An Assimilation Process Arguably Enables Apparent Motion, the Accuracy of Perceived Features, Classical and Instrumental Conditioning, Fear Reduction in Young Animals by the Mother, Contrast, and Additional General Results

An Assimilation Process Arguably Enables Apparent Motion,

the Accuracy of Perceived Features, Classical and

Instrumental Conditioning, Fear Reduction in

Young Animals by the Mother, Contrast,

and Additional General Results

Donald L. King

donleeking@gmail.com

16192 W 66th Cir, Arvada CO, 80007

     The following paper is a completion of the previous post entitled Assimilation Enables Diverse Perceptions.  The paper was submitted to Psychological Review for publication in April 2023.

Abstract

A proposition:  A perception assimilates toward (becomes similar to) another perception which enables diverse general results.  Backing for this proposition includes support for the following statements.  Assimilation enables a perceived location to become similar to another perceived location.   Assimilation enables an average perceived location.  Assimilation of a less accurate perceived location toward a more accurate perceived location enables e.g. apparent motion.  Assimilation of the accuracy of perceived features toward the accuracy of their perceived location enables e.g. a briefly processed object’s less accurate perceived features.  Assimilation enables perceived locations to become similar when their perceived three-dimensional distances differ.  Assimilation of a perceived conditioned stimulus toward the retained perceived unconditioned stimulus enables the conditioned response.  Complete assimilation of a perceived response-correlated stimulus to a retained perceived response-correlated stimulus of a previous instrumental response enables the instrumental response to occur again.  Assimilation of a perceived response-correlated stimulus toward a retained perceived demonstrator’s response-produced stimulus enables delayed imitation.  Assimilation of a young animal’s perceived fear toward the perceived calmness produced by its mother’s stimuli enables its perceived fear to be reduced.  Assimilation enables contrast (dissimilarity) between perceptions.  Another proposition that is supported:  A perceived (more precisely, encoded) location enables diverse perceptions. 

 

Key words:  assimilation, location, conditioning, fear reduction, contrast

 

A proposition is that an assimilation process enables apparent motion, the accuracy of perceived features, classical and instrumental conditioning, fear reduction in young animals by the mother, contrast, and additional general results.  Assimilation is basically defined as occurring when a perception becomes similar to including the same as another perception.  Presumably assimilation is brought about by a single process of assimilation.  Here enables means essential to bringing about but that other factors may also contribute to the bringing about. 

Illustrative evidence of assimilation is that the violet of a rectangle and the green of a contiguous rectangle were perceived as one integrated color that could not be discriminated between (Eskew & Boynton, 1987).  The violet and green probably became sufficiently assimilated (similar) to each other that one color was perceived. 

Concentration is often also on a second proposition.  Put roughly, it is that a perceived location enables diverse perceptions.  Nevertheless, a perceived location is a consequence and hence cannot enable a perception.  Moreover, a location is often unlikely to be consciously perceived.  Even when two objects appear and viewing conditions are good, one object’s location may not be consciously perceived, one object’s location may be perceived less accurately, the assimilation that involves perceived locations that this article often considers may result in an assimilation-produced perceived location instead, features may be perceived instead, and there are other possibilities.  Hence it is more accurate to claim that an encoding for a perceived location, that is, neural information for a perceived location, enables another perception.  In addition, the encoding tends to result in a location that is perceived under some conditions.  Accordingly, the text will frequently indicate that an encoded-perceived (EP) location enables a perception.  This second proposition is largely consistent with Gogel’s (1990) theory of phenomenal geometry, as will be touched on. 

A summation is that this article supports the two propositions that an assimilation process and EP location enable diverse general results. 

This article is divided into the present Introduction and subsequent divisions.  Divisions are frequently divided into sections.  Divisions and sections are numbered in order to readily refer to them.  One section includes subsections. 

Divisions 1-3 and 5 involve the occurrence of assimilation between perceived locations.  Evidence that this assimilation occurs includes that an object’s perceived location becomes similar to (assimilates toward) the physical location of another object.  “Attraction” (e.g. Cicchini, Binda, Burr, & Morrone, 2013; Ganz, 1964; Li, Shim, & Cavanagh, 2014; Smith, 1954) and “spatial compression” (e.g. Born, Kruger, Zimmermann, & Cavanagh, 2016) are also said to occur.  Division 1 defines assimilation as occurring between EP (recollect, encoded-perceived) locations.  In accord, when this assimilation is involved, text will usually refer to an EP location including in this Introduction. 

Each of the following paragraphs touches on the gist of a single division. 

Division 1 provides evidence that assimilation between EP locations occurs.  It also reasons that assimilation between objects’ EP locations enables the perception of about the average of objects’ physical locations. 

Division 2 concludes that a less accurate EP location assimilates more than a more accurate EP location.  It also reasons that this more assimilation enables the binding of perceived features to a perceived location, apparent motion, and three more results. 

Division 3 concludes that an association (similarity) exists between the accuracy of a perceived location and the accuracy of perceived features at this perceived location.   It also supports the theory that this association is enabled by assimilation of the accuracy of perceived features to the accuracy of their perceived location.  For example, division 3 proposes that assimilation of the accuracy of perceived features toward the low accuracy of the EP location of a briefly processed singleton object enables the features at this location to be perceived less accurately. 

Division 4 supports the theory that two EP locations enable the perceived length of the interval that they flank. 

Division 5 speculates that assimilation enables a time-2 target’s less accurate EP location to become more similar to a cognitively sourced more accurate time-1 EP location that matches the physical location that a time-1 cue (nontarget) predicts.  The consequence is that the time-2 target’s perceived location and hence also its perceived features become more accurate.       

Division 6 reasons that assimilation enables an EP three-dimensional (3D) location to become similar to another EP 3D location in perceived 3D distance. 

Division 7 supports the theory that in classical conditioning, assimilation enables the conditioned stimulus (CS) to be perceived as similar to the retained perceived unconditioned stimulus (US).  Also, this perception of the CS results in the conditioned response (CR). 

Division 8 supports the theory that in instrumental conditioning, assimilation enables a perceived response-correlated stimulus to become very similar to (match) a retained perceived instrumental-response-correlated stimulus.  The occurrence of this match means that the instrumental response is executed again.

Division 9 supports the theory that in delayed imitation, assimilation enables a perceived response-correlated stimulus to become similar to a retained perceived stimulus produced by the demonstrator’s response and hence the imitated response occurs. 

Division 10 supports the theory that assimilation enables a young animal’s perceived fear to become similar to the perceived calmness produced by stimuli of the mother and hence its perceived fear is reduced. 

Division 11 indicates how assimilation may enable contrast.  Contrast essentially is a decrease in the similarity between the perceived parts of different objects.      

1. Assimilation Enables an EP Location

to Become Similar to Another EP Location  

This division begins by indicating a result that provides evidence that assimilation between EP (recollect, encoded-perceived) locations (positions) occurs, relating this evidence to a definition and theory of this assimilation, and pointing out that this assimilation supports the article’s two propositions than an assimilation process and EP location enable diverse general results.   (The Introduction highlights these propositions.)  The division touches on aspects of perceived location.  It supports the conclusion that the aim of a saccade is a measure of perceived location (this conclusion is subsequently relied on).  It supports the conclusion that assimilation between EP locations occurs (this assimilation is not only illustrated).  It supports the definition of assimilation between EP locations.  It supports the conclusion that assimilation between EP locations enables a perceived location that is about the average of objects’ physical locations.  This support means that this article’s two propositions are supported again.  The conclusion that assimilation is indeed between EP—not physical—locations is supported.  The conclusion that assimilation between EP locations occurs rapidly is supported. 

1.1.  Assimilation between EP Locations

A result that is evidence that assimilation between EP (encoded-perceived) locations occurs is described.  The relation of this type of evidence of assimilation between EP locations to a definition of this assimilation and a theory of it are covered. 

A result that is evidence that assimilation between EP locations occurs is that the perceived location of a line became similar to the physical location of an adjacent square per a judgment task (Ganz, 1964).  This result suggests that the perceived location of the line when it is also a singleton object became similar to (assimilated toward) the perceived location of the square when it is also a singleton object.  A singleton object is one that appears individually (alone). 

Nevertheless, the location of the line when it is a singleton object is probably usually not consciously perceived when the assimilation occurs.  A strong reason is that the line’s assimilation-produced location is probably often consciously perceived instead. 

Hence assimilation occurs between encoded locations that tend to be perceived under some conditions.  That is, assimilation occurs between EP locations.  Accordingly, the definition of assimilation between EP locations is that an EP location becomes similar to including the same as another EP location.  Also, both EP locations can become similar to each other.  Additionally, an assimilation-produced EP location (one that becomes more similar) often results in a consciously perceived location.  Accordingly, an assimilation-produced perceived location will often be referred to.   An implication of this definition is that encodings for perceived locations, that is, neural information for them, also becomes similar to each other. 

An ensuing theory of assimilation between EP locations is that an assimilation process enables an EP location to become similar to another EP location.  Hence both an assimilation process and EP location enable this assimilation.  Thus this article’s two propositions that an assimilation process and EP location enable diverse general results are supported.  

1.2.  Location and Direction

The definition and theory of assimilation between EP locations in section 1.1 assigns import to perceived location (position).  Accordingly, the present section supports this definition and theory with a bit of evidence of perceived location’s importance to visual perception.  This evidence is in the next three paragraphs.  Aspects of egocentric direction become relevant. 

Presumably, although not often explicitly stated, perceived location is basic to an understanding of visual perception.  A theory of perceived location is that it is frequently enabled by an egocentric direction and a perceived 3D distance (more precisely, an encoded egocentric direction and an encoded 3D distance).  Similar thinking is that a perceived location often results in the encoded (neural information of) egocentric direction and encoded 3D distance that determines this location. 

Support for the theory of perceived location comes from traditional explanations of the size constancy and Emmert’s Law results.  A drawing that is used to explain these results can have a tilted line between a point at the bottom of the drawing and an end point of a horizonal line that is at the top of the drawing.  The bottom point represents a midsagittal point of the body, the physical location of the end point of the horizontal line represents this end point’s perceived location, the tilt of the line represents an egocentric direction to the represented perceived location, and the length of the vertical interval from the bottom point to the horizontal line represents a perceived 3D distance to the represented perceived location.  These representations imply that together an egocentric direction and a perceived 3D distance enable the end point’s perceived location.  In addition, the end point’s perceived location is integral to an understanding of the line’s perceived length.

Support for the theory of perceived location also comes from Gogel’s (1990) evidence for his theory of phenomenal geometry.  Gogel states that “perceived space …  is specified in terms of … the perception of direction, the perception of distance,” (and also “the perception of the observer’s own position or motion”), p. 105, and “perceived space” essentially means perceived location.

The possibility that assimilation is between egocentric directions is thought unlikely.  A primary reason is that two objects in the same egocentric direction can be at different perceived 3D distances.

For most of the results that are covered, the relevant locations are at the same perceived 3D distance.  Hence the amount of a difference in egocentric direction and the amount of a difference in perceived location are usually very highly associated.  Consequently distinguishing between perceived location and egocentric direction will usually be deemphasized.

From now on egocentric direction will be called perceived direction. 

1.3 Terminology

The present section involves terminology. 

Assimilation between EP locations will be written about in different ways.  Consistent with a previous statement, an assimilation-produced perceived location will often be indicated to occur.  Also, an object will often be said to assimilate toward or to the EP location of a second object, and on occasion similar statements will be made.  “Assimilation” and “assimilates” will also be used to refer to assimilation between EP locations. 

A measure of the magnitude of assimilation between EP locations is the absolute amount of the difference between a physical location and an assimilation-produced perceived location.  Another measure of the magnitude of assimilation is this absolute amount divided by the maximum possible amount of this assimilation that can occur.  When the amount of assimilation between EP locations is considered subsequently, it will be the absolute amount.  Another measure of the magnitude of assimilation between EP locations is the frequency with which it occurs.  Accordingly, more, less, extent of, increase in, and decrease in assimilation will refer to both the absolute amount and frequency of assimilation. 

Text will state an “object” quite frequently.  Here an object usually means a physical entity that is relatively small with physical components (elements) that are relatively homogenous.  Examples of an object are both a dot and a rectangle.  An object is conceived of as tending to produce the perception of a location.  An object’s physical components also lead to the perception of features.  The perceived location of these features tends to be the object’s perceived location—binding of features occurs.

Here two objects mean an object like the one that the preceding paragraph describes and a second such object.  In addition, the elements (components) of these objects are spatially separated including not contiguous. 

Initial and subsequent objects will usually referred to as time-1 and time-2 objects. 

Both a target and a nontarget will frequently be referred to.  A target is an object whose location and/or features are task-relevant and hence often measured.  A nontarget is an object whose location and features are task-irrelevant and hence less likely to be measured. 

The proximity between physical locations will be referred to as near, less near, and the like.  Also, the proximity between perceived and EP locations will be referred to as close, less close, and the like. 

A perceived location and a physical location will sometimes not be explicitly distinguished between when it is likely that the perceived location is accurate.

1.4.  The Aim of a Saccade Is a Measure of Perceived Location

The aim (landing) of a saccade will be used as a measure of perceived location.  Accordingly, the current section supports the conclusion that the aim of a saccade is a measure.  Evidence for the conclusion will primarily be that an association exists between the aim of a saccade and traditional measures of perceived location.  The latency of a saccade and the momentary aim (trajectory) of a saccade will also be used as measures of perceived location, as the current section also considers.  Accordingly, this article will often indicate measures of perceived location that experiments employ and thereby sometimes inform that saccade and traditional measures of perceived location are associated. 

Because the saccade aim, saccade latency, and the momentary aim of a saccade measures will be used to indicate the occurrence of assimilation between EP locations, the assimilation-produced location of a target will often not be consciously perceived.   One reason is that a saccade is rapidly executed and is often quickly preceded and followed by other saccades.  A second is that often other objects appear at the same or slightly different times and one or more of their locations may be consciously perceived instead.  A third is that the momentary aim (trajectory) of a saccade quickly changes over time. 

The amount of a difference in perceived direction and the amount of a difference in perceived location are highly associated when perceived 3D distances are the same per section 1.2.  Hence the aim of a saccade, although directional in nature, can be a measure of perceived location. 

Evidence of an association between the aim of a saccade and traditional measures of perceived location comes next.  This association occurs per results from the same studies (Aitsebaomo & Bedell, 1992; Miller, 1980; van Heusden, Rolfs, Cavanagh, & Hogendoorn, 2018; Vishwanath & Kowler, 2003).  For example, the perceived location of a briefly retained target was relatively accurate per both the aim of a saccade toward its location and the reproduction of its location (Miller). 

The indicated association also occurs per the results of different studies.  The perceived location of a briefly processed target was relatively inaccurate per both the aim of a saccade toward the target (Aitsebaomo & Bedell, 1992) and additional measures of a target’s perceived location (Adam, Paas, Ekering, & van Loon, 1995; Atkinson & Braddick, 1989; Donk & Meinecke, 2001; Prinzmetal, 2005).  A perceived location approximated the unweighted average of two objects’ physical locations per the aim of a saccade toward this average location (Coren & Hoenig, 1972; Findlay, 1982; Van der Stigchel & Nijboer, 2013) and per the reproduction of this average location (Hazeltine, Prinzmetal, & Elliott, 1997). 

The latency of a saccade will also be used as a measure of perceived location.  One reason is that a faster saccade implies that less time is needed for an accurate perceived location to occur.  A second reason is evidence that the latency of a saccade and traditional measures of perceived location are associated.  Evidence follows.  A target assimilated toward the EP location of a nontarget with the same color more than toward the EP location of a nontarget with a different color per both the latency of a saccade that aimed at the target and a choice of location measure (Ludwig & Gilchrist, 2002).  A target’s perceived location was less accurate when a target’s and a nontarget’s physical locations were nearer per the latency of the aim of a saccade toward the target (McSorley, Cruickshank, & Inman, 2009; Theeuwes, Kramer, Hahn, Irwin, & Zelinsky, 1999 (a control condition result)) and also per both the judgment of location (Ganz, 1964) and reproduction of location (Rentschler, Hilz, & Grimm, 1975).  A time-2 target’s perceived location was more accurate when it appeared by chance in about the same physical location as a time-1 nontarget per both the latency of the aim of a saccade toward the time-2 target (Adler, Bala, & Krauzlis, 2002) and choice of location measures (Donk & Soesman, 2010; Joseph & Optican (1996). 

The momentary aim (trajectory) of a saccade that occurs while it is being executed will also be used as a measure of perceived location.  Evidence for this use follows.  An instruction was to saccade toward a target (McSorley et al., 2009; McSorley, Haggard, & Walker, 2006; Mulckhuyse, Van der Stigchel, & Theeuwes, 2009; van Zoest & Kerzel, 2015).  A nontarget also appeared.  It turned out that the saccade’s momentary aim deviated toward the nontarget’s physical location.  An interpretation is that the target’s EP location assimilated toward the nontarget’s EP location, and the saccade’s momentary aim was toward the target’s momentary assimilation-produced perceived location (more precisely, EP location, because this assimilation-produced location was almost certainly not consciously perceived).  Hence there is support for using a saccade’s momentary aim as a measure of perceived location.  More support for this use follows.  First, a manual response also momentarily aimed toward a nontarget’s physical location (van Zoest & Kerzel, 2015).  Second, nearer physical locations of a target and a nontarget resulted in a less accurate perceived location of the target per the momentary aim of a saccade (McSorley et al., 2009), the aim (not momentary) of a saccade (McSorley et al., 2009), the latency of a saccade (Theeuwes et al., 1999 (a control condition result)), judgment of location (Ganz 1964), and reproduction of location (Rentschler et al., 1975). 

1.5. Assimilation between Perceived Locations Occurs

In agreement with section 1.1’s definition of assimilation between EP locations and its illustration of evidence of this assimilation, evidence that this assimilation occurs includes the result that an object’s perceived location becomes similar to another object’s physical location. 

This result occurs (Ganz, 1964; Maddox, Prinzmetal, Ivry, & Ashby,1994; Prinzmetal, 2005; Rentschler et al., 1975).  For example, a target vertical line assimilated toward (became similar to) the physical location of a nontarget vertical line per a reproduction of location measure Rentschler et al.  An analogous result occurs with diplopic percepts (Rose & Blake, 1988; Werner, 1937).

This result also occurs when a target and a nontarget onset at different times (Born, Kruger, Zimmermann, & Cavanagh, 2016; Cicchini et al., 2013; Eagleman & Sejnowski, 2000; Morrone Ross Burr, 1997; F. Ono & Watanabe, 2011; Smith, 1954; Yoshida 1952-1953, as cited in Sagara and Oyama, 1957).  For example, F. Ono and Watanabe’s results suggest that each of two time-1 vertical lines assimilated toward the physical location of a time-2 nearer disk when the stimulus onset asynchrony (SOA) was 200 ms per a judgment measure. 

A note is that assimilation between EP locations is associated with the binding of features.  This is because the perceived location of an object’s perceived features is frequently the same as the object’s assimilation-produced perceived location instead of the same as the object’s physical location.  This binding is vouched for by the way that an assimilation-produced perceived location is often measured.  For example, the task to move “the screen cursor (with the mouse) to the location of the small target dot” (Prinzmetal, 2005, p. 65) implies that the perceived features of this dot were at the dot’s perceived location. 

1.6.  Support for the Definition of Assimilation between EP Locations

The definition of assimilation between EP locations is supported.  The definition of assimilation between EP locations in section 1.1 is basically that an EP location becomes similar to including the same as another EP location and it results in an assimilation-produced perceived location.  Per this definition, although an assimilation-produced perceived location can become the same as a second perceived location, it can never proceed to become less similar to it.  Likewise, when a green color assimilates toward a yellow color, the green color never becomes orange.  The definition is supported because a target’s perceived location became very similar to including the same as a nontarget’s physical and hence presumably perceived location but did not proceed to become less similar to the nontarget’s physical location per reproduction and judgment measures (Born et al., 2016; Cicchini et al., 2013; Morrone et al., 1997). 

The definition of assimilation between EP locations is additionally supported.  The definition means that when two EP locations are rather close (similar), the absolute amount of assimilation between EP locations that can possibly occur is rather small.  For example, per the definition, when a target’s and a nontarget’s EP locations are 4 and 5, respectively, then the maximum absolute amount of the target’s assimilation toward the nontarget’s EP location that is possible is 5 – 4 = 1 and hence relatively small, but when these EP locations are 1 and 5, then this maximum absolute amount is 5 – 1 = 4 and hence relatively large.  The definition is supported, because when the physical locations of two objects were rather near and hence when their EP locations were rather close, a relatively small absolute amount of assimilation between EP locations occurred per results of Born et al. (2016) and McSorley et al. (2009).  One result is that a 2 deg difference between a target’s and a nontarget’s physical location resulted in less than half of the absolute amount of the target’s assimilation toward the nontarget’s physical location than a 6 deg difference per a reproduction measure (Born et al. (figure 1D)). 

1.7.  Assimilation between EP Locations Enables a Single Unweighted Average Perceived

Location 

The current section supports the conclusion that assimilation between two EP locations often and readily enables a single perceived location that is an approximate unweighted average of two physical locations.  Presumably each EP location is relatively accurate.  Also, because the average is unweighted, each EP location is assumed to assimilate toward the other EP location to the same extent.  An ancillary supposition is that the two EP locations become sufficiently assimilated (similar) to each other that an average of these locations and hence a single perceived location occurs instead.  This sufficient similarity supposition is supported by the result that different perceived features can also be perceived as a single feature.  For example, two colors resulted in a single integrated perceived color (Eskew & Boynton, 1987), as was indicated at this article’s outset. 

This assimilation-based conclusion underlies an explanation of the result that two objects eventuate in a single perceived location that is an about unweighted average of their physical locations.  This result occurred per the findings of Coren and Hoenig (1972), Hazeltine et al. (1997), and Van der Stigchel and Nijboer (2013) according to section 1.4.  One section 1.4 result was that when a target and nontarget were moderately near and a saccade was initiated upon the target’s and nontarget’s onset, the saccade aimed toward an about unweighted average location (Coren & Hoenig).  According to the assimilation-based conclusion, the EP locations of the target and nontarget assimilated.  This putative assimilation is likely to have occurred because a moderate nearness tends to result in more assimilation between EP locations per section 2.6, and so does the brief processing that occurs when a saccade is initiated upon a stimulus’s onset per section 2.1.  Also, the aim of a saccade is a measure of perceived location per section 1.4.  The sufficient similarity supposition then accounts for the single perceived location that occurred.  Because the conclusion, including the ancillary sufficient similarity supposition, are explanatory, they are supported. 

The conclusion also claims that the single unweighted average perceived location occurs often and readily.  This claim is supported by the result that a saccade aimed toward about an unweighted average of the physical locations of a target and a nontarget even though the instruction was to fixate or move the eyes to the target (Coren & Hoenig, 1972; Van der Stigchel & Nijboer, 2013). 

The assimilation-based conclusion also underlies an explanation of the single unweighted average perceived location that occurs when the two eyes’ perceived locations are different.  A relatively large disparity tends to result in two eyes’ perceived locations that are different, as is revealed by the diplopic percepts that both an object in space (Vieth, 1818, as cited in Howard, 2002) and dichoptic objects (Wheatstone, 1838, as cited in Howard, 2002) result in.  In addition, a relatively small disparity tends to frequently and readily result in a single perceived location that is an unweighted average of the two eyes’ different perceived locations.  The two eyes’ perceived locations can also be different because two objects are in different physical locations in space and it is arranged for each object to be viewed by one eye (Hering, 1879; Le Conte, 1871; Wells, 1792, as cited in Ono & Mapp, 1995).  In addition, when these objects are viewed binocularly, the result is a frequently and readily perceived single location that is an unweighted average of the two physical locations.  Per this section’s assimilation-based conclusion, including the ancillary sufficient similarity supposition, the two eyes’ different EP locations assimilate hence enabling a single unweighted average perceived location.  The conclusion is supported, because prototypical assimilation between the two eyes’ different EP locations also occurs per results of Rose and Blake (1988) and Werner (1937), and because this assimilation makes it more likely that assimilation between the two eyes’ different EP locations can also enable a single unweighted average perceived location. 

The assimilation-based conclusion accounts for a related result.  A task was essentially to indicate the unweighted average of the physical locations of two lines as well as possible.  The result was that the perceived average of these locations was extremely accurate (Klein & Levi, 1985; Westheimer, Crist, Gorski, & Gilbert, 2001).  Presumably the extreme accuracy was enabled by assimilation between the EP locations of the two objects and a match between the ensuing single unweighted average perceived location and the unweighted average of the two physical locations.  In addition, the extreme accuracy implies that a single unweighted average perceived location occurs often and readily. 

1.8.  Assimilation between EP Locations Enables a Single Weighted Average Perceived

Location 

The current section supports the conclusion that assimilation between two EP locations often and readily enables a single perceived location that is a weighted (not unweighted) average of two corresponding physical locations.  A weighted average perceived location is closer to one of the physical locations than the second.  A claim that accords with the conclusion is that the single weighted average perceived location can be the same as one of the two physical locations; the two weights can be 0% and 100%.   Presumably the two EP locations are relatively accurate.  Also, because the average is weighted, presumably the two EP locations assimilate toward each other by unequal (not equal) extents.  In addition, one EP location may completely assimilate to a second EP location to result in 100% assimilation.  The conclusion also invokes the preceding section’s sufficient similarity supposition:  The assimilation between the two EP locations makes them sufficiently similar that a single average location is perceived instead. 

The conclusion explains single weighted (not unweighted) average perceived location results.  Such results occur per findings of Findlay (1982), Findlay and Gilchrist (1997), and Morrone et al. (1997).  One finding is that a saccade aimed at the weighted average of the physical locations of two objects contrary to the instruction that one of these objects was the target (Findlay & Gilchrist).  Recollecting, this aim is evidence that the perceived location is the one at which the saccade aims per section 1.4.  Because the finding was contrary to the instruction, it is also evidence that a single weighted average perceived location occurs often and readily.  The conclusion maintains that the two objects’ EP locations assimilated toward each other to unequal extents, and the sufficient similarity supposition accounts for the eventuating single perceived location.  Because the conclusion explains these single weighted average perceived locations, it is supported. 

Another weighted average perceived location result occurs when dichoptic objects produce disparity (Mansfield & Legge, 1976).  For example, stereoscopic viewing of dichoptic low luminance and high luminance objects that produced disparity resulted in a single perceived location that was closer to the high luminance object’s monocularly perceived location (Verhoef, 1933, as cited in Mansfield and Legge).  Per the conclusion, the disparity resulted in EP locations for the two eyes that were different, these locations assimilated, and a single weighted average perceived location eventuated.

1.9.  Assimilation between EP locations That Derive from Multiple Physical Points

Enables a Single Unweighted Average Perceived Location

The current section provides evidence that the single location of the approximate center of an angle or typical regular shape is perceived.  This result is called the perceived-center–location result.  The current section also provides an explanation of the perceived-center-location result.  The explanation maintains that this result is enabled by assimilation between EP locations that derive from multiple physical points. 

The perceived-center-location result occurs (He & Kowler, 1991; Henderson, 1993; Kaufman & Richards, 1969; Melcher & Kowler, 1999; Nuthmann & Henderson, 2010; Vishwanath & Kowler, 2003).  For example, when the task was to aim a saccade at the “target as a whole,” the saccade aimed at approximately the center of the target of a square ring (Vishwanath & Kowler).  Also, when the task was to align an object with the position of the square ring, the object was aligned to about the center of the square ring. 

The perceived-center-location result is thought to occur often and readily.  One reason is that there are multiple additional locations of angles and typical regular shapes that might be perceived instead.  

The explanation of the perceived-center-location result uses a circle for exposition.  Assimilation between two rather close EP locations results in a rather small extent of assimilation between them per section 1.6.  Because an EP location ordinarily approximates the physical location from which it derives, two near points on the circumference of a circle should result in a rather small extent of assimilation between their EP locations.  Hence the explanation disregards these near points.  Two points on the circumference of a circle that are on its opposite sides such as a circle’s top and bottom points are less near.  Thus the EP locations of two opposite-side points result in a rather large extent of assimilation between them.  This is the case for multiple pairs of opposite-side points.  This assimilation is taken to be unweighted.  The sufficient similarity supposition that section 1.7 introduced is also invoked.  Accordingly, the EP locations of two opposite-side points are claimed to become sufficiently assimilated (similar) to each other that an unweighted average of these locations hence a single perceived location eventuates.  Also, this is the case for multiple pairs of opposite-side points.  The unweighted average of two opposite-side points is the circle’s center.  In conclusion, unweighted assimilation between the two EP locations of multiple pairs of opposite-side points enables the perceived location of the circle’s center.  Generalizing, assimilation between two less close EP locations of multiple pairs of opposite-side points of lines of angles and perimeters of typical regular shapes often enables a single approximately unweighted average perceived location that approximates the center of these objects.

1.10. Assimilation Is Indeed between EP Locations

The definition of assimilation between EP locations in section 1.1 is basically that an EP location becomes similar to another EP—not physical–location.  The current section supports this EP location aspect of the definition.  The support comes now because it relies on the preceding section’s perceived-center-location result and its explanation. 

Support is that the perceived location of a small object that was inside of a circle became similar to the physical location of the circle’s center (Denisova, Singh, & Kowler, 2006).  In addition, a physical object did not appear at the circle’s center.  This result is support, because an EP location that is the circle’s center may have occurred per the preceding section’s explanation of the perceived-center-location result, and hence the small object could have assimilated toward this EP—not physical—location.  More support comes from the corresponding result that the perceived location of a dot that was near to a side of a Kanizsa square was toward the square’s center (Guttman & Kellman, 2004; Pomerantz, Goldberg, & Golder, 1981). 

1.11.  Assimilation between EP Locations Occurs Rapidly

The conclusion that assimilation between EP locations occurs rapidly is supported. 

The rapidity of assimilation between EP locations makes it more likely that an assimilation-produced perceived (more precisely, encoded) location enables other perceptions.  This is because other perceptions probably occur more slowly. 

Support for the conclusion that assimilation between EP locations occurs rapidly is that a saccade rapidly aimed toward about the average of the physical locations of two objects (Findlay, 1982; Findlay & Gilchrist, 1997; Heeman, Van der Stigchel, & Theeuwes, 2017; Van der Stigchel & Nijboer, 2013).  This result is support, because a single average perceived location is enabled by assimilation between EP locations per sections 1.7-1.9.  The saccade latency was as fast as about 135 ms (Findlay). 

The momentary aim (trajectory) of a saccade that is toward a nontarget instead of toward a target is evidence that the target assimilates toward the nontarget’s EP location per section 1.4.  Hence a rapid momentary aim of a saccade toward a nontarget also supports the conclusion that assimilation between EP locations occurs rapidly.  This momentary aim was in fact rapid (McSorley et al., 2009; McSorley et al., 2006; van Zoest, Donk, & Van der Stigchel, 2012; van Zoest & Kerzel, 2015).  For example, latencies were as fast as about 160 ms (van Zoest & Kerzel) (and about 210 ms for the aim of a manual response).  

2. Assimilation Enables Diverse Results

Because a Less Accurate EP Location Assimilates More

This division supports the conclusion that a less accurate EP location assimilates toward another EP location more than a more accurate EP location does.  This conclusion is called the less–accurate-EP-location-more-assimilation conclusion.  This conclusion is supported by results indicating that factors that make a singleton object’s perceived location less accurate often also result in an object assimilating more toward another EP location.  There is support, because presumably an object’s EP location continues to be less accurate when it assimilates toward another EP location. 

This division also relies on the less-accurate-EP-location-more-assimilation conclusion for explanations of the binding of features to a perceived location, apparent motion, the result that nearer physical locations of objects often result in more assimilation between the objects’ EP locations, the result that more similar features of objects often result in more assimilation between the objects’ EP locations, and the result that a time-1 nontarget often makes a less accurate time-2 target’s perceived location become more accurate when the time-1 EP location and the time-2 physical location match by chance.  Because the less-accurate-EP-location-more-assimilation conclusion is relied on for these explanations, it is additionally supported. 

Because the less-accurate-EP-location-more-assimilation conclusion is relied on for explanations of these results, this article’s proposition that an assimilation process enables diverse general results is also supported.  Because the processes underlying the accuracy of perceived location and perceived location itself should be closely related, this article’s proposition that EP location enables diverse general results is also supported.

The support for the less-accurate-EP-location-more-assimilation conclusion is in sections 2.1-2.3.  The explanations are in sections 2.4-2.8.

2.1.  Brief Processing Makes a Singleton Object’s Perceived Location Less Accurate and

Results in More Assimilation

In accord with this division’s opening paragraph, the current section supports the less-accurate-EP-location-more-assimilation conclusion with evidence that brief processing makes a singleton object’s perceived location less accurate and evidence that brief processing results in more assimilation between EP locations. 

Brief processing of an object tends to occur when its duration is relatively short, when the stimulus onset asynchrony (SOA) between it and a time-2 object is relatively short, and when the response to the object is relatively fast. 

Singleton-object perceived location evidence for the less-accurate-EP-location-more-assimilation conclusion is that briefer processing made a singleton target’s perceived location less accurate per the aim of a saccade toward it (Aitsebaomo & Bedell, 1992) and per a manual aim toward it (Adam, Paas, Ekering, & van Loon, 1995).  Also, briefer processing made a peripheral target’s perceived location less accurate per the reproduction of its location when a central target for a different task was also present (Prinzmetal, 2005). 

Assimilation evidence for the less-accurate-EP-location-more-assimilation conclusion is the result that a time-2 target’s perceived location was almost the same as a time-1 nontarget’s physical location when the time-2 target’s duration was 20 ms and was near to its own physical location when its duration was 100 ms per a reproduction of location measure (Born et al., 2016).  This result is evidence, because the perceived location of the 20-ms duration time-2 target is explained as follows.  The time-2 target’s 20 ms duration resulted in a less accurate EP location, this location almost completely assimilated toward the time-1 nontarget’s EP location, and hence the time-2 target’s assimilation-produced perceived location was close to the nontarget’s physical location.  In addition, this almost complete assimilation means that at best the time-1 nontarget hardly assimilated toward the time-2 target’s EP location. 

More assimilation evidence for the less-accurate-EP-location-more-assimilation conclusion is the result that the aim of a saccade was closer to the average of the locations of a target and a nontarget when the latency of the saccade was faster (Bucker, Belopolsky, & Theeuwes, 2015; Findlay & Gilchrist, 1997; McSorley et al., 2009).  One reason for this support is that, recollecting, the aim of a saccade toward a location can indicate the location’s perceived location per section 1.4.  A second reason is that a single average perceived location is enabled by assimilation between EP locations per sections 1.7-1.9.  A third reason is that the faster latency indicates that the processing was briefer. 

2.2.  Lower Luminance Makes a Singleton Object’s Perceived Location Less Accurate

and Results in More Assimilation

The less-accurate-perceived-location-more-assimilation conclusion is supported in the same way as in the preceding section with a lower luminance object in place of a more briefly processed one.   

Singleton-object perceived location support for the less-accurate-perceived-location-more-assimilation conclusion is that a lower luminance made a singleton target’s perceived location less accurate per results of Doma and Hallett (1988), Heeman, Van der Stigchel, Munoz, & Theeuwes (2019), and Reuter-Lorenz, Hughes, and Fendrich (1991).  Heeman et al. varied the location of a singleton disk over trials and instructed participants to quickly make an eye movement toward it.  A lower luminance singleton disk resulted in a saccade that was less accurate and slower, which attests to this disk’s less accurate perceived location. 

Assimilation support for the less-accurate-perceived-location-more-assimilation conclusion is that a lower luminance line assimilated toward the EP location of a higher luminance line per a reproduction measure according to results of Rentschler et al. (1975).  In addition, the preceding paragraph’s evidence advises that the lower luminance line’s EP location was less accurate when the higher luminance line was also present.  More assimilation support is that a time-2 low contrast target bar assimilated toward the EP location of a time-1 nontarget bar more than did a time-2 high contrast target bar per a reproduction measure according to results of Born et al. (2016). 

More assimilation support is that a lower luminance dichoptic object assimilated toward a higher luminance dichoptic object’s EP location more than vice versa on the basis of Verhoef’s (1933) result that was considered in section 1.8. 

2.3.  A Less Foveal Retinal Image Makes a Singleton Object’s Perceived Location Less

Accurate and Results in More Assimilation

The less-accurate-perceived-location-more-assimilation conclusion is supported for a less foveal retinal image in the same way as for a more briefly processed and a lower luminance object.  Here a less foveal retinal image occurs when an object is more eccentric (peripheral).  The object is said to be less foveal.

Singleton-object perceived location support for the less-accurate-EP-location-more-assimilation conclusion follows.  A less foveal singleton object’s perceived location was less accurate than a more foveal singleton object’s perceived location per reproduction (Adam, Huys, van Loon, Kingma, & Paas, 2000), manual aim (Adam et al., 1995), and both judgment and manual aim (Ma-Wyatt & McKee, 2006) measures of perceived location. 

Assimilation support for the less-accurate-perceived-location-more-assimilation conclusion follows.  The perceived location of a less foveal horizontal target bar became similar to the vertical location of two flanking horizontal nontarget bars per a judgment measure (Greenwood, Bex, & Dakin, 2009).  Hence the nonfoveal target probably assimilated toward the vertical EP location of the nontargets.  Another result is that a small object was more likely to be inaccurately perceived at the vertical contour of the side of a square or edge of a strip that was more foveal than at the vertical contour that was less foveal (Chastain, 1982; Wolford & Shum, 1980).  Presumably the small object was more likely to assimilate toward the more accurate EP location of the more foveal contour than toward the less accurate EP location of the less foveal contour, perhaps in part because the less foveal contour’s EP location was also less accurate and hence also assimilated more.  Another result is that a spot’s perceived location became similar to a point’s physical location by a greater extent when it was less foveal than more foveal (Mateeff & Gourevich, 1983).  The point was foveal, fixated, and at the average horizontal location of a ruler-like stimulus.  Hence the spot’s perceived location was most likely less accurate than the point’s perceived location.  Thus the spot assimilated toward the more accurate EP location of the point and by a larger extent when the spot was less foveal and therefore when’s its perceived location was less accurate.  Another result is that two near dots resulted in one perceived location when they were less foveal and two perceived locations when they were more foveal (Thorson, Lange, & Biederman-Thorson, 1969).  A single perceived location was attributed to assimilation between two EP locations in sections 1.7-1.8.  Thus an explanation is that the less foveal dots resulted in more assimilation between their EP locations and therefore were also more likely to result in one perceived location. 

Less foveal retinal images that are due to disparity are more likely to result in a single average perceived location instead of the two perceived locations of diplopic percepts than are more foveal retinal images (Howard, 2002, p. 273).  The preceding paragraph’s explanation of the Thorson, Lange, and Biederman-Thorson (1969) result applies because diplopic percepts and two perceived near dots are alike. 

2.4.  Binding of Features:  A Feature’s EP Location is Less Accurate, It Completely 

Assimilates to Its Object’s More Accurate Perceived Location, and Hence Binding Occurs

The current section provides an explanation of the binding of features.  It relies on the present division’s less-accurate-perceived-location-more-assimilation conclusion that sections 2.1-2.3 supported. 

The explanation follows.  A claim is that early in the processing for the perception of an object, the object results in a more accurate EP location than the EP locations of its individual features.  This claim is supported by the seemingly reasonable possibility that the totality of an object’s stimulus brings about its more accurate perceived location.  Another claim is that the encoding for a feature and the encoding for a feature’s location are neurally connected.  A critical claim is that each feature’s less accurate EP location completely assimilates to (becomes the same as) the object’s more accurate EP location.  This claim is supported by the less-accurate-perceived-location-more-assimilation conclusion.  Because each encoded feature is neurally connected to an encoded location, each feature is also at the object’s more accurate perceived location.  Hence the binding of features occurs.  Lastly, this explanation applies to an object’s assimilation-produced location in that this location is conceived of as having been established. 

2.5.  Apparent Motion:  An EP Location Is Less Accurate and It Assimilates toward

a More Accurate EP Location 

The current section supports an account of apparent motion.  The account relies on this division’s less-accurate-perceived-location-more-assimilation conclusion. 

2.5.A.  The Account

The account of apparent motion claims that earlier in the time course of apparent motion, the time-1 object’s EP location is more accurate than the time-2 object’s EP location.  It also claims that earlier in this time course, the time-2 EP location assimilates toward the time-1 EP location.  This latter claim is supported by this division’s less-accurate-perceived-location-more-assimilation conclusion. 

The account also claims that the weighted averaging type of assimilation between EP locations occurs early in the time course of apparent motion.  This type was considered in section 1.8.  Consistent with this claim, the assimilation of the time-2 EP location toward the time-1 EP location results in a single weighted average location that is close to the time-1 EP location.   This single weighted average location will also be called an EP location because ordinarily apparent motion is consciously perceived instead. 

The account also claims that later in the time course of apparent motion, the time-1 EP location is less accurate than the time-2 EP location.  It also claims that later in this time course, the time-1 EP location assimilates toward the time-2 EP location.  This latter claim is also supported by the less-accurate-perceived-location-more-assimilation conclusion. 

The account also claims that the weighted averaging type of assimilation between EP locations also occurs later in the time course of apparent motion.  Because the time-2 EP location is now more accurate, this claim means that the single average weighted location is close to the time-2 EP location.  This single average weighted location will also be called an EP location. 

The account also claims that the change in the assimilation-produced single weighted average EP location from the time-1 location to the time-2 location during the course of apparent motion is the immediate enabler of apparent motion including that it starts at the time-1 location and proceeds to the time-2 location.  This claim is supported by the theory that a rapid change in EP location enables perceived motion in general.  This theory is called the EP-location-enables-perceived-motion theory.  It is largely consistent with the theory of phenomenal geometry (Gogel, 1990).  It is supported because it helps to explain apparent motion.  It will be additionally supported in subsection 2.5.D.  Hence this article’s proposition that EP location enables diverse general results is also supported.

It is known that apparent motion is associated with assimilation between the perceived features of the time-1 and time-2 objects.  Hence by generalization this assimilation between features supports the account’s claimed assimilation between EP locations.  The account is now additionally supported. 

2.5.B.  Support for the Account for Earlier during the Time Course of Apparent Motion

The account’s claims for earlier during the time course of apparent motion are supported. 

The account’s claim that earlier during the time course of apparent motion the time-1 perceived location is more accurate is supported.  First, earlier during this time course, the time-1 object is processed for a longer time than the time-2 object, because the time-2 object has hardly begun to be processed.  Second, a longer processing time frequently results in a more accurate perceived location per section 2.1.  Hence the claim is supported.

The same claim is also supported because an explanation of an apparent motion result is similarly based on the accuracies of the perceived locations of time-1 and time-2 objects.  The result is that when the time-2 object’s luminance was higher than the time-1 object’s luminance, apparent motion started at about the physical location of the time-2 object instead of at the physical location of the time-1 object (Korte, 1915, as cited in Anstis, 1970).  The perceived location of a higher luminance object is more accurate per section 2.2.  Hence in accord with the less-accurate-EP-location-more-assimilation conclusion, early in the time course of apparent motion the lower luminance time-1 object’s less accurate EP location assimilated toward the higher luminance time-2 object’s more accurate EP location.  The account’s claimed single weighted average perceived location would then be initially close to the higher luminance time-2 object’s EP location, meaning that the apparent motion would start at about this location, as to be explained.

The same claim is also supported because an explanation of another apparent motion result is similarly based on the accuracies of perceived locations.  Two flashes alternated in time of occurrence.  Briefer stimulus durations of the two flashes, for example, 10 ms, resulted in less optimal apparent motion than longer stimulus durations, for example, 90 ms (Neuhaus, 1930, as cited in Kolers, 1972; Kolers, 1964).   The briefer stimulus durations mean that a preceding flash was more briefly processed.  Hence, per section 2.1, the preceding flash’s EP locaton was less accurate.  Thus the succeeding flash was less likely to assimilate toward the EP location of the preceding flash.  Therefore, per the account of apparent motion, apparent motion would be less optimal, completing the explanation.  The same claim is also supported by the result that a briefer stimulus duration (24 ms) resulted in more optimal apparent motion when the interstimulus interval between the two flashes was longer (Kolers, 1964).  The key to this result’s explanation is that the longer interstimulus interval made the preceding flash’s EP location more accurate.

The account’s claim that earlier in the time course of apparent motion the time-2 EP location assimilates toward the time-1 EP location is also supported.  Support is that assimilation toward a time-1 EP location also occurred per results of Born et al. (2016), Morrone et al. (1997), and Yamada, Kawabe, and Miura (2008). 

The account’s claim that the assimilation of the time-2 EP location toward the time-1 EP location results in a single weighted average perceived location is also supported.  Support is that a time-2 object’s EP location completely or almost completely assimilated to a time-1 object’s EP location, that is, resulted or nearly resulted in a single perceived location, per results of Born et al. (2016) and Morrone et al. (1997). 

The account’s claim that the perception of apparent motion occurs at about the same moment as the assimilation of the time-2 EP location toward the time-1 EP location is also supported.  A time-1, time-2, and a time-3 disk were all in a row (Li, Shim, & Cavanagh, 2014).  Apparent motion was readily perceived.  In addition, the disks themselves were perceived.  Hence their perceived locations could be determined.  It turned out that the time-2 disk’s perceived location was toward the time-1 disk’s perceived location per a judgment measure (“position attraction” was said to occur).  Hence apparent motion was perceived and there is evidence that assimilation toward the time-1 EP location occurred at about the same moment.  Therefore the claim is supported. 

2.5.C.  Support for the Account for Later during the Time Course of Apparent Motion

The account’s claims for later during the time course of apparent motion are supported.

The account’s claim that later during the time course of apparent motion the time-2 EP location becomes more accurate than the time-1 EP location is supported.  First, later during the time course of apparent motion the processing of the time-2 object is longer.  Second, hence the time-2 object’s EP location becomes more accurate per section 2.1. 

The same claim is additionally supported.  A target and a nontarget appeared simultaneously, and when a saccade was faster it aimed (landed) toward the nontarget and when it was slower it aimed toward the target (Donk & van Zoest, 2011).  This result is evidence that a slightly longer time interval was associated with a rapid decrease in the accuracy of the nontarget’s perceived location.  Another result:  A target and a nontarget appeared simultaneously, and when a saccade was faster it momentarily aimed toward (its trajectory was toward) the nontarget more than when it was slower (van Zoest et al., 2012).  This result is also evidence that a slightly longer time interval was associated with a rapid decrease in the accuracy of the nontarget’s perceived location.  Generalizing, a slightly longer time interval can make an object’s perceived location less accurate when a second object is present.  Hence for apparent motion, a slightly longer time interval since the time-1 object’s onset may make its EP location less accurate than the time-2 object’s EP location.  Thus the claim is supported. 

The account’s claim that later in the time course of apparent motion, the time-1 EP location assimilates toward the time-2 EP location is also supported.  Support is that a time-1 EP location can in fact assimilate toward a time-2 EP location per results of Cicchini et al. (2013), Eagleman and Sejnowski (2000), and F. Ono and Watanabe (2011). 

The account’s claim that the perception of apparent motion later in its time course occurs at about the same time as assimilation of the time-1 EP location toward the time-2 EP location is also supported.  Time-1, time-2, time-3, time-4, and time-5 disks appeared in a row (Li et al., 2014).  One result is that apparent motion was perceived.  A second is that the perceivable time-3 disk assimilated toward the EP locations of the time-4 and time-5 disks per a judgment measure.  Support ensues because the time-4 and time-5 disks correspond to a time-2 object.  There is more support.  Apparent motion of a time-1 small square toward the physical location of a time-2 large triangle was perceived (Anstis & Ramachandran, 1985).  Then the time-1 small square was perceived as being at the time-2 large triangle’s perceived location while being occluded by it.  This perception is evidence that the time-1 square’s EP location completely assimilated to the time-2 triangle’s EP location, and this complete assimilation advises that assimilation was also occurring while apparent motion was perceived a moment previously.

2.5.D.  EP-location-enables-perceived-motion Theory

The account claims that the putative change in the assimilation-produced single weighted average EP location from about the time-1 EP location to about the time-2 EP location is the immediate enabler of apparent motion (subsection 2.5.A).  The account also maintains that this claim is supported by the EP-location-enables-perceived-motion theory that a rapid change in EP location enables perceived motion in general.  Accordingly, the present subsection supports this theory.  It  does so by indicating that it is a key to explaining the following three perceived motion results. 

Movement of the eyes resulted in perceived movement of an afterimage in the same direction as the eyes (Mack & Bachant, 1969).  Because the retinal image is fixed, movement of the eyes should rapidly change the afterimage’s EP location.  Hence EP-location-enables-perceived-motion theory is a key to explaining the afterimage’s perceived motion.  Thus it is supported. 

A, for example, stationary straight ahead upright finger is viewed for a long duration first by one eye and then by the second eye.  The result is that many people perceive the finger in one location and then in a different horizontal location.  A second result is that a switch to viewing by the second eye frequently results in the perception of the finger moving horizontally.  Hence apparent motion is perceived.  The long duration result is evidence that time-1 and time-2 EP locations occur when the apparent motion is perceived.  Per the account of apparent motion, assimilation between these EP locations results in a single weighted average EP location that rapidly changes.  This change then enables the perceived motion per EP-location-enables-perceived-motion theory.  Thus this theory is a key to explaining the apparent motion.  Therefore it is supported.  This explanation is consistent with results and analyses of H. Ono and Gonda (1978), H. Ono and Weber (1981), and Park and Shebilske (1991). 

A stationary object is midsagittal, physically near in 3D distance, and due to this nearness, its perceived 3D distance is overestimated (Gogel, 1982).  Also, when the head is to one side and stationary, the midsagittal object’s perceived location is toward the other side and vice versa per a manual aim measure.  Additionally, when the head moves to one side, the object is perceived to move toward the opposite side, that is, toward the same side as indicated by the manual aim.  The explanation by EP-location-enables-perceived-motion theory is that the head movement rapidly changes the object’s EP location and this change enables the object’s perceived motion.  Because the theory is a key to explaining the perceived motion, it is supported.

2.6.  Closer EP Locations are Claimed to Be Less Accurate, and They Assimilate More

Two more proximal physical locations are referred to as nearer.  Two more proximal perceived and also EP locations are referred to as closer.  This was indicated in section 1.3.

The current section provides evidence that two objects with nearer physical locations often result in more assimilation between their EP locations.  Accordingly, a nearer-physical-locations-more-assimilation result is concluded to occur. 

The explanation of the nearer-physical-locations-more-assimilation result relies on a new claim.  It is that two closer EP locations are associated with the perception of at least one of these locations as less accurate.  This claim is called the closer-EP-locations-are-less-accurate claim.  This claim is rationalized.  Closer EP locations are equivalent to more similar EP locations.  Perhaps then two more similar EP locations are more likely to be “confused” by the nervous system.  Also, this confusion makes the EP locations less accurate. 

The combination of the current section’s closer-EP-locations-are-less-accurate claim and this division’s less-accurate-EP-location-more-assimilation conclusion means that closer EP locations should be associated with more assimilation between them.  This association is called the closer-EP-locations-more-assimilation association.  Nearer physical locations usually result in closer EP locations.  Hence per the closer-EP-locations-more-assimilation association, nearer physical locations often result in more assimilation, which is the result to be explained.

This explanation of the nearer-physical-locations-more-assimilation result has been based on the current section’s closer-EP-locations-are-less-accurate claim and this division’s less-accurate-EP-location-more-assimilation conclusion.  Being explanatory, this claim and this conclusion are supported. 

A qualification to the nearer-physical-locations-more-assimilation result is that more similar physical locations do not result in more assimilation when these locations are rather near to begin with.  This is because then an additional nearness does not result in more assimilation per section 1.6. 

The remainder of the current section provides evidence that the nearer-physical-locations-more-assimilation result occurs.  To begin, when a line was nearer to an adjacent rectangle, its perceived location became similar to the rectangle’s physical location by a larger extent than when the line was less near to this rectangle per the judgment of location (Ganz, 1964).  This result is evidence that a line that was nearer to an adjacent rectangle resulted in more assimilation of its EP location toward the rectangle’s EP location.  Nearer physical locations also resulted in more assimilation beween EP locations per the reproduction of a target’s location results of Rentschler et al. (1975),  the latency of a saccade results of Theeuwes et al. (1999 (a control condition result)), and both the aim of a saccade and the momentary aim of saccade results of McSorley et al. (2009). 

More evidence is that nearer physical locations more frequently resulted in a single average perceived location (Coren & Hoenig, 1972; Ottes, Van Gisbergen, & Eggermont, 1984; Van der Stigchel & Nijboer, 2013).  This result is more evidence, because a single average perceived location attests to the occurrence of assimilation between EP locations per sections 1.7-1.9.   

The nearer-physical-locations-more-assimilation result and the closer-EP-locations-more-assimilation association of five paragraphs past correspond.  Hence support for this association also supports this result.  Accordingly, this association is now supported.  Less disparity is known to be more likely to result in perceived locations of the two eyes’ diplopic percepts that are closer.  Less disparity is also known to be more likely to result in a single average perceived location.  This single average perceived location stems from assimilation between the EP locations of diplopic percepts per section 1.7.  In sum, less disparity results in closer perceived locations and more assimilation between their corresponding EP locations.  Hence the closer-EP-locations-more-assimilation association is supported.

2.7.  The EP Locations of Objects with More Similar Features Are Claimed to Be Less

Accurate, and They Assimilate More

The current section provides evidence that two objects with more similar features (e.g., colors) often result in more assimilation between their EP locations.  Accordingly, this result is concluded to occur.  It is called the more-similar-features-more-assimilation result. 

The explanation of the more-similar-features-more-assimilation result relies on a new claim.  It is that the EP locations of objects with more similar features are less accurate.  This claim is called the more-similar-features-EP-locations-are-less-accurate claim.  A seemingly reasonable possibility that supports this claim is that the nervous system is more likely to “confuse” two EP locations when the neurally connected encodings for their perceived features are more similar.  Also, this confusion makes the two EP locations less accurate.  

The current section’s more-similar-features-EP-locations-are-less-accurate claim and the preceding section’s closer-EP-locations-are-less-accurate claim accord.  This is because both maintain that two more similar aspects of objects (their locations and their features) result in the nervous system “confusing” EP locations thereby making them less accurate. 

The combination of the current section’s more-similar-features-EP-locations-are-less-accurate claim and this division’s less-accurate-EP-location-more-assimilation conclusion means that an association should exist between EP locations that derive from objects with more similar features and the occurrence of more assimilation between these locations.  Given this association, two objects with more similar features should result in more assimilation between their EP locations, which is the result to be explained. 

Hence together both the current section’s claim and this division’s conclusion are explanatory.  Thus they are supported. 

A presumption has been that similar physical features are ordinarily also perceived as similar.  Accordingly, the text has not distinguished between physical and perceived features. 

The remainder of the current section provides evidence that the more-similar-features-more-assimilation result occurs.  The perceived location of a white line became more similar to the physical location of a white square than to the physical location of a black square per a judgment measure (Ganz, 1964).  This finding is evidence that a white line assimilated toward the EP location of a white square more than it assimilated toward the EP location of a black square.  A time-1 vertical target often completely assimilated to the EP location of a time-2 vertical nontarget, but it hardly assimilated toward the EP location of a horizontal time-2 nontarget per a reproduction measure according to results of Cicchini et al. (2013).  A target assimilated toward a nontarget with the same color more than to a nontarget with a different color per both a choice of location measure and the latency of a saccade that aimed at the target according to results of Ludwig and Gilchrist (2002).  A center line and angles of the outgoing angle Muller Lyer stimulus that were the same color resulted in a greater overestimation of the center line’s perceived length than a center line and angles that were different in color (Lamy, Segal, & Ruderman, 2006; Mukerji, 1957).  Because this overestimation is enabled by assimilation between EP locations per division 4, the same color resulted in more of this assimilation.  The lines and angles of similar stimuli that were the same color also resulted in a larger illusory effect on perceived length (Miyahara, 2006; Sadza & de Weert, 1984).   

More evidence for the similar-features-more-assimilation result is that binocular viewing of disparity producing dichoptic objects with the same features is known to result in a single average perceived location more often than disparity producing dichoptic objects with less similar features.  Also, this single average perceived location stems from assimilation between the two eyes’ different EP locations per section 1.7.   Hence two dichoptic objects with the same features result in more assimilation between EP locations, thus evidencing the similar-features-more-assimilation result. 

2.8.  A Less Accurate Time-2 EP Location Assimilates toward a Time-1 EP Location That

by Chance Matches the Time-2 Physical Location and Hence the Time-2 Perceived Location

Becomes More Accurate

A time-1 nontarget can make a time-2 target’s perceived location more accurate when this target appears by chance in the same physical location as the time-1 nontarget.  Also, this result occurs when the time-2 target’s perceived location would ordinarily (under different circumstances) be less accurate than the time-1 nontarget’s perceived location.  This result is called the more-accurate-perceived-location result.  The current section explains it.  

The explanation of the more-accurate-perceived-location result relies on the present division’s less-accurate-perceived-location-more-assimilation conclusion.   Hence exogenous attention to the time-2 target is not posited to enable the more-accurate-perceived-location result. 

Evidence that the more-accurate-perceived-location result occurs comes next.  Its explanation follows. 

A time-1 nontarget resulted in a faster saccade toward a time-2 target when the time-2 target appeared by chance in the same physical location as the time-1 nontarget than when the time-1 nontarget did not occur (Adler et al., 2002).  The faster saccade is evidence that the time-2 target’s perceived location was more accurate.  The faster saccade is also evidence that the time-2 target was briefly processed.  This brief processing advises that the time-2 target’s perceived location would ordinarily be less accurate than the time-1 nontarget’s perceived location on the basis that brief processing results in a less accurate perceived location per section 2.1.  In conclusion, a more-accurate-perceived-location result occurred.

Another result is that a time-1 nontarget with a feature that differed from a feature of additional time-1 nontargets made a time-2 target’s perceived location more accurate when the time-2 target appeared by chance in the same physical location as this time-1 nontarget per choice of location measures (Donk & Soesman, 2010; Joseph & Optican, 1996).  The time-2 target of at least the Joseph and Optican research was processed relatively briefly.  This brief processing again advises that the time-2 target’s perceived location would ordinarily be less accurate than the time-1 nontarget’s perceived location.  Hence another more-accurate-perceived-location result occurred. 

Another result is that a time-2 target’s perceived location was more accurate per a faster saccade toward it when it appeared by chance at the average of the locations of two (also four) time-1 nontargets (Christie, Hilchey, Mishra, & Klein, 2015).  The faster saccade also informs that the time-2 target was more briefly processed than the time-1 nontargets.  Hence the time-2 target’s perceived location would again be ordinarily less accurate.  Thus another more-accurate-perceived-location result occurred.  Further, a time-1 physical object was not at the average location, which is evidence that a time-1 EP location instead of a different type of encoding that a physical object brings about enabled this result.

An explanation of the more-accurate-perceived-location result follows.  The time-2 target’s less accurate EP location assimilates toward the time-1 nontarget’s more accurate EP location on the basis of this division’s less-accurate-perceived-location-more-assimilation conclusion.  In addition, because the time-1 nontarget’s EP location and the time-2 target’s physical location match, the time-2 target’s assimilation-produced perceived location becomes closer to its physical location.  Equivalently, the time-2 target’s perceived location becomes more accurate, as to be explained.  This explanation is supported by the preceding paragraph’s evidence that a time-1 EP location enabled the more-accurate-perceived-location result.

3.  Assimilation Enables the Accuracy of Perceived Features

to Become Similar to the Accuracy of Their Perceived Location

This division supports the occurrence of an association (a similarity) between the accuracy of a perceived location and the accuracy of perceived features at this perceived location.  The association is called the perceived–location-perceived-features-similar-accuracies association.

This division also supports the theory that an assimilation process enables the accuracy of perceived features to become similar to (assimilate toward) the accuracy of their EP location.  The theory is called the assimilation-enables-accuracy-of-perceived-features theory.  It is supported because it explains the perceived-location-perceived-features-similar-accuracies association. 

This division’s section 3.1 additionally supports the assimilation-enables-accuracy-of-perceived-features theory.  Its sections 3.2-3.4 provide one type of support for the perceived-location-perceived-features-similar-accuracies association.  This type is basically evidence that a singleton object’s less accurate perceived location is associated with less accurate perceived features at this perceived location.  This type of support will be called singleton-object support.  Section 3.5-3.10 provide evidence that an assimilation-produced hence less accurate perceived location is associated with less accurate perceived features at this perceived location.  An assimilation-produced perceived location can also be more accurate per section 2.8.  Accordingly, section 3.11 indicates that time-2 perceived features can also be more accurate.  In sum, sections 3.5-3.11 provide assimilation support for the perceived-location-perceived-features-similar-accuracies association.  This type of support will be called assimilation support.

This division’s support for the perceived-location-perceived-features-similar-accuracies association and assimilation-enables-accuracy-of-perceived-features theory means that this article’s two propositions that an assimilation process and EP location enable diverse general results are also supported.

The accuracy of a perceived feature is taken to be indicated by the ability to detect a feature, identify a feature, and discriminate between features.  Discriminations between features, including successive discriminations, should be a measure, because presumably the accuracy of a perceived feature is associated with how well it is discriminated from another feature.

3.1.  Support for the Assimilation-enables-accuracy-of-perceived-features Theory

This division’s introduction indicated that the assimilation-enables-accuracy-of-perceived-features theory is supported because it explains the perceived-location-perceived-features-similar-accuracies association.  The current section additionally supports the theory.  It also touches on two related theories. 

Evidence that an accurate location is perceived rather rapidly supports the assimilation-accuracy-of-perceived-features theory.  This is because then the accuracy of an EP location probably precedes the perception of features and hence is capable of enabling the accuracy of this perception.  Evidence comes from the latency of saccade measure of perceived location as follows.  The aim of a saccade toward a target that appeared randomly to the left or right was more accurate than chance when its latency was close to 100 ms (Heeman et al., 2019).  This result is notable.  This is because the afferent to efferent neural transmission time for a saccade is about 80 ms (Heeman et al.).  More evidence is that monkeys successfully aimed their saccades toward a target that appeared randomly to the left and right with a latency of about 185 ms (Dorris & Munoz, 1995). 

An assimilation-produced perceived location is rapidly perceived per section 1.11.  This rapidity also supports the assimilation-accuracy-of-perceived-features theory.  This is because the rapidity of an assimilation-produced perceived location advises that it probably precedes the perception of features at this location and hence can enable their accuracy. 

The assimilation-enables-accuracy-of-perceived-features theory’s claim that the accuracy of an EP location enables the accuracy of perceived features at this location is also supported via generalization by the evidence in divisions 2 and 4 that the accuracy of an EP location enables perceived motion and perceived length, respectively.  Because the accuracy of a perceived location and a perceived location itself are related perceptions, the theory is also supported via generalization by evidence for this article’s proposition that EP location enables diverse general results. 

The assimilation-enables-accuracy-of-perceived-features theory also claims that an assimilation process is enabling.  Hence the theory is supported via generalization by the support for this article’s proposition that an assimilation process enables diverse general results.

van der Heijden (1993) essentially reasons that an EP location enables the perception of features at that location.  Another theory is somewhat similar.  It maintains that “activated features generate attention-calling “interrupt” signals, specifying only location; attention then retrieves the properties at that location” (Johnston & Pashler, 1990, p. 843).  Hence activated features have precedence over location, location is the source for perceived features, and attention is involved.

3.2.  Brief Processing Makes a Singleton Object’s Perceived Location and Perceived Features

Less Accurate

The current section is the first of this division’s remaining sections that supports its perceived-location-perceived-features-similar-accuracies association.  The type of support is the singleton-object support that this division’s introduction described.

Section 2.1 provided evidence that brief processing makes a singleton object’s perceived location less accurate.  In addition, it is known that brief processing also makes a singleton object’s perceived features less accurate.  For example, it is known that brief processing makes a singleton object harder to detect.  In sum, brief processing makes both a singleton object’s perceived location and perceived features less accurate.  Hence there is singleton-object support for this division’s perceived-location-perceived-features-similar-accuracies association. 

Support for this association also comes from data on perceived location and perceived features from the same singleton object that is obtained as roughly the same time.  Hence the “perceived features at this perceived location” aspect of the perceived-location-perceived-features-similar-accuracies association is supported.  In a Bloem and van der Heijden (1995) experiment, a disk appeared either to the left or right and it was one of four possible colors.  The time available to process the disk was reduced to result in sufficient errors.  The task was to name the color and location of the disk.  When the choice of location was corrrect, the probability that the choice of color was correct was .511, and when the choice of location was incorrect, the probability that the choice of color was correct was .269, which was close to chance.  Hence an association occurred between a less accurate perceived location and a less accurate perceived feature of the same object.  The results were rather similar when the tilts of the singleton target were different (Brouwer & van der Heijden, 1997).  Results for tilt were reasonably similar (Dick & Dick, 1969).  Results were similar when the stimulus (display) was not a singleton object (Johnston & Pashler, 1990; Kovacs & Harris, 2019; Treisman & Gelade, 1980 (experiment 9).)

3.3.  Lower Luminance Makes a Singleton Object’s Perceived Location and Perceived

Features Less Accurate

Section 2.2 provided evidence that lower luminance makes a singleton object’s perceived location less accurate.  Evidence that lower luminance makes a singleton object’s perceived features less accurate is the familiar result that lower luminance makes a singleton object difficult to detect.  Hence the combined evidence amounts to singleton-object support for this division’s perceived-location-perceived-features-similar-accuracies association.

3.4.  A Less Foveal Retinal Image Makes a Singleton Object’s Perceived Location and

Perceived Features Less Accurate

A less foveal singleton object results in a less accurate perceived location per section 2.3.  It also results in less accurate perceived features per the current section.  Hence there is singleton-object support for this division’s perceived-location-perceived-features-similar-accuracies association. 

Supporting results for perceived features follow.  A singleton less foveal letter was identified less accurately than a more foveal one (Bouma, 1970).  Also, a dscrm between two oppositely tilted small lines was poorer when each of them was less foveal (Donk & Meinecke, 2010).  Because the dscrm was successive, a single tilted line appeared on a trial.  In addition, this tilted line was like a singleton object because it appeared with a number of regularly arranged vertical small lines that approximated a background.

3.5.  Brief Processing Results in More Assimilation Hence a Less Accurate Perceived

Location, and the Perceived Features at the Assimilation-produced Perceived Location

Are also Less Accurate

The current section is the first of this division’s remaining sections that provide the assimilation type of support for the perceived-location-perceived-features-similar-accuracies association that this division’s introduction described. 

Section 2.1 indicated that a briefly processed object often assimilates toward the EP location of another object.  As has been indicated, an assimilation-produced perceived location is less accurate.  The current section provides evidence that the perceived features at the briefly processed object’s assimilation-produced perceived location are also less accurate.  Hence the present section provides assimilation support for the perceived-location-perceived-features-similar-accuracies association.  Evidence comes next.

The perceived location of a vertical line became similar to the physical location of an adjacent square (Ganz, 1964).  This result was previously indicated to be evidence of assimilation between EP locations.  Due to this assimilation, the line’s perceived location became less accurate.  The line’s perceived features also became less accurate when the square was present according to the result that this line was detected less accurately.  Because the assimilation and detection data came from the same line and rectangle and the nearness between them, the line probably assimilated toward the EP location of the square when its detectability was measured.  The durations of the line and square were .106 sec.  In conclusion, brief processing resulted in an assimilation-produced less accurate perceived location and the perceived features at this perceived location were also less accurate.  This conclusion constitutes assimilation support for the perceived-location-perceived-features-similar-accuracies association including its “perceived features at this perceived location” aspect.    

More assimilation support for this association follows.  Two objects that are briefly processed often result in a single average perceived location per section 1.11.  A single average perceived location is enabled by assimilation between EP locations per sections 1.7-1.9.  A single average perceived location is less accurate, because it differs from the physical locations of the target and nontarget.  Perceived features at the single average perceived location are not indicated to be perceived (Bucker et al., 2015; Coren & Hoenig, 1972; Findlay & Gilchrist, 1997; McSorley et al., 2009).  For example, when two objects were both asterisks, an asterisk was not indicated to be perceived at about the average location that a saccade aimed at (Coren & Hoenig).  This no indication is evidence that the perceived features at the single average perceived location are less accurate.  A summation is that an assimilation-produced hence less accurate perceived location is associated with less accurate perceived features at this location.  Thus there is assimilation support for the association including its “perceived features at this perceived location” aspect.

3.6.  Lower Luminance Results in More Assimilation Hence a Less Accurate Perceived

Location, and the Perceived Features at the Assimilation-produced Perceived Location

Are Also Less Accurate

Section 2.2 provided evidence that a lower luminance object often assimilates toward the EP location of a higher luminance object.  Hence the lower luminance object’s perceived location often becomes less accurate when a higher luminance object is also present.  The current section provides evidence that when a higher luminance object is also present, the perceived features at the lower luminance object’s assimilation-produced perceived location also often become less accurate.   Thus there is assimilation support for the perceived-location-perceived-features-similar-accuracies association.  In addition, a general result provides evidence and it is explained.

  This general result is that a lower luminance object’s perceived features are often less accurate when a higher luminance object is simultaneously present (or nearly so) (e.g. Alpern, 1953; Chung, Levi, & Legge, 2001; Mounts & Gavett, 2004).  This result along with the section 2.2 evidence about luminance, assimilation, and an ensuing assimilation-produced less accurate perceived location that the preceding paragraph indicated constitutes assimilation support for the perceived-location-perceived-features-similar-accuracies association.  Similarly, this general result is explained by assimilation between EP locations, the ensuing assimilation-produced less accurate perceived location, and the perceived-location-perceived-features-similar-accuracies association. 

The “perceived features at this perceived location” aspect of the perceived-location-perceived-features-similar-accuracies association is also supported.  A lower luminance vertical bar and an adjacent higher luminance vertical bar resulted in a shorter perceived length of the interval between them than when the two bars were the same in luminance (Watt & Morgan, 1983).  The shorter perceived length attests to the occurrence of more assimilation between the EP locations of the two bars per division 4.  The lower luminance bar assimilated toward the perceived location of the higher luminance bar more than vice versa on the basis of evidence in section 2.2.  Thus the lower luminance bar’s perceived location became less accurate.  The lower luminance and higher luminance bars were also less accurately resolved.  This result is evidence that the lower luminance bar’s perceived features also became less accurate.   Therefore there is assimilation support for the “perceived features at this perceived location” aspect of the association.

3.7.  A Less Foveal Retinal Image Results in More Assimilation Hence a Less Accurate

Perceived Location, and the Perceived Features at the Assimilation-produced

Perceived Location Are Also Less Accurate

Section 2.3 provided evidence that a less foveal object often assimilates toward the EP location of another object.  Hence a less foveal object’s perceived location often becomes less accurate when another object is also present.  A general result is that a less foveal object’s perceived features also often become less accurate when another object is present (e.g. Bouma, 1970; Pelli, Palomares, & Majaj, 2004).  Thus an assimilation-produced less accurate perceived location is associated with less accurate perceived features at this location.  Therefore there is assimilation support for the perceived-location-perceived-features-similar-accuracies association.  Likewise, the general result is explained:  Assimilation, an ensuing assimilation-produced less accurate perceived location, and the perceived-location-perceived-features-similar-accuracies association account for it. 

3.8.  Apparent Motion Is Associated with Assimilation Hence a Less Accurate Perceived

Location, and the Perceived Features at the Assimilation-produced Perceived Location

Are Also Less Accurate 

Section 2.5 concluded that the perceived location of an object in apparent motion is assimilation-produced.  Hence this perceived location is less accurate.  For example, this perceived location is least accurate about midway between the physical locations of the time-1 and time-2 objects that eventuate in apparent motion.  The current section provides evidence that the perceived features of the time-1 and time-2 objects are often also least accurate about midway between these physical locations.  These considerations amount to evidence that an assimilation-produced least accurate perceived location is associated with least accurate perceived features at this location.  Thus there is assimilation support for the perceived-location-perceived-features-similar-accuracies association including its “perceived features at this perceived location” aspect.  Some evidence follows. 

When a time-1 vertical bar and a time-2 horizontal bar that together approximate the letter “L” appear, a bar apparently moves while also rotating downward from the 12:00 o’clock location to the 3:00 o’clock location (Rock, 1975, p. 202).  Hence this bar’s perceived location is least accurate at about the midway (1:30) location.  The bar’s perceived tilt at the 1:30 location is about 45 deg and hence about least accurate in that this tilt is maximally different from the bar’s physical vertical and horizontal tilts.  The bar’s least accurate perceived location is assimilation-produced per the preceding paragraph’s recollection.  In conclusion, an assimilation-produced least accurate perceived location and a least accurate perceived feature at this location occurred.  More evidence follows.  When a large circle and a small circle with the same physical centers appeared at different times, the large circle apparently moved while shrinking toward the size of the small circle (Higginson, 1926).  Hence at the circle’s midway and thus about least accurate perceived location, the circle’s perceived size was in between the circles’ two physical sizes and thus also about least accurate.  Additional evidence is that when a blue and a green disk appeared at different times and resulted in apparent motion, the perceived disk’s color was cyan at this motion’s midway and hence about least accurate perceived location (Chong, Hong, & Shim, 2014).

3.9.  Nearer Physical Locations Result in More Assimilation Hence a Less Accurate

Perceived Location, and the Perceived Features at the Assimilation-produced Perceived

Location Are Also Less Accurate

Section 2.6 provided evidence that the nearer physical locations of objects often result in more assimilation between the objects’ EP locations.  This more assimilation means that these nearer physical locations often result in an object’s assimilation-produced location that is less accurate.  The current section provides evidence that these nearer physical locations frequently result in perceived features at the assimilation-produced location that are also less accurate.  Hence there is assimilation support for the perceived-location-perceived-features-similar-accuracies association.   Some of this support comes from a general result.  Accordingly, an explanation of it is indicated. 

The general result is that nearer physical locations of a target and nontarget frequently result in the target’s perceived features being less accurate (e.g. Bouma, 1970; Dresp & Bonnet, 1993; Eriksen & Rohrbaugh, 1970; Flom, Weymouth, & Kahneman, 1963; Mounts & Gavett, 2004; Theeuwes et al., 1999 (a control condition result)).  The preceding paragraph recollected that nearer physical locations of objects often result in more assimilation.  Hence the perceived location of a target of the general result would probably be assimilation-produced.  Thus it would probably be less accurate.  In conclusion, a target’s perceived location and perceived features are both less accurate.  Therefore there is assimilation support for the perceived-location-perceived-features-similar-accuracies association.  The general result is also explained:  Assimilation, an ensuing assimilation-produced less accurate perceived location, and the perceived-location-perceived-features-similar-accuracies association explain it. 

The “perceived features at this perceived location” aspect of the perceived-location-perceived-features-similar-accuracies association is also supported as follows.  Nearer physical locations of a line and an adjacent square resulted in more assimilation of the line toward the square’s EP location (Ganz, 1964).  Hence the perceived location of the line became less accurate.  These nearer physical locations also resulted in less accurate detection of the line.  Because the assimilation and detection data came from the same line and rectangle and nearness between them, the line probably assimilated toward the square’s perceived location when its detection was ascertained.  Thus there is assimilation support for the “perceived features at this perceived location” aspect of the association.

There is more such support.  Nearer physical locations of two objects made the perception of a single average perceived location more likely (Coren & Hoenig, 1972; Ottes et al., 1984; Van der Stigchel & Nijboer, 2013), as section 2.6 indicated.  This perceived location is assimilation-produced per sections 1.7-1.9.  Hence it is also less accurate.  There was no indication that the objects’ features were perceived at the single average perceived location.  Thus the perceived features at an assimilation-produced hence less accurate perceived location were probably also less accurate.  Therefore there is assimilation support for the perceived-location-perceived-features-similar-accuracies association including for its “perceived features at this perceived location” aspect. 

There is additional such support.  Less disparity is known to result in the perceived locations of the two eyes’ diplopic percepts being closer.  This result is relevant, because nearer physical locations also result in two perceived locations being closer.  Less disparity is also known to tend to result in a single unweighted average perceived location instead of diplopic percepts.  This single average perceived location is due to assimilation between the EP locations of the two eyes’ diplopic percepts per section 1.7.  Being assimilation-produced, this single average perceived location is also less accurate.  One set of features is perceived at this assimilation-produced single average perceived location, not the two sets of features of diplopic percepts.  Hence the perceived features at this assimilation-produced single average perceived location are also less accurate.  Thus there is assimilation support for the perceived-location-perceived-features-similar-accuracies association including for its “perceived features at this perceived location” aspect.

3.10.  Objects with More Similar Features Result in More Assimilation Hence a Less Accurate

Perceived Location, and the Perceived Features at the Assimilation-produced Perceived

Location Are Also Less Accurate

Objects with more similar features often result in more assimilation between their EP locations per section 2.7.  As previously, an assimilation-produced perceived location is less accurate.  Hence objects with more similar features also often result in less accurate perceived locations.  The current section provides evidence that objects with more similar features frequently result in perceived features that are also less accurate.  In conclusion, this section provides assimilation support for the perceived-location-perceived-features-similar-accuracies association. 

Evidence for objects with more similar features comes from a general result.  Accordingly, the result is explained.  The general result is that objects with more similar features frequently result in perceived features that are less accurate (e.g. Carter, 1982; Ivry & Prinzmetal, 1991; Kooi, Toet, Tripathy, & Levi, 1994; Neisser, 1963).  For example, the time taken to search for a purplish target was slower when nontargets were purplish red than when they were green (Carter).  Per the preceding paragraph, objects with more similar features often result in assimilation-produced hence less accurate perceived locations.  Thus there is assimilation support for the perceived-location-perceived-features-similar-accuracies association.  In addition, an explanation of the general result follows:  Assimilation, an ensuing less accurate assimilation-produced perceived location, and the perceived-location-perceived-features-similar-accuracies association provide the explanation.

Evidence for the “perceived features at this perceived location” aspect of the perceived-location-perceived-features-similar-accuracies association follows.  A line assimilated toward the EP location of an adjacent square more when they were the same color than different colors (Ganz, 1964), as section 2.7 also indicated.  Hence the line’s assimilation-produced perceived location was less accurate when the line and square were the same color.  The detection of the line was also less accurate when it and the square were the same color.  Because the perceived location and detection data came from the same line and rectangle in the same physical locations, the line was likely to have assimilated more toward the EP location of the same color square when its detection was measured.  Thus it is likely that less accurate features were perceived at the same location that was perceived as less accurate.  Therefore the “perceived features at this perceived location” aspect of the association as well as the association itself is supported. 

There is more evidence.  Dichoptic objects with the same features that produce disparity are known to be relatively likely to result in a single average perceived location and one set of perceived features at this location instead of diplopic percepts.  This single average perceived location is assimilation-produced per section 1.7.  Accordingly, it is less accurate.  The perceived features at the assimilation-produced single average perceived location are also less accurate.  This is because one set of features is perceived instead of the two sets of features of diplopic percepts.  Hence more similar features result in an assimilation-produced less accurate perceived location and less accurate perceived features at this perceived location.  Thus there is support for the “perceived features at this perceived location” aspect of the association in addition to support for the association itself. 

3.11.  A Less Accurate Time-2 EP Location Assimilates toward a Time-1 EP Location That

by Chance Matches the Time-2 Physical Location, and the Perceived Features at the

Assimilation-produced Perceived Location Are Also More Acccurate

Per section 2.8’s assimilation-based analysis, a time-2 target’s less accurate EP location assimilates toward a time-1 nontarget’s more accurate EP location that by chance matches the time-2 physical location, and hence the time-2 target’s assimilation-produced perceived location becomes more accurate.  Per the current section, a general result is that the time-2 target’s perceived features also become more accurate.  Hence the current section provides assimilation support for the perceived-location-perceived-features-similar-accuracies association.     

This support is a reason to doubt that the general result occurs because a time-2 target’s perceived features become more accurate due to the direction of exogenous attention to the time-2 target. 

Evidence for the perceived-location-perceived-features-similar-accuracies association follows.  Section 2.8 indicated that a time-2 target’s perceived location was more accurate when it appeared by chance in the same physical location as a time-1 nontarget.  The preceding paragraph also indicated that an assimilation-based analysis accounts for this increase in accuracy.  General result findings also occurred:  The perceived features of the time-2 target also became more accurate according to how well it was detected (Donk & Soesman, 1996; Joseph & Optican, 1996).  Also, the perceived location and detection accuracy results came from the same objects, making it more likely that when detection was determined, the time-2 target’s perceived location also became more accurate.  Hence there is assimilation support for the perceived-location-perceived-features-similar-accuracies association. 

More evidence for the perceived-location-perceived-features-similar-accuracies association follows.  General result findings are that a time-2 target’s perceived features became more accurate when this target appeared by chance in the same physical location as a time-1 nontarget (Jonides, 1981; Kim & Cave, 1999, 2001; Montagna, Pestilli, & Carrasco, 2009).  In addition, the time-2 target’s perceived location probably also became more accurate.  This is because the section 2.8 assimilation-based analysis applies, since the time-2 target’s EP location was probably less accurate than the time-1 nontarget’s EP location per the next three sentences.  The response to the time-2 target was speeded (Jonides; Kim & Cave, 1999, 2001), hence it was briefly processed and thus its EP location was relatively inaccurate.  Also, the time-2 target was not a singleton object, whereas the time-1 nontarget was (Jonides; Montagna et al.).  Additionally, the SOA between the time-1 nontarget and the time-2 target was 120 ms or longer Montagna et al.).  In conclusion, these general result findings also provide assimilation support for the association. 

A summation that pertains to this entire division is that the perceived-location-perceived-features-similar-accuracies association is supported in its sections 3.2-3.11, and this association is explained by the assimilation-accuracy-of-perceived-features theory that was considered in its introduction and section 3.1.

4.  Two EP Locations Enable the Perceived Length

of the Interval that They Flank

Two nearer (less near) physical locations usually result in a smaller (larger) perceived length of the interval between these locations.  Hence two closer (less close) EP locations are usually associated with a shorter (longer) perceived length of the interval between these locations.  An “EP location” is referred to, because the two locations may frequently not be consciously perceived, for example, because perceived length is instead.  Accordingly, the association is called the EP-location-perceived-length assocation. 

An ensuing theory is that two EP locations enable the perceived length of the interval between these locations.  It is called the EP-location-enables-perceived-length theory.  This theory is subsumed by Gogel’s (1990) theory of phenomenal geometry.

This division concentrates on supporting the EP-location-enables-perceived-length theory.  An aim is to thereby also support this article’s proposition that EP location enables diverse general results both when an assimilation process is integrally involved and when it is not. 

An EP location also enables perceived motion without an assimilation process being integrally involved per the EP-location-enables-perceived-motion theory.  This theory was supported in section 2.5. 

The EP-location-enables-perceived-length theory is supported, because two physical locations determine the physical length of the interval between them, hence increasing the probability that two EP locations enable the perceived length of the interval between them.  This theory is also supported, because the physical length of an interval does not determine its two flanking physical locations, hence increasing the probability that an encoding for perceived length, that is neural information of it, is not capable of enabling the two flanking EP locations. 

The remainder of this division continues to support the EP-location-enables-perceived-length theory.  It does so by providing evidence that the EP-location-perceived-length association holds when one or both of the flanking EP locations is inaccurate.  This evidence is supporting, because an inaccurate location is an EP location instead of a physical one. 

Evidence for the theory comes from the Emmert’s Law result.  This result indicates, for example, that the length of a perceived horizontal line is overestimated.  Hence the EP locations of the line’s flanking left and right ends are less close.  Thus the EP-location-perceived-length association is supported.  In addition, the flanking EP locations of these left and right ends are also inaccurate.  Thus this association holds when the flanking EP locations are inaccurate.  Therefore the EP-location-enables-perceived-length theory is supported according to the preceding paragraph. 

Evidence for the theory also comes from the Mueller-Lyer stimulus  Aiming a saccade or a manual response toward the location of an end point (and/or vertex) of an outgoing angle Mueller-Lyer stimulus results in an aim that is somewhat toward the center location of this angle (Binsted & Elliott, 1999; Delabarre, 1897, as cited in McCarley, Kramer, & DiGirolamo, 2003; Gentilucci, Daprati, Gangitano, & Toni, 1997; Welch, Post, Lum, & Prinzmetal, 2004).  This aim means that the perceived location of this end point is inaccurate.  This aim also means that the EP locations of this end point and the Mueller-Lyer stimulus’s opposite end point are less close.  The length of the interval between the locations of these two end points is then perceived as longer per the EP-location-perceived-length association.  In fact, this perceived length is longer.  It is the longer perceived length that the outgoing angle Mueller-Lyer stimulus results in.  The import is that the EP-location-perceived-length association holds when a flanking EP location is inaccurate and hence the perceived-location-enables-perceived-length theory is supported.

An aside is that the result that the end point’s perceived location is somewhat toward the center location of the near outgoing angle advises that this end point assimilates toward an EP location of this angle, e.g. its average location.  Thus a different message is that assimilation between EP locations most likely enables the outgoing angles Mueller-Lyer illusion. 

The current and next two paragraphs provide similar evidence for the theory.  When one vertical bar was higher in luminance than a second adjacent vertical bar, the perceived length of the interval between these bars was shorter (Watt & Morgan, 1983).  The lower luminance bar assimilated toward the EP location of the higher luminance bar on the basis of evidence in section 2.2.  Hence the two bars’ EP locations became closer.  Thus closer EP locations were associated with a shorter perceived length of the interval between them.  Therefore the EP-location-perceived-length association is supported.  Also, the lower luminance bar’s perceived location was inaccurate due to the indicated assimilation.  Consequently this association prevailed when a flanking perceived location was inaccurate.  So the EP-location-enables-perceived-length theory is supported. 

Viewing an object that is, say, an upright midsagittal finger, with first one eye and then the other eye frequently results in the perception of the finger in one horizontal location and then in a different horizontal location per subsection 2.5.D.  Hence at least one of the two perceived horizontal locations is inaccurate.  The length of the interval between these locations is perceived.  Thus moderately close EP locations are associated with a moderate perceived length of the interval between these locations.  Therefore the EP-location-perceived-length association holds when at least one flanking EP location is inaccurate.  Consequently the EP-location-enables-perceived-length theory is supported. 

When the head is to one side, the perceived location of a midsagittal target whose perceived 3D distance is overestimated is to the opposite side and vice versa (Gogel, 1982), as subsection 2.5.D indicated.  The length of the interval between the target’s inaccurate left and right EP locations is also perceived.  In addition, a reproduction measure of this perceived length was associated (negatively) with the closeness between the inaccurate left and right perceived locations.  Hence the EP-location-perceived-length association held when two flanking EP locations were inaccurate.  Thus the perceived-location-enables-perceived-length theory is supported.

5.  Assimilation Enables a Time-2 Target’s Less Accurate EP Location

to Become More Similar to a Cognitively Sourced More Accurate

Time-1 EP Location and One More Speculation

Because of past support for this article’s two propositions that an assimilation process and EP location enable diverse general results, the two following speculations are also supported. 

A speculation is that a time-1 cue (nontarget) that correctly predicts the physical location of a time-2 target results in a rather accurate cognitively sourced encoding for this location.  In addition, assimilation enables the time-2 target’s less accurate EP location to become similar to this more accurate cognitively sourced encoded location, and hence the time-2 target’s perceived location becomes more accurate.  This more accurate location occurred per both a choice of location measure (Zehetleitner, Krummenacher, Geyer, Hegenloh, & Muller 2011) and the latency of a saccade (Adler et al., 2002).  The general result that the time-2 target’s perceived features become more accurate (e.g. Posner, Snyder, & Davidson, 1980) is then accounted for by the perceived-location-perceived-features-similar-accuracies association of division 3. 

A second speculation is that the extent of the accuracy of an EP location enables the extent to which salience is perceived at the location.

6.  Assimilation Enables an EP 3D Location to Become Similar to

Another EP 3D Location in Perceived 3D

Obviously, the perceived 3D (three-dimensional distance) of a singleton object can be different from the perceived 3D of another singleton object.  The perceived location of such a singleton object will also be emphasized.  This emphasis follows from the theory in section 1.1 that perceived location is frequently enabled by a perceived (egocentric) direction and a perceived 3D distance (more precisely, an encoded perceived direction and an encoded 3D distance) and the thought in the same section that a perceived location often results in the encoded (neural information of) perceived direction and 3D distance that determines this location. 

When two (or more) objects with different perceived 3Ds when they are singletons appear together at about the same time, each object’s singleton location will be referred to as an EP (recollecting, encoded-perceived) 3D location.  The reason for referring to an EP location is the same as in the Introduction and section 1.1. 

The present division provides evidence that the EP 3D location of an object becomes similar to (assimilates toward) another EP 3D location in perceived 3D (not in perceived direction).  Accordingly, assimilation between EP 3D locations will be said to occur.  Also, an assimilation-produced perceived 3D location will be said to occur.  

 Presumably an assimilation process enables an EP 3D location to become similar to another EP 3D location in perceived 3D.  Hence this division’s evidence supports this article’s proposition that an assimilation process enables diverse general results.  Because an EP 3D location is similar to an EP location, this article’s proposition that EP location enables diverse perceptions is also supported.

Research refers to evidence of assimilation between EP 3D locations in different ways without mentioning assimilation.  An exception is “an assimilation of their disparities” (Westheimer & Levi, 1987). 

Evidence of assimilation between EP 3D locations comes from Gogel (1965).  One piece of evidence is that light from a projector is perceived at the location of a viewing screen.  An interpretation is that the light’s EP 3D location is where the projector is and the light’s assimilation-produced 3D location is very similar (completely assimilated) to the screen’s EP 3D.  A second piece is that an afterimage’s perceived 3D location becomes very similar to the 3D location of a frontal surface.  A third piece is that monocular viewing of white threads at different physical 3D distances resulted in the perception of them at the same perceived 3D (Judd, 1893, as cited in Gogel 1965).  Presumably, assimilation-produced averaging of different EP 3D locations occurred.  A fourth is that perceived slant was underestimated according to 18 articles. 

Evidence of assimilation between EP 3D locations also comes from effects of disparity on perceived 3D per results of Foley and Richards (1978), Westheimer (1986), and Westheimer and Levi (1987).  For example, dichoptic lines that produced crossed disparity and dichoptic lines that produced uncrossed disparity resulted in the perception of two lines at the same perceived 3D (Foley & Richards).  Presumably, assimilation-produced averaging of different EP 3D locations occurred. 

More evidence comes from drawings that afffect the perceived 3D of locations.  One observation is that the perceived 3D location of an internal white area of a line drawing of a Necker cube is fairly similar to the inaccurate EP 3D location of a rather close point on a line of the drawing.  Hence this white area presumably assimilates toward the EP 3D location of this point.  Evidence of this assimilation is that when the perceived 3D of this point reverses, the perceived 3D of the white area changes in the same manner. 

Also, an assimilation-produced EP 3D location can enable another perception.  It enabled perceived depth (Gogel, 1964).

7.  Assimilation Enables a CS to Be Perceived

as Similar to a Retained Perceived US

This division supports the theory “that the CS assimilates to the US” (D. L. King, 2001, p. 35).  Likewise, assimilation enables the CS to be perceived as similar to the retained perceived US.  Also, this perception of the CS results in the CR.  The following support for this assimilation theory of classical conditioning also supports this article’s proposition that an assimilation process enables diverse general results.

Support for this theory is that pigs that perceived a coin and then perceived food came to root the coin (Breland & Breland, 1961), that is, came to make the same response that pigs make to perceived food.  The theory is supported, because due to the coin-food occurrences, the pigs could have perceived the coin as sufficiently similar to the retained perception of food to root it.

Similar support for this theory is that CS-US pairings can result in a CR that is highly similar to the unconditioned response (UR), in other words, the response that the perception of the US produces.  There is support, because this high CR-UR similarity may be due to the CS being perceived as highly similar to the retained perception of the US.  One supporting result is that pairing the ring of a bell with food resulted in dogs looking at the location of the bell (Zener, 1937), as dogs look when they perceive food.  A second is that pairing the illumination of a plastic response key with food made pigeons peck the key, as pigeons peck when they perceive food (Brown & Jenkins, 1968; Jenkins & Moore, 1973).   A third is that pairing the insertion of a response lever into an experimental enclosure with food made rats lick, paw, gnaw, and bite the response lever (Peterson, Ackil, Frommer, & Hearst, 1972; Stiers & Silberberg, 1974), as rats do when they perceive food.  A fourth is that pairing the entering of a ball bearing into an experimental enclosure with food made rats put the ball bearing into their mouths (Timberlake, Wahl, & D. A. King, 1982), as rats do when they perceive food. 

A CS is known to result in less dramatic CRs than the ones of the previous paragraph.  Nevertheless, the theory continues to apply.  An illustration of why is the following explanation of the classical conditioning of salivation using food.  The CS results in the partial perception of food, that is, an image of food, and this partial perception produces the salivation.  In addition, this explanation has support:  When humans partially perceive (imagine) food, they tend to salivate.  Furthermore, this explanation works in general, because “images of stimuli lead to responses similar to the ones produced by real stimuli” (D. L. King, 1973, p. 403).  Likewise, “The idea that the CR is due to a CS-produced image of the UCS is supported by findings that suggest that images of stimuli result in responses similar to the ones produced by real stimuli” (D. L. King, 1979, p. 31). 

More evidence for the theory follows.  First, a CS results in verbal descriptions of a US, verbal responses suggesting that the US is perceived, and a judgment of which direction a moving object rotates that all suggest that the CS is perceived as similar to the US per results of Davies, Davies, and Bennett (1982), Ellson (1941), Haijiang, Saunders, Stone, and Backus (2006), and Powers, Mathys, and Corlett (2017).  Second, a verbal response was associated with activation of a brain region that is activated by the US (Powers et al.). 

More evidence for the theory is that a nontarget that was paired with the eventual receipt of a larger financial award resulted in a slower or less accurate saccade toward a target than a nontarget that was paired with the eventual receipt of a smaller financial award (Bucker et al., 2015; Le Pelley, Pearson, Griffiths, & Beesley, 2015).  Humans probably tend to aim a saccade at a physically present larger reward more than at a physically present smaller reward.  Hence these results are evidence that the nontarget for a larger financial award was a CS and that its perception became similar to the forthcoming perception of the US of a larger financial reward.

8.  Assimilation Enables a Response-Correlated Stimulus

to Be Perceived as Very Similar to a

Retained Perceived Instrumental-Response-Correlated Stimulus

The present division supports an assimilation theory of instrumental conditioning.  Hence this article’s proposition that an assimilation process enables diverse general results is also supported.  The reward learning type of instrumental conditioning is covered.

The theory of instrumental conditioning maintains that assimilation enables a response-correlated stimulus to be perceived as very similar to, that is, match, a retained perceived instrumental-response-correlated stimulus.  Also, a retained perceived instrumental-response-correlated stimulus exists, because this stimulus was perceived when the instrumental response was previously executed.  In addition, the occurrence of the match means that the instrumental response is made again.  Similar theoretical statements follow.  “Successively closer approximations to the stimuli produced by the instrumentally conditioned response” occur, “this response thereby eventuating” (D. L. King, 1974, p. 1115).  Also, “the animal brings about a match between a response-produced stimulus and an image of the same stimulus” (D. L. King, 1979, p. 449) (an image of a response-produced stimulus and a retained perceived instrumental-response-correlated stimulus are alike.)  Additionally, “the mechanism for matching may be essentially identical to the one for assimilation” (D. L. King, 2001, p. 36). 

The assimilation theory of instrumental conditioning is supported by classical conditioning’s occurrence as follows.  The instrumental-response-correlated stimulus is essentially a CS, because it is paired with the reward that the instrumental response brings about.  Hence classical conditioning should occur between “the response-produced stimuli and the goal” (King, 1974, p. 1115).  An animal looks at a CS, puts it in its mouth, and so on per the preceding division.  That is, an animal responds in order to better perceive a CS.  Thus an animal should attempt to perceive the CS of the instrumental-response-correlated stimulus.   Presumably this attempt is successful, because this success explains the occurrence of the instrumental response.  Finally, the reason that this attempt is successful is that assimilation enables a perceived response-correlated stimulus to match the retained perceived instrumental-response-correlated stimulus, which is as the theory maintains per the preceding paragraph.

9.  Assimilation Enables a Response-Correlated Stimulus

to Be Perceived as Similar to a

Retained Perceived Stimulus Produced by a Demonstrator’s Response

As previously, a perceived response-correlated stimulus means that the response in question is being executed.  Hence imitation occurs when an observer produces a response-correlated stimulus that is perceived as similar to the perceived stimulus produced by a demonstrator’s response.  Similarly, an animal “matches the stimulus produced by his or her own response to the stimulus provided by the demonstrator’s response” (D. L. King, 1979, p. 449).  Thus imitation reveals that a perception becomes similar to another perception.  Accordingly, a theory of imitation is that assimilation enables an observer’s response-correlated stimulus to be perceived as similar to the perceived stimulus produced by a demonstrator’s response.  Also, this “perceived as similar” means that the imitated response is executed.  Support for this assimilation theory of imitation means that the article’s proposition that an assimilation process enables diverse general results is also supported.

This division concentrates on delayed imitation.  This is mainly because an assimilation theory of delayed imitation and division 8’s assimilation theory of instrumental conditioning are about analogous. 

An assimilation theory also explains classical conditioning per division 7.  Also, classical conditioning’s occurrence supports the assimilation theory of instrumental conditioning per division 8.  The upshot is that related assimilation theories explain classical conditioning, instrumental conditioning, and imitation.  Hence support for each of these theories also supports the other two theories.

Evidence that delayed imitation occurs is outlined.  Delayed imitation of visually perceived responses by chimpanzees and gorillas occurs (Moore, 1992, a review).  Delayed imitation of visually perceived responses by rats and dogs occurred (Will, Pallaud, Soczka, & Makikowski, 1974 and Fugazza & Miklosi, 2014, respectively).  A familiar result is that delayed imitation of sounds by birds occurs.  Delayed imitation of visually perceived responses by a parrot (Moore, 1992) and quails (Akins & Zentall, 1996) occurred.  For example, when a demonstrator rat pressed a lever only once during a brief period that food could be obtained, afterward an observer rat was more likely to press a lever only once during a brief period (Will et al.).  Another example is that when a human made a hand wave, afterward a parrot imitated the hand wave by moving its wings (Moore, 1992). 

The assimilation theory of imitation for specifically delayed imitation is that assimilation enables an observer’s response-correlated stimulus to be perceived as similar to a retained perceived stimulus that the demonstrator’s response produces.  The theory of instrumental conditioning is that assimilation enables a response-correlated stimulus to be perceived as very similar to (match) a retained perceived instrumental-response-correlated stimulus.  Hence the two theories are about analogous.  Similarly, “The matching involved in delayed imitation appears to be quite similar to the matching that occurs in straightforward instrumental conditioning” (D. L. King, 1979, p. 449).  Also, “Delayed imitation … involves a closely related type of matching” (D. L. King, 2001, p. 36). 

Because the assimilation theory of delayed imitation and the assimilation theory of instrumental conditioning are about analogous, the theory of instrumental conditioning is supported.  A reason is that delayed imitation is most likely more difficult than instrumental conditioning.  Similarly, the “more difficult … matching in delayed imitation definitely supports the possibility that the corresponding matching occurs in straightforward instrumental conditioning” (D. L. King, 1979, p. 449).  Likewise, “The occurrence of a difficult process should increase the probability that a related easier process occurs” (D. L. King, 2001, p. 36).  Delayed imitation is most likely more difficult than instrumental conditioning, because in imitation an observer’s perceived response-correlated stimulus can be fairly dissimilar to the stimulus produced by a demonstrator’s previous response, which should make it more difficult to extract the similarity between these two stimuli.  An example of a dissimilarity for delayed imitation is that when a parrot imitated the previous hand waving of a human by moving its wings (Moore, 1992), the parrot could hardly visually perceive this wing movement. 

Another reason the theory of instrumental conditioning is supported by delayed imitation’s occurrence is that an observer’s delayed imitation response is frequently obvious.  This is because a delayed imitation response and an instrumentally conditioned response correspond, and because the obviousness of a delayed imitation response then increases the probability that the instrumental conditioning response also occurs via assimilation.

10.  Assimilation Enables a Young Animal’s Perceived Fear

 to Become Similar to the Perceived Calmness Produced by Stimuli of the Mother

A young animal’s perception of fear is produced by a novel (strange) stimulus and also by a punishing stimulus such as shock (a first conclusion).  A young animal’s perception of calmness is produced by stimuli of a mother or substitute mother (a second conclusion).   A young animal’s perception of fear is decreased by stimuli of a mother or substitute mother (a third conclusion). 

The third conclusion is explained by an assimilation theory.  The theory posits that the perceived fear becomes similar (assimilates) to the perceived calmness and that is why the perceived fear is decreased.  This theory is supported because it explains the decrease in fear.  Hence the present article’s proposition that an assimilation process enables diverse general results is also supported. 

The first, second, and third conclusions of two paragraphs past are briefly supported in sequence.   Humans, monkeys, dogs, and birds are covered.

The first conclusion is supported because it is known that the perception of fear is produced by a punishing stimulus such as shock.  It is also supported because the perception of fear is produced by a novel stimulus per the following.  The perception of fear in human infants was produced by a strange room per more crying and autistic behavior and less playing with objects (Arsenian, 1943), by a stranger per more crying and gaze aversion (Bronson, 1972), and by a stranger per more frowning (Campos, Emde, Gaensbauer, & Henderson, 1975).  The perception of fear in young monkeys was produced by a strange object such as a moving toy bear per crouching and rocking (Harlow & Zimmermann, 1959) and also by a human face per grimacing (Kenney, Mason, & Hill, 1979).  The perception of fear in young dogs was produced by a strange quiet human per the dogs’ withdrawal from the human (Freedman, King, & Elliot, 1961) and was produced by a strange pen per the dogs’ more frequent whining (Elliot & Scott, 1961).  The perception of fear in young but not very young birds was produced by a strange frequently moving inanimate object of intermediate size per flight from it (Jaynes, 1957) and per more avoidance, disress calls, and startle responses (Moltz & Stettner, 1961). 

The second conclusion is supported by the result that a young animal tends to approach and remain close to a mother when the perception of fear does not occur.  This result is supporting because this approach and closeness are presumably due to the perception of calmness.   A human infant is known to frequently approach and remain close to the mother when the perception of fear does not occur.  Young monkeys frequently made tactual contact with a cloth mother per a measure of hours spent on her when the perception of fear did not occur (Harlow & Zimmermann, 1959).  Young dogs did likewise (Igel & Calvin, 1960).  Very young birds exposed to an inanimate moving object tended to remain close to and follow it including at a later age, likewise, imprinting occurred (e.g. Jaynes, 1957). 

The third conclusion is supported including by the result that young animals that perceive a fear producing stimulus approach, remain close to, and/or contact the mother.  The interpretation of this result is that these responses occur because they increase the perception of calmness likewise decrease the perception of fear.  When human infants were in a strange room, the presence of the mother reduced crying and autistic behavior and increased playing with objects (Arsenian, 1943).  When a stranger was present, infants that were held by their mother infrequently cried and older infants often crawled toward their mother (Bronson, 1972).  When young monkeys were shown a novel object, they approached a cloth mother and tactually contacted her more than a wire mother (Harlow & Zimmermann, 1959).  Young monkeys with a cloth mother also crouched and rocked less and eventually explored the novel object more.  When blasts of air came from a cloth mother, young monkeys made more tactual contact with it (Rosenblum & Harlow, 1963).  Young dogs that were both physically punished and rewarded by an experimenter were more likely to remain close to and in contact with the experimenter than young dogs that were only rewarded (Fisher 55, as cited in Rajecki, Lamb, & Obmascher, 1978).  Young birds exposed to novel stimuli exhibited less signs of fear when they remained close to their imprinting object (Moltz, 1960, p. 301).  Young birds in an unfamiliar open field peeped loudly less frequently when their imprinting object was present (Stettner & Tilds, 1966).  Young birds often remained close to their imprinting object even though they were therefore also closer to a strange doll (Stettner & Tilds, 1966).  Young birds were more likely to follow their imprinting object when they were previously shocked in the same enclosure (Moltz, 1963). 

These three conclusions are additionally supported because their validity would result in an evolutionary advantage (D. L. King, 1965).  A mother and her young children hardly perceive novel dangerous stimuli such as those produced by a nearby fire, because if they did their survival would be less likely.  Hence the stimuli of the mother decrease her offspring’s perception of fear of novel stimuli that are not dangerous.  Thus when her offspring are now adults and they perceive novel stimuli, these stimuli tend to be dangerous.  The perception of novel stimuli produces escape and avoidance.  Therefore adults escape and avoid novel–and dangerous—stimuli.  So an evolutionary advantage ensues.

11.  An Assimilation Process May Enable Contrast

This division provides an account of how an assimilation process may enable the general result that the similarity between the perceived parts of different objects decreases.  This decrease in similarity is frequently referred to as contrast, as it will be here.  In this division, a perceived part includes both a perceived location and a perceived feature.  An example of evidence of contrast is that the perceived location of a line became less similar to the physical location of an adjacent square (Ganz, 1964) (this result occurred when the line and square were less near).  The account of how an assimilation process may enable contrast follows.

A single physical element results in multiple neural values that are on the same neural dimension.  For example, a point that is low in intensity results in these multiple neural values.  The nervous system also computes an average of these multiple neural values.  This average is called a neural average.   An average is a single event.  Hence the neural average is a single neural event.  Critically, the neural average results in a single perceived part. 

Accordingly, two elements frequently result in two sets of multiple neural values that are on the same neural dimension.  Hence two ensuing neural averages that are on the same neural dimension frequently occur.  Thus these two neural averages result in two perceived parts.  When the two neural averages are on the same neural dimension, the two perceived parts are on the same perceptual dimension.

For exposition, a first element results in two neural values on a neural dimension.  Also, these neural values are 0 and 6.  Hence the first element results in a neural average of 3.  Thus the element-produced first perceived part is 3 when the element occurs individually (alone).  Additionally, for exposition, a second element also results in two neural values that are on the same neural dimension.  Also, these neural values are 7 and 13.  Therefore the second element results in a neural average of 10.  Consequently, the element-produced second perceived part is 10 when the element occurs individually.  Accordingly, these two perceived parts are on the same perceptual dimension.

In addition, an assimilation process operates on neural values that are on the same neural dimension.  Also, this assimilation process operates in the way that assimilation between EP locations occurs.  This last statement means that the accuracy of a neural value can also vary.  Recollecting, a less accurate EP location often assimilates toward a more accurate EP location and often the reverse assimilation does not occur per division 2.  Thus the same statement also means that an assimilation process may change an element’s neural values or it may not. 

In accord with the preceding paragraph, the first element’s neural values of 0 and 6 are, for exposition, considered to be less accurate than the second element’s neural values of 7 and 13.  Also in accord, when the first and second elements appear at about the same time, the neural values of 0 and 6 assimilate toward (become similar to) the neural values of 7 and 13, whereas the neural values of 7 and 13 are unchanged.  The amount of this assimilation is called moderate.  This moderate assimilation results in the first element’s neural values of 0 and 6 becoming, for exposition, 2 and 8, respectively. 

The first element’s assimilation-produced neural value of 8 is larger than the second element’s unchanged neural value of 7.  Critically, consequently the neural value of 8 no longer affects the neural average that the first element results in.  The first element’s sole remaining neural value is 2.  Hence the first element’s neural average is also 2.  Thus the first element produces a first perceived part of 2. 

Summing, when the first element appears individually, the first perceived part is 3.  Also, when a second element appears at about the same time and hence an assimilation process operates, the first perceived part is 2.  Additionally, the second perceived part continues to be 10.  Hence the first perceived part of 2 is less similar to the second perceived part of 10 when an assimilation process operates than when it does not.  Thus the possibility that an assimilation process enables contrast between perceived parts is supported. 

The described assimilation process also brings about assimilation.  The same two elements and their neural values when these elements occur individually are used for exposition.  Now the first element’s two neural values assimilate toward the second element’s two neural values by a larger extent.  Accordingly, the extent of this assimilation is called large.  The second element’s two neural values are again unchanged.  The large assimilation results in the first element’s neural values of 0 and 6 becoming, for exposition, 4 and 10.  The first element’s neural value of 10 is larger than the second element’s neural value of 7.  Critically, therefore the first element’s neural value of 10 no longer affects the neural average that the first element results in (analogous to the claim for moderate assimilation).  The first element ’s sole remaining neural value is 4.  Hence the first element’s neural average is also 4.  Thus the first perceived part is 4. 

Summing, when the first element appears individually, the first perceived part is 3.  Also, when the second element also occurs and when the assimilation is large, the first perceived part is 4.  Additionally, the second perceived part continues to be 10.  The perceived part of 4 is more similar to the perceived part of 10 than is the perceived part of 3.  Hence the first perceived part assimilates toward (becomes similar to) the second perceived part, as to be explained.

How an assimilation process may result in contrast has been indicated.

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