ASSIMILATION AND PERCEIVED DIRECTION: A PERCEPTION IS HYPOTHESIZED TO ASSIMILATE TO A PERCEIVED DIRECTION OR ASPECT OF IT SUCH AS ITS ACCURACY

Two corrections of the text of the “7.1 Introduction” section were made on 6/5/22. In both cases, the corrected text is in bold.

ABSTRACT

Evidence is indicated that often or typically an object’s perceived direction assimilates (becomes similar) to another object’s perceived direction, the perceived direction of an object’s perceived features is extremely similar to (the same as) the object’s assimilation-produced perceived direction, the accuracy of a singleton object’s perceived features is similar to the inaccuracy of its perceived direction, the accuracy of an object’s assimilation-produced perceived direction is similar to the inaccuracy of its singleton perceived direction, the accuracy of an object’s perceived features is similar to the inaccuracy of its assimilation-produced perceived direction, the accuracy of an object’s perceived features is also similar to the increased—not decreased—accuracy of its assimilation-produced perceived direction, and the unitized perception of features is similar to the assimilation-produced unitized perception of directions.  Condensing, a perception is similar to an object’s perceived direction or aspect of it.  The ensuing hypothesis is that a perception is similar to an object’s perceived direction or aspect of it because it assimilates (becomes similar) to this direction or aspect.  Evidence is largely from briefly processed, low contrast, and small objects.  The process for assimilation may also enable contrast per an explanation.

1 INTRODUCTION

The present paper provides evidence that the following results occur either often or typically.  The divisions of the paper in which the evidence appears are numbered.  An object’s perceived direction becomes similar to another object’s perceived direction in other words assimilation between perceived directions occurs (2), the perceived direction of an object’s perceived features is extremely similar to (the same as) the object’s assimilation-produced perceived direction (3), the accuracy of a singleton object’s perceived features is similar to the inaccuracy of its perceived direction (4), the accuracy of an object’s assimilation-produced perceived direction is similar to the inaccuracy of its singleton perceived direction (5), the accuracy of an object’s perceived features is similar to the inaccuracy of its assimilation-produced perceived direction (6), the accuracy of an object’s perceived features is also similar to the increased—not decreased—accuracy of its assimilation-produced perceived direction (7), and the unitized perception of features is similar to the assimilation-produced unitized perception of perceived directions (8).  The perceived direction under consideration is egocentric.    

Condensing, a perception is similar to an object’s perceived direction, the accuracy of its perceived direction, or the unitized perception of perceived directions.  Additionally condensing and in conclusion, a perception is similar to an object’s perceived direction or aspect of it.  

The majority of the evidence for this conclusion will come from briefly processed, low contrast, and small objects.  The effects of a unique feature, an object that onsets in a new direction, a cue that predicts the direction or features of a second object, an instruction to attend to an object, divided attention, and so on will not be covered. 

The interpretation of the conclusion that a perception is similar to an object’s perceived direction or aspect of it is that the perception is hypothesized to assimilate to a perceived direction or aspect of it and this is why the perception is similar.  Assimilation means a perception becomes similar to another perception, likewise, the similarity between two perceptions increases.  An illustration of the interpretation is that the accuracy of a briefly processed, low contrast, and small singleton object’s perceived features is hypothesized to assimilate to this object’s inaccurate perceived direction and this is why these perceived features are similarly (also) inaccurate.  The interpretation is supported by all divisions.  The interpretation will be referred to as Division 1’s hypothesis.  (Accordingly, the present introduction will be referred to as Division 1.) 

A theory is that one–always the same–process enables a perception to assimilate to another perception.  Enables means is essential to bringing about.  The perception can be of different types.  The theory will be called assimilation theory.  The process will be called the assimilation process.   Because Division 1’s hypothesis is that a perception is hypothesized to assimilate to a perceived direction or aspect of it, when Division 1’s hypothesis explains a perception, assimilation theory maintains that this perception is enabled by the assimilation process.  Because assimilation theory explains a perception’s assimilation to another perception, it supports Division’s 1 hypothesis.  Because assimilation theory is explanatory, it too is supported.   The assimilation process is also reasoned to enable contrast such as the contrast that occurs between different tilts (Division 9). 

A final division (10) summarizes support for Division 1’s hypothesis and also supports previously indicated conclusions and explanations.  It also integrates and extrapolates results.

“Perceived direction” will frequently be referred to when it is more precise to refer to “neural information for perceived direction.”  Referring to this neural information can be more precise, because the direction under consideration may not be consciously perceived, for example, because another direction is.  This reference can also be more precise in that this neural information can affect another perception whereas “perceived direction” is akin to a dependent variable.  This note also applies to a perceived feature, for it too may not be consciously perceived and is akin to a dependent variable. 

The paper’s main parts are referred to as divisions and numbered.  Accordingly, parts of a division are referred to as sections and also numbered.  Numbering helps to discriminate among both divisions and sections and also helps to refer to them. 

Presumably, the perception of the tilt, shape, and size of an object is associated with the perceived directions of the different points that comprise the object.  Nevertheless, the perception of tilt, etc. is treated as the perception of a feature. 

The physical proximity between two objects can also be referred to as the similarity between the physical directions of two objects.  This is because this proximity and similarity are associated.    Referring to physical proximity instead of the similarity between physical directions may reduce confusion between physical directions and perceived directions.  Accordingly, physical proximity will often be referred to.

Another note bears on successively appearing objects.  An initial object will tend to be referred to as a S1 object and a subsequent one as a S2 object.

2  A PERCEIVED DIRECTION ASSIMILATES TO ANOTHER PERCEIVED DIRECTION 

2.1 Evidence for Assimilation between Perceived Directions

The present division provides evidence that an object’s perceived direction assimilates toward (becomes similar to) another object’s perceived direction and frequently vice versa.  Assimilation between perceived directions is also often referred to.  Illustrative evidence of assimilation between perceived directions is that the perceived direction of a vertical white line became similar to the physical direction of an adjacent proximal white rectangle (Ganz, 1964). 

When assimilation between perceived directions is under consideration, an object’s perceived direction is distinguished from its assimilation-produced perceived direction.  An object’s perceived direction is its perceived direction that would occur if it appeared alone, that is, if it were a singleton object.  Likewise, an object’s perceived direction is not its assimilation-produced perceived direction.  Because an object’s singleton perceived direction tends to be accurate, when assimilation between perceived directions occurs, an object’s perceived direction is presumed to also tend to be accurate.  Thus, it is considered appropriate to maintain that the preceding paragraph’s vertical white line assimilated toward the perceived direction of the white rectangle (as well as toward its physical direction). 

Evidence that assimilation between perceived directions occurs are results indicating that assimilation between perceived features occurs (e.g., Helson & Rohles, 1959; Oyama, 1975).  This is because by generalization the occurrence of assimilation between features increases the likelihood that assimilation between perceived directions occurs. 

More evidence that assimilation between perceived directions occurs follows.  The occurrence of this assimilation means that when a first and a second object’s perceived directions are, for example, 1 and 5, respectively, the first object’s assimilation-produced perceived direction can become 2, 3, 4, and 5 but never dissimilar to 5, for example, never 6.  Thus, evidence that assimilation between perceived directions occurs is that an object’s perceived direction became very similar to a second object’s physical (hence presumably perceived) direction while not also becoming dissimilar to it (Rentschler, Hilz, & Grimm, 1975; Watt & Morgan, 1983; Morrone, Ross, & Burr, 1997; Born, Kruger, Zimmermann, & Cavanagh, 2016). 

There is more evidence.  When, for example, a first and a second object’s perceived directions are 4 and 5, respectively, then per the meaning of assimilation between directions, the maximum absolute amount of assimilation of the first object’s perceived direction toward the second object’s perceived direction that is possible is 5 – 4 = 1 and thus small.  Also, when these perceived directions are 1 and 5, then the maximum absolute amount of the assimilation between perceived directions that is possible is 5 – 1 = 4 and thus large.  So, evidence that assimilation between perceived directions occurs is that a relatively high similarity between the physical and hence presumably perceived directions of two objects results in a relatively small absolute amount of assimilation between these directions (Coren & Hoenig, 1972; Rentschler et al., 1975; Watt & Morgan, 1983; Morrone et al., 1997; McSorley, Cruickshank, & Inman, 2009; Born et al., 1916).  (The evidence of Coren and Hoenig and McSorley et al. comes from a result that the next paragraph considers.)

Evidence of assimilation between directions also comes from an averaging of directions result.  This result occurs when a perceived direction is an average of two or more objects’ physical directions.  One such result is that a first object’s perceived direction was about the average of its physical direction and a second object’s physical direction according to the reproduced direction of the first object (Hazeltine, Prinzmetal, & Elliott, 1997).  Another such result occurred when the instruction was to saccade toward a first object and saccades landed (aimed) at about the average of its physical direction and a second object’s physical direction (e.g., Coren & Hoenig, 1972).  This is because a saccade’s aim tends to indicate the direction that is currently perceived.  This statement is supported by the result that averaging of directions also occurred according to a reproduction measure of perceived direction per two sentences past.  More support for this statement starts in Division 3.  An explanation of the averaging of directions result for two objects then is that each object’s perceived direction (that approximates its physical direction) assimilates toward the second object’s perceived direction by a sufficiently high percentage that these two perceived directions are averaged, the consequence being one perceived direction that is the average of the two objects’ perceived directions.  Per this explanation, a perceived direction assimilates toward a second perceived direction and vice versa.  Thus, the result and its explanation provide evidence of assimilation between directions. 

Four types of evidence of assimilation between perceived directions have been indicated.  In conclusion, assimilation between perceived directions is considered to occur.

2.2  Imports of Assimilation between Perceived Directions

Imports of the occurrence of assimilation between perceived directions are covered.  There are also comments. 

The occurrence of assimilation between perceived directions supports Division 1’s hypothesis that a perception is hypothesized to assimilate to a perceived direction or aspect of it.  First, the occurrence of assimilation between directions means that a perception actually (really) assimilates toward (becomes similar to) a perceived direction.  Second, by generalization, this actual assimilation supports the occurrence of the hypothesized assimilation of Division 1’s hypothesis. 

The occurrence of assimilation between perceived directions means that there should be a source for each object’s perceived–not assimilation-produced perceived–direction.  Thus, it is inferred that each object results in neural information for a perceived direction that approximates the perceived direction that occurs when it is a singleton object (appears alone).  A singleton object’s perceived direction will often be referred to as a singleton perceived direction.  Thus, the occurrence of assimilation between perceived directions supports the inference that each of two or more simultaneously present objects results in neural information for a perceived direction that approximates its singleton perceived direction.  This inference is called the neural-information inference. 

The measurement of the extent of assimilation between perceived directions that occurs is considered.  Per the preceding section, the similarity between the perceived directions of two objects is associated with the amount of absolute assimilation between these directions that occurs.  Thus, it can be more appropriate to refer to the percentage of assimilation between perceived directions that occurs.  Accordingly, this percentage was also referred to in the preceding section.  An example of a percentage of assimilation is that when a first object’s perceived direction is 1, a second object’s perceived direction is 5, and the first object’s assimilation-produced perceived direction toward the second object is 3, the percentage of the first object’s assimilation is (3 – 1)/(5 – 1) or 50%.    

Assimilation between perceived directions, an assimilation-produced perceived direction, and assimilation toward the perceived direction of a second object will frequently be referred to.  Similar terms, including an increase in the similarity between perceived directions, will also be used.  Truncations of these terms will also be used.  For example, just assimilation may be mentioned. 

Assimilation between perceived directions is also referred to as attraction (e.g., Ganz, 1964):  An object is attracted to the direction of another object.  Also, evidence of assimilation between perceived directions is conceived of as evidence of the occurrence of spatial compression (e.g., Born et al. 2016). 

3  THE PERCEIVED DIRECTION OF PERCEIVED FEATURES IS THE SAME AS AN ASSIMILATION-PRODUCED PERCEIVED DIRECTION (BINDING OCCURS) 

The present division considers the result that the perceived direction of an object’s perceived features is the same as the object’s assimilation-produced perceived direction.  In other words, it considers the result that an object’s perceived features are bound to its assimilation-produced perceived direction. 

This binding is evidenced when an assimilation-produced perceived direction is measured by indicating the direction of an object’s features.  An example of such a measurement is the task to move “the screen cursor (with the mouse) to the location of the small target dot” (Prinzmetal, 2005, p. 65).  This is because it seems that the cursor is moved to the perceived direction of this dot’s perceived features. 

Division 1’s hypothesis explains this binding.  Recollecting, this hypothesis is that a perception is hypothesized to assimilate to a perceived direction or aspect of it.  Presumably, this assimilation can be complete.  Thus, the perceived direction of an object’s perceived features is hypothesized to completely assimilate to (become the same as, become bound to) the object’s assimilation-produced perceived direction and this is why the object’s perceived features are perceived at its assimilation-produced perceived direction.  Because Division 1’s hypothesis is explanatory, it is supported.

Division 1’s hypothesis also explains the general binding result.  This result is that the perceived direction of an object’s features is ordinarily at the object’s perceived direction regardless of whether assimilation between perceived directions occurs or not.  Per Division 1’s hypothesis, the perceived direction of an object’s perceived features is hypothesized to completely assimilate to (become the same as, become bound to) the object’s perceived direction. 

Per Division 1, assimilation theory maintains that the same assimilation process enables a perception to assimilate to another perception for different types of perception.  Accordingly, per assimilation theory, the hypothesized complete assimilation of the perceived direction of an object’s perceived features to an object’s perceived direction is enabled by the assimilation process.  Thus, assimilation theory supports Division 1’s hypothesis and, being explanatory, is supported itself. 

Because Division 1’s hypothesis is that a perception is hypothesized to assimilate to a perceived direction or aspect of it, it is maintaining that a perceived direction or aspect of it has precedence over another perception.  Thus, a corollary of Division 1’s hypothesis is that a perceived direction or aspect of it precedes another perception.  The corollary will be referred to as the precedence corollary.  The precedence corollary is supported by the present division’s result that an object’s features are perceived at its assimilation-produced perceived direction.   This is because there seems to be no reason to suspect that an object’s perceived features are the basis for their being at a specific perceived direction including an assimilation-produced one. 

4  THE ACCURACY OF A SINGLETON OBJECT’S PERCEIVED FEATURES IS SIMILAR TO THE INACCURACY OF ITS PERCEIVED DIRECTION

4.1  Introduction

The present division provides evidence that the accuracy of a briefly processed, low contrast, and small singleton object’s perceived features is similar to the inaccuracy of its perceived direction.  That is, it provides evidence that the perceived features of a briefly processed, etc. singleton object are also inaccurate. 

Division 1’s hypothesis explains why the accuracy of a briefly processed, etc. singleton object’s perceived features is similar to the inaccuracy of its perceived direction.  Recollecting, Division 1’s hypothesis is that a perception is hypothesized to assimilate to a perceived direction or aspect of it and this is why the perception is similar.  The aspect includes the accuracy of a perceived direction.  Thus, per Division 1’s hypothesis, the accuracy of a briefly processed, etc. singleton object’s perceived features is hypothesized to assimilate to the inaccuracy of its perceived direction and this is why these perceived features are also inaccurate.  Because this features inaccuracy is explained by Division 1’s hypothesis, Division 1’s hypothesis is supported. 

Per the assimilation theory that Division 1 also considered, the hypothesized assimilation is enabled by the assimilation process.  Thus, assimilation theory supports Division 1’s hypothesis, and being explanatory, is supported itself.    

4.2  Brief Processing 

The present section provides evidence that the accuracy of a briefly processed singleton object’s perceived features is similar to the inaccuracy of its perceived direction.  That is, per this evidence, these perceived features are also inaccurate.  The present section also explains this features inaccuracy using Division 1’s hypothesis. 

One way to produce brief processing is to present an object for a brief duration.  A second way is to use a short stimulus onset asynchrony (SOA) between an object and a mask.  

The present section also supports the conclusion that the accuracy of a saccade’s landing (aim) toward an object is a measure of the object’s perceived direction.  A saccade’s latency is also concluded to be a measure of an object’s perceived direction.   

Inaccurately perceived direction results are covered first, starting with those of Prinzmetal (2005).  The singleton object was a small disk.  Over trials, its stimulus duration was either 67 ms or 500 ms.  Its physical direction also varied over trials.  The disk did not appear on some trials.  The perceived direction task was to reproduce the disk’s location hence direction.  The 67 ms stimulus duration resulted in a much larger difference between the reproduced and physical directions of the disk than the 500 ms duration.  This result is evidence that the briefly processed disk’s perceived direction was relatively inaccurate.  Another task was to judge when the disk did not appear.  Participants’ judgements indicated that the disk was usually perceived.  Therefore, it is unlikely that guessing brought about the relatively inaccurate perceived direction. 

A briefer processing time also resulted in a relatively inaccurate perceived direction per a saccadic measure and also a psychophysical measure of perceived direction (Aitsebaomo & Bedell, 1992).  In the saccade experiment, a singleton object, a small vertical line, appeared to the right.  Over trials, the line’s stimulus duration varied from 17-200 ms.  The line was immediately followed by a mask.  The instruction was to saccade toward the line.  A briefer stimulus duration resulted in a saccadic landing (aim) that was more inaccurate.  This result is evidence that a more briefly processed line’s perceived direction was relatively inaccurate per the next paragraph.  A psychophysical task was to indicate whether the perceived direction of a target line that was in the right visual field was less or more eccentric than the direction of a reference line in the left visual field.  The stimulus durations and masking conditions for the target object were comparable to those of the saccade experiment.  The reference object was continuously visible and it was separated from the target object by more than 10 deg.  Thus, the target object is thought to function as a singleton object.  A more briefly processed target object’s perceived direction was relatively inaccurate according to this psychophysical measure. 

The conclusion that a saccade’s landing (aim) toward an object is a measure of its perceived direction of three paragraphs past is supported.  First, the results of Aitsebaomo and Bedell (1992) indicate that briefer processing resulted in an object’s perceived direction being relatively inaccurate per both a saccadic aim measure and a psychophysical measure.  Second, the saccade aim result of Aitsebaomo and Bedell and the psychophysical result of Prinzmetal (2005) of two paragraphs past indicate the same joint inaccuracy.  Third, per Division 2, the averaging of directions result occurs according to a saccade’s aim and also to a reproduction measure of perceived direction.  A saccade’s latency is also concluded to be a measure of an object’s perceived direction providing that its aim is accurate.  This is because a short (long) saccadic latency is evidence that less (more) processing time is needed for an object’s direction to be accurately perceived.

Evidence that a saccade’s landing (aim) is a measure of perceived direction will be accumulating.  This is also the case for a saccade’s latency. 

Perceived features are now considered.  It is well known that briefer processing of a singleton object results in a more inaccurate perception of its features.  An illustrative result is that the briefer stimulus duration of 9 ms increased a singleton disk’s contrast threshold (Barlow, 1956).  This result is evidence of this more inaccurate perception of features, because it means that when the stimulus duration was 9 ms, the disk’s contrast had to be increased in order to reduce errors in detecting its features. 

Summing, a briefly processed singleton object’s perceived direction and perceived features are both relatively inaccurate.  Thus, Division 1’s hypothesis applies:  The accuracy of a briefly processed singleton object’s perceived features is hypothesized to assimilate to the inaccuracy of its perceived direction and this is why these perceived features are also inaccurate.

4.3  Contrast

The present section provides evidence that the accuracy of a low contrast singleton object’s perceived features is similar to the inaccuracy of its perceived direction, meaning that these perceived features are also inaccurate.  Thus, the present section’s evidence is like the preceding section’s evidence.  Accordingly, Division 1’s hypothesis applies essentially as previously. 

Contrast will refer to the similarity between an intensity and a second intensity.  A low (high) similarity is equivalent to a high (low) contrast. 

Saccadic latency evidence for perceived direction comes from results of Doma and Hallett (1988).  The intensity of a singleton object varied over trials.  The intensity of the background was still lower.  On a trial, the singleton object appeared in either of two directions.  The instruction was to saccade to the object.  A lower intensity hence lower contrast object resulted in longer saccadic latencies than a higher intensity hence higher contrast object.  The preceding section concluded that the latency of a saccade can be a measure of perceived direction.  Thus, the result is evidence that a lower contrast singleton object’s perceived direction was relatively inaccurate. 

Saccadic landing evidence for perceived direction comes from Heeman, Van der Stigchel, Munoz, and Theeuwes (2019).  On each trial, a singleton object appeared that was higher in intensity than the background by either a low amount or a high amount.  Over trials, this low or high intensity hence low or high contrast singleton object appeared at one direction or a second direction.  The instruction was for an eye movement to land (aim) at the object.  The saccades aimed toward the high contrast singleton object more accurately than toward the low contrast singleton object.  The preceding section concluded that the aim of a saccade can be a measure of perceived direction.  Thus, the low contrast singleton object’s perceived direction was relatively inaccurate.

The contrast of a singleton Gabor object was also varied (White, Kerzel, & Gegenfurtner, 2006).  Over trials, this object appeared either to the left or right.  The task was to make an eye movement to its center upon its appearance.  A lower contrast object resulted in longer saccadic latencies than a higher contrast object.  Thus, a lower contrast Gabor object’s perceived direction was relatively inaccurate. 

Regarding perceived features, it is known that a low contrast singleton object’s perceived features are relatively inaccurate.  This inaccuracy is evidenced, for example, by determining the contrast threshold of a singleton object.  This is because when this threshold is determined, a decrease in the singleton object’s intensity and hence contrast makes its detection and thus the perception of its features more inaccurate. 

Thus, a low contrast singleton object’s perceived features and perceived direction are both relatively inaccurate.  Division 1’s hypothesis explains why:  The accuracy of a low contrast singleton object’s perceived features is hypothesized to assimilate to the relative inaccuracy of its perceived direction and this is why its perceived features are also relatively inaccurate. 

4.4  Size

The present section covers the effect of size.  It otherwise corresponds to the preceding two sections. 

Evidence for perceived direction comes from Van der Stigchel, Heeman, & Nijboer (2012).  The singleton object was a circle.  Its size varied over trials.  The circle’s physical direction also varied over trials.  The instruction was to move the eyes to the stimulus on the monitor.  A smaller circle resulted in a wider distribution of saccadic landings (aims) toward it than a larger circle.  Thus, a smaller singleton object’s perceived direction was relatively inaccurate per a saccadic aim measure of perceived direction. 

In another experiment, the spatial frequency of a singleton Gabor object varied over trials (Ludwig, Gilchrist, & McSorley, 2004).  The physical direction of this object also varied over trials.  Participants saccaded toward the direction of this object.  A higher spatial frequency resulted in a longer saccadic latency.  A higher spatial frequency tends to result in the perception of stripes that are narrower (smaller).  Thus, the perceived direction of a singleton object that tends to result in smaller perceived stripes was relatively inaccurate per a saccadic latency measure of perceived direction. 

Regarding perceived features, it is known that a smaller singleton object results in a relatively inaccurate perception of its features.   For example, the contrast threshold for a smaller singleton object was higher than for a larger singleton object (Barlow, 1956).  That is, for the same extent of contrast, a smaller singleton object’s perceived features were more inaccurate. 

Supporting evidence for perceived features also comes from a discrimination result (Schultz & Eriksen, 1978).  A singleton letter appeared on each trial.  Its size varied over trials.  Its identity also varied over trials.  On each trial, the task was to make one or a second rapid response depending on the identity of the singleton letter.  Smaller singleton letters resulted in slower response times.  Most likely an accurate discrimination between letters is enabled by an accurate perception of their features.  Thus, the smaller singleton objects probably resulted in slower response times because their features were less accurately perceived and so more time was needed to accurately perceive them. 

Summing, a small singleton object’s perceived features and perceived direction are both relatively inaccurate.  Per Division 1’s hypothesis, the accuracy of these perceived features is hypothesized to assimilate to the inaccuracy of this perceived direction and this is why these perceived features are also relatively inaccurate. 

5  THE ACCURACY OF AN OBJECT’S ASSIMILATION-PRODUCED PERCEIVED DIRECTION IS SIMILAR TO THE INACCURACY OF ITS SINGLETON PERCEIVED DIRECTION

5.1  Introduction

The present division provides evidence that a briefly processed, low contrast, and small  object assimilates toward the direction of another object more than a lengthily processed, high contrast, and large object does.  About equivalently, it provides evidence that a briefly processed, etc. object tends to assimilate toward the direction of another object. 

An assimilation-produced perceived direction is inaccurate.  Per the preceding paragraph, a briefly processed, low contrast, and small object tends to assimilate toward the direction of another object.  Thus, a briefly processed, etc. object’s assimilation-produced perceived direction is relatively inaccurate.  A briefly processed, etc. singleton object’s perceived direction is also relatively inaccurate per Division 4.  So, the accuracy of a briefly processed, etc. object’s assimilation-produced perceived direction is similar to the inaccuracy of a briefly processed, etc. object’s singleton perceived direction.  That is, both these perceived directions are relatively inaccurate.

Per Division 1’s hypothesis, the accuracy of a briefly processed, etc. object’s assimilation-produced perceived direction is hypothesized to assimilate to the inaccuracy of its briefly processed, etc. singleton object’s perceived direction and this is why the briefly processed, etc. object’s assimilation-produced perceived direction is also relatively inaccurate.  Because Division 1’s hypothesis explains the inaccuracy of the assimilation-produced perceived direction, it is supported. 

The indicated assimilation is enabled by the assimilation process, which is as previously.  Also as previously, thus both Division 1’s hypothesis and assimilation theory are supported. 

Because two or more objects are present when assimilation between perceived directions occurs, a singleton object is not actually present.  Nevertheless, per the neural-information inference of Division 2, each of two or more objects results in neural information of a perceived direction that approximates its singleton perceived direction.  So, this neural information should (is presumed to) enable a briefly processed, etc. object’s assimilation-produced direction to also be relatively inaccurate. 

5.2  Brief Processing

The present section provides evidence that a briefly processed object tends to assimilate toward the perceived direction of another object.  Because an assimilation-produced perceived direction is inaccurate per the preceding section, a briefly processed object’s tendency to assimilate toward the perceived direction of another object means that its assimilation-produced perceived direction is relatively inaccurate.  Thus, Division 1’s hypothesis applies:  The accuracy of a briefly processed object’s assimilation-produced perceived direction is hypothesized to assimilate to the inaccuracy of a briefly processed singleton object’s perceived direction, and this is why a briefly processed object’s assimilation-produced perceived direction is relatively inaccurate, equivalently, this is why it tends to assimilate toward the perceived direction of another object.   The present section’s evidence of this tendency to assimilate follows.   

In an experiment of Badcock and Westheimer (1985), the stimulus consisted of top and bottom vertical vernier lines and another bottom vertical line.  These lines were identical.  The other bottom line was adjacent and proximal to the bottom vernier line.  Over trials, the other bottom line was either to the left or right of the bottom vernier line.  Also, over trials, the stimulus duration of the other bottom line varied from being less than the duration of the vernier lines to the same duration as these lines.  The task was to judge whether one vernier line was to the left or right of the second vernier line.  The judgement results are evidence that as the stimulus duration of the third line decreased, it was more likely to assimilate toward the perceived direction of the bottom vernier line instead of vice versa. 

In an experiment of Born et al. (2016), a S1 vertical bar appeared and quickly thereafter a S2 adjacent vertical bar appeared.  Recollecting, per Division 1, an initial object will tend to be referred to as a S1 object and a subsequent one as a S2 object.  The task was to reproduce S2’s perceived direction.  The briefest stimulus duration of S2 (20 ms) resulted in a much larger percentage of S2’s assimilation toward the perceived direction of S1 than the longest stimulus duration of S2 (100 ms). 

Evidence also comes from the averaging of directions result.  This result occurs when a perceived direction is the average of the perceived directions of two or more objects per Section 2.1.  Also, Section 2.1 reasoned that the averaging of directions result is enabled by assimilation among the objects’ perceived directions.  Thus, the result that briefer processing was associated with more averaging of directions (Findlay & Gilchrist, 1997; Godijn & Theeuwes, 2002; McSorley et al. 09) is evidence that briefer processing results in more assimilation between perceived directions.  An experiment of Findlay and Gilchrist is covered in order to indicate how processing time varied.  On a trial, two squares appeared.  The instruction was to saccade to one of them.  This square was denoted by its physical direction.  Saccades with shorter latencies landed (aimed) at about the average of the directions of the two squares more frequently than saccades with longer latencies.  A saccade’s aim toward an object is a measure of its perceived direction per Division 4.  A shorter saccadic latency means that processing time is briefer.  So, briefer processing of the two squares was associated with more averaging of their perceived directions and therefore more assimilation between their perceived directions.   

Evidence also comes from the result that responses momentarily deviate (aim) toward another object instead of to the object that is to be aimed at.  This momentary deviation is taken as evidence that the object to be aimed at fleetingly assimilates toward the perceived direction of the other object.  Processing time varied in the same way as in the preceding paragraph.  Briefer processing was associated with a larger momentary deviation of both a saccade’s aim (McSorley, Haggard, & Walker, 2006; McSorley et al., 2009; van Zoest & Kerzel, 2015) and a manual response’s aim (van Zoest & Kerzel, 2015) toward the direction of the other object.  Thus, briefer processing of the object that was to be aimed at was associated with a larger amount of its fleeting assimilation toward the other object’s perceived direction. 

5.3  Contrast

The present section provides evidence that a low contrast object tends to assimilate toward the perceived direction of a higher contrast object.  The interpretation of this evidence is as previously.  Key considerations follow.  The tendency of a low contrast object to assimilate means that its assimilation-produced perceived direction is relatively inaccurate and thus similar to the relative inaccuracy of a low contrast singleton object’s perceived direction.  Thus, the accuracy of a low contrast object’s assimilation-produced perceived direction is hypothesized to assimilate to the inaccuracy of its singleton perceived direction and thus also become inaccurate.   The evidence comes next. 

A low intensity vertical line assimilated toward the direction of an adjacent high intensity otherwise identical vertical line and there was no indication that the high intensity line assimilated toward the direction of the low intensity line (Rentschler et al., 1975).  The background was lower in intensity.  Thus, a low contrast line assimilated toward the perceived direction of a high contrast line.  The perceived direction of the low contrast line was measured by participants using a third object to match its apparent direction.  Per Fig. 2, when the proximity between the two lines was about 2 min and hence high, the extent of the low contrast line’s assimilation toward the direction of the high contrast line was about 1.2 min or 60% and hence also high. 

A low intensity vertical bar assimilated toward the perceived direction of a high intensity vertical bar but not vice versa on the basis of results of Watt and Morgan (1983).  Two top vertical bars were adjacent.  Two bottom vertical bars were superimposed.  They tended to be perceived as a single bar.  Except for their intensities, these bars were identical.  Over trials, the ratio of the intensities of the two top bars was varied.  The intensity of the background was lower still.  The task was a resolution one:  It was to decide whether the top stimulus or the bottom stimulus consisted of two bars.  Accordingly, the proximity between the two top bars was varied in order to determine the proximity that yielded above chance performance.  A higher ratio between the intensities of the two top bars resulted in a higher resolution threshold.  That is, when the intensity of one top bar was higher than the second, these bars had to be less proximal in order for them to be resolved.  An explanation follows.  When a top bar that was higher in intensity and hence higher in contrast occurred, the top bar that was lower in intensity and thus lower in contrast assimilated toward the perceived direction of the higher in contrast bar.  This assimilation made the perceived directions of the two top bars quite similar.  Thus, it was less likely that the two top bars could be perceived (resolved), as to be explained.  So, the explanation’s assumption that the lower in contrast bar assimilated toward the perceived direction of the higher in contrast bar is supported.  Fig. 3 reveals that the highest ratio of intensities between the two top bars about doubled the size of the resolution threshold.  Therefore, the percentage of the assimilation of the lower in contrast bar toward the perceived direction of the higher in contrast bar was relatively high. 

A low contrast S2 bar assimilated toward the perceived direction of a S1 bar more than a high contrast S2 bar did per results of Born et al. (2016).  The proximity between the two bars was, for example, 6 deg, thus lower than in the Rentschler et al. (1975) and Watt and Morgan (1985) experiments.  The perceived direction of the S2 bars was indicated by participants clicking on a location in the visual field.  

5.4  Size

The present section provides evidence that a small object tends to assimilate toward the perceived direction of a larger object.  Previous analysis applies to this evidence.  The evidence follows.     

A smaller object assimilated toward the direction of a larger object per results of Ganz (1964) and Prinzmetal (2005) and there was no indication that the larger object assimilated toward the direction of the smaller object.  Prinzmetal’s small and large objects were otherwise identical.  The small object’s perceived direction was measured by reproducing it. 

A small object tended to assimilate toward the direction of a large object per results of Findlay (1982).  A small and a large square that were otherwise identical appeared.  Over trials, the small square was to the left or right of the large square.  Tasks required a saccade toward the two squares.  The saccades landed (aimed) closer to the direction of the large square than to the direction of the small square.  This result is considered to be an averaging of directions result in which the averaging is weighted instead of unweighted.  Averaging of directions stems from assimilation between perceived directions per Division 2.  Thus, the small square assimilated toward the perceived direction of the large square more than vice versa. 

A small object assimilated toward the direction of a large object when observation was prolonged per results of Greene (1998).  Two identical dots that were separated by a gap appeared on a page.  It was easy to perceive the tilt of an imaginary line that connected these two dots.  One of the two dots was proximal to a large circle.  Participants looked at a page and indicated their perception of the tilt of the imaginary line that connected the two dots.  The circle affected the perceived tilt of the imaginary line.  How is illustrated.  Suppose that one dot was at the 9 direction on a clock face and the second dot was at 3.  Also, a large circle was below and proximal to the dot that was at 3.  Due to this circle, the perceived tilt of the imaginary line that connected the two dots was from 9 to 4 instead of from 9 to 3.  For this illustration, the interpretation is that the dot at the 3 direction assimilated toward the perceived direction of the large circle, and this dot’s inaccurate assimilation-produced perceived direction accounts for the 9 to 4 perceived tilt. 

6.  THE ACCURACY OF A TARGET’S PERCEIVED FEATURES IS SIMILAR TO THE  INACCURACY OF ITS ASSIMILATION-PRODUCED PERCEIVED DIRECTION WHEN A NONTARGET IS NOT VERY PROXIMAL

6.1  Introduction

The present division provides evidence that when a briefly processed, low contrast, and small object assimilates toward the perceived direction of a not very proximal object, the briefly processed, etc. object’s perceived features are relatively inaccurate.  As Division 5 points out, the indicated assimilation between perceived directions means that the briefly processed, etc. object’s assimilation-produced perceived direction is relatively inaccurate.  Summing, the briefly processed, etc. object’s perceived features are relatively inaccurate and this inaccuracy is similar to the inaccuracy of its assimilation-produced perceived direction.  The briefly processed, etc. object will frequently be referred to as the target and the not very proximal object will frequently be referred to as the nontarget. 

Division 1’s hypothesis explains the inaccuracy of the target’s perceived features:  The accuracy of the target’s perceived features is hypothesized to assimilate to the inaccuracy of its assimilation-produced perceived direction and this is why the target’s perceived features are also inaccurate.  This explanation is supported, because it is unlikely that the inaccurate perception of the target’s features leads to the inaccurate perception of the target’s direction, due to the evidence that the inaccurate perception of direction is assimilation-produced instead.  Because Division 1’s hypothesis is explanatory, it is supported. 

Per assimilation theory, the assimilation process enables the accuracy of the target’s perceived features to assimilate to the inaccuracy of its assimilation-produced perceived direction.  Thus, both Division 1’s hypothesis and assimilation theory are supported in the same way as previously. 

The nontarget is not very proximal, because then the absolute amount of the target’s assimilation toward the nontarget’s perceived direction can be relatively large, meaning that the inaccuracy of the target’s assimilation-produced perceived direction can also be relatively large.  Evidence that a large absolute amount of assimilation of a target toward a not very proximal nontarget can occur is that this assimilation was about 5 deg and more (Morrone et al. 1997; Godijn & Theeuwes, 2002; Van der Stigchel & Nijboer, 2013; Born et al., 2016). 

6.2  Brief Processing

The present section provides evidence that a briefly processed target assimilates toward the direction of a not very proximal nontarget and the target’s perceived features are relatively inaccurate.  Recollecting, this assimilation means that the target’s perceived direction is also relatively inaccurate.  Thus, the target’s perceived features are relatively inaccurate and this inaccuracy is similar to the inaccuracy of its assimilation-produced perceived direction.  Division 1’s hypothesis then explains the perceived features inaccuracy as the next paragraph considers. 

Evidence of both assimilation between directions and inaccurately perceived features comes from varying the number of the nontargets that are also present per results of Cameron, Tai, Eckstein, and Carrasco (2004) and Dukewich and Klein (2009).  Their displays consisted of a small target object and multiple small nontarget objects.  The target and nontargets were not very proximal.  The number of the nontargets varied over trials.  The target was briefly processed in that the stimulus duration of the display was 54 ms (Cameron et al.) and the task called for a rapid response (Dukewich & Klein).  The target’s direction varied over trials.  The perceived direction tasks were to choose the direction at which the target appeared (Cameron et al.) and to indicate whether the target was to the left or right of the display (Dukewich & Klein).  The feature perception tasks were to decide whether a target was present or absent while also telling apart the target from the nontargets and to indicate which one of two targets appeared on a trial  (both Cameron et al. and Dukewich & Klein).  A larger number of nontargets, that is, a larger set size, increased the inaccuracy of both the target’s perceived direction and perceived features.  Interpretation follows.  The target assimilated toward the perceived directions of the simultaneously appearing nontargets.  In support of this claim, the target was briefly processed, and a briefly processed target tends to assimilate toward the perceived direction of another object per Division 5.  In addition, both the target and nontargets were moderately proximal, relatively small, and fairly similar in their features, and these conditions frequently result in an object assimilating toward the direction of another object (e.g., Ganz, 1964; Coren & Hoenig, 1972; Hazeltine et al., 1997; Prinzmetal, 2005; Born et al., 2016).  A larger number of nontargets should provide more opportunities for the target to assimilate toward the perceived direction of a nontarget.  Thus, presumably, a larger number of nontargets resulted in a larger absolute amount of assimilation of the target toward the directions of the nontargets.  So, a larger number of nontargets also resulted in the target’s assimilation-produced perceived direction being increasingly inaccurate.  Division 1’s hypothesis then explains the target’s increasingly inaccurate perceived features:  The accuracy of these perceived features is hypothesized to have assimilated to the target’s increasingly inaccurate assimilation-produced perceived direction and this is why these perceived features also became increasingly inaccurate. 

6.3  Contrast

The present section provides evidence that a low contrast target assimilates toward the perceived direction of a not very proximal higher contrast nontarget and the target’s perceived features are relatively inaccurate.  Recollecting, an assimilation-produced perceived direction in inaccurate.  Thus, the accuracy of the target’s perceived features is similar to the inaccuracy of its assimilation-produced perceived direction.  So, this evidence and the preceding section’s evidence correspond.  Therefore, Division 1’s hypothesis applies as previously. 

Evidence of both assimilation between perceived directions and inaccurate perceived features comes from results of Mounts and Gavett (2004), and an explanation of this evidence by Division 1’s hypothesis is indicated.  Over trials, a target was either low or high in contrast and a nontarget was also either low or high in contrast.  The proximity between the target and nontarget also varied over trials.  The highest proximity was 22.5 deg.  There were two targets that differed in tilt.  On a trial, one or the other of these targets appeared.  The task was to discriminate between these two targets by making one of two responses.  One discrimination result was that the low contrast target and the high contrast nontarget resulted in a more inaccurate discrimination than the low contrast target and the low contrast nontarget.  A second discrimination result was that a higher proximity between a target and a nontarget resulted in a more inaccurate discrimination.  Interpretation comes next.  The low contrast target assimilated toward the direction of the high contrast nontarget by a larger absolute amount than toward the direction of the low contrast nontarget.  In support of this claim, a low contrast object tends to assimilate toward the direction of a high contrast object per Division 5.  Thus, the low contrast target’s assimilation-produced perceived direction was more inaccurate when the high contrast nontarget occurred than when the low contrast nontarget occurred.  As for features, the first discrimination result indicates that the perceived features of the low contrast target were more inaccurate when the high contrast nontarget occurred than when the low contrast nontarget occurred.  Summing, when the high contrast nontarget occurred, both the low contrast target’s perceived direction and perceived features were more inaccurate.  Division 1’s hypothesis then applies:  The accuracy of the low contrast target’s perceived features is hypothesized to have assimilated to the greater inaccuracy of its assimilation-produced perceived direction and this is why these perceived features were also more inaccurate.  The second discrimination result is now considered.  As long as the proximity between two objects is not too high, a higher proximity between them increases the absolute amount of assimilation between their perceived directions (Ganz, 1964; Rentschler et al., 1975; McSorley et al., 2009; Van der Stigchel & Nijboer, 2013).  Extrapolating on the basis of this result, a higher proximity between the low contrast target and the high contrast nontarget increased the absolute amount of the target’s assimilation toward the perceived direction of the nontarget.  So, the inaccuracy of the target’s assimilation-produced perceived direction was increased.  The second discrimination result indicates that this higher proximity increased the inaccuracy of the target’s perceived features.  (This features inaccuracy result is also explained by Division 1’s hypothesis.)  Concluding, the second discrimination result is evidence that the low contrast target assimilated toward the direction of the high contrast nontarget.

6.4  Size

The present section provides evidence that a small target assimilates toward the perceived direction of a not very proximal larger nontarget and the small target’s perceived features are relatively inaccurate.  Thus, the small target’s perceived features and assimilation-produced perceived direction are similarly inaccurate once again.  So, Division 1’s hypothesis applies as previously. 

Evidence of both assimilation between perceived directions and inaccurately perceived features comes from Ganz (1964).  A smaller vertical white line and the center of a larger white rectangle were not very proximal.  The smaller line assimilated toward the perceived direction of the larger rectangle per Division 2.  In addition, the contrast threshold of the smaller line was higher when the larger rectangle was present than when it was not.  These results support the inference that when the smaller line assimilated toward the direction of the larger rectangle, its perceived features were more inaccurate.  This features inaccuracy is then explained by Division 1’s hypothesis.

Evidence also occurred when the size of the nontarget varied per results of Dresp and Bonnet (1993).  The target was a pixel and hence quite small.  The nontargets were larger disks.  The disks varied in size over trials.  The pixel and the centers of the disks were not very proximal.  The proximity between the pixel and disks varied over trials.  A larger disk worsened detection of the pixel more than a smaller disk per the pixel’s contrast threshold.  A second result was that a higher pixel-disk proximity worsened detection of the pixel more than a lower pixel-disk proximity.  Interpretation follows.  A smaller object tends to assimilate toward the perceived direction of a larger object per Division 5.  Thus, the pixel assimilated toward the direction of each disk and by a larger absolute amount when a disk was larger.  So, the pixel’s assimilation-produced perceived direction was more inaccurate when a disk was larger.  The detection result indicates that the pixel’s perceived features were also more inaccurate when a disk was larger.  Summing, the pixel’s assimilation-produced perceived direction and perceived features were comparably inaccurate.  The perceived features inaccuracy is then explained by Division 1’s hypothesis.  The second result corresponds to the preceding section’s result of Mounts and Gavett (2004) that a higher proximity between a target and a nontarget worsened discrimination.  The preceding section reasons that this result is evidence that the target assimilated toward the perceived direction of the nontarget.  Thus, the second result supports the present interpretation’s inference that the pixel assimilated toward the perceived direction of each disk. 

Mounts and Gavett (2004) varied the size of the nontarget as well as the target.  On a trial, either a small or large S1 target appeared and either an equally small or large S1 nontarget also appeared.  The target and nontarget were not very proximal.  Also, the proximity between the target and nontarget varied over trials.  On the same trial, either of two S2 objects that differed in tilt appeared.  The task was to discriminate between these different tilts.  The S1-S2 SOA was 80 ms.  One result was that the small S1 target and the large S1 nontarget resulted in the most inaccurate S2 tilt discrimination.  A second result was that a higher proximity between the target and nontarget resulted in a more inaccurate S2 tilt discrimination.  Analysis follows.  A smaller object tends to assimilate toward the direction of a larger object per Division 5.  Thus, the small S1 target assimilated toward the perceived direction of the large S1 nontarget more than toward the perceived direction of the small S1 nontarget.  So, the small S1 target’s assimilation-produced perceived direction was more inaccurate when the large S1 nontarget occurred.  This more inaccurate perceived direction persisted over the S1-S2 SOA.  Therefore, when a S2 object appeared at the small S1 target’s physical direction and the large S1 nontarget also occurred, the S2 object’s perceived direction was more inaccurate.  Per eight sentences past, the same S1 and S2 conditions resulted in the most inaccurate S2 tilt discrimination.  Consequently, for these conditions, both S2’s assimilation-produced perceived direction and perceived features were most inaccurate.  The perceived features inaccuracy is then explained by Division 1’s hypothesis.  The second result, namely that a higher target-nontarget proximity resulted in a more inaccurate discrimination, corresponds to the effect of a higher target-nontarget proximity on the discrimination of Mounts and Gavett (2004) (the preceding section) and on the detection of Dresp and Bonnet (1993) (the preceding paragraph).  As was indicated, these previous effects of target-nontarget proximity are evidence that targets did indeed assimilate toward the perceived direction of nontargets.  Ergo, the present experiment’s effect of a higher target-nontarget proximity is also evidence of this assimilation. 

7  THE ACCURACY OF A TARGET’S PERCEIVED FEATURES IS SIMILAR TO THE INCREASED ACCURACY OF ITS ASSIMILATION-PRODUCED PERCEIVED DIRECTION WHEN A NONTARGET IS VERY PROXIMAL

7.1  Introduction 

The present division provides evidence that the accuracy of a briefly processed, low contrast, and small object ’s perceived direction is often increased when a more lengthily processed, higher contrast, and larger object is very proximal.  It does the same for a briefly processed, etc. object’s perceived features.  Thus, the accuracy of a briefly processed, etc. object’s perceived features is similar to the increased accuracy of its assimilation-produced perceived direction.  The briefly processed, etc. object will frequently be referred to as the target and the not very proximal object will frequently be referred to as the nontarget. 

The increased accuracy of the target’s perceived direction is accounted for with the following assimilation based explanation.  Per Division 4, a briefly processed, low contrast, and small object’s singleton perceived direction is relatively inaccurate.  Per the neural-information inference of Division 2, when two objects are present, each object results in neural information of a perceived direction that approximates its singleton perceived direction.  Thus, when both a target and nontarget are present, the briefly processed, etc. target results in neural information that its perceived direction is relatively inaccurate.  The preceding paragraph indicates that the present division’s nontargets are more lengthily processed, higher in contrast, and larger than the target.  So, when both the target and nontarget are present, the more lengthily processed, etc. nontarget results in neural information that its perceived direction is relatively accurate.  Therefore, when two or more objects are present, the perceived direction of a more lengthily processed, etc. object, etc. should be relatively accurate, and this result was found to happen for a more lengthily processed object (Atkinson & Braddick, 1989; Donk & Meinecke, 2001) and a higher contrast object (Beutter, Eckstein, & Stone, 2003).  Per Division 5, a briefly processed, etc. object tends to assimilate toward the perceived direction of a more lengthily processed, etc. object.  Accordingly, the assimilation based explanation posits that the briefly processed, etc. target assimilates toward the relatively accurate perceived direction of the more lengthily processed, etc. nontarget.  Recollecting, the target and nontarget are very proximal.  Consequently, when the briefly processed, etc. target assimilates toward the relatively accurate perceived direction of the more lengthily processed, etc. nontarget, it also assimilates toward its own physical direction.  This assimilation means that the briefly processed, etc. target’s perceived direction is relatively accurate, likewise, its accuracy is increased.  Concluding, even though the briefly processed etc. target results in neural information that its perceived direction is relatively inaccurate, its perceived direction is relatively accurate. 

The increased accuracy of the target’s perceived features that also occurs is explained by Division 1’s hypothesis:  The accuracy of the target’s perceived features is hypothesized to assimilate to the increased accuracy of its assimilation-produced perceived direction and this is why the accuracy of the target’s perceived features is also increased.   In support of this explanation, it is unlikely that the increased accuracy of the target’s perceived features leads to the increased accuracy of its perceived direction, because the latter increased accuracy is accounted for by the assimilation based explanation. 

As previously, assimilation theory attributes the assimilation of Division 1’s hypothesis to the assimilation process.  Thus, both Division 1’s hypothesis and assimilation theory are supported as previously.

7.2  Brief Processing Time

The present section provides evidence that the accuracy of both the perceived direction and perceived features of a briefly processed target is often increased when a more lengthily processed nontarget is very proximal.  Likewise, the accuracy of this target’s perceived features is similar to the increased accuracy of its perceived direction.  The preceding section’s assimilation based explanation and Division 1’s hypothesis explanation of these jointly increased accuracies is adhered to.  The targets are S2 objects and the nontargets are S1 objects. 

The perceived direction of a briefly processed S2 target increased in accuracy when a more lengthily processed S1 nontarget was very proximal per results of Joseph and Optican (1996) and Donk and Soesman (2010).  In a Donk and Soesman experiment, a 29 X 21 S1 grid of regularly positioned small lines appeared.  One S1 line was dissimilar in tilt from the remaining identical S1 lines.  (A more dissimilar line was also used although the evidence was not as clear.)  On a trial, the S1 grid terminated and afterward a small S2 target appeared at the physical direction of either the dissimilar S1 nontarget line or the physical direction of another S1 nontarget line.  The S2 target’s physical direction was not predictable.  The S1-S2 SOA varied over trials.  The task was to rapidly indicate the direction of the S2 target by pressing the “7” on a keypad when it appeared in the upper left, pressing the “9” on the keypad when it appeared in the upper right, and so on.   When the S2 target appeared in the same physical direction as the dissimilar S1 nontarget line, likewise, when this S2 and S1 were very proximal, a 158 ms SOA resulted in a faster response to this S2 than a 42 ms SOA, meaning that the 158 ms SOA resulted in this S2’s perceived direction being more accurate.  The assimilation based explanation of this division’s introduction works for this result as follows.  Due to the rapid response instruction, the S2 target was briefly processed.  Thus, the S2 target resulted in neural information that its perceived direction is inaccurate.  Nevertheless, the S2 target assimilated toward the perceived direction of the dissimilar S1 nontarget.  This is because a briefly processed target tends to assimilate toward the direction of another object per Divisions 5 and 6.  In addition, when the SOA was 158 ms and hence when the dissimilar nontarget was lengthily processed, this nontarget’s perceived direction was relatively accurate.  Recollecting, on some trials, the S2 target appeared at the same physical direction as the dissimilar S1 nontarget.  This means that for these trials and when the SOA was 158 ms, the S2 target assimilated toward the dissimilar S1 nontarget’s accurately perceived direction and so toward its own physical direction.  Therefore, for these conditions, the accuracy of the S2 target’s perceived direction was increased, as to be explained. 

The perceived features of a briefly processed S2 target also increased in accuracy when a more lengthily processed S1 nontarget was very proximal per results of Joseph and Optican (1996), Henderson and Macquistan (1993), and Donk and Soesman (2010).   For Donk and Soesman’s result, the same S2 target and same S1 nontargets appeared as in the preceding paragraph except that on some trials the S2 target did not appear.  The task was to rapidly respond whenever the S2 target appeared.  When the S2 target appeared at the same physical direction as the dissimilar S1 nontarget and the SOA was 158 ms, the response to the S2 target was faster than when the SOA was 42 ms.  Thus, for the indicated conditions, the detection of the S2 target was better.  So, the indicated conditions increased the accuracy of S2’s perceived features, as to be explained. 

Per two paragraphs past, when the S2 target appeared at the same physical direction as the dissimilar S1 nontarget and the SOA was 158 ms, the accuracy of S2’s perceived direction increased.  Per the preceding paragraph, for the same conditions, the accuracy of S2’s perceived features also increased.  Division 1’s hypothesis then explains the perceived features result:  The accuracy of S2’s perceived features is hypothesized to have assimilated to the increased accuracy of S2’s assimilation-produced perceived direction and this is why the accuracy of S2’s perceived features also increased. 

Henderson and Macquistan (1993) were cited two paragraphs past.  A S1 nontarget was a small object, and a S2 target was either the letter X or O depending on the trial.  The contrasts of the S1 nontarget and the S2 target were the same and their sizes were fairly similar.  The directions of the S1 nontarget and the S2 target varied over trials.  The S1 nontarget did not predict the direction of the S2 target.  The S1-S2 SOA was 100 ms.  The S2 target’s stimulus duration was briefer than the S1 nontarget’s stimulus duration and the S2 target was followed by a mask.  The task was to discriminate between the two S2 letters by rapidly making one or a second response.  In a comparison condition, eight S1 nontargets appeared, each S1 being at one of the different locations that the primary condition’s single S1 could appear on a trial.  Also, the S2 target appeared in the same way as in the primary condition.  In the primary condition, on a proportion of the trials, the S2 target appeared at the S1 nontarget’s physical direction.  For these trials, the physical directions of the S1 nontarget and S2 target partially overlapped.  On these trials, the response to the S2 target (either letter) was faster and more accurate than it was in the comparison condition.  Thus, in the primary condition and when the S1 nontarget and S2 target were very proximal, the accuracy of the S2 target’s perceived features increased.  The assimilation based explanation is used.  The S2 target was briefly processed due to the rapid responding, its briefer duration, and the mask that followed.  A briefly processed object tends to assimilate toward the direction of more lengthily processed object per Divisions 5 and 6.  Also, the 100 ms SOA provided enough processing time for the perceived direction of the primary condition’s S1 nontarget to be accurate.  So, in the primary condition, the S2 target assimilated toward the S1 nontarget’s accurately perceived direction.  Therefore, on those trials when the S1 nontarget and S2 target were very proximal, the S2 target also assimilated toward its own physical direction.  Consequently, on those trials, the S2 target’s perceived direction increased in accuracy.  Recollecting, for the same trials, the S2 target’s perceived features also increased in accuracy.  This increased accuracy in features is then explained by Division 1’s hypothesis. 

7.3  Contrast

The present section provides evidence that the accuracy of the perceived features of a low contrast target is often increased when a high contrast nontarget is very proximal.  The accuracy of the perceived direction of this target is also increased per the assimilation based explanation.  Thus, the target’s perceived features accuracy is similar to the target’s perceived direction increased accuracy.  Division 1’s hypothesis applies.  This is the case even though now the target and nontarget occur simultaneously.   

The features of a low contrast target were perceived more accurately when a high contrast nontarget was very proximal than when the low contrast target was a singleton (appeared alone) per results of Kapadia, Ito, Gilbert, and Westheimer (1995) and King, Robinson, and Roberts (1996).  In an experiment of King et al., one stimulus consisted of a bottom horizontal dotted line  and a top horizontal solid line.  The dotted line was the target and the solid line was the nontarget.  The dotted line was directly below the solid line.  The proximity between them was 12 min.  These lines were both black and otherwise identical.  The background was white.  Thus, the dotted line was lower in contrast than the solid line.  A discrimination between the dotted and solid lines together and the solid line alone resulted in fewer total errors than a discrimination between the dotted line alone and an empty field (blank).  In addition, errors on the discrimination between the dotted line alone and the blank consisted of mostly misses of the dotted line.  Thus, the presence of the solid line increased the accuracy of the perceived features of the dotted line.  The assimilation based explanation applies as follows.  Per the neural-information inference, when both a low contrast object and another object are present, the low contrast object results in the same neural information for inaccurate perceived direction that it results in when it is a singleton object.  Nevertheless, a low contrast object tends to assimilate toward the direction of a high contrast object per Divisions 5 and 6.  Thus, the low contrast dotted line assimilated toward the perceived direction of the very proximal high contrast solid line.  The perceived direction of the very proximal high contrast solid line was accurate.  So, when the low contrast dotted line assimilated toward the perceived direction of the very proximal high contrast solid line, it also assimilated toward its own physical direction.  Therefore, the accuracy of the low contrast dotted line’s perceived direction increased.  In support of this conclusion, the preceding section indicates that the accuracy of a briefly processed target’s perceived direction also increased according to the measurement of its perceived direction.  Recollecting, the discrimination result points out that the high contrast solid line increased the accuracy of the perceived features of the low contrast dotted line.  Division 1’s hypothesis explains why:  The accuracy of the dotted line’s perceived features is hypothesized to have assimilated to the increased accuracy of its assimilation-produced perceived direction and this is why the accuracy of the dotted line’s perceived features also increased. 

7.4  Size 

The present section provides evidence that the accuracy of the perceived features of a small target is often increased when a large nontarget is very proximal.  The explanation of this increased accuracy adheres to previous ones. 

In an experiment of Dresp (1993), the target was a small disk and the nontarget was a relatively long (hence large) vertical line.  The horizontal directions of the disk and the line were the same.  The disk was below the bottom end of the line.  The proximity between the disk and this bottom end was less than 5 min.  The task was to discriminate the presence of the disk from its absence both when the line was present and when the disk was a singleton (appeared alone).  The presence of the line resulted in a more accurate discrimination.  Thus, the line increased the accuracy of the perceived features of the disk.  Explanation comes next.  Because the disk was small, per the neural-information inference, it resulted in neural information that its perceived direction was inaccurate when the line was also present.  Nevertheless, a small object tends to assimilate toward the perceived direction of a larger object per Divisions 5 and 6.  So, the disk assimilated toward the perceived direction of the line.  Because the line was large, its perceived direction was relatively accurate.  The horizontal physical directions of the disk and line were the same and their vertical directions were rather similar.  Therefore, when the disk assimilated toward the perceived direction of the line, it also assimilated toward its own physical direction.  Consequently, the accuracy of the disk’s perceived direction was increased.  In support, a briefly processed target’s perceived direction similarly increased in accuracy according to measures of perceived direction per Section 7.2.  The above result that the line increased the accuracy of the disk’s perceived features is then explained by Division 1’s hypothesis:  The accuracy of the disk’s perceived features is hypothesized to have assimilated to the increased accuracy of its assimilation-produced perceived direction, and this is why the accuracy of the disk’s perceived features increased. 

A small target line’s perceived features also increased in accuracy when it and a large nontarget line were very proximal in that they formed a right angle (King, Hicks, & Brown, 1993).  The stimuli and the discrimination results correspond to those of King et al. (1996) that the preceding section describes.  Accordingly, the four stimuli were a right angle that consisted of a shorter (smaller) horizontal black line and a longer (larger) black vertical line, the short line alone hence a singleton object, the long line alone hence also a singleton object, and a blank (empty field).  The left end of the short line intersected with the top point of the long line to form the right angle.  A discrimination between the right angle and the short singleton line resulted in fewer total errors than a discrimination between the short singleton line and the blank.  For this latter discrimination, the errors were mostly due to misses of the short line.  Thus, the presence of the long line (the nontarget) increased the accuracy of the perceived features of the small line (the target).  The explanation is as previously.  Essentially, the short line’s perceived direction would be relatively inaccurate except that it assimilated toward the accurately perceived direction of the long line, so also toward its own physical direction, meaning that the accuracy of its perceived direction increased.  Division 1’s hypothesis then explains the increased accuracy of the short line’s perceived features. 

The size of the nontarget was also varied (Dresp 1993; Mounts & Gavett, 2004).  In the Mounts and Gavett experiment, one S1 nontarget was a large disk and the second was a small disk.  On each trial, a S2 target appeared at the center of a S1 nontarget.  Thus on each trial the target and the nontarget were very proximal.  The S2 targets were smaller than the S1 nontargets.  There were two S2 targets.  They differed in tilt.  Over trials, either the small or large S1 nontarget appeared and either of the two S2 targets appeared.  The S1-S2 SOA was 80 ms.  The task was to discriminate between the different tilts of the S2 targets by making one response or a second response.  The larger S1 nontarget resulted in a higher percentage of correct responses on this discrimination than the smaller S1 nontarget.  The explanation is much as previously.  In brief, because a small object tends to assimilate toward the direction of a larger object, the small S2 target assimilated toward the perceived direction of the large S1 nontarget.  Also, because the large S1 nontarget’s perceived direction was accurate, the small S2 target also assimilated toward its own physical direction.  So, the accuracy of the small S2 target’s perceived direction increased.  The accuracy of the small S2 target’s perceived features also increased when the large S1 nontarget occurred per the above discrimination result.  The increased accuracy of these perceived features is then explained by Division 1’s hypothesis. 

8.  THE UNITIZATION OF PERCEIVED FEATURES IS HIGHLY SIMILAR TO THE ASSIMILATION-PRODUCED UNITIZATION OF PERCEIVED DIRECTIONS

8.1  Introduction

The present division provides evidence that the unitization of the perceived features of two or more objects is highly similar to (duplicates) the assimilation-produced unitization of these objects’ perceived directions.  That is, these perceived features are also unitized.  The core result that is covered is that a briefly processed, low contrast, and small object and another rather proximal object can be perceived as one object. 

The interpretation of the core result follows.  The perception of one object means that despite the occurrence of two objects, there is one unitized perceived direction and one unitized set of perceived features at this direction.  Regarding this one perceived direction, the briefly processed, etc. object assimilates to the perceived direction of the other object.  The percentage of this assimilation is very high.  Because of this very high percentage and also because the two objects are rather proximal to begin with, the two perceived directions become so similar that one unitized direction is perceived.  When this assimilation between perceived directions occurs, the perceived features of the briefly processed, etc. object remain bound to this object’s perceived direction and thus they are at the perceived direction of the other object, which follows from Division 3.  Consistent with Division 1’s hypothesis, the perceived features of the briefly processed, etc. object and the other object are hypothesized to highly assimilate (become highly similar) to the unitization of perceived directions and this is why the unitization of these perceived features occurs.  This assimilation is enabled by the assimilation process per assimilation theory.  Thus, as previously, assimilation theory supports Division 1’s hypothesis and, being explanatory, is supported itself.   Because the briefly processed, etc. object’s directions are not actually perceived, it is more precise to maintain that the increase in similarity of the neural information of the briefly processed, etc. object’s perceived direction to the neural information of the other object’s perceived direction is enough for one unitized perceived direction to occur.  This comment also applies to features. 

The interpretation’s assumption that the percentage of assimilation of a briefly processed, low contrast, and small object to the perceived direction of a rather proximal other object can be very high and thus result in one unitized perceived direction is supported.  Divisions 5 and 6 indicate that a briefly processed, etc. object tends to assimilate toward the direction of another object, thus increasing the likelihood that the percentage of this assimilation can be very high.  Division 2 reasons that the percentage of assimilation between directions can be sufficiently high that the one perceived direction that characterizes the averaging of directions result occurs.  The percentage of assimilation between the perceived directions of two objects was high when they were rather proximal (Rentschler et al., 1975; Watt & Morgan, 1983) and also when they were less proximal (Morrone et al., 1997; Born et al., 2016).  A high percentage of assimilation between directions is associated with the perception of one object (Watt & Morgan, 1983, per Section 5.3). 

8.2  Brief Processing

In an experiment of Herzog and Koch (2001), the S1 stimulus consisted of one pair of two colinear bars with a small gap between them that were tilted clockwise.  The stimulus duration was 30 ms.  The S2 stimulus consisted of three pairs of two colinear bars with a small gap between them that were vertical.  The S2 three pairs were in a row.  The stimulus duration was 300 ms.  The centers of S1 and S2 were the same.  The S1 and S2 bars were identical, for instance, in length.  The size of the gaps between two colinear bars were also identical.  S1 was briefly processed because its stimulus duration was 30 ms and it was followed by the S2 with an ISI of 0 ms.  The perception was of three pairs of colinear bars that were tilted clockwise instead of vertical also meaning that one pair of colinear bars was missing.  

The explanation of this perception adheres to the preceding section’s interpretation and is as follows.  The S1 tilted colinear bars assimilated to the perceived directions of the S2 three colinear vertical bars.  In addition, the percentage of this assimilation was sufficiently high that only the directions of the S2 three colinear bars was perceived.  That is, the perceived directions of S1 and S2 were unitized.  The preceding section supports this possibility, for example, with evidence that the percentage of assimilation between two perceived directions can be high.  Also, the perceived features of S1 were bound to its assimilation-produced perceived directions and thus they were at the perceived directions of the S2 three colinear bars.  The clockwise tilt feature of S1 and the vertical tilt feature of S2 became unitized, explaining why the vertical tilt feature was not perceived.  Consistent with Division 1’s hypothesis, the perceived features of S1 and S2 are hypothesized to have highly assimilated (become highly similar) to the unitization of the perceived directions of S1 and S2 and this is why the unitization of these perceived features also occurred.  Concluding, the disappearance of S1’s perceived direction and the perceived clockwise tilt of the S2 three colinear vertical lines is explained. 

8.3  Contrast 

A masking result of Fehrer and Smith (1962) is considered because the masked object and the two masking objects differed in contrast but not in both processing time and size and other features.  Three identical squares appeared in a row.  These squares were contiguous.  Accordingly, the middle square shared a border with both flanking squares.  The middle square’s intensity was lower than the flanking squares’ equal intensities.  The intensity of the background was lower still.  The stimulus durations of the three squares were all 50 ms.  The detection of the middle square (its discrimination from background) was somewhat below chance. 

An explanation comes next.  The low intensity middle square assimilated to the perceived directions of both high intensity flanking squares.  In addition, the percentage of this assimilation was sufficiently high that only the directions of the flanking squares were perceived.  These possibilities are supported in Section 8.1.  For example, Section 8.1 indicates that assimilation between perceived directions can lead to one perceived direction.  More support for these possibilities is that assimilation toward the perceived direction of a square’s center occurs on the basis of the results that the perceived direction of a contour of a Kanizsa square was toward the direction of its center (Guttman & Kellman, 2004) and the perceived direction of a small object that was inside of a circle was toward the direction of the circle’s center (Denisova, Singh, & Kowler, 2006).   Regarding perceived features, the middle square’s perceived features were bound to its assimilation-produced perceived directions and thus they were at the perceived directions of the flanking squares.  In addition, consistent with Division 1’s hypothesis, the perception of the middle square’s perceived features and each flanking square’s perceived features are hypothesized to have highly assimilated to the unitization of perceived directions that occurred and this is why these perceived features also unitized.  In support of this possibility, the middle square’s and flanking squares’ features did not result in a perceptual summation of features, because this summation would result in above chance detection.  Per this explanation, both the perceived direction and perceived features of the middle square disappeared, thus explaining its below chance detection. 

8.4  Size 

In an experiment of Eskew and Boynton (1987), on each trial two rectangles were left and right with horizontally aligned centers, contiguous, and always the same size.  Thus, the inside vertical border of these two rectangles was the same (shared).  The hues of the two rectangles were different.  The size of the two rectangles varied over trials.  Viewing was prolonged.  One result was that for some conditions observation indicated a “melting border”:  The hue of portions of one rectangle were perceived to bleed across the inside border, that is, be at the perceived direction of the other rectangle, and vice versa.  A second result was that for some conditions a single rectangle was perceived.  Its perceived area was about the same as the combined area of the two rectangles and its hue was the same.  A third result was that two smaller rectangles resulted in the perception of this one rectangle more frequently than two larger rectangles.   

An explanation follows.  The melting border (first) result means that portions of one rectangle assimilated to the perceived direction of portions of the second rectangle by a sufficiently high percentage that these portions were perceived at the direction of portions of the second rectangle and vice versa.  This is because the hue of a portion is bound to its assimilation-produced perceived direction and thus indicates this perceived direction.  More support for this assimilation between perceived directions is in Section 8.1.  More support is that assimilation toward the perceived direction of the center of a square occurs per the preceding section.  Presumably, the assimilation-produced perceived direction of the portion of one rectangle and the identical unchanged perceived direction of a portion of the second rectangle often resulted in one unitized perceived direction.  Regarding the perception of the two rectangles as having the same hue (the second result), Division 1’s hypothesis is explanatory:  The different hues of portions in the same perceived direction are hypothesized to have highly assimilated to the unitization of these portions’ perceived directions and this is why unitization of these different hues also occurred.  Presumably, the extent of the unitization of hues was enough for the one rectangle to be perceived.  The size and perceived one rectangle result (the third result) occurred because two smaller rectangles assimilated toward each other’s perceived direction by a higher percentage than two larger rectangles on the basis of evidence that a smaller object tends to assimilate toward the perceived direction of another object in Divisions 5 and 6.  In addition, consistent with Division 1’s hypothesis, this higher percentage of assimilation between perceived directions led to more frequent unitizations of the different hues of portions and thus a more frequent perception of the one rectangle. 

9.  ASSIMILATION MAY ENABLE CONTRAST

The present division explains how the assimilation process may also enable contrast between perceived features, for example, the contrast that occurs between two tilts.  The explanation follows.

A component of a singleton object that is on a physical dimension results in multiple neural values that are on the same neural dimension.  An average of these multiple neural values also exists.  This average is called the final neural value.  The final neural value results in a specific perceived feature of an object on a perceptual dimension.  The neural and perceptual dimensions are related.  An example of a specific perceived feature is a certain perceived length. 

For exposition, a singleton object results in two neural values.  Thus, the average of these two neural values is the final neural value. 

For exposition, a first singleton object results in two neural values that are 0 and 6, and a second singleton object results in neural values on the same dimension that are 7 and 13.  Thus, the first singleton object’s final neural value is 3 and the second singleton object’s final neural value is 10.  So, the first singleton object results in a perceived feature of 3 on a perceptual dimension and the second singleton object results in a perceived feature of 10 on the same perceptual dimension. 

The process of assimilation operates on neural values.  Also, the process operates in the way that assimilation between perceived directions occurs.  Accordingly, because the accuracy of a singleton perceived direction varies, the accuracy of a singleton object’s neural values also varies.  In addition, because a less accurate perceived direction may assimilate toward a more accurate perceived direction but not vice versa, the process of assimilation may change an object’s neural values or it may not. 

For exposition, the first singleton object’s neural values of 0 and 6 are considered to be more inaccurate than the second singleton object’s neural values of 7 and 13.  In accord with the preceding paragraph, when the first and second objects are both present, 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 extent of this assimilation is called moderate.  This moderate assimilation results in the first object’s neural values of 0 and 6 becoming, for exposition, 2 and 8, respectively. 

The first object’s assimilation-produced neural value of 8 is larger than the second object’s unchanged neural value of 7.  Accordingly, the neural value of 8 no longer affects the first object’s final neural value.  Thus, the first object’s final neural value is 2.  So, the final neural value of 2 results in a perceived feature of 2. 

Summing, when the first object is a singleton, its perceived feature is 3.  Also, when the process of assimilation operates, its perceived feature is 2.  Recollecting, the second object’s perceived feature is 10.  The perceived feature of 2 is less similar to the perceived feature of 10 than is the perceived feature of 3.  Thus, the possibility that the process of assimilation enables contrast between perceived features is supported. 

The explanation of assimilation (not contrast) between perceived features is quite similar.  The same two objects and their neural values are used for exposition.  The first object’s neural values assimilate toward (increase in similarity to) the second object’s two neural values by a larger extent.  Accordingly, the amount of this assimilation is called large.  The second object’s two neural values are unchanged.  The larger extent of assimilation results in the first object’s neural values of 0 and 6 becoming, for exposition, 4 and 10.  The first object’s assimilation-produced neural value of 10 is larger than the second object’s neural value of 7.  Accordingly, the neural value of 10 no longer affects the first object’s final neural value.  Thus, the first object’s final neural value is 4.  Therefore, the first object’s perceived feature is also 4. 

Summing, when the first object is a singleton, its perceived feature is 3.  Also, when the extent of assimilation is large, its perceived feature is 4.  Recollecting, the second object’s perceived feature value is 10.  The perceived feature of 4 is more similar to the perceived feature of 10 than is the perceived feature of 3.  Thus, the first object’s perceived feature becomes similar to (assimilates toward) the second object’s perceived feature, as to be explained.

These explanations of contrast and assimilation are quite similar.  This high similarity supports the claim that the process of assimilation may also enable contrast.

10.  ADDITIONAL SUPPORT FOR DIVISION 1’S HYPOTHESIS, CONCLUSIONS, AND EXPLANATIONS, ALSO INTEGRATIONS AND EXTRAPOLATIONS

10.1  Support for Division 1’s Hypothesis

The present section provides a summary of support for Division 1’s hypothesis.  It also provides additional support for it.

Each heading of Divisions 3-8 describes a result that Division 1’s hypothesis explains.  The result is about perceived features for Divisions 3-4 and 6-8 and is about perceived direction for Division 5.  Because Division 1’s hypothesis explains these results, it is supported. 

Division 1’s hypothesis is that a perception assimilates to a perceived direction or aspect of it.  By generalization, Division 1’s hypothesis is supported by evidence that assimilations occur.  Evidence of assimilation between directions begins in Division 2.  Evidence of assimilation between perceived features is indicated by their unitization as in Division 8 and also by increases in their similarity without unitization also occurring (e.g., Helson & Rohles, 1959).  Assimilation also occurs if it enables contrast between perceived features which is as Division 9 advises. 

Per assimilation theory, the assimilation process enables assimilation between perceived directions (Division 2), the different perceptions of Divisions 3-8 that are hypothesized to stem from assimilation per Division 1’s hypothesis, assimilation between perceived features, and possibly contrast between perceived features (Division 9).  Because assimilation theory contributes to explaining how different perceptions come about, it is supported.  Because assimilation theory is parsimonious, it is also supported.  Because assimilation theory is supported and because the assimilation process enables the different perceptions that are hypothesized to stem from assimilation per Division 1’s hypothesis, Division 1’s hypothesis is supported in turn.

A corollary of Division 1’s hypothesis is that a perceived direction or aspect of it precedes another perception according to Division 3.  This corollary was called the precedence corollary.  Thus, support for the precedence corollary amounts to support for Division 1’s hypothesis.  Support for the precedence corollary is that an object’s features are perceived at (are bound to) its assimilation-produced perceived direction per Division 3.  More support for the precedence corollary comes from the explanations of experimental results in Divisions 6-8.  This is because per these explanations’ assimilation between perceived directions occurs directly, readily, and quickly and is followed by effects on perceived features.  More support for the precedence corollary is that a briefly processed, low contrast, and small object tends to assimilate toward the direction of another object per Divisions 5-8, equivalently, a briefly processed, etc. object’s assimilation-produced perceived direction tends to be relatively inaccurate.  This is because a briefly processed, etc. singleton object’s perceived direction is relatively inaccurate per Division 4 and neural information of this inaccuracy exists when two or more objects are present per the neural-information inference of Division 2. 

10.2  Additional Support for the Conclusions of Divisions

Similar conclusions mean that by generalization each conclusion supports the other conclusions.  Each of Divisions 2-8 provides evidence for a conclusion that is described by its heading.  This type of conclusion is referred to as a heading conclusion.  Similarities among these heading conclusions exist.  Thus, each heading conclusion supports a heading conclusion to which it is similar.  So, in order to additionally support the heading conclusions, conclusions that are similar are indicated. 

The heading conclusions of Divisions 2-8 are similar because they maintain that a perception is similar to a perceived direction or aspect of it.  The heading conclusions of Divisions 4-8 are similar because they are supported by results with briefly processed, low contrast, and small objects.  The heading conclusions of Divisions 4 and 6-8 are similar because they maintain that the accuracy of perceived features is similar to the accuracy of perceived directions. 

10.3  Additional Support for the Explanations of the Conclusions of Divisions 

Similar explanations mean that by generalization each explanation supports the other explanations.  Similar explanations of the heading conclusions of different divisions are indicated in order to additionally support these explanations. 

As previously indicated, explanations of the heading conclusions of Divisions 3-8 are similar because they hypothesize that a perception assimilates to a perceived direction or aspect of it and this is why the perception occurs.  Explanations of the heading conclusions of Divisions 3 and 6-8 are similar because they maintain that assimilation between perceived directions enables a perceived features result.  The explanations of Divisions 6-8 are additionally similar because they maintain that assimilation between perceived directions enables the accuracy of perceived features to change. 

10.4  Integrations

Explanations of Divisions 6 and 7 indicate that assimilation between perceived directions can enable both the inaccurate and accurate perception of a target’s features.   Thus, these explanations amount to an integration. 

Division 6 indicates an essentially identical explanation of results that are considered to be influenced by attention (Cameron et al., 2004; Dukewich & Klein, 2009; Mounts & Gavett, 2004) and of results that are not considered in terms of attention (Ganz, 1964; Dresp & Bonnet, 1993).  Thus, this essentially identical explanation amounts to an integration.

Division 7 indicates an essentially identical explanation of results that are considered to be influenced by attention (Joseph & Optican; 1996; Henderson & Macquistan, 1993; Mounts & Gavett, 2004; Donk & Soesman, 2010), and of results that are not considered in terms of attention (Dresp, 1993; King et al., 1993; Kapadia et al., 1995; King et al., 1996).   Thus, this essentially identical explanation amounts to an integration.  In addition, because this and the preceding paragraph’s integrations are similar, they support one another. 

Division 8 indicates an essentially identical explanation of a result (Herzog & Koch, 2003) that resembles a typical metacontrast result, a result (Fehrer & Smith, 1962) that is a typical masking result, and a result (Eskew & Boynton, 1987) that probably tends to be considered in terms of color perception.  Thus, another integration is indicated.   

10.5  Extrapolations

Per Divisions 3 and 6-8, assimilation between perceived directions enables different types of perceptions.  Extrapolating, assimilation between perceived directions may enable a large number of different types of perceptions.  An explanation that is unconventional and thus is a hint that assimilation enables a large number of different perceptions follows.  Perhaps objects that are to the left and right in space continue to assimilate to each other’s perceived directions over time, these perceived directions continue to be averaged over time, thus one midsagittal direction continues to be perceived, and this perceived direction is essentially equivalent to the perception that the egocenter’s horizontal direction is midsagittal. 

A briefly processed, low contrast, and small singleton object result in a relatively inaccurate perceived direction per Division 4.  A briefly processed, etc. object tends to assimilate toward the direction of another object (Division 5) and this assimilation leads to the inaccurate perception of the briefly processed, etc. object’s features (Division 6), the accurate perception of the briefly processed, etc. object’s features (Division 7), and the unitization of the briefly processed, etc. objects’ perceived directions and perceived features with those of another object (Division 8).  A monocularly viewed, peripheral (eccentric), and unattended long duration singleton object also tend to result in a relatively inaccurate perceived direction.  Extrapolating, when two objects occur, perhaps a monocularly viewed, etc. object also tends to assimilate to the perceived direction of another object and this assimilation likewise leads to effects on perceived features.  For example, perhaps monocular viewing of dichoptic objects increases the tendency for these objects to assimilate toward each other’s perceived direction, and this tendency increases the frequency of the unitization of these objects’ perceived directions and perceived features, that is, increases the frequency of binocular fusion. 

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