The current manuscript was completed in Jan 2024. Nevertheless, included in it are small changes that were made in Mar 2024. The current manuscript is a revision of a manuscript that was completed in Nov 2023 and published in Visual Perception Science on Nov 6 2023. The title of this earlier manuscript is “Attention: Basically, the Time-2 Target’s Inaccurate Perceived Location Assimilates to a Time-1 Perceived Location That Approximates the Time-2 Target’s Physical Location and Hence Becomes More Accurate.” The current manuscript is basically the same as the Nov 2023 manuscript. On the other hand, it should be a bit more precise and readable than the Nov 2023 manuscript.

Abstract

An initial object that is by chance in the same location as a subsequent object’s (target’s) physical location is called a cue.  Information that indicates a subsequent target’s physical location is also called a cue.  The exogenous attention result is that the same-location cue makes the subsequent target’s perceived location and perceived features more accurate.  The endogenous attention result is that the information cue does the same.  An assimilation-location theory explains these results.  This theory relies on the following supported premises.  A:  The cue produces a perceived location that mirrors the target’s physical location.  B:  The target’s perceived location is less accurate than the cue-produced perceived location.  C:  Because the target’s perceived location is less accurate than the cue-produced perceived location, the target’s perceived location assimilates (becomes more similar) to the cue-produced perceived location.  D:  An object’s more accurate perceived location enables its features to be more accurate.  Per Premises A-C, via assimilation the target’s perceived location becomes more similar to the cue-produced perceived location, hence also becomes more similar to its own physical location, and thus becomes more accurate, as to be explained.  Per Premise D, the target’s perceived features also become more accurate, as also to be explained.

An initial object that is by chance in about the same location as a subsequent object’s (target’s) physical location will be called a cue.  This cue tends to make the subsequent target’s perceived location more accurate, for example, per a choice of location measure (Joseph & Optican, 1996).  This cue also tends to make the subsequent target’s features more accurate, for example, per an improved successive discrimination between features of two different targets (Jonides, 1981).  Consistent with the research literature, both this perceived location outcome and this perceived features outcome are considered to constitute the exogenous attention result.

Information that indicates a subsequent object’s (target’s) physical location will also be called a cue.  As for the exogenous attention result, this cue tends to make the subsequent target’s perceived location and perceived features more accurate.  Consistent with the research literature, both this location outcome and this feature outcome are considered to constitute the endogenous attention result.  The endogenous attention result tends to occur when an initial object (the cue) predicts a subsequent target’s physical location (e.g. Posner, Nissen, & Ogden, 1978).  The endogenous attention result also tends to occur when, for example, a verbal communication (the cue) informs about a subsequent target’s physical location (e.g. Butler, 1980).  The endogenous attention result also tends to occur in additional ways that probably also inform about a subsequent target’s physical location (e.g. LaBerge, 1983).  An information cue does make a subsequent target’s perceived location more accurate, for example, per a choice of location measure (e.g. Bashinski & Bacharach, 1980), and it does make a subsequent target’s perceived features more accurate, for example, per a detection measure (e.g. Posner et al., 1978).

This paper introduces and supports a theory of both the exogenous and endogenous attention results.  The theory is called assimilation-location theory.  This theory’s account (explanation) of the exogenous and endogenous attention results is in Section 1.

Evidence that the location toward which a saccade aims and the currently perceived location are frequently approximately equivalent is in Section 2.  Evidence about the speed of a saccade is also considered in Section 2.  This evidence is relied on in Sections 3-7.  

Evidence of the exogenous attention and endogenous attention results’ outcome that the target’s perceived location becomes more accurate is indicated in Section 3.  Evidence of these results’ outcome that the target’s perceived features become more accurate is not indicated.  The primary reason is that this outcome is presumably relatively familiar.

Assimilation-location theory relies on four premises (A-D).  Premises A-D are considered in Section 1.  They are additionally considered including supported in Sections 4-7, respectively. 

Sections and also subsections are numbered to readily refer to them.

1. Assimilation-Location Theory

The present section indicates assimilation-location theory’s account of the exogenous attention and endogenous attention results.

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

Consistent with the present paper’s assimilation related approach to attention, assimilation’s role in psychology may be significant.  One possibility is that via assimilation “classical conditioning increases the perceived similarity of the CS to the US” (King, 2001, p. 35).   Another possibility is that a young animal’s fear assimilates (becomes similar) to the perceived absence of fear produced by a mother’s stimuli and hence the young animal’s fear is reduced.

An assimilation-induced perceived location will sometimes be referred to (e.g. Ganz’s line came to have an assimilation-induced perceived location).  Also, sometimes an object’s perceived location will be said to assimilate toward another object’s perceived location.  Simply assimilation will sometimes be mentioned. 

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

Assimilation-location theory maintains that an assimilation-induced perceived location enables the exogenous attention and endogenous attention results.  (More precisely, an assimilation-induced encoded location is enabling.)  Also, enables means essential to bringing about but that other factors can also contribute to the bringing about.  Recollecting, both the exogenous attention and endogenous attention results include the outcome that the target’s perceived location becomes more accurate and also the outcome that the target’s perceived features become more accurate. 

Assimilation-location theory does not involve attention.  In accord, 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.  The theory relies on four premises, as the Introduction noted.  These premises, A-D, will be additionally considered including supported in Sections 4-7, respectively, as the Introduction also noted. 

Premise A is that the cue produces a perceived location that mirrors the target’s physical location.  For the exogenous result, the cue’s physical location approximates the target’s physical location (the Introduction).  Accordingly, for the exogenous result, the perceived location that mirrors the target’s physical location is assumed to stem from the cue’s physical location.  For the endogenous result, the cue is information that indicates a subsequent target’s physical location (the Introduction).  Accordingly, the cue-produced perceived location that mirrors the target’s physical location is assumed to be enabled by a cognitive process.  This assumption is called the cognition assumption.

 Premise B is that for both the exogenous and endogenous results, the target’s perceived location is less accurate than the cue-produced perceived location (i.e., less accurate up to the moment that the target’s perceived location becomes more accurate).   

Premise C is that because the target’s perceived location is less accurate than the cue-produced perceived location (per premise B), the target’s perceived location assimilates (becomes more similar) to the cue-produced perceived location.  This assimilation means that the target also assimilates (becomes more similar) to a perceived location that mirrors its physical location per Premise A.  In other words, the target’s perceived location becomes more accurate.  Hence assimilation-location theory accounts for the exogenous and endogenous results’ outcome that the target’s perceived location becomes more accurate.     

Premise D is that the accuracy of an object’s perceived (more precisely, encoded) location enables a similar (comparable) accuracy of its perceived features.  Both the exogenous attention and endogenous attention results include the outcome that the target’s perceived location becomes more accurate.  Hence it follows from premise D that the target’s perceived features also become more accurate.  Thus assimilation-location theory also accounts for the exogenous and endogenous results’ outcome that the target’s perceived features become more accurate.  

The following synopsis of assimilation-location theory’s account may help to understand it.  Because the cue-produced perceived location approximates the target’s physical location and also because the target’s perceived location assimilates toward the cue-produced perceived location, the target’s perceived location becomes more similar to its physical location, that is, becomes more accurate.  Then Premise D applies. 

2. Saccade-Location-Perceived-Location Evidence

and Saccade-Speed-Perceived-Location Evidence

The main purpose of the present section is to support the use of a saccade’s aim toward a location and a saccade’s speed to indicate a perceived location and/or the accuracy of a perceived location in Sections 3-7.  Support for using a saccade’s aim toward a location is in Subsection 2.1, and support for using a saccade’s speed is in Subsection 2.2.  An ensuing inference is considered in Subsection 2.3.

2.1. Saccade-Location-Perceived-Location Evidence

The present subsection supports the conclusion that the location toward which a saccade aims and the currently perceived location are frequently approximately equivalent.  The essential support for this conclusion consists of evidence that the location to which a saccade aims is approximately equivalent to the currently perceived location according to presumably accepted measures of perceived location.  This evidence is called saccade-location-perceived-location evidence.  This evidence is now indicated. 

Results advise that when the task is to aim a saccade toward an object, the aimed at location is approximately equivalent to the object’s perceived location per an accepted measure of perceived location (Aitsebaomo & Bedell, 1992; Miller, 1980; Vishwanath & Kowler, 2003).  For example, when the task was to saccade toward an object, the saccade’s aimed at location was approximately equivalent to the object’s perceived location per a reproduction measure (Miller).  Hence these results provide saccade-location-perceived location evidence.

Also, less time to process an object decreased the accuracy of a saccade’s aim toward an object’s location (Aitsebaomo & Bedell, 1992), and it also decreased the accuracy of an object’s perceived location per presumably accepted measures of perceived location (Adam, Paas, Ekering, & van Loon, 1995; Atkinson & Braddick, 1989; Prinzmetal, 2005), for instance, per the accuracy of manual pointing toward an object (Adam et al.).   This correspondence between the accuracy of a saccade’s aim toward a location and the accuracy of the perception of a location amounts to saccade-location-perceived-location evidence. 

Additionally, when a first and a second object were present, a saccade that was to be aimed toward the first object’s location aimed somewhat toward the second object’s location (Findlay & Gilchrist, 1997; McSorley, Cruickshank, & Inman, 2009), and when a first and a second object were again present, the first object’s perceived location was somewhat toward the second object’s location per accepted measures of the first object’s perceived location (Ganz, 1964; Rentschler, Hilz, & Grimm, 1975), for instance, per a judgment of the first object’s location (Ganz).   Hence a location that a saccade aimed toward and a perceived location indicated by presumably accepted measures of perceived location correspond.  Thus there is more saccade-location-perceived-location evidence.

Further, a saccade aimed toward the unweighted average of the locations of a first object that was to be saccaded toward and a second object (e.g. Coren & Hoenig, 1972), and an unweighted average of the locations of a first object that was responded to and a second object was perceived per a reproduction measure of the first object’s perceived location (Hazeltine, Prinzmetal, & Elliott, 1997).  Hence a location that a saccade aimed toward and a perceived location indicated by a reproduction measure of perceived location correspond.    Hence there is additional saccade-location-perceived-location evidence.

2.2. Saccade-Speed-Perceived-Location Evidence

The present subsection supports the conclusion that the speed of a saccade’s aim toward an object’s location is frequently a measure of the accuracy of the object’s perceived location (providing that when a saccade’s speed is faster, the accuracy of its aim does not decline).  This conclusion will be supported by evidence that an association exists between the speed of a saccade that is intended to aim toward an object’s location and the accuracy of this object’s perceived location according to presumably accepted measures of perceived location.  This association evidence is called saccade-speed-perceived-location evidence.  This evidence follows and hence the just indicated conclusion is supported. 

One result is that a saccade was to be aimed toward a first object’s location, and a second object that was the same in color resulted in both a slower saccade toward the first object’s location and a less accurate choice of this location than a second object that was different in color (Ludwig & Gilchrist, 2002).  Hence a slower saccade that was intended to be toward an object’s location was associated with a less accurate perception of this location per a presumably accepted measure of perceived location.  Thus the result provides saccade-speed-perceived-location evidence.

Also, a saccade was to be aimed toward a first object’s location, and the saccade toward this location was slower when a second object was closer to it than less close to it (Theeuwes, Kramer, Hahn, Irwin, & Zelinsky, 1999 (a control condition result)).  Additionally, a first object’s perceived location was less accurate when a second object was closer to it than less close to it per both judgment of location (Ganz, 1964) and reproduction of location (Rentschler et al., 1975) measures of perceived location.  Together, these two findings advise that an association exists between the speed of a saccade that was intended to be toward an object’s location and the accuracy of this object’s perceived location.  Hence they provide saccade-speed-perceived-location evidence.

More saccade-speed-perceived-location evidence and also more saccade-location-perceived-location evidence:  A saccade aimed toward a single (sole) lower contrast object more slowly (Doma & Hallett, 1988; Heeman, Van der Stigchel, Munoz, & Theeuwes, 2019), a saccade aimed toward a single lower contrast object less accurately (Heeman et al., 2019), and the perceived location of a single lower contrast object was less accurate per a judgment of location measure (Hadani, Meiri, & Guri, 1984).

Additional saccade-speed-perceived-location evidence:  A cue that by chance was in the same physical location as a subsequent target and also a cue that indicated the subsequent target’s physical location accelerated a saccade that aimed toward the target (Adler, Bala, & Krauzlis, 2002), and a cue also makes a subsequent target’s perceived location more accurate per accepted measures of perceived location per Section 3. 

2.3. An Ensuing Inference

Some of the evidence in the previous two subsections comes from an instruction to saccade toward a feature or features—not a location.  One such instruction was to saccade to 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) the feature of an object enables its location to be perceived.

3. Evidence for the Outcome That the Target’s Perceived Location

Becomes More Accurate

The exogenous and endogenous results include the outcome that the target’s perceived location becomes more accurate.  The Introduction indicated that evidence for this outcome is forthcoming, including for both the exogenous and endogenous results.  Accordingly, such evidence follows. 

3.1. The Exogenous Result

Evidence for the exogenous result is covered.  A target’s perceived location was more accurate when it appeared by chance in the same location as a cue per choices of location measures (Donk & Soesman, 2010; Joseph & Optican, 1996).  A target’s perceived location was also more accurate when it appeared by chance in the same location as a cue per a faster saccade that aimed toward it (Adler et al., 2002) by virtue of saccade-speed-perceived location evidence according to Section 2.  Also, a target’s perceived location was more accurate when it appeared by chance in the same location as a cue that occurred on the preceding trial per a saccade’s more accurate aim toward the target’s location (Talcott & Gaspelin, 2020), because this more accurately aimed at location advises a more accurately perceived location by virtue of saccade-location-perceived-location evidence according to Section 2.

3.2. The Endogenous Result

Evidence for the endogenous result is also covered.  A target’s perceived location was more accurate when a cue predicted the target’s location than when the initial object did not predict the target’s location per choice of location measures (Bashinski & Bacharach, 1980; Muller & Rabbit, 1989), per a manual pointing measure (Tsal & Bareket, 1999), and per a faster saccade that aimed toward a target’s location  (Adler et al., 2002; Crawford & Muller, 1992; Senturk, Greenberg, & Liu, 2016) by virtue of saccade-speed-perceived-location evidence according to Section 2.  A target’s perceived location was also more accurate when a verbal cue informed about the target’s location per the number of additional display objects that were mislocalized as being at the target’s location (Butler, 1980) and per a judgment of location measure (Egly & Homa, 1984).

4. Premise A

Premise A was previously considered in Section 1.  Premise A is that the cue produces a perceived location that mirrors the target’s physical location.  The present section supports this premise for both the exogenous and endogenous results.

4.1. The Exogenous Result

 Premise A is supported for the exogenous result.  Recollecting, for the exogenous result, the cue is an object that appears by chance in about the same physical location as the subsequent target.  Hence when the cue-produced perceived location is reasonably accurate, it mirrors the target’s physical location.  Thus evidence that the cue-produced perceived location is reasonably accurate supports Premise A (that the cue produces a perceived location that mirrors the target’s physical location).  Such evidence follows.

The cue is frequently a single (sole) object (e.g. Adler et al., 2002; Anderson & Druker, 2013; Henderson & Macquistan, 1993; Jonides, 1981; Posner & Cohen, 1984).  The perceived location of a single object is known to tend to be accurate.  In addition, the cues (single objects) of the just cited research were not processed for a relatively short time.  Hence their perceived location would be expected to tend to be accurate per evidence about processing time that is in Subsection 5.1. 

The exogenous result also occurs when the cue is an object with an unique feature, that is, a feature that is dissimilar to a feature on the same dimension that additional initial objects have in common (Donk & Soesman, 2010; Joseph & Optican, 1996; Kim & Cave, 1999).   The perceived location of an object with an unique feature is relatively accurate per Subsection 5.2.  Hence there is additional evidence that the cue-produced perceived location is reasonably accurate.

4.2. The Endogenous Result

Premise A is supported for the endogenous result.  For the endogenous result, a cognition assumption is also involved, as Section 1 mentioned.  Accordingly, the present subsection also considers including supports the cognition assumption. 

The endogenous result occurs when the cue predicts the subsequent target’s physical location (e.g. Posner et al., 1978).  Recollecting, Premise A is that the cue produces a perceived location that mirrors the target’s physical location.  Hence Premise A is supported via generalization by evidence that under a different condition the prediction of a physical location results in this location being perceived.   Such evidence follows.  When the instruction was to saccade toward an object and the object was more likely to appear in one (the predicted) physical location instead of a second physical location, a saccade tended to aim toward the predicted physical location (He & Kowler, 1989), and thus the perceived location approximated the predicted physical location by virtue of saccade-location-perceived-location evidence according to Section 2.           

The endogenous result also occurs when the cue verbally informs about the target’s physical location (Butler, 1980; Egly & Homa, 1984).  Hence this informed location is also perceived per Premise A.  Thus Premise A is supported via generalization by evidence that a cue that informs of a subsequent object’s physical location results in the perception of this location.  Some evidence follows.  An instruction to saccade toward a subsequently appearing particular object rather than toward other simultaneously appearing objects resulted in a saccade that aimed toward the particular object’s location (Deubel & Schneider, 1996; Kowler, Anderson, Dosher, & Blaser, 1995).  Hence the saccade’s aim toward a location was relatively accurate.  In addition, this relatively accurately aimed at location advises a more accurately perceived location by virtue of saccade-location-perceived-location evidence according to Section 2.   In conclusion, the location that was informed via instruction was perceived relatively accurately.  

The cognition assumption is that, for the endogenous result, the cue-produced perceived location that mirrors the target’s physical location is enabled by a cognitive process.  Hence the cognition assumption accounts for how a cue-produced perceived location mirrors the target’s physical location.  Accordingly, support for the cognition assumption follows. 

The cognition assumption is supported, because results advise that preparation for an aim of a saccade need not enable the endogenous result, making it more likely that cognition does.  Klein (1980) arranged for a saccade to be prepared to aim toward one side (left or right) for an entire block.  Also, on a trial (not a block), a stimulus that was to be detected appeared either to the left or right.  The finding was that detection was no better when the side that was prepared to be aimed at with a saccade and the stimulus’s side were the same than when they were opposite.  In conclusion, preparation for the saccade’s aim did not enable the endogenous result.  Additional research (Wollenberg, Deubel, & Szinte, 2018) basically showed that when two initially appearing objects were in different locations (X and Y) and a factor resulted in a saccade that aimed toward a third location (Z) instead of the X or Y location, the detection of a subsequent object was worse when it appeared in the Z location than in the X or Y location.  Hence preparation for the aim of a saccade was associated with worse instead of enhanced detection of a subsequent object that appeared where the saccade aimed.

5. Premise B

Premise B was indicated in Section 1.  Premise B is that for both the exogenous and endogenous results, the target’s perceived location is less accurate than the cue-produced perceived location.  Premise B is a basis for Premise C.  The present section supports Premise B for both the exogenous and endogenous results.

5.1. Time to Process an Object

Less time to process an object decreases the accuracy of its perceived location per the next paragraph.  When the exogenous and endogenous results occur, the target is ordinarily processed for a shorter time than the cue per two paragraphs henceforth.  Together, these two conclusions amount to evidence that when the exogenous and endogenous results occur, the target’s perceived location is less accurate than the cue-produced perceived location.  Hence  Premise B is supported. 

Less time to process an object decreases the accuracy of its perceived location as follows.  Processing a single (sole) object for less time decreased the accuracy of its perceived location per a judgment of location measure (Aitsebaomo & Bedell, 1992), a choice of location measure (Atkinson & Braddick, 1989), a manual pointing measure (Adam et al., 1995), and the accuracy of a saccade’s aim toward the object’s location (Aitsebaomo & Bedell, 1992) because this decreased accuracy in aimed at location advises a less accurately perceived location by virtue of saccade-location-perceived-location evidence according to Section 2.   

When the exogenous and endogenous results occur, the target is usually processed for a shorter time than the cue.  Evidence follows.  The target was responded to about as quickly as possible (Donk & Soesman, 2010; Jonides, 1981; Kim & Cave, 1999; Posner et al., 1978; Senturk et al., 2016), and rapid responding shortens the time to process an object.  Hence the target was processed for a relatively short time.  Also, the target’s stimulus duration was noticeably less than the cue’s stimulus duration (Bashinski & Bacharach, 1980).   Additionally, the target’s duration was less than the cue’s duration, and the target was more similar to the objects that appeared with it than the cue was similar to the objects that appeared with it (Joseph & Optican, 1996).  Further, the target appeared along with eight other nontargets for 100 ms whereas there was sufficient time to understand the initial information (cue) about the target’s location (Butler, 1980).  Similarly, the duration of the target was relatively brief and it was masked whereas there was sufficient time to understand the initial information (cue) about the target’s location (Egly & Homa, 1984).

5.2. An Unique Feature

Per Subsection 4.1, the exogenous result occurs when the cue is an object with an unique feature (Donk & Soesman, 2010; Joseph & Optican, 1996; Kim & Cave, 1999).  The perceived locations of the targets of these papers were relatively inaccurate because they were briefly processed per the preceding paragraph.  Also, the perceived location of an object with an unique feature is relatively accurate per the next paragraph.  Hence, for these papers, the target’s perceived location was less accurate than the cue-produced perceived location.  Thus Premise B is supported.

Evidence that the perceived location of an object with an unique feature is relatively accurate follows.  The perceived location of an object (X) with an unique feature was more accurate than the perceived location of an object (Y) with a feature that was relatively similar to a feature of simultaneously appearing additional objects per a manual pointing measure (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 red object was more accurate than the perceived location of a yellowish green object when the color of the large number of simultaneously appearing additional objects was green per a choice of location measure (Zehetleitner et al., 2011b).

6. Premise C

Section 1 considered Premise C.  Premise C is that because the target’s perceived location is less accurate than the cue-produced perceived location (per premise B), the target’s perceived location assimilates (becomes more similar) to the cue-produced perceived location.  The present section supports Premise C in its subsections. 

The present section finishes the support for assimilation-location theory’s account of the exogenous and endogenous results’ outcome that the target’s perceived location (not features) becomes more accurate.  This is because this outcome is accounted for by Premises A-C per Section 1, and also because, with the present section’s evidence, these three premises are supported. 

Assimilation-location theory’s account of the outcome that the target’s perceived location becomes more accurate is retold.  Premise A is that the cue produces a perceived location that mirrors the target’s physical location.  Premise B is  that the target’s perceived location is less accurate than the cue-produced perceived location.  Premise C is that because the target’s perceived location is less accurate than the cue-produced perceived location (per premise B), the target’s perceived location assimilates (becomes more similar) to the cue-produced perceived location.  This assimilation means that the target’s perceived location also becomes more similar to its physical location (since the cue-produced perceived location mirrors the target’s physical location).  In other words, the target’s perceived location becomes more accurate, which is the outcome to be accounted for.

6.1. Time to Process and Assimilation

The present and next subsection’s support for Premise C consists of evidence for the outcome that an object’s perceived location is more likely to assimilate toward a more accurate perceived location than toward a less accurate perceived location in general.  This outcome is called the assimilation-is-toward-accuracy outcome.  Generalizing on the basis of the assimilation-is-toward-accuracy outcome, it becomes more likely that the target assimilates to the more accurate cue-produced perceived location.  Hence Premise C is supported. 

Accordingly, evidence for the assimilation-is-toward-accuracy outcome is indicated.  This evidence consists of results that advise that assimilation is toward the physical location of an object that is processed for a longer time.  These results are evidence, because an object’s perceived location is more accurate when it is processed for a longer time per Subsection 5.1.  Premise C is supported in turn per the preceding paragraph.

The just mentioned evidence is indicated.  Object X’s stimulus duration was less than object Y’s, and object X’s perceived location assimilated completely (by 100%) to object Y’s physical location per a judgment of location measure (Morrone, Ross, & Burr, 1997).  (Most likely object X was also processed for less time because it appeared at about the same time as a saccade.)  A similar result:  Object X’s stimulus duration was less than object Y’s, and object X’s perceived location assimilated almost completely to object Y’s physical location per a reproduction of location measure (Born et al., 2016).  Another similar result occurred per a judgment of location measure (Eagleman & Sejnowski, 2000).  Additionally, the appearance of a mask at about the same time as object X increased the assimilation of object X’s perceived location toward object Y’s physical location per a judgment of location measure (Zimmermann, Fink, & Cavanagh, 2013). 

6.2. 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 relatively accurate per Section 5.2.   Recollecting, the assimilation-is-toward-accuracy outcome is that an object’s perceived location is more likely to assimilate toward a more accurate perceived location than toward a less accurate perceived location in general.  Hence the assimilation-is-toward-accuracy outcome is supported by evidence that an object tends to assimilate toward the physical location of an object with an unique feature.  Recollecting, Premise C is supported in turn. 

The just mentioned evidence is described.  An object, X, and a number of additional objects appeared simultaneously (van Zoest, Donk, & Van der Stigchel, 2012).  Another object also appeared.  It was either an object with a feature that was unique relative to a feature on the same dimension of the additional objects or it was a comparison object.  The task called for saccading toward object X.  As might be expected, the saccade tended to aim toward the location of object X.  But it also aimed somewhat toward the location of the object with the unique feature, including more than it did toward the location of the comparison object.  Hence the perceived location of object X was somewhat similar to the location of the object with the unique feature and more so than it was similar to the location of the comparison object by virtue of saccade-location-perceived-location evidence according to Section 2.  Thus object X’s perceived location assimilated toward the location of the object with the unique feature and more so than it assimilated toward the location of the comparison object.  Therefore object X also assimilated more toward the object with the more accurately perceived location (when it is recollected that the perceived location of an object with a unique feature is relatively accurate).  So the assimilation-is-toward-accuracy outcome is supported.  There is more support:  When the task was to manually point to a comparable object X, the outcome was also comparable (van Zoest & Kerzel, 2015).

7. Premise D

Section 1 considered Premise D.  Premise D is that the accuracy of an object’s perceived (more precisely, encoded) location usually enables a similar (comparable) accuracy of its perceived features.  The present section supports Premise D in its subsections.

The present section finishes the support for assimilation-location theory’s account of the exogenous and endogenous results as follows.  First,  the target’s perceived location becomes more accurate per Section 3.  Second, this greater accuracy in perceived location was previously accounted for by supporting and applying Premises A-C (the account is in Section 1 and also in Section 6’s introduction).  Third, this greater accuracy in perceived location enables the target’s perceived features to also be more accurate per the present section’s Premise D.

Premise D is counter to feature integration theory’s claim that “features come first in perception” and subsequently “stimulus locations are processed serially” (Treisman & Gelade, 1980, p. 98).  This is because if, as Premise D supposes, the accuracy of an object’s perceived location usually enables a similar accuracy of its perceived features, it becomes more likely that an encoded location comes first in perception. 

The basic assimilation location result also counters feature integration theory’s claim.  First, this result means that a first object’s perceived location assimilates toward a second object’s perceived location.  Second, the first object’s features are perceived at the object’s assimilation-produced perceived location (the binding of features occurs), not at or about the first object’s physical location.  Third, hence the location of the first object’s perceived features is predicted by the assimilation-produced perceived location.  Fourth, the third point makes it more likely that location comes first in perception. 

That the basic assimilation in location result is evidence that supports location comes first in perception theory was not considered by papers that support this theory, for example, Cave (2001), Kovacs and Harris (2019), and van der Heijden (1993).  Aditionally, the evidence in Subsection 7.1 and Subsections 7.3-7.7 that supports location comes first in perception theory was also not considered in these papers.   

Much prior support for location comes first in perception theory has faced the problem that an experiment’s locations may only be more discriminable than its features (e.g. van der Heijden, 1993).   However, evidence that a factor that changes the accuracy of a perceived location also changes the accuracy of a perceived feature in Subsections 7.3-7.7 does not face this problem. 

7.1. The Accuracy of a Perceived Location Is Enabling

Section 6’s assimilation-is-toward-accuracy outcome is that an object’s perceived location is more likely to assimilate toward a more accurate perceived location than toward a less accurate perceived location in general.  Presumably this outcome is enabled by the accuracy of perceived (more precisely, encoded) locations.  Generalizing, it becomes more likely that the accuracy of an object’s perceived location also enables the accuracy of its perceived features, which is as Premise D maintains.  Thus Premise D is supported. 

7.2. Accurate Perceived Location, Hence Accurate Perceived Features

A perceived feature of an object was more accurate when this object’s perceived location was more accurate (e.g. Brouwer van der Heijden, 1997; Dick & Dick, 1969; Johnston & Pashler, 1990).  Also, there was essentially no indication that the identical object’s perceived location was more accurate when a perceived feature of this object was more accurate.  These results advise that an object’s more accurate perceived (more precisely, encoded) location enables its features to be perceived more accurately.  Hence Premise D is supported. 

7.3. Accurate Saccade Aim, Hence Accurate Perceived Location, Hence Accurate Perceived

Features

A result is that preparation for the accurate aim of a saccade toward a goal object was associated with a better detection of an object that appeared at the goal object’s location with a 20% chance than the detection of this object when it appeared instead at the fixation location with a 80% chance (Posner, 1980, pp. 16-17).  A similar result is that preparation for an accurate aim of a saccade toward a goal object was associated with a better successive discrimination between two objects that appeared at the goal object’s location with a 25% chance than the successive discrimination that occurred when these two objects appeared instead at a cued location with a 75% chance (Hoffman & Subramaniam, 1995).  A saccade’s more accurate aim toward an object’s location advises that this location is more accurately perceived by virtue of saccade-location-perceived-location evidence according to Section 2.  Hence these two results are evidence that a more accurately perceived location was associated with more accurately perceived features at this location.  Thus this more accurately perceived (more precisely, encoded) location may have enabled these more accurately perceived features.  Therefore Premise D is supported.

7.4. Accurate Perceived Features, Hence Accurate Perceived Location, Hence Additional

Accurate Perceived Features

Tasks that called for perceiving a feature of an object X made the perception of a feature of a close (near) simultaneously appearing object Y more accurate than the feature of a less close simultaneously appearing object Z (Hoffman & Nelson, 1981; Tsal & Lavie, 1988).  This result occurred with fixation on a central object.  The following interpretation of this result supports Premise D.

A first supposition is that the task to perceive a feature of object X resulted in an accurate perceived location of this object.  This supposition is supported by the inference in Subsection 2.3 that an accurately perceived (more precisely, encoded) feature of an object enables the accurate perception of its location.

A second supposition is that object X’s accurately perceived (more precisely, encoded) location enabled the accurate perception of object Y’s location but not object Z’s location.

A third supposition is that the accurately perceived (more precisely, encoded) location of object Y enabled the accurate perception of its features, which is the result to be explained.  Being explanatory, the third supposition is supported.

Also, the third supposition and Premise D are alike.  Hence Premise D is also supported.

7.5. Assimilation-Induced Inaccurate Perceived Location, Hence Inaccurate Perceived

Features: Same-Research Evidence

More support for Premise D stems from the occurrence of assimilation between perceived locations, as follows.  When a first object’s perceived location assimilates toward a second object’s perceived location, ordinarily the first object’s assimilation-induced perceived location is not its physical location.  Hence ordinarily an assimilation-induced perceived location is inaccurate.  Thus, according to Premise D, the first object’s assimilation-induced inaccurately perceived (more precisely, encoded) location enables a similar inaccuracy of its perceived features.  An ensuing prediction is that an object’s assimilation-induced inaccurately perceived location is associated with an inaccurate perception of its features.  This prediction is called the assimilation-features prediction.

The present subsection supports the assimilation-features prediction when the same research measures both the accuracy of an object’s perceived location and its features.  Because this prediction is underpinned by Premise D per the preceding paragraph, Premise D is also supported. 

A result is that multiple bars that were in different physical locations and appeared at about the same time as a saccade resulted in the perception of a single bar at the physical location of the goal object for the saccade (Morrone et al., 1997).  The perception of the bars at the goal object’s physical location is evidence that the bars’ perceived locations assimilated (by 100%) to the goal object’s physical location.  Hence the assimilation-induced perceived location of each bar was rather inaccurate.  The perception of the features of only one bar advises that the perceived features of the bars were also rather inaccurate.  Hence an association occurred between assimilation-induced inaccurately perceived locations of objects and the inaccurate perception of their features.   This association supports the assimilation-features prediction and thus also the underpinning Premise D. 

The just indicated association did not stem from the features of the four bars.  This is because when the four bars (hence their features) and the saccade occurred at less similar times, the perception of one bar at the location of the goal object did not occur.  Hence it becomes more likely that the just indicated association was enabled by the assimilation-induced inaccurately perceived (more precisely, encoded) location.  Thus Premise D is additionally supported. 

Related findings follow.  A line assimilated more toward the perceived location of a rectangle when the rectangle was closer to the line than less close per a judgment of location measure (Ganz, 1964).  Hence the line’s assimilation-induced perceived location was less accurate when the rectangle was closer to the line.  Also, the line’s perceived features were also less accurate when the rectangle was closer to the line per a detection measure.  Thus the assimilation-features prediction is supported and therefore also the underpinning Premise D. 

Also, when the line and rectangle were less close, the assimilation and the poorer detection did not occur.  Nevertheless, the features of the line and rectangle were the same.  Hence when the association between more assimilation and worse detection did occur, it was not because of features.  Thus, it becomes more likely that this association was enabled by the assimilation-induced inaccurately perceived (more precisely, encoded) location that occurred, which is more support for Premise D.

7.6. Assimilation-Induced Inaccurate Perceived Location, Hence Inaccurate Perceived

Features: Closeness Evidence

Support for the assimilation-features prediction supports Premise D per Subsection 7.5.  Accordingly, the present subsection also supports the assimilation-features prediction and thereby Premise D.   Recollecting, the assimilation-features prediction is that an object’s assimilation-induced inaccurately perceived location is associated with an inaccurate perception of its features.

An Outcome X is that a first object’s assimilation-induced perceived location is less accurate when a second object is physically closer (nearer) to it.  An Outcome Y is that a first object’s perceived features are also less accurate when a second object is physically closer to it.  Hence, together, Outcomes X and Y support the assimilation-features prediction.

Accordingly, the present section backs both Outcomes X and Y.  An ensuing explanation of Outcome Y is also indicated.  To be complete, qualifications of both Outcomes X and Y are also indicated. 

Outcome X (the assimilation, less accurate perceived location, and closer outcome) is backed as follows.  First, a first object assimilated more to the physical location of a second object when the second object was closer than less close per a judgment of the first object’s perceived location (Ganz, 1964) (the preceding subsection also indicates this).  Hence the first object’s assimilation-induced perceived location was less accurate when the second object was closer.  Second, more assimilation and less accuracy also occurred when a second object was closer per a reproduction measure (Rentschler et al., 1975).  Third, a saccade that was to be aimed at a first object tended to aim toward it but it also aimed toward a second object (McSorley et al., 2009).  In addition, the saccade aimed more toward the second object when it was closer to the first object instead of less close to it.  An analysis of a somewhat analogous result (van Zoest et al., 2012) is in Section 6.2.  This analysis advises that for the McSorley et al. results, the first object’s perceived location assimilated more toward the second object’s perceived location when the second object was closer.  Thus the first object’s  assimilation-induced perceived location was less accurate when the second object was closer.  Fourth, a result that is similarly interpretable is that a saccade’s aim was more likely to be toward a location that was in between the physical locations of two objects when they were closer than less close (Ottes, Van Gisbergen, & Eggermont, 1984). 

Now Outcome Y (the less accurate perceived features and closer outcome) is backed.  It is backed by arguably broad evidence that a first object’s perceived features are less accurate when a second and/or additional objects are closer to it rather than less close to it (e.g. Bouma, 1970; Eriksen & Hoffman, 1972; Flom, Weymouth, & Kahneman, 1963; Ganz, 1964 (as the preceding subsection also indicates); Parlee, 1969).  

The previously mentioned ensuing explanation of Outcome Y comes next.  Outcome X (that a first object’s assimilation-induced perceived location is less accurate when a second object is physically closer) has been supported.  Premise D (that the accuracy of an object’s perceived (more precisely, encoded) location usually enables a similar (comparable) accuracy of its perceived features) has also been supported.  Hence an explanation of Outcome Y, namely, that a first object’s perceived features are less accurate when a second object is physically closer, is that this lesser accuracy is enabled by the first object’s less accurate assimilation-induced perceived (more precisely, encoded) location that occurs when a second object is physically closer. 

The previously mentioned qualification of Outcome X is indicated.  It is that a first object does not consistently assimilate more to the location of a physically closer second object when the measure of the amount of assimilation is an absolute one.  For example, when the closeness between a first object and a second object is, say, 5 mm, the maximum absolute amount by which the first object can assimilate to the second object is only this 5 mm.  In contrast, the first object can assimilate to this second object by as much as 100% per a percentage measure. 

The previously noted qualification of Outcome Y is also indicated.  It is that a first object’s perceived features can be more accurate instead of less accurate when a first object’s location and a second object’s location are rather close including overlapping (Dresp & Bonnet, 1993; King, Mose, & Nixon, 1995; Novak & Sperling, 1963).  In addition, when or if the first object appeared alone, its features were or would be poorly perceived because, for example, its contrast was low. 

7.7. Assimilation-Induced Inaccurate Perceived Location, Hence Inaccurate Perceived

Features: Similarity between Features Evidence

The present subsection largely parallels Subsection 7.6.  Accordingly, the present section backs an Outcome X that a first object’s assimilation-induced perceived location is less accurate when the similarity between its features and a second object’s features is higher.  It also backs an Outcome Y that a first object’s perceived features are also less accurate when the similarity between its features and a second object’s features is higher.  Hence the assimilation-features prediction (that an object’s assimilation-induced inaccurately perceived location is associated with the inaccurate perception of its features) is supported.  Thus the underpinning Premise D is also supported.   Also, an ensuing explanation of Outcome Y is indicated.

Outcome X (the assimilation, less accurate perceived location, and higher similarity between features outcome) is backed.  One result is that a line assimilated more to the location of an adjacent rectangle when the line and rectangle’s colors were the same then when they were different per a judgment of location measure (Ganz, 1964).  Hence the line’s assimilation-induced perceived location was less accurate when the similarity between its features and the rectangle’s features was higher.  Thus Outcome X is backed.  Another result that was described in Section 5.2 is that a yellowish green object’s perceived location was less accurate than a red object’s perceived location when the color of a large number of simultaneously appearing additional objects was green per a choice of location measure (Zehetleitner et al., 2011b).  This lesser accuracy in perceived location presumably stemmed from the yellowish green object’s perceived location assimilating more to the perceived locations of the green objects than to the perceived locations of the red objects.  In conclusion, the yellowish green object’s assimilation-induced perceived location was less accurate when the similarity between features was higher.  Hence Outcome X is backed.   Another result is that a saccade that was to be aimed at a first object tended to aim toward the first object’s location, but it also aimed somewhat toward a same-color second object’s location and more so than to a different-color second object’s location (Findlay & Gilchrist, 1997).  An analysis of a somewhat analogous result (van Zoest et al., 2012) is in Section 6.2.  This analysis advises that for the Findlay and Gilchrist results, the first object’s perceived location assimilated more toward the same-color object’s perceived location than to the different-color object’s perceived location.  Hence the first object’s perceived location was less accurate when the second object was the same-color one.  The same-color object was the one with the more similar features.  In conclusion, the first object’s assimilation-induced perceived location was less accurate when the similarity between features was higher.  Therefore Outcome X is backed.

Outcome Y (the less accurate perceived features and higher similarity between features outcome) is also backed.   It is backed by the arguably broad evidence that a feature of a first object is perceived less accurately when the similarity between this feature and a feature on the same dimension of a second and/or additional objects is higher (e.g. Carter, 1982; Duncan & Humphreys, 1989; Fehrer, 1966; Harms & Bundesen, 1983; Ivry & Prinzmetal, 1991; Krueger & Chignell, 1985; Zehetleitner, Krummenacher, & Muller, 2009). 

The previously mentioned ensuing explanation of Outcome Y comes next.  Outcome X has been supported and Premise D remains supported.  Hence an explanation of Outcome Y’s first object’s less accurately perceived features is that it is enabled by the first object’s assimilation-induced less accurately perceived (more precisely, encoded) location. 

8. Review

Assimilation-location theory accounts for the exogenous and endogenous results’ outcome that the target’s perceived location becomes more accurate per both Section 1 and Section 6’s introduction.  Assimilation-location theory accounts for the exogenous and endogenous results’ outcome that the target’s perceived features become more accurate per both Section 1 and the preceding section.  Hence assimilation-location theory accounts for the exogenous and endogenous results.

This paper has supported additional statements including the following ones.  The location toward which a saccade aims and the currently perceived location are frequently approximately equivalent.  The cue produces a perceived location that mirrors the target’s physical location.  For the endogenous result, the cue-produced perceived location that mirrors the target’s physical location is enabled by a cognitive process.  The target’s perceived location is less accurate than the cue-produced perceived location.  An object’s perceived location is more likely to assimilate toward a more accurate perceived location than toward a less accurate perceived location.  The target’s perceived location assimilates toward the cue-produced perceived location.  The accuracy of an object’s perceived (more precisely, encoded) location usually enables a similar accuracy of its perceived features.  Location comes first in perception.

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