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Finding the “odd one out”:
Memory color effects and the logic of appearance
J.J. Valenti and Chaz Firestone
Johns Hopkins University
Header: Memory Color And Perceptual Logic
Version: 4/3/19 — in press, Cognition
Word Count: 10920
Address for correspondence:
Chaz Firestone (chaz@jhu.edu)
Department of Psychological & Brain Sciences
Johns Hopkins University
3400 N Charles St
Baltimore, Maryland 21218
MEMORY COLOR AND PERCEPTUAL LOGIC 2
Abstract
Can what we know change what we see? A line of research stretching back nearly a century suggests
that knowing an object’s canonical color can alter its visual appearance, such that objectively gray
bananas appear to be tinged with yellow, and objectively orange hearts appear redder than they really
are. Such “memory color” effects have constituted the strongest and most complete evidence that
basic sensory processing can be penetrated by higher-level knowledge, and have contributed to
theories of object perception in psychology, neuroscience, and philosophy. Are such phenomena
truly perceptual? Or could they instead reflect shifts in judgments and responses without altering
online color perception? Here, we take a novel approach to this question by exploiting a “logic” that
is inherent in visual processing but that higher-level cognition often cannot follow. In four
experiments spanning both classical and contemporary work, we exhaust the predictions of memory
color theories, by exploring scenarios where memory color accounts make tortuous and difficult-to-
grasp hypotheses that should nevertheless be easily accommodated by visual processing. We show
that such conditions eliminate or even reverse memory color effects in ways unaccounted-for by
their underlying theories — especially in a novel “odd one out” paradigm that may help distinguish
visual appearance from higher-level judgment in a powerful and general way. We suggest that prior
knowledge can influence color judgments in real and robust ways, but that such influences may not
truly reflect changes in visual appearance per se. We further discuss the general utility of this
approach for isolating perception from judgment, both for memory color effects and beyond.
Keywords: memory color, color perception, top-down effects, cognitive penetrability, modularity
MEMORY COLOR AND PERCEPTUAL LOGIC 3
What we see can change what we believe — but can what we believe change what we see? In
contrast to a traditional “modular” view of perception, recent work has suggested that higher-level
cognitive states can reach down into visual processing and change how the world appears to us. For
example, it has been reported that recalling unethical behavior can change the perceived brightness
of a room (Banerjee, Chatterjee, & Sinha, 2012), that impressive or powerful people appear larger
(Duguid & Goncalo, 2012; Masters et al., 2010), and that frightening objects appear closer (Harber
et al., 2011). Such work goes beyond the more widely accepted notion that higher-level expectations
can modulate attention, eye movements, or object categorization (Bar, 2004; Malcolm et al., 2014);
instead, the force of these results is their claim to directly alter the way a given object looks to us, at
the level of basic visual properties such as color, size, or distance.
The ground-shaking consequences implied by these claims have made them extremely
influential, but they have also attracted skepticism for the same reasons, on at least three general
fronts. First, the studies used to motivate these claims are often “one-off” results rather than
integrated parts of a broader literature: With rare exceptions (e.g., Dunning & Balcetis, 2013;
Proffitt, 2006; Witt, 2011; but see also Durgin et al., 2011; Firestone 2013a), many of these claims
draw from only one source of evidence, use only one sort of task, and have rarely been replicated or
extended by other researchers and laboratories. Second, these studies frequently arise from outside
the field of vision science, and as a result may overlook certain controls expected of perception
studies, such as matching stimuli on important low-level properties (e.g., Harber et al., 2011; van
Ulzen et al., 2008). Third, many of these claims are theoretically puzzling and even implausibly
maladaptive. For example, given the degree to which visual processing relies on representing a
scene’s lighting conditions, it would seem odd at best (and actively unhelpful at worst) for the mind
to adjust a room’s perceived brightness when the perceiver has recently recalled an unethical vs.
ethical action (Banerjee et al., 2012) — an effect that has no clear adaptive function and could even
mislead perceivers about their visual environment. These and other concerns have motivated
reviewers of this literature to ask whether there is truly any evidence that cognition can penetrate
visual perception (Firestone & Scholl, 2016; Lammers, de Haan, & Pinto, 2017; Machery, 2015; for
more classical discussions of modularity and cognitive impenetrability; see Fodor, 1983; Pylyshyn,
1999).
MEMORY COLOR AND PERCEPTUAL LOGIC 4
The highest-hanging fruit
In the entire literature on top-down effects of cognition on perception, one class of findings
stands apart in straightforwardly overcoming many of the above weaknesses: a collection of results
known as “memory color” effects. Memory color effects are said to occur when one’s prior belief
about the color of an object changes the color one actually experiences that object to be. For
example, an orange-red heart may appear redder than it really is (Delk & Fillenbaum, 1965), or a gray
banana may appear tinged with yellow (Hansen et al., 2006; Olkkonen et al., 2008), because the
perceiver knows the objects’ canonical colors (Figure 1).
Memory color effects withstand many of the criticisms raised against other top-down effects
of cognition on perception. First, they have been observed for nearly a century and have been
replicated in various ways since their initial discovery (e.g., Adams, 1923; Bannert & Bartels, 2013;
Bruner, Postman, & Rodrigues, 1951; Delk & Fillenbaum, 1965; Duncker, 1939; Hansen et al., 2006;
Lupyan, 2015b; White & Montgomery, 1976; Witzel, 2016; for a review, see Adeyefa-Olasupo &
Flombaum, 2018). Second, though some classical memory color effects may have had
methodological shortcomings by today’s standards, the research program has been revived by
modern vision science laboratories that pay careful attention to many important methodological
details, including various controls for the stimuli used in the experiments, the manner in which the
measurements are taken, and experimenter bias (e.g., Hansen et al., 2006; Olkkonen et al., 2008;
Witzel et al., 2011; Witzel, 2016). Third, the findings make sense in a way that so many other alleged
top-down effects on perception do not: If the perceiver knows something about the typical color of
an object, then incorporating that prior information into the visual system’s computation of that
object’s color doesn’t seem so unreasonable (and may perhaps be consistent with ‘Bayesian’ norms
of inference; Witzel, Olkkonen, & Gegenfurtner, 2018).
MEMORY COLOR AND PERCEPTUAL LOGIC 5
Figure 1. Schematic illustration (and exaggeration) of memory color effects. (A) Objectively
gray bananas may appear tinged with yellow. (B) Hearts may appear redder than they really
are.
For these reasons and others, the memory color effect is considered by many researchers to
be among the most promising candidates for a genuine top-down effect of cognition on perception.
Indeed, effects of knowledge on color appearance have played a central role in recent arguments for
the cognitive penetrability of perception (e.g., Macpherson, 2012; Newen & Vetter, 2017; Vetter &
Newen, 2014), have helped to motivate new perspectives on cognitive architecture more generally
(e.g., Barsalou, 2008; Lupyan, 2015a), and have even appeared in popular perception textbooks (e.g.,
Goldstein & Brockmole, 2016; Schwartz & Krantz, 2017).
A seed of doubt?
At the same time that memory color effects have been so robust and influential, there is also
reason to wonder whether they truly reflect changes in perception — how an object looks, per se — vs.
changes in subjects’ behavioral responses, which may occur without altering what is actually seen. In
other words, might it possible that subjects give responses that are in line with memory color theories,
even if they don’t literally see objects as having those colors? In particular, one might doubt a
perceptual interpretation of these effects for at least three reasons:
Effect sizes. First, memory color effects are surprisingly large — so large that they should be
subjectively apparent even when casually viewing the experimental stimuli (as in Figure 1a, where
memory color theory predicts that the gray banana shown there should look yellow to you, the
reader, right now). For example, many modern studies of memory color effects measure their
presence using the method of “achromatic adjustment”, whereby subjects adjust a stimulus’s color
MEMORY COLOR AND PERCEPTUAL LOGIC 6
until it appears to be a neutral gray (e.g., Hansen et al., 2006; Lupyan, 2015b; Olkkonen et al., 2008;
Witzel et al., 2011). In the case of a yellow banana, for example, subjects in fact make the banana a
bit blue — with the idea being that the visual system is independently adding some extra yellow to
the image’s perceived color, such that the banana image must be objectively blue (yellow’s opponent
color) in order to cancel out the extra yellow and thereby appear gray to the subject. What is striking
about such effects is just how much color subjects add to the images: In the original studies, the
effects were as high as 13% relative to the images’ typical color settings (with a mean of 8%; Hansen
et al., 2006), and follow-up work has adjusted this value even higher, estimating the memory color
effect for grayscale photographs of bananas to be 22% (Olkkonen et al., 2008). This essentially
implies that an objectively gray banana should appear to be 22% as colorful as a real-life, naturally
colored yellow banana. Hansen et al. note that a finding of this magnitude “amounts to an effect
that is approximately three to five times above the threshold of discrimination” (p.1368); but on
reflection this seems like a problem, because an effect of this size just does not comport with the
subjective experience of seeing a gray banana — which, fairly plainly, looks gray (as in Figure 1a). In
other words, speaking purely subjectively, gray bananas just don’t look yellow to the degree suggested
by memory color studies. (For a more sustained treatment of the role of phenomenology in
evaluating top-down effects, see Firestone & Scholl, 2015a.)
Conflicting mechanisms. Second, there may be inconsistencies across memory color studies as to
their underlying mechanisms — in particular, as to whether memory color effects are driven by
explicit higher-level beliefs or instead by low-level statistical associations between shapes and colors.
For example, it has been reported that blurring a fruit image reduces its memory color effect even
when subjects still know the fruit’s identity (Olkkonen et al., 2008). This suggests a fairly low-level
learning mechanism for memory color effects, since even when the subject’s high-level knowledge is
preserved (i.e., even when the subject still knows they are viewing a banana), the blurring procedure
reduces the memory color effect (see Olkkonen et al., 2008, for a more detailed interpretation of this
finding along these lines). At the same time, however, the largest memory color effects of all are
typically observed for branded objects with very generic shapes, where the effect seems to be driven
by exactly the sort of higher-level knowledge that earlier studies seemed to have ruled out. For
example, a simple disk does not produce a memory color effect on its own; but when the disk is
branded with the logo for Nivea (a popular brand of skin lotion with dark blue containers), a large
memory color effect occurs, such that the additional writing on the surface of the tin reportedly
causes the whole tin to appear blue (Witzel et al., 2011). This result suggests a higher-level source of
MEMORY COLOR AND PERCEPTUAL LOGIC 7
memory color effects (what those researchers call “object knowledge”), since a rounded tin is a very
generic shape, and it’s only the addition of meaningful writing that now produces a large memory
color effect. Though these somewhat conflicting patterns do not by themselves undermine the
relevant studies, they may well be a reason to seek alternative explanations for many of these effects.
Unconstrained tasks. Third, the vast majority of contemporary memory color studies use tasks
that rely on the subjects’ pre-existing notions of where “gray” and other colors are located in color
space, in a potentially problematic way. For example, rather than show subjects a gray object and ask
them whether a gray banana looks like that, most memory color studies show subjects a colored
banana and ask subjects to make it gray, leaving it to the subjects themselves to determine the gray
standard on their own. This open-ended design may be especially susceptible to biases in judgments
and responses, especially since there are usually no countermeasures in place to prevent subjects
from inferring the purpose of these studies (which, given their designs, plainly concern the
connection between familiar objects and their typical colors). Just like any color term, “gray” does
not correspond to a single point in color space, but instead to a continuous region within that space:
As one discovers in a paint store, for example, many different colors answer to “gray”, including not
only dark grays and light grays but also warm grays and cool grays, which have other hues mixed in
but are still accepted as instances of “gray”. Just as asking a subject to adjust something to be “red”
leaves open the precise shade of red they should choose — and even gives the subject leeway to
choose different reds for different objects depending on each object’s canonical red — asking a
subject to make something “gray” permits the subject to choose a different gray for different
objects, or to use different strategies for different objects, even if all such objects are perceived
identically (and if that subject’s own subjective gray standard is measured in advance). Indeed, one
distinct possibility is that subjects who adjust bananas to be a bit blue do so because their strategy is
to stay a safe distance away from the object’s canonical color — as if thinking, “Let me make certain
there’s not even a speck of yellow in this banana” — and so tend to overshoot towards that color’s
opponent (here, blue). In other words, if subjects wish to make a banana look gray, and in so doing
make a special effort to avoid yellowish grays, then a banana might elicit a bluish estimate for
strategic reasons (“let me reduce yellow a bit more, just to be safe”) rather than because of how the banana
visually appears.
1
(For discussion of a similar worry, see Zeimbekis, 2013.)
1
Indeed, if subjects take this approach to the achromatic adjustment task, then this might even explain why memory
color effects revealed by that task have typically been stronger for colors on the daylight axis (e.g., blues and yellows)
than for other colors, especially reds (e.g., a strawberry image in Olkkonen et al., 2008; though see Delk & Fillenbaum,
1965, who do find memory color effects for red objects). Since color discrimination is poorer along the blue-yellow
MEMORY COLOR AND PERCEPTUAL LOGIC 8
Of course, these issues do not by themselves show that memory color effects are not
perceptual, and they certainly do not undermine the reality or robustness of such effects. But they
do raise the question: Might such effects not reflect how a given object visually appears in the
moment, but instead how the subject responds in certain experimental conditions?
Separating seeing from thinking through the “logic of appearance”
How could we distinguish biases in perception from biases in post-perceptual judgment? Our
approach here is to take advantage of a kind of “logic” that is automatically employed by visual
processing (Rock, 1983) but that operates more slowly and less reliably (if at all) in higher-level
cognition. In particular, truly perceptual phenomena typically arise not only in reports about the
stimuli undergoing those phenomena, but also in our experience of how those stimuli relate to other
objects and events in the environment.
For example, ask yourself: “If a teal object had its color move roughly half the distance
towards red in color space, and another teal object had its color move roughly half the distance
towards green, and they both appeared beside a light purple object, which of the three objects would
look the most different from the other two?” While you find yourself working through this problem
in your head, look at Figure 2 to see the answer for yourself. Figure 2a shows two objectively
identical teal ovals (center) whose appearance has been altered by the Munker illusion: The oval on
the left looks purplish, and the oval on the right looks greenish — and if subjects were asked to
explicitly report the colors of these ovals, they would surely say so. Additionally, however, the same
sort of effect can be revealed by comparison: When the two ovals appear next to an objectively purple
oval (Figure 2b), the greenish-looking oval now looks different from the other two. If you were asked
to identify the “odd color out” from the display, you could easily point to the rightmost, greenish-
looking oval.
daylight axis (Pearce et al., 2014), it may be easier to discriminate purely achromatic gray from a slightly greenish gray
than it is to discriminate purely achromatic gray from a slightly bluish gray. In that case, subjects who are asked to make
a banana “gray” are able to stray relatively far into blue territory while still judging the blue-gray sample to be acceptably
gray; by contrast, subjects who are asked to make a strawberry “gray” will tolerate only just a bit of green in the sample,
because anything more would be easily noticed. The relative weakness or absence of memory color effects for red
objects has sometimes been taken as evidence for their perceptual nature (e.g., Block, 2016); but in fact, even this fairly
specific pattern of results can still be explained by biased responding, once other baseline aspects of perceptual
discrimination are taken into account (in particular, baseline differences in the discriminability of different colors).
MEMORY COLOR AND PERCEPTUAL LOGIC 9
Figure 2. An example of “logic” in perceptual comparison. (A) Objectively, the two ovals are
identical shades of teal, but the Munker illusion causes the left one to appear purplish and the
right one to appear greenish. (B) Next to an objectively purple oval, the green-looking oval
not only looks green but also appears to the “odd one out” in the triplet in terms of its hue.
Note that this is true even without a perfect hue match; even if the two purplish-looking ovals
in panel B don’t look identical, they still may look similar enough to seem different than the
greenish-looking one.
Notice that this straightforward experience of one object standing out from the rest reflects
a kind of “logical” relationship among otherwise-basic perceptual processes: First, multiple stimuli
undergo the Munker illusion, in which a stimulus is assimilated to the color of its foreground; then,
the stimuli that now carry these illusory colors are each compared to one another and to a third
stimulus, which looks as it does for independent reasons; finally, one of these pairwise comparisons
comes out “same” while two of them come out “different”, resulting in one object standing out
from the rest. When reading the riddle-like question that began the previous paragraph, one finds
oneself laboring through this logic, as if slowly and tentatively solving a puzzle; but that same logic is
implemented flawlessly and near-instantaneously in visual processing, as you can see in Figures 2b
and 2c.
Crucially for our purposes here, note that the “odd one out” judgments you can make in
Figures 2b and 2c never require you to actually name the color that the objects are. Indeed, a distinct
advantage of this approach is that one can obtain evidence that the illusion is working without ever
asking which color the objects appear to be; given the logic of these comparisons, all that is required
is a judgment about which object looks most different from the others.
The present studies: The logic of appearance in memory color effects
Here, we exploit this perceptual logic for the case of memory color effects. Rather than ask
subjects to report the colors they see, and rather than make subjects apply a pre-conceived color
MEMORY COLOR AND PERCEPTUAL LOGIC 10
standard, we show subjects sets of objects that have or don’t have canonical colors, and we ask
subjects to identify similarities and differences between them. Experiments 1 and 2 apply this multi-
step logic of comparison to contemporary memory color effects discovered in recent years, while
Experiments 3 and 4 explore classical memory color effects from the middle of the last century. In
all cases, we ask whether such effects persist when their underlying theories make predictions that
would be difficult for subjects to follow or provide strategic answers for.
In other words, we ask: Do memory color effects obey the logic of appearance?
Experiment 1: The “odd-one-out” task
If memory color effects are genuinely perceptual, then they should reveal themselves not only
through direct reports of an object’s color, but also through “odd-one-out” comparisons of the sort
in Figure 2. (For other perception studies employing analogous tasks in other domains, see Adams,
Kerrigan, & Graf, 2016; Robilotto & Zaidi, 2004.) Experiment 1 ran such a test for the now-classic
case of yellow-looking bananas.
Recent work has established that the memory color effect for such stimuli can be measured
not only through achromatic adjustment (as in Hansen et al., 2006), but also through a much simpler
forced-choice task in which subjects are shown an objectively gray banana next to an objectively
bluish banana whose color matches the particular shade of blue that independent subjects selected
when making a banana gray. When asked which of the two objects is truly “gray”, subjects tend to
select the objectively bluish banana more often than the objectively gray banana — however,
subjects do not do this for bluish and gray disks (Witzel, 2016). The interpretation of this pattern was
that, due to memory color effects, blue bananas look gray and gray bananas look yellow, such that
subjects select the bluish banana as “gray”; but since disks don’t have canonical colors, there is no
similar effect in those cases.
This method, helpfully named the “Easy Way to Show Memory Color Effects” (by Witzel,
2016), does indeed have several advantages over earlier methods. Notably, its design and key
comparisons mean that the experiment does not depend on an elaborate setup with sensitive
equipment, precise calibration, and a lengthy experimental session (as earlier investigations of
memory color have required); indeed, this new forced-choice method was run over the Internet,
using whatever display the subjects happened to have at home. This advance allows for a
MEMORY COLOR AND PERCEPTUAL LOGIC 11
straightforward and highly standardized design that can be easily replicated across laboratories, and
also permits much larger samples than have been used in previous studies, given the ease of online
data collection. Partly for these reasons, this new approach involving direct comparison between
objects has motivated especially strong claims about separating perception from judgment, as it has
been explicitly argued that such experiments “measure a bias in perception rather than memory or
judgment biases” (Witzel & Gegenfurtner, 2018, p.480).
Here, we make a simple change to the forced-choice task used in such experiments: Rather
than select the “gray” object among two choices, we ask subjects to select the “odd color out”
among three choices. For example, we ask subjects to select which object among a bluish disk, a
bluish banana, and a gray disk appears to be a different color than the other two (Figure 3). If bluish
bananas of this particular blue tend to look gray (as predicted by memory color theories and
reported in previous work), then the bluish banana and the gray disk should look similar, leaving the
bluish disk appearing to be the odd color out among the three. But if subjects simply see the colors
roughly as they are (as predicted by modular theories), then they should select the gray disk as the
odd color out.
Method
Subjects
220 subjects were recruited online from Amazon Mechanical-Turk and were monetarily
reimbursed. (For discussion of this subject pool’s reliability, see Crump et al., 2013; for other
investigations of color perception run online, see Haberman, Brady, & Alvarez, 2015; Lafer-Sousa,
Hermann, & Conway, 2015; Witzel, 2016; Witzel et al., 2017). This sample size followed Witzel
(2016, Study 2), which ran 210 subjects; we slightly increased this number (both in this study and in
Experiment 2) because of an “attention check” we added that we expected would lead to slightly
more exclusions than in previous work.
Stimuli
The same four images as used in Witzel (2016) served as stimuli in the present experiment: a
gray disk, a gray banana, a bluish disk, and a bluish banana, presented on a neutral gray background.
2
The particular blue of the bluish objects was used in previous work because it approximates the
2
We thank Christoph Witzel for generously providing these stimuli.
MEMORY COLOR AND PERCEPTUAL LOGIC 12
color that subjects adjust a banana to be when asked to make it “gray”; importantly, this previous
work showed that subjects consider the bluish banana to be a better example of “gray” than even
the objectively gray banana.
From these four images, we created four trial types corresponding to the four unique triplets
that can be made from them. Each triplet comprised three side-by-side images, displayed in a newly
randomized left-to-right order each time they were presented (for a “screenshot” of the task, see
Figure 3). Due to the nature of online data collection, we cannot be sure of the exact color, size, or
brightness (etc.) of the images as they appeared to subjects during the experiment; however, any
distortions or miscalibrations caused by a given subject’s monitor would have been held constant
across conditions (just as in earlier online studies using these stimuli).
In addition to these experimental trials, the final trial of the experiment was a “catch trial”
consisting of a triplet that included a green square, a blue square, and a blue circle whose colors were
much more saturated than those of the experimental stimuli; the purpose of this trial was to ensure
that the subjects were paying attention (see below).
Figure 3. An example triplet from Experiment 1. On each trial, subjects saw three images in a
random order, and selected whichever image appeared to have a different color than the other
two. This particular trial shows a gray disk (left), blue banana (middle), and blue disk (right),
and so the objectively “correct” answer would be to select the left-most image. By contrast,
memory color theories predict that the blue disk (right) should appear to be the odd color out
(or, at least, the most different in hue), since the blue banana has exactly the right amount of
blue to appear gray (as measured and validated in previous studies).
Procedure
Subjects were first shown an instruction page which informed them that they would see
three objects on each of many subsequent pages, and that they should “judge which one looks to be
a slightly different color from the other two, by clicking on that object.” The instructions page also
Which is the ‘odd color out’?
MEMORY COLOR AND PERCEPTUAL LOGIC 13
showed subjects an “easy” practice triplet that included a (much more saturated) blue circle, yellow
square, and yellow circle; subjects were told, for this example, that they “should select the blue circle,
since it is a different color from the other two objects”, but also that “the real experiment will be
much harder than this, though! The colors will be very hard to tell apart, so look closely.”
In the experiment itself, subjects completed the odd-color-out task 10 times for each of the
four trial types, for a total of 40 experimental trials; the trials appeared in blocks of four (one for
each of the four trial types), with the trial order randomized within each block. The relative position
of each individual image within the triplet (i.e. left, middle, or right) was randomly chosen for each
trial. Subjects could only advance to the next trial after clicking on one of the three images displayed.
There was no time limit on responses. After making a selection, all of the images disappeared from
the screen, followed by a 2000ms interval before the next trial’s images appeared.
After all 40 experimental trials, the “catch” trial appeared; this was later used as an exclusion
criterion to ensure that subjects understood the task.
Readers can experience the task for themselves at http://perceptionresearch.org/bananas.
Results and Discussion
21 subjects were excluded either for failing to provide a complete dataset (4/220) or for
failing to correctly answer the “catch” question (17/220), leaving 199 subjects with usable data.
However, none of the results reported here depended on these exclusions (i.e. all of the effects
below remain statistically significant, in the same direction, even without excluding these subjects).
For each triplet type, we can consider the prediction made by the memory color view
(according to which blue bananas appear gray, and gray bananas appear yellow) and the prediction
made by the “modular” view (according to which color knowledge does not affect color
appearance), and compare the data to those predictions.
3
To foreshadow the general pattern, every
triplet yielded the result predicted by the modular view, and none of them yielded the result
predicted by the memory color view (Figure 4).
3
Given that there were 10 repetitions of each triplet, it was possible for subjects to respond inconsistently across
repetitions, which may have been a marker of low engagement on the part of the subject; to ensure that random or
unthoughtful responses did not contaminate the results, we considered responses only from those subjects who
consistently selected the same triplet-member a majority of the time across repetitions (i.e. >5 times out of 10
opportunities). This left 148 subjects (from the original 199). Once again, however, none of the results depended on
such exclusions: All of the contrasts and inferential statistics reported here remain statistically significant even when
these subjects are not excluded.
MEMORY COLOR AND PERCEPTUAL LOGIC 14
For the triplet consisting of {gray disk, bluish banana, bluish disk}, memory color theory
predicts that the blue banana should appear gray, and thus that subjects should pick the bluish disk
as the odd color out; by contrast, the modular view predicts that subjects should pick the gray disk
as the odd color out, since the bluish banana should look similar to the equally blue disk (Figure 4a).
In fact, 68.9% of subjects selected the gray disk as the odd color out (the choice consistent with the
modular view), and only 1.4% of subjects selected the blue disk as the odd color out (the choice
consistent with memory color), χ2(2, N=148)=102.32, p<.001; the remaining 29.7% of subjects
selected the bluish banana as the odd color out, which is predicted by neither view. (Given the
subtlety of the differences in color for these images, we suspect that subjects who couldn’t detect a
meaningful difference in color between the three images simply defaulted to picking the odd shape
out, which in this triplet was the bluish banana. Another possibility is that, being unable to detect
any difference in hue, subjects considered the difference in shading of this third object to be a
relevant difference in “color”, and so chose it for that reason. As is clear below, other conditions
reveal a similar odd-shape-out pattern.)
MEMORY COLOR AND PERCEPTUAL LOGIC 15
Figure 4. Results from Experiment 1. (A) Subjects accurately identified a gray disk as the “odd
color out”, even though memory color theories predict that the blue disk should be perceived
as the odd color out (because the blue banana should appear gray). (B) Across all trial types,
the most popular selection was always the perceived odd color out predicted by a modular
view, and never the perceived odd color out predicted by memory color theory.
For the triplet consisting of {bluish banana, gray disk, gray banana}, memory color theory
predicts that the blue banana should appear gray (like the gray disk), and the gray banana should
appear yellow, and thus that subjects should pick the yellow-looking gray banana as the odd color
What color it really is gray blue
How it should look if
distorted by Memory Color
blue
gray gray blue
0
20
40
60
80
100
perceived odd-color-out
if seen “objectively”
perceived odd-color-out
if distorted by Memory Color
What color
it really is blue gray gray
How it should look
if distorted by
Memory Color
gray
gray yellow
odd-color-out if
seen “objectively”
odd-color-out if
distorted by
Memory Color
% chosen as odd color out
0
20
40
60
80
100
blue gray gray
blue yellow gray
odd-color-out if
seen “objectively”
(under Memory
Color distortion, all
three look different)
bluegray blue
yellow blue gray
odd-color-out if
seen “objectively”
(under Memory
Color distortion, all
three look different)
% chosen as odd color out
A
B
MEMORY COLOR AND PERCEPTUAL LOGIC 16
out; by contrast, the modular view predicts that subjects should pick the bluish banana as the odd
color out, since the gray banana should look similar to the equally gray disk, and the bluish banana
should look blue. In fact, 64.8% of subjects selected the bluish banana as the odd color out (the
choice consistent with the modular view), and only 4.1% of subjects selected the gray banana as the
odd color out (the choice consistent with memory color); χ2(2, N=148)=82.52, p<.001. The
remaining 31.1% of subjects selected the gray disk as the odd color out, which is predicted by
neither view and is again consistent with deferring to an “odd shape out” strategy.
For the triplet consisting of {bluish disk, gray banana, gray disk}, memory color theory predicts
that the objects should appear to be three different colors — the gray banana should appear yellow,
the gray disk should appear gray, and the bluish disk should appear blue — and thus that there
should be no salient “odd color out”; in that case, any option should perhaps be equally likely as
another. By contrast, the modular view straightforwardly predicts that subjects should pick the
bluish disk as the odd color out, since the other two objects are gray. In fact, there was a salient odd
color out: 69.6% of subjects selected the bluish disk as the odd color out (the choice consistent with
the modular view), whereas 0 subjects selected the blue banana as the odd color out, and 30.4% of
subjects selected the gray banana as the odd color out; χ2(2, N=148)=108.20, p<.001.
For the triplet consisting of {gray banana, bluish disk, bluish banana}, memory color theory
predicts that the objects should appear to be three different colors — the gray banana should appear
yellow, the bluish banana should appear gray, and the bluish disk should appear blue — and thus
that there should be no salient “odd color out”; in that case, any option should perhaps be equally
likely as another. By contrast, the modular view straightforwardly predicts that subjects should pick
the gray banana as the odd color out, since the other two objects are blue. In fact, there was a salient
odd color out as indicated by subjects’ responses: 68.9% of subjects selected the gray banana as the
odd color out (the choice consistent with the modular view), whereas 0.7% of subjects selected the
blue banana as the odd color out, and 31.4% of subjects selected the bluish banana as the odd color
out; χ2(2, N=148)=104.06, p<.001.
In other words, across these four triplets, subjects’ responses always favored the modular
account and never favored the memory color account, even when memory color theories made clear
predictions about which objects should look different than the others in a given triplet.
Indeed, even if the memory color effects in our study somehow varied in strength relative to
previous studies (even though we used the same stimuli as Witzel, 2016, under closely matched
conditions), it is striking just how unpopular the memory color theory’s predicted “odd-one-out”
MEMORY COLOR AND PERCEPTUAL LOGIC 17
was for subjects. For example, suppose that for the triplet consisting of {gray disk, bluish banana, bluish
disk}(shown in Figure 4a), it turned out that the memory color effects was somehow weaker than in
previous work, such that the bluish banana was perceptually biased only halfway towards achromatic
gray, rather than completely towards achromatic gray as in previous studies. Even then, memory
color theories should predict that the gray disk and bluish disk should be chosen roughly equally
often, and that the bluish banana should be chosen least often (since it would be most perceptually
similar to the other two images); but this pattern was not observed either — instead, subjects just
behaved as though they saw the relative coloring accurately and without distortion.
Overall, we took these general patterns of results as initial evidence that memory color
effects fail to obey the “logic” expected of bona fide perceptual effects.
Experiment 2: “Where were the bananas?”
Experiment 1 suggested that subjects fail to respond according to the memory color theory in cases
with clear predictions about which objects should look similar and which should look different.
However, one possibility is that our task caused subjects to focus too closely on the particular colors
of certain pixels on the display, and perhaps thereby fail to represent the images as objects with
known colors. This could undermine the validity of the results, since it is critical to memory color
effects that subjects represent canonically colored objects as those objects — i.e. that they are
representing the banana as a banana while viewing it.
To give memory color effects the best chance of revealing themselves in this task,
Experiment 2 included a secondary task after each odd-color-out judgment, in which the objects
disappeared from the screen and subjects had to identify the locations of all the banana images that
had been present a moment earlier. Since the images were no longer on the display during this
secondary task, accurate performance on it required subjects to have earlier noticed which objects
were bananas and which weren’t (or, at least, to have encoded their shapes in some way, rather than
just the colors of a few pixels). This encouraged subjects to represent the bananas as bananas while
making color judgments about them, since subjects knew at that time of viewing the stimuli that
they would later have to report the locations of the bananas from memory.
4
This experiment also
4
We thank Molly O'Rourke-Friel for a comment that inspired this design.
MEMORY COLOR AND PERCEPTUAL LOGIC 18
served as a replication of Experiment 1 (and otherwise proceeded in exactly the same way), to
ensure the reliability of the relevant patterns.
Method
This experiment was identical to Experiment 1 except as follows. A new group of 250
subjects participated. (We conservatively increased the sample size because of an additional
exclusion criterion related to the secondary task.) After making each odd-color-out judgment, the
images disappeared and were replaced 500ms later by three empty boxes in the same locations as the
trial images. Subjects were asked “Where were the bananas?”, and could click as many or as few of
the boxes as they liked; when they were satisfied with their answer, subjects clicked a button labeled
“I’ve chosen the bananas”, after which the boxes disappeared for 2000ms and were then replaced by
the images for the next trial (Figure 5).
To ensure that we only analyzed data from subjects who were representing the bananas as
bananas, we excluded any subject who failed to perform above 90% accuracy across all of the
“Where were the bananas?” trials; this resulted in the additional exclusion of 7 subjects (2.8% of the
total sample).
Figure 5. Design of Experiment 2. After picking the odd color out from the display, subjects
were asked to recall the locations of the banana(s) that had been on the screen. This required
subjects to focus on the identity of the objects while making their initial choice, thereby
encouraging subjects to represent the banana images as bananas.
Which is the ‘odd color out’?
Where were the bananas?
Time
MEMORY COLOR AND PERCEPTUAL LOGIC 19
Results and Discussion
Every finding from Experiment 1 was replicated in Experiment 2.
For the triplet consisting of {gray disk, bluish banana, bluish disk}, 73.9% of subjects selected
the gray disk as the odd color out (the choice consistent with the modular view), and only 2.5% of
subjects (just two subjects in the entire sample) selected the blue disk as the odd color out (the
choice consistent with memory color).
For the triplet consisting of {bluish banana, gray disk, gray banana}, 70.8% of subjects selected
the bluish banana as the odd color out (the choice consistent with the modular view), and only 5.0%
of subjects selected the gray banana as the odd color out (the choice consistent with memory color).
For the triplet consisting of {bluish disk, gray banana, gray disk}, 75.6% of subjects selected the
blue disk as the odd color out (the choice consistent with the modular view); memory color predicts
that all three objects should appear different colors, and thus that any option should be as likely a
response as any other.
For the triplet consisting of {gray banana, bluish disk, bluish banana}, 73.9% of subjects selected
the gray banana as the odd color out (the choice consistent with the modular view); memory color
predicts that all three objects should appear different colors, and thus that any option should be as
likely a response as any other.
In other words, every triplet showed the pattern predicted by the modular view, and none of
them showed the pattern predicted by the memory color view, even among subjects who were
actively representing the bananas as bananas. Indeed, if anything, these patterns were stronger here
than in Experiment 1, despite the increased focus on the bananas’ identities.
This result further suggests that memory color effects do not obey the “logic” expected of
genuine perceptual effects, and instead behave exactly as they should if they are simply perceived
without this sort of distortion. For example, if bluish bananas truly look gray, then they should
resemble gray disks (recall that blue shade used here was specifically chosen by memory color
researchers to match the shade that subjects choose for a banana to be “gray”); however, we found
the opposite pattern — subjects’ answers were least consistent with the memory color theory, and
most consistent with the traditional view that blue objects look blue and gray objects look gray, no
matter the subject’s knowledge about their canonical colors.
MEMORY COLOR AND PERCEPTUAL LOGIC 20
Experiment 3: Perceptual logic in classical memory color effects
The previous experiments explored a new way to study alleged effects of knowledge on perception,
by asking whether memory color effects obey a “logic” that should be expected of genuinely
perceptual phenomena. In focusing on the strongest and most recent work on memory color effects,
however, these studies dealt with only one sort of stimulus, and only one sort of claim. How
generally can this strategy be applied?
To answer this question, Experiment 3 turned from contemporary work on memory color
effects to the classical investigations that inspired this more recent work — in particular, a report
from the middle of the last century that heart-shapes appear redder than identically colored shapes
that don’t have strong color associations (Delk & Fillenbaum, 1965). In that study, subjects viewed
shapes cut out of orange-red cardboard, which appeared against a color-adjustable background. The
subjects’ task was to adjust the background to match the color of the presented shape (by giving
instructions to an experimenter), and the results showed that subjects selected a redder background
for the heart than they did for shapes without canonical colors (e.g., circles, triangles, or rectangles).
On one hand, this earlier result may seem weaker than more recent memory color work, in
that the study relied on methods that seem especially prone to bias: For example, the experimenters
themselves operated the dials that adjusted the background’s color, which could have contaminated
the results in favor of the experimenters’ hypotheses (Gilder & Heerey, 2018). At the same time, one
relative strength of these studies is that they involved matching the colors of two stimuli, rather than
adjusting one stimulus to some internal standard (cf. the achromatic adjustment method of Hansen
et al., 2006). As noted earlier, relying on the subject’s own notions of such color categories can pose
problems for isolating perceptual effects per se, given the contextual flexibility of such subjectively
defined color standards. Perceptual matching tasks such as these may also be less susceptible to
alternative explanations based on differences in memory rather than perception (Cooper et al., 2012;
Firestone & Scholl, 2015b), since they involve affirming the similarity of two currently visible
stimuli. In light of these factors, and in light also of this classic study’s prominence in contemporary
debates over cognitive (im)penetrability (Brogaard & Gatzia, 2017; Deroy, 2013; Gatzia, 2017; Gross
et al., 2014; MacPherson, 2012; Stokes, in press; Vetter & Newen, 2014; Zeimbekis, 2013), we asked
whether this phenomenon might also be susceptible to a test of perceptual “logic”.
MEMORY COLOR AND PERCEPTUAL LOGIC 21
El Greco, juiced-up
Our study in this vein is a variant on the “El Greco fallacy” — an episode from art history
that has also become a technique for separating perception from judgment (Firestone, 2013b;
Firestone & Scholl, 2014; Martin et al., 2016). El Greco famously painted figures that were unusually
elongated, and it was once theorized that this reflected a distortion in the Spanish renaissance artist’s
vision due to unusually severe astigmatism, which was said to vertically blur his perception of the
world. However, if El Greco truly experienced a vertically stretched-out world, then he would also
have experienced a vertically stretched-out canvas, and the distortions would have ‘canceled out’. So,
whether or not El Greco had astigmatism, that couldn’t explain the distortions in his paintings. For
perception research, the moral is the same: If an alleged effect is truly perceptual, and if the
‘equipment’ used to measure this effect it itself similarly susceptible to the manipulation, then the
effect should disappear when the manipulation is applied to both the stimulus and the measuring
equipment.
Here, we develop an even stronger and more comprehensive version of the El Greco fallacy
than has been used in previous research, to ask whether classical memory color effects obey the
“logic” of perception: We run four conditions of the original Delk & Fillenbaum study, ratherthan
two, corresponding to all possible pairs of backgrounds and foregrounds made up of hearts and
rectangles. In other words, subjects not only saw hearts and rectangles on rectangle-shaped
backgrounds (as in the original study), but also hearts and rectangles on heart-shaped backgrounds
5
(Figure 6).
5
We thank Eli Shupe for a comment that inspired this design. Gross et al. (2014) also take a similar approach.
MEMORY COLOR AND PERCEPTUAL LOGIC 22
Figure 6. Design of Experiment 3. (A) Subjects saw a shape on a color-adjustable background,
and estimated its color by continuously adjusting the color of the background shape to match
the color of the foreground shape. (B) The four trial types included a rectangle on a rectangular
background, a heart on a rectangular background, a rectangle on a heart-shaped background,
and a heart on a heart-shaped background.
The shape of the background itself is relevant because, if hearts look redder than rectangles,
then heart-shaped backgrounds should themselves appear redder than rectangle-shaped backgrounds,
and subjects’ color matching judgments should incorporate this distortion too. However, while
memory color theories make clear and strong predictions about such cases, those predictions can be
difficult to quickly and reliably wrap one’s mind around. For example, try to quickly determine how
estimates for an orange-red rectangle on a heart-shaped background should differ from estimates for
an orange-red heart on a rectangle-shaped background. Memory color theory is committed to just as
strong a prediction about such a case as it is in the original case, but we may find ourselves
struggling to immediately and confidently articulate this prediction. (The answer is that a rectangle
on a heart-shaped background should produce an objectively more orange estimate than a heart on a
A
B
MEMORY COLOR AND PERCEPTUAL LOGIC 23
rectangle-shaped background, in part owing to the extra redness present in the adjustable
background.) Indeed, for each of the pairwise comparisons between these conditions, the memory
color theory makes an equally strong prediction; the present experiment exhausts these predictions
and asks whether they are confirmed.
Method
Subjects
400 subjects were recruited online from Amazon Mechanical-Turk and were monetarily
reimbursed.
Stimuli
The stimuli in this experiment consisted of either a love-heart shape or a rectangle, both
appearing in a red-orange fill with a thin black outline. The precise shapes and colors used in the
original Delk and Fillenbaum study were either unknown or difficult to reproduce on a computer
monitor; however, we chose a conventional love-heart shape for the heart, and we chose an orange-
red color for the foreground shapes corresponding to RGB(242,59,13), or its equivalent
HSV(12°,95%,95%). This color is naturally judged as an example of “red” — and is often called
“orange red” in web color guides — but still leaves room in the red-ward direction of the color
space. (In HSV color space, red is conventionally located at 0°, and orange is conventionally located
at 30°; our sample was located at 12°.) The background against which these shapes appeared was
either a larger rectangle, or a larger version of the same heart shape. As earlier, the nature of online
data collection means that we cannot be sure of the exact color, size, or brightness (etc.) of the
images as they appeared during the experiment; however, any distortions or miscalibrations caused
by a given subject’s monitor would have been held constant across conditions (just as in previous
work studying memory color effects online; Witzel, 2016).
Procedure
Subjects were instructed to “adjust the color of the background until it looks the same as the
color of the object in the middle”, and they completed one trial of each of four trial types,
corresponding to the four pairs of foreground and background shapes: {rectangle-background, rectangle-
foreground}, {rectangle-background, heart-foreground}, {heart-background, rectangle-foreground}, {heart-
background, heart-foreground} (Figure 6). The trials appeared in a newly randomized order for each
subject.
MEMORY COLOR AND PERCEPTUAL LOGIC 24
On each trial, the background began colored in black, and subjects clicked a button to reveal
a color palette through which they could navigate using their cursor; as the cursor moved through
the space, the background’s color changed to match the cursor’s location in the color space. Subjects
clicked a button to indicate that they were satisfied with the match, at which point the next trial
appeared.
Readers can experience the task for themselves at http://perceptionresearch.org/hearts.
Results and Discussion
Following previous work (Gross et al., 2014), we analyzed responses in terms of the degree-
difference in hue within the HSV color space, which allows the analysis to collapse over differences
in saturation or brightness and instead isolate the “redness” vs. “orangeness” of responses. The
degree-value of a given color response represents its angular position within a cylindrical color
space: 0° is red, 60° is yellow, 120° is green, etc.
Given the sensitivity of color matching to extreme values (where a single “random” response
by a single subject can throw off dozens or hundreds of subtle responses by other subjects), we
excluded any subject whose response on any trial was more than 60° away from the object’s true
color; this is equivalent to answering that a deeply blue object is pink, or a purely red object is
yellow, and so would seem to indicate a lack of engagement or understanding on the part of the
subject. We also excluded any subject who failed to contribute a complete dataset. This left 363
subjects of the original 400. (We also used these exact same exclusion criteria in a replication
experiment; see Experiment 4.)
The results of all four conditions appear together in Figure 7a, and are plotted as the bias in
hue toward red from the foreground image’s true hue (which was 12° in every condition).
6
Below, we
consider the various pairwise comparisons that are possible between these conditions, and whether
the memory color prediction was in fact observed.
Replication of Delk and Fillenbaum
We first examined the effect from the original Delk and Fillenbaum study, which had found
that hearts are judged as redder than familiar shapes that don’t have strong color associations; in our
6
To determine the mean H value of subjects’ color settings, rather than the red-ward bias we report here, you could
subtract the values in Figure 7a from 12°; for example, for the {rectangle-background, rectangle-foreground} condition, the red-
ward bias was 1.39°, which means subjects set the background to an average H value of 12° – 1.39° = 10.61°.
MEMORY COLOR AND PERCEPTUAL LOGIC 25
experiment, this was equivalent to the {rectangle-background, heart-foreground} vs. {rectangle-background,
rectangle-foreground} contrast (Figure 7b, comparison i). We successfully replicated this effect: In our
sample too, subjects adjusted the background rectangle to be redder when the foreground was a
heart than when the foreground was a square: 2.84° red-ward vs. 1.39° red-ward, t(362)=4.17,
p<.001. Though this effect is rather small in terms of raw degrees of hue, this result establishes the
reliability of Delk and Fillenbaum’s original finding — and indeed this may be the first study in
several decades to do so. Color estimates for hearts truly are redder than estimates for identically
colored squares.
Exhausting the predictions of memory color theories
Is this effect truly perceptual? Having established the reliability of the key rectangle vs. heart
contrast, we can now examine other contrasts about which the memory color theories make equally
strong predictions. For example, consider the contrast between {heart-background, heart-foreground} and
{rectangle-background, rectangle-foreground} (Figure 7b, comparison ii): In both cases, a given foreground
shape is matched to an identical background shape, and so there should be no effect of the shapes’
identity; if hearts appear redder than rectangles, then both the foreground heart and the background
heart should appear redder, and the effects should cancel out, since the mind would also have added
some extra redness to the background heart. However, we did observe an effect between these two
conditions: Subjects judged a heart to be redder than a rectangle even when the background of the
heart was itself a heart: 2.41° red-ward vs. 1.39° red-ward, t(362)=2.82, p=.005. This pattern
exemplifies the characteristic “El Greco fallacy” result; if hearts truly look redder, then there should
have been no difference between these two cases.
Importantly, however, the design of this experiment permits even more comprehensive and
powerful tests of the memory color theory’s predictions. Even beyond the “El Greco” pattern, we
can consider other contrasts — for example, the contrast between {rectangle-background, rectangle-
foreground} and {heart-background, rectangle-foreground} (Figure 7b, comparison iii). Here, with the
foreground shape held constant, subjects should adjust the heart-shaped background to be more
orange (i.e., less red) than the rectangle-shaped background, to account for the added redness that the
mind allegedly adds to hearts. However, we did not observe this effect, and indeed if anything we
observed the opposite effect: Subjects adjusted the background to be redder in the {heart-background,
rectangle-foreground} condition than in the {rectangle-background, rectangle-foreground} condition: 2.32° red-
ward vs. 1.39° red-ward, t(362)=2.12, p=.03 — the reverse of the memory color prediction. (Note that
it is not particularly crucial that this “opposite” effect be statistically significant; the key result is
MEMORY COLOR AND PERCEPTUAL LOGIC 26
simply that it fails to differ in the other direction.) This result is perhaps even more powerful
evidence against a perceptual interpretation than the canonical “El Greco”-style result, because it is a
minimal pair with the original Delk and Fillenbaum (1965) result: Switching the heart from the
foreground to the background should produce the opposite of the original effect, but it does not.
Figure 7. Results of Experiment 3. Whereas a simple contrast of heart vs. rectangle (on a
rectangular background) produced the effect expected by memory color theories, other
contrasts failed to produce the effects predicted by memory color theories, or even produced
opposite effects. Error bars for each contrast are ± 1 SE of the difference between conditions.
Memory Color
Prediction Red-ward Bias (°H)
0 0.5 1 1.5 2 2.5
should be
redder than Successful Delk &
Fillenbaum replication
should be
redder than
Memory Color
Result?
should be
same as
should be
redder than
A
B
Red-ward Bias (°H)
i.
ii.
iii.
iv.
0
0.5
1
1.5
2
2.5
3
3.5
3 3.5
MEMORY COLOR AND PERCEPTUAL LOGIC 27
Consider further the contrast between {heart-background, heart-foreground} and {heart-background,
rectangle-foreground} (Figure 7b, comparison iv); this contrast should behave exactly like the original
Delk and Fillenbaum contrast of {rectangle-background, rectangle-foreground} vs. {rectangle-background, heart-
foreground}, with a redder estimate for the foreground heart than for the foreground rectangle —
since the background is held constant across both conditions, and only the foreground shape has
changed. However, there was no effect in this case — 2.41° red-ward vs. 2.32° red-ward,
t(362)=0.24, p>.80 — even though we had indeed observed a robust effect in the {rectangle-
background, rectangle-foreground} vs. {rectangle-background, heart-foreground} case.
We can also consider {rectangle-background, heart-foreground} vs. {heart-background, heart-
foreground}; here, {rectangle-background, heart-foreground} should produce a redder estimate (since the
foreground is constant but the rectangular background has no added redness), but in fact there was
no effect: 2.84° red-ward vs. 2.41° red-ward, t(362)=1.25, p=.21. (However, we note that this non-
significant trend was indeed in the direction predicted by memory color theory, and it could emerge
with greater statistical power; for this reason, we do not wish to read too much into this non-effect
here.)
Finally, {rectangle-background, heart-foreground} vs. {heart-background, rectangle-foreground} should
have produced the largest effect of all, with {rectangle-background, heart-foreground} producing the
reddest estimate of all conditions and {heart-background, rectangle-foreground} producing the least red
estimate of all conditions; however, there was no effect here too: 2.84° red-ward vs. 2.32° red-ward,
t(362)=1.23, p=.22. Although this trend was in the direction predicted by memory color theory, we
note that it was numerically smaller than the effect it was supposed to be significantly larger than: The
difference between {rectangle-background, rectangle-foreground} and {heart-background, rectangle-foreground}
was 1.45°, and so the difference between {rectangle-background, heart-foreground} vs. {heart-background,
rectangle-foreground} should have been even larger than that difference, according to memory color
theories; but instead the {rectangle-background, heart-foreground} vs. {heart-background, rectangle-foreground}
difference was only 0.51°. In other words, even if this 0.51° effect were statistically significant in a
larger sample, it is still the wrong kind of effect to vindicate the memory color theory’s prediction.
Thus, whereas we successfully replicate the original heart vs. rectangle effect on a rectangle-
shaped background — exactly the kind of hypothesis that might be easier for subjects to follow —
we repeatedly fail to confirm the memory color prediction for other cases, or we even actively find
the opposite pattern. Indeed, just a single failed prediction among the set above would be enough to
frustrate the memory color account; however, we found that the memory color theory’s prediction
MEMORY COLOR AND PERCEPTUAL LOGIC 28
was wrong about a majority of its predictions, just as would be expected if the relevant effects were
not perceptual.
Alternative explanations?
One possible alternative explanation for some of the above results is that we’ve
mischaracterized the role of the added redness of the background heart. In particular, perhaps the
added redness of a heart-shaped background subsumes whatever shape appears inside of it, making it
appear redder as well (as if the foreground were “inside” the heart-shaped background, taking on the
heart’s reddish glow). This could, perhaps, explain why heart-shaped backgrounds don’t drive
judgments orange-ward, since they also imbue their foreground shapes with an equal amount of
added redness.
However, this alternative is contradicted by other results: For example, if the effect of a
heart-shaped background is additive with whatever is in the foreground, then a heart on a heart-
shaped background should have been judged as redder than a rectangle on a heart-shaped
background; but this was not the case (indeed, these conditions were the most similar of any
condition we tested). And if the effect is not additive — i.e. if the foreground shape gets as much
extra redness as it would ever get as long as there is one heart in the foreground or the background
— then this alternative fails to explain why a heart on a rectangle-shaped background produced a
response no different than a heart on a heart-shaped background. Moreover, both such accounts fail
to explain the redder judgment in {heart-background, rectangle-foreground} than in {rectangle-background,
rectangle-foreground}.
Another possibility is that background hearts are somehow not recognized as hearts, or are
not attended to as strongly, in such a way that memory color effects don’t apply to them. Could this
explain our results? First, we note that this account seems unmotivated from the perspective of the
memory color framework; to our knowledge, there has not been any prior evidence or suggestion
that attention was required for memory color effects. Indeed, memory colors are meant to assist
color processing across a whole scene; so if it turned out that memory color effects were hyper-local
in this way — applying to one small region of an image but not to the immediately surrounding
region — then memory color effects would not be nearly as useful for perception as they are meant
to be. But second, this account would fail to explain our results even if it were the case that memory
color effects don’t apply to the background shapes. For example, it would fail to explain why there
was a large square vs. heart difference when the background was rectangular (Figure 7b, comparison
MEMORY COLOR AND PERCEPTUAL LOGIC 29
i), but no square vs. heart difference when the background was heart-shaped (Figure 7b, comparison
iv); if the background is ignored for the purposes of memory color effects, then those two contrasts
should have produced similar results.
Overall, we thus took this general pattern of results as promising evidence against a
perceptual interpretation of classical memory color effects, which seem not to behave as they should
if they were genuinely perceptual.
Experiment 4: Replication
Experiment 3 produced results that were inconsistent with what a memory color account would
predict; but what explains those results? Examining the totality of the data collected (e.g., Figure 7a),
it is difficult to find a single unifying explanation. However, one plausible account that seems to
qualitatively cover the relative judgments made in the various conditions is a simple estimation
strategy that might be summarized as follows: “If there is a heart on the display, give a redder estimate”. This
simple rule, if implemented by subjects, could account for the fact that every condition involving a
heart produced a response that was redder than the baseline {rectangle-background, rectangle-foreground}
condition. And it could also explain why the more fine-grained predictions made by memory color
theories failed to come true: The subjects simply weren’t making the sophisticated and often
tortuous inferences implied by the theory. However, whereas we had actively predicted that many of
the conditions from Experiment 3 would disconfirm the predictions made by memory color theory,
our present “if it has a heart, answer red” hypothesis was generated post-hoc, having occurred to us
only after looking at the data.
Thus, to further support this interpretation, Experiment 4 replicated Experiment 3, but
asked each subject to contribute more estimation data, and also debriefed subjects about the
purpose of the experiment; this allowed us both to determine the reliability of the pattern observed
in Experiment 3 and also to gain further insight into the thought process of subjects completing the
experiment.
Method
All methods in Experiment 4 were identical to Experiment 3 except as noted here. 500
subjects were recruited online from Amazon Mechanical-Turk and were monetarily reimbursed. (We
MEMORY COLOR AND PERCEPTUAL LOGIC 30
conservatively increased the sample size here because we expected to exclude more subjects; see
below.) Rather than complete only one trial of each trial type, subjects completed 10 trials of each
trial type; the trials appeared in blocks of four (one for each of the four trial types), with the trial
order randomized within each block.
Given the role of demand characteristics in producing related sorts of effects (Durgin et al.,
2009), subjects were also debriefed about the purpose of the experiment once they had completed
all the trials. In particular, they were asked yes-or-no questions about various hypotheses, after the
open-ended question, “What did you think was the purpose of this study? Please answer in two
sentences”.
Results and Discussion
Every result from Experiment 3 replicated in Experiment 4.
We applied the same exclusion criteria as in Experiment 3, excluding any subject who ever
gave a response whose hue was more than 60° off the foreground image’s true color, or who failed
to contribute a complete dataset; since each subject completed 40 trials instead of 4, this inevitably
resulted in a higher exclusion rate, leaving 398 subjects of the original 500.
As in Experiment 3, {rectangle-background, heart-foreground} vs. {rectangle-background, rectangle-
foreground} replicated Delk and Fillenbaum (1965): t(397)=2.63, p<.01. {heart-background, heart-
foreground} vs. {rectangle-background, rectangle-foreground} produced an “El Greco” fallacy: t(397)=2.21,
p=.028. {rectangle-background, rectangle-foreground} vs. {heart-background, rectangle-foreground} failed to
produce an effect in the direction predicted by memory color theories, and if anything again
produced an effect in the “wrong” direction: t(397)=2.30, p=.022. {heart-background, heart-background}
vs. {heart-background, rectangle-foreground} showed no effect where there “should” have been one:
t(397)=0.09, p>.90. {rectangle-background, heart-foreground} vs. {heart-background, heart-foreground} also
produced no effect where there “should” have been one: t(397)=0.24, p>.80). Finally, {rectangle-
background, heart-foreground} vs. {heart-background, rectangle-foreground} showed no effect where there
“should” have been the largest effect: t(397) = 0.15, p>0.85. These results, though overall weaker in
magnitude, confirmed the pattern of results from Experiment 3.
Subjects’ hypotheses
The present results were also consistent with an estimation strategy that connects the
presence of a heart with redder estimates. In Experiment 4, only the condition without a heart in it
MEMORY COLOR AND PERCEPTUAL LOGIC 31
— {rectangle-background, rectangle-foreground} — had an estimate that was less red than any other
condition (though, again, other comparisons could reveal reliable alternative effects with larger
samples).
This account is also consistent with responses given by subjects when asked about the
purpose of the study. Though we do not attempt a systematic coding and analysis of these open-
ended responses here, we note anecdotally that many subjects explicitly articulated Delk and
Fillenbaum’s original hypothesis, with striking clarity, when simply asked in an open-ended way what
they thought the experiment was testing. For example:
“maybe people tend to put the heart a little more red”
“To see if the shape of the object changed our perceptions of the color of it”
“If you associated red with the heart shaped item, even if the color was more orange”
“To see how peoples perceptions of color changes with shapes. Maybe people see hearts as a darker red.”
“I think this study was about how shapes affect color perception.”
“To see if people make the heart shapes more red colored even if they are more orange in hue.”
“If the shape affected the color choice. Like maybe I see hearts as more red.”
“It was maybe about shape and how we perceive its color. For example we usually instinctively think red
when we see a heart.”
“If it's a heart you're more likely to choose a more red color. If it's a square, you'd pick more orange.”
“Maybe to see if the shape affected the color choice”
“I think the purpose of the study was to see whether shapes affect color perception, maybe”
“You probably were looking to see a relationship between color matching and the type of shape.”
“to see if i would rate hearts as more red in color”
Taken together, these results imply that memory color effects of this sort may not reflect
changes in visual appearance: Not only do these effects fail to obey various “logical” constraints, but
there are available explanations of the effects in terms of strategic or compliant responding by
subjects.
General Discussion
Does knowing an object’s typical color change its color appearance? Whereas a long-standing
research tradition suggests that it does, we extended such claims to new scenarios and circumstances
MEMORY COLOR AND PERCEPTUAL LOGIC 32
where the underlying theories make strong and specific predictions that are nevertheless tortuous
and difficult to grasp. Across new experiments spanning classical and contemporary work, we found
that such scenarios fail to produce the effects expected by memory color theories — and often
produce the opposite effects. Instead, all such results implied that subjects simply saw the objects’
colors in a manner undistorted by their beliefs or prior knowledge, and that any distorted responses
that did arise could be readily explained by strategic or compliant responding.
These results may bear on discussions in unusually diverse fields. In vision science, memory
color effects have been studied not only as a phenomena unto themselves, but also contributors to
color constancy and other core processes of color perception (Witzel & Hansen, 2015; Witzel &
Gegenfurtner, 2018). Although our results do not entail — and we do not argue — that color
appearance cannot be affected by this sort of color knowledge, we contend that pre-existing data,
tasks, and stimuli fail to settle the issue, such that more work would be required to show that color
knowledge plays this kind of active role in color perception. (For different notions of how higher-
level cognition might interact with color perception, see Webster & Kay, 2012, and Winawer et al.,
2007, both of whom also use sets of colored objects but in rather different designs.) Beyond this,
though, these findings reach further into cognitive science more generally, where memory color
effects have been near the center of broader disputes over the cognitive (im)penetrability of
perception (Lammers, de Haan, & Pinto, 2017; Lupyan, 2015a; Vetter & Newen, 2014) — and even
to philosophy, where the influence of higher-level cognition on color perception is discussed not
only with respect to the relationship between cognition and perception (Deroy, 2013; Gatzia, 2017;
Macpherson, 2012; Zeimbekis, 2013) but also the rational formation of perceptual beliefs (Siegel,
2012), and even the nature of aesthetic experience (Stokes, 2014). Indeed, philosophical discussions
of memory color effects are often particularly concerned, as we are here, with the question of
whether memory color effects occur at the level of perceptual phenomenology per se; our results
address this question directly and suggest reasons not to accept such claims given the available
evidence.
Generally applicable
Beyond the particular implications of the present results, we note further that the
experimental design strategy employed here is perfectly general, and could be applied to many other
alleged cases of top-down effects on visual appearance. Just as a yellow-distorted blue object should
MEMORY COLOR AND PERCEPTUAL LOGIC 33
look more similar to gray objects than to blue objects, an object that allegedly appears darker, larger,
or closer due to cognitive factors should also show the same pattern.
For example, if positive words truly appear bright and negative words truly appear dark
(Meier et al., 2007), then perhaps a positive word presented next to both (a) a neutral word of the
same brightness, and (b) a neutral word that is objectively brighter, should appear to resemble the
brighter word, and thus the equally bright neutral word should stand out as differently bright. If
dartboards truly look larger after a subject hits them with darts (Cañal-Bruland et al., 2010), then a
recently hit dartboard presented next to both (a) an un-hit dartboard of the same size, and (b) an un-
hit dartboard that is objectively larger, should appear to resemble the larger dartboard object in size,
such that the equally sized un-hit dartboard should stand out as different in size. If objects truly look
closer when they are desired (Balcetis & Dunning, 2010), then a desired object presented near (a) a
neutral object of the same distance, and (b) a neutral object that is objectively closer, should
resemble the closer object in distance, and the equally distant neutral object should stand out as
different in distance (so too with other reported spatial distortions; Caparos et al., 2015; Fini, Brass,
& Committeri, 2015; Harber et al., 2011). Any of these findings would strengthen the case for those
alleged top-down effects of cognition on perception (though there may of course be other pitfalls
lurking in the background; Firestone, 2013a; Firestone & Scholl, 2016).
Indeed, this strategy is applicable even outside questions of how cognition does or does not
affect perception: As exemplified by the color illusion in Figure 2, just about any effect on
appearance can be studied using “odd one out” tasks of this sort.
Generally
interpretable
Another notable property of the present strategy — and in particular of the “odd one out”
task explored in Experiments 1-2 — is that the data it yields are interpretable in an unusually broad
and powerful way. One unfortunate feature of many investigations of top-down effects on
perception — and indeed of many studies in psychology as a whole — is that statistically significant
“positive” effects are typically easier to interpret than “null” effects. For example, if a study finds
that wearing a heavy backpack makes hills look steeper (a la Bhalla & Proffitt, 1999), one might
tentatively conclude that a real effect is present; but if you don’t find this result, you might attribute
such a failure to other factors, such as a lack of statistical power or a failure to properly apply the
manipulation. Indeed, this issue can even afflict strategies such as the “El Greco fallacy” (Firestone
& Scholl, 2014) to at least some degree: If you find an effect in an “El Greco” condition, you may
MEMORY COLOR AND PERCEPTUAL LOGIC 34
infer that a given effect may not be perceptual; but if you don’t obtain that result, some other factor
could again be the culprit (including even statistical power, as perhaps was the case in Gross et al.,
2014, who report a study similar in spirit to our Experiment 3 but who fail to replicate the general
Delk and Fillenbaum result in a sample of 25 subjects).
By contrast, the data from the “odd-color-out” task used here are interpretable on multiple
outcomes, since they can produce statistically reliable results both for or against the relevant theory.
For example, consider the {gray disk, bluish banana, bluish disk} triplet from Experiment 1, where
memory color theory predicts that the blue banana should appear gray (and thus that subjects should
pick the bluish disk as the odd color out), and where a modular view predicts that the bluish banana
should look similar to the equally blue disk (and so subjects should pick the gray disk as the odd
color out). Either of these two contrary predictions could be positively supported by a statistically
reliable preference to choose one object over another: If subjects pick the blue disk as the odd color
out, then that result actively supports memory color theory; but if subjects pick the gray disk as the
odd color out (as occurred in our studies), then that result actively opposes memory color theory
and supports the modular view. (Perhaps the only hard-to-interpret result would be completely noisy
or random responding.) This is a relative strength of this strategy over previous investigations of
perception vs. judgment (including Firestone & Scholl, 2014, 2015c), and it makes “odd one out”
tasks a promising strategy for the durable challenge of separating perception from post-perceptual
judgments and responses (Goldstone et al., 2015; Witt et al., 2015), including even in domains that
go beyond questions of modularity and cognitive impenetrability.
Conclusions
How can we separate what we see from what we judge? Though experimentally distinguishing
perception from judgment is often difficult, here we have explored one such way, relying on the
“logic” that is obeyed by perception but followed only inconsistently or unreliably by higher-level
reasoning. This strategy takes seriously the underlying claims of the relevant theories, and simply
exhausts their predictions by testing them in more varied scenarios. We suggest that these results not
only recast extant claims about how knowledge does or does not affect perception (here, of color),
but also point toward a new and broadly applicable strategy for investigating visual appearance.
MEMORY COLOR AND PERCEPTUAL LOGIC 35
Acknowledgements
For comments on previous drafts, we thank Bart Anderson, Jacob Beck, David Delijani,
Steven Gross, and Maria Olkkonen; for discussion, we thank members of seminars and reading
groups at Johns Hopkins, UMass-Amherst, UNSW, Yale, and York.
MEMORY COLOR AND PERCEPTUAL LOGIC 36
Data Availability
All data and materials supporting the experiments in this paper are available at
https://osf.io/9tebu/.
MEMORY COLOR AND PERCEPTUAL LOGIC 37
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