurate perceived location than to a less accurate perceived location under other circumstances.  An object’s perceived location is more accurate when it is processed for a longer time per section 4.1.  Hence the premise is supported with evidence that a target is more likely to assimilate to the perceived location of an object that is processed for a longer time than the target.  This evidence comes next. 

A target with a briefer duration assimilated completely (by 100%) to the perceived location of a nontarget with a longer duration per a judgment of location measure (Morrone, Ross, & Burr, 1997).  (Most likely the target was also processed for less time because it appeared at about the time of a saccade.)  Because the assimilation was complete, the reverse assimilation, that is, the nontarget’s assimilation to the target’s perceived location, did not occur.  A similar result:  The stimulus duration of a target was less than the stimulus duration of a nontarget, and the target assimilated almost completely to the nontarget’s perceived location per a reproduction of location measure (Born et al., 2016).  Also, a brief duration target assimilated to a subsequent nontarget’s perceived location per a judgment of location task and there was no indication that the reverse assimilation occurred (Eagleman & Sejnowski, 2000).  Additionally, the appearance of a mask at about the same time as a target increased the target’s assimilation to the perceived location of a preceding nontarget per a judgment of location measure (Zimmermann, Fink, & Cavanagh, 2013).  Further, the aim of a saccade that was to be toward a target was similar to the location of a nontarget and more so when the saccade was faster (McSorley et al., 2009).  Hence the target’s perceived location was more similar to the location of the nontarget when the saccade was faster per the saccade aim measure of perceived location.  Thus the target assimilated to the perceived location of the nontarget and more so when the faster saccade decreased the time to process the target.

5.2. An Unique Feature and Assimilation

The perceived location of an object with an unique feature, that is, a feature that is dissimilar to a feature on the same dimension of a number of simultaneously appearing objects, is more accurate per section 4.2.   Recollecting, support for the current section’s premise that the time-2 target assimilates to the more accurate time-1 perceived location consists of evidence that a target is more likely to assimilate to a more accurate perceived location than a less accurate perceived locaation under other circumstances.  Hence this premise is supported by results advising that a target tends to assimilate to the perceived location of an object with an unique feature.  This support comes next. 

A target and a number of nontargets appeared simultaneously (van Zoest, Donk, & Van der Stigchel, 2012).  One other object also appeared.  It was either a nontarget with a feature that was rather unique relative to a feature on the same dimension of the other nontargets or it was a comparison nontarget.  The task was to aim a saccade toward the target.  The result was that the saccade aimed toward the location of the nontarget with the rather unique feature more than toward the comparison nontarget.  As when the McSorley et al.  (2009) result was considered in the preceding (5.1) subsection, a saccade’s aim is considered to indicate a target’s perceived location and this perceived location can indicate that a target assimilated toward the nontarget’s perceived location.  Hence the saccade aim result advises that the target assimilated to a more accurate perceived location more than to a less accurate perceived location.  Thus the premise is supported.  A similar result is covered next.  The task was to manually point to a target (van Zoest & Kerzel, 2015).  As in the van Zoest et al. (2012) research, a target, a number of nontargets and either a nontarget with a unique feature or a comparison nontarget appeared simultaneously.  Manual pointing to the target was slower when the unique nontarget appeared than when the comparison nontarget appeared.  Also, manual pointing was more often toward the location of the unique nontarget than toward the location of the comparison nontarget.  Both manual response results advise that that the target assimilated more to the perceived location of the nontarget with a unique feature than to the perceived location of the comparison nontarget.  Recollecting, the perceived location of an object with a unique feature is relatively accurate.  Therefore the premise is supported by both these saccade aim and manual pointing results. 

6.0. The Premise that the Accuracy of a Perceived Location Enables

the Accuracy of Perceived Features at This Location

The current section supports assimilation-location theory’s premise that the accuracy of a perceived location (more precisely, its encoding) enables the accuracy of perceived features that are at this location.  The Introduction indicated this premise and called it the location-accuracy-enables-features-accuracy premise.

An increase in the accuracy of the perceived location of the exogenous and endogenous results’ time-2 target occurs per section 2.0.  This increase in accuracy enables an increase in the accuracy of the time-2 target’s perceived features by application of the location-accuracy-enables-features-accuracy premise that the current section supports.  Hence assimilation-location theory accounts for the exogenous and endogenous results’ increased accuracy of the time-2 target’s perceived features.  Assimilation-location theory also accounts for the exogenous and endogenous results’ increased accuracy of the time-2 target’s perceived location (e.g., the introduction of the preceding section (5.0)).  An upshot is that the current section completes the support for assimilation-location theory’s account of the exogenous and endogenous results.

6.1. Support for the Location-accuracy-enables-features-accuracy Premise

One type of support for the location-accuracy-enables-features-accuracy premise is that a target’s perceived feature was more accurate when the same target’s perceived location was more accurate (e.g. Brouwer van der Heijden, 1997; Dick & Dick, 1969; Johnston & Pashler, 1990).  In addition, there was essentially no indication that the target’s perceived location was more accurate when the same target’s perceived feature was more accurate.  This result supports the possibility that the accuracy of the target’s perceived location (more precisely, its encoding) enabled the accuracy of its perceived features.  Hence the location-accuracy-enables-features accuracy premise is supported.

A second type of support for the premise is that the task to perceive a feature of a target increased the perception of a feature of a close (near) object but not a less close object (Hoffman & Nelson, 1981; Tsal & Lavie, 1988).  One implication of this result is that the perception of the target’s feature (more precisely, its encoding) enabled the perception of the target’s location and also the perception of the close object’s location.  A second implication is that the perception of the close object’s location (more precisely, its encoding) enabled the perception of the features of this object.  It is this second implication that supports the premise.  In addition, the first implication is supported by an inference that was reached in subsection 1.3, namely, that the perception of an object’s features enables its location to be perceived.

6.2. Assimilation Support for the Location-accuracy-enables-features-accuracy Premise

More support for assimilation-location theory’s location-accuracy-enables-features-accuracy premise stems from the occurrence of assimilation between perceived locations, as follows.  When a first object assimilates toward the perceived location of a second object, ordinarily the first object’s perceived location is its assimilation-produced one rather than its physical one.  Hence ordinarily an assimilation-produced perceived location is inaccurate.  Thus per the location-accuracy-enables-features-accuracy premise, the first object’s assimilation-produced inaccurate perceived location enables its perceived features to also be inaccurate.  An ensuing prediction is that the accuracy of an object’s assimilation-produced perceived location is associated with the accuracy of the same or a comparable object’s perceived features.  Also, an object is comparable when, say, object A is close to one nontarget and object B is close to a different nonarget.  In this case, object B is comparable to object A.

Accordingly, three of the current section’s remaining subsections support the preceding paragraph’s prediction.  Moreover, because this prediction is underpinned by the location-accuracy-enables-features-accuracy premise, this premise is also supported.  The two remaining sections indicate ensuing suggestions. 

6.3. Same-research Assimilation Support

Support for the preceding section’s prediction that the accuracy of an object’s assimilation-produced perceived location is associated with the accuracy of the same or a comparable object’s perceived features occurs when both these accuracies are measured in the same research.  This support comes next.

Multiple target bars in different physical locations that appeared at about the time of a saccade were perceived as a single bar at the location of the goal for the saccade (Morrone et al., 1997).  The perception of the bars at the goal’s location is evidence that the bars assimilated (by 100%) to the perceived location of the goal.  Hence the assimilation-produced perceived location of each of these bars was rather inaccurate.  The perception of only one bar means that these bars’ perceived features were also rather inaccurate (the number of perceived features was inaccurately small).  Hence an assimilation-produced inaccurate perceived location was associated with inaccurate perceived features at this location, in support of the prediction.   

Also, a target line assimilated more to the perceived location of a nontarget rectangle when the nontarget rectangle was closer to the target line than less close per a judgment of location measure (Ganz, 1964).  Hence the target line’s assimilation-produced perceived location was less accurate when the nontarget rectangle was closer to the target line.  The accuracy of the target line’s perceived features was also less when the nontarget rectangle was closer to the target line per a detection measure.  Hence perceived location and perceived features accuracies were associated, in support of the prediction.  More evidence of the predicted association:  Both more assimilation and worse detection also occurred when the colors of the target line and nontarget rectangle were the same instead of different.

Additionally, a target horizontal bar assimilated to the higher (or lower) perceived location of two horizontal bars that were to the left and right (Greenwood, Bex, & Dakin, 2012 (actually, each horizontal bar was a component of a larger object that looks like a cross)).   Also, the perceived tilt of a similar but now tilted target bar was perceived less accurately when left and right now tilted bars were present per a discrimination between tilts task.  Presumably the now tilted target bar again assimilated to the perceived locations of the left and right tilted bars, meaning that the target bar’s location was perceived less accurately.  Hence these results suggest that both the target bar’s location and tilt were perceived less accurately and thus these accuracies were associated, in support of the prediction. 

6.4. Closeness Assimilation Support

The statement that a target assimilates more to the perceived location of a closer (nearer) nontarget than to the perceived location of a less close (farther) nontarget is evidenced.  Hence the target’s assimilation-produced perceived location is less accurate when the perceived location of the nontarget is closer.  A second statement, that the accuracy of a target’s perceived feature is less when a nontarget is closer than less close, is also evidenced.  Hence the accuracy of a target’s perceived location and the accuracy of its perceived features at this location are associated.  Thus the prediction that the accuracy of an object’s assimilation-produced perceived location is associated with the accuracy of the same or a comparable target’s perceived features is again supported.  Recollecting, because the prediction is underpinned by the location-accuracy-enables-features-accuracy premise, this premise is also supported.  The current subsection also qualifies both of this paragraph’s statements. 

The preceding paragraph’s statement that there is more assimilation to a closer perceived location is evidenced first.  A target assimilated more to a perceived closer nontarget than to a perceived less close nontarget per a judgment of the target’s perceived location (Ganz, 1964) (as subsection 6.3 also indicates).  This effect of closeness also occurred per a reproduction measure (Rentschler et al., 1975).  A saccade that was to be aimed at a target aimed more toward a closer nontarget than toward a less close nontarget (McSorley et al., 2009).  Hence the target’s perceived location became more similar to the closer nontarget’s location than to the less close nontarget’s location per the saccade aim measure of perceived location.  This more similarity is then evidence that the target assimilated more to the perceived closer nontarget than to the perceived less close nontarget.  A similar result is that a saccade’s aim was more likely to be in between a target’s and a nontarget’s location when the target and nontarget were closer than less close (Ottes, Van Gisbergen, & Eggermont, 1984).  Hence the target’s perceived location became more similar to the closer nontarget’s location than to the less close nontarget’s location per the saccade aim measure of perceived location.  This more similarity is then again evidence that the target assimilated more to the perceived closer nontarget than to the perceived less close nontarget.  Another result is that a saccade that aimed at a target was slower when a nontarget was closer than less close (Theeuwes et al., 1999 (a control result)).  A slower saccade that aims at a target indicates that a target’s perceived location is less accurate per the saccade speed measure of perceived location.  Presumably the target’s less accurate perceived location was assimilation produced.  Hence this slower saccade result is also evidence that a target assimilated more to a perceived closer nontarget than to a perceived less close nontarget.

Now the statement about features that is in the current subsection’s first paragraph is evidenced.  That is, evidence that the accuracy of a target’s perceived feature is less when a nontarget (or more than one nontarget) is closer to the target than less close is indicated.  Extant evidence is both fairly familiar and broad (e.g. Bouma, 1970; Eriksen & Hoffman, 1972; Flom, Weymouth, & Kahneman, 1963; Ganz, 1964 (as the preceding subsection also indicates); Parlee, 1969; Werner, 1935). 

The accuracy of a target’s assimilation-produced perceived location is also less when a nontarget is closer than less close to the target per two paragraphs past.  Hence the prediction that the accuracy of a target’s assimilation-produced perceived location is associated with the accuracy of the same or a comparable target’s perceived features is supported.  Thus the premise is also supported per the current subsection’s first paragraph.

The current subsection’s first paragraph also notes that its statement about assimilation would be qualified.  The qualification is that a target does not consistently assimilate more to the perceived location of a closer nontarget than to a less close one when the measure of the amount of assimilation that occurs is an absolute one.  For example, when the closeness between a target and a nontarget is, say, 5 mm, the maximum absolute amount by which the target can assimilate to the nontarget is also 5 mm.  In contrast, the percentage of the amount of assimilation of the target to a 5-mm distant nontarget can still be large, for instance, 100%.  In regards to the current subsection’s assimilation evidence, most likely a target assimilated to a perceived closer nontarget more than to a perceived less close nontarget per both these measures of amount of assimilation.

The current subsection’s first paragraph also notes that its statement about perceived features would be qualified.  The statement is qualified because a target’s perceived features were more accurate instead of less accurate when the locations of a target and nontarget overlapped or were very close (Dresp & Bonnet, 1991; King, Mose, & Nixon, 1995; Novak & Sperling, 1963).  In addition, the target’s perceived contrast was less than the nontarget’s perceived contrast. 

6.5. A Suggestion

A suggestion that is an aside stems from subsection 6.4’s evidence that an association exists between the accuracy of a target’s assimilation-produced perceived location and the accuracy of its perceived features.  In light of this association, the suggestion is that the perceived features evidence of Bouma (1970), Eriksen and Hoffman (1972), Flom, Weymouth, and Kahneman (1963), Ganz (1964), Parlee (1969), Werner (1935), and other researchers may be enabled by the target assimilating to the perceived location of the nontarget(s). 

6.6. Similarity between Features Assimilation Support

Evidence is indicated that when the features of a target and a simultaneous or almost simultaneous nontarget are more similar, the target assimilates more to the nontarget’s perceived location.  Evidence is also indicated that when the features of a target and a simultaneous or almost simultaneous nontarget are more similar, the target’s features are perceived less accurately.  Recollecting, an assimilation-produced perceived location is ordinarily inaccurate, Hence the prediction in subsection 6.2 that the accuracy of a target’s assimilation-produced perceived location is associated with the accuracy of the same or a comparable target’s perceived features is supported once more.  Since this prediction is underpinned by the location-accuracy-enables-features-accuracy premise, this premise is also supported.

The evidence that when the features of a target and a simultaneous or almost simultaneous nontarget are more similar, the target assimilates more to the nontarget’s perceived location follows.  A target assimilated more to a same-color nontarget’s perceived location than to a different-color nontarget’s perceived location per a judgment of location measure (Ganz, 1964) (as also indicated in subsection 6.3)).  More evidence:  A saccade that was to be aimed at a target aimed more toward a same-color nontarget’s location than to a different-color nontarget’s location (Findlay & Gilchrist, 1997).  Hence the target’s perceived location become more similar to the same-color nontarget’s location than to the different-color nontarget’s location per the saccade aim measure of perceived location.  Thus this saccade aim result is evidence that the target assimilated more to the same-color nontarget’s perceived location than to the different-color nontarget’s perceived location.  Additional evidence:  A vertical target assimilated toward a nontarget’s perceived location when the nontarget’s tilt was vertical but not when it was horizontal per a reproduction of location measure (Cicchini, Binda, Burr, & Morrone, 2013).  Further evidence:  A target assimilated more to a same-color nontarget than to a different-color nontarget per a choice of location measure and also per the result that a saccade that aimed at the target was slower when the nontarget was the same color (Ludwig & Gilchrist, 2002).   Congruent evidence is that manual reaching toward a tilted target was both less accurate and slower when the similarity between the target’s tilt and the tilt of multiple nontargets was higher than lower (Zehetleitner et al., 2011a).  More congruent evidence is that the similarity between the contrasts of a target and multiple nontargets affected manual reaching comparably (Zehetleitner et al., 2011a).  Additionally, using a choice of location measure yielded parallel results (Zehetleitner et al., 2011b).  Hence the target’s perceived location was less accurate when the similarity between its feature and the feature of the multiple nontargets was higher.  Presumably this lesser accuracy was due to the target assimilating more to the perceived locations of the nontargets when this similarity between features was higher. 

Now evidence about perceived features is indicated.  The evidence is fairly familiar and broad:  When the similarity between the feature of a target and the feature of one or more nontargets was higher, the perception of the target’s feature was less accurate (e.g. Carter, 1982; Duncan & Humphreys, 1989; Fehrer, 1966; Harms & Bundesen, 1983; Ivry & Prinzmetal, 1991; Zehetleitner, Krummenacher, & Muller, 2009).  The effect of the similarity between features was analogous when two objects were both targets (e.g. Krueger & Chignell, 1985).

6.7. Another Suggestion

Section 6.6 provides similarity between features evidence that an association exists between the accuracy of a target’s assimilation-produced perceived location and the accuracy of its perceived features.  In light of this association, an ensuing suggestion is that assimilation between the perceived locations of a target and one or more additional objects enables the effect of the similarity between features on the accuracy of perceived features found by the research that the preceding paragraph cites and comparable research. 

7.0. Conclusion

Section 6.0 supported assimilation-location theory’s location-accuracy-enables-features-accuracy premise.  It also pointed out that this premise accounts for the exogenous and endogenous results’ increased accuracy of the time-2 target’s perceived features.  The increased accuracy of the exogenous and endogenous results’ time-2 target’s perceived location is also accounted for by assimilation-location theory (e.g., see section 5.0’s introduction).  In conclusion, the exogenous and endogenous results are accounted for by assimilation-location theory.

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