intellecton/papers/project_paper_4_fbt/references/Hoffman2015.txt

The Interface Theory of Perception:

Natural Selection Drives True Perception To Swift Extinction

Donald D. Hoffman



1

The Interface Theory of Perception

A goal of perception is to estimate true properties of the world. A goal of
categorization is to classify its structure. Aeons of evolution have shaped
our senses to this end. These three assumptions motivate much work on
human perception. I here argue, on evolutionary grounds, that all three are
false. Instead, our perceptions constitute a species-specific user interface
that guides behavior in a niche. Just as the icons of a PC’s interface hide
the complexity of the computer, so our perceptions usefully hide the com-
plexity of the world, and guide adaptive behavior. This interface theory of
perception offers a framework, motivated by evolution, to guide research in
object categorization. This framework informs a new class of evolutionary
games, called interface games, in which pithy perceptions often drive true
perceptions to extinction.

1.1 Introduction

The jewel beetle Julodimorpha bakewelli is category challenged [11, 12]. For
the male of the species, spotting instances of the category desirable female
is a pursuit of enduring interest and, to this end, he scours his environment
for telltale signs of a female’s shiny, dimpled, yellow-brown elytra (wing
cases). Unfortunately for him, many males of the species Homo sapiens, who
sojourn in his habitats within the Dongara area of Western Australia, are
attracted by instances of the category full beer bottle but not by instances of
the category empty beer bottle, and are therefore prone to toss their emptied
“stubbies” unceremoniously from their cars. As it happens, stubbies are
shiny, dimpled, and just the right shade of brown to trigger, in the poor
beetle, a category error. Male beetles find stubbies irresistible. Forsaking all
normal females, they swarm the stubbies, genitalia everted, and doggedly try
to copulate despite repeated glassy rebuffs. Compounding misfortune, ants

1


2
The Interface Theory of Perception

of the species Iridomyrmex discors capitalize on the beetles’ category errors;
the ants sequester themselves near stubbies, wait for befuddled beetles, and
consume them, genitalia first, as they persist in their amorous advances.
Categories have consequences. Conflating beetle and bottle led male J.
bakewelli into mating mistakes that nudged their species to the brink of ex-
tinction. Their perceptual categories worked well in their niche: Males have
low parental investment and thus their fitness is boosted if their category
desirable mate is more liberal than that of females (as predicted by the the-
ory of sexual selection, e.g., [7, 39]). But when stubbies invaded their niche,
a liberal category transformed stubbies into Sirens, 370 milliliter amazons
with matchless allure.
The bamboozled bakewelli illustrate a central principle of perceptual cat-
egorization, the

Principle of Satisficing Categories: Each perceptual category of an or-
ganism, to the extent that the category is shaped by natural selection, is a
satisficing solution to adaptive problems.

This principle is key to understanding the provenance and purpose of percep-
tual categories: They are satisficing solutions to problems such as feeding,
mating, and predation that are faced by all organisms in all niches. How-
ever, these problems take different forms in different niches and therefore
require a diverse array of specific solutions. Such solutions are satisficing in
that (1) they are, in general, only local maxima of fitness and (2) the fitness
function depends not just on one factor, but on numerous factors, including
the costs of classification errors, the time and energy required to compute
a category, and the specific properties of predators, prey and mates in a
particular niche. Furthermore, (3) the solutions depend critically on what
adaptive structures the organism already has: It can be less costly to co-opt
an existing structure for a new purpose than to evolve de novo a structure
that might better solve the problem. A backward retina, for instance, with
photoreceptors hidden behind neurons and blood vessels, is not the “best”
solution simpliciter to the problem of transducing light but, at a specific
time in the phylogenetic path of H. sapiens, it might have been the best
solution given the biological structures then available. Satisficing in these
three senses is, on evolutionary grounds, central to perception and therefore
central to theories of perceptual categorization.
According to this principle, a perceptual category is a satisficing solution
to adaptive problems only “to the extent that the category is shaped by
natural selection.” This disclaimer might seem to eviscerate the whole prin-


1.2 The Conventional View
3

ciple, to reduce it to the assertion that perceptual categories are satisficing
solutions, except when they’re not.
The disclaimer must stand. The issue at stake is the debate in evolution-
ary theory over adaptationism: To what extent are organisms shaped by
natural selection versus other evolutionary factors, such as genetic drift and
simple accident? The claim that a specific category is adaptive is an empir-
ical claim, and turns on the details of the case. Thus, this disclaimer does
not eviscerate the principle; instead, it entails that, although one expects
most categories to be profoundly shaped by natural selection, each specific
case of purported shaping must be carefully justified in the normal scientific
manner.

1.2 The Conventional View

Most vision experts do not accept the principle of satisficing categories, but
instead, tacitly or explicitly, subscribe to a different principle, the

Principle of Faithful Depiction: A primary goal of perception is to re-
cover, or estimate, objective properties of the physical world. A primary goal
of perceptual categorization is to recover, or estimate, the objective statistical
structure of the physical world.

For instance, Yuille and B¨ulthoff [44] describe the Bayesian approach to
perception in terms of faithful depiction: “We define vision as perceptual
inference, the estimation of scene properties from an image or sequence of
images . . . there is insufficient information in the image to uniquely de-
termine the scene. The brain, or any artificial vision system, must make
assumptions about the real world. These assumptions must be sufficiently
powerful to ensure that vision is well-posed for those properties in the scene
that the visual system needs to estimate.” On their view, there is a phys-
ical world that has objective properties and statistical structure (objective
in the sense that they exist unperceived). Perception uses Bayesian estima-
tion, or suitable approximations, to reconstruct the properties and structure
from sensory data. Terms such as estimate, recover, and reconstruct, which
appear throughout the literature of computational vision, stem from com-
mitment to the principle of faithful depiction.
Geisler and Diehl [8] endorse faithful depiction: “In general, it is true
that much of human perception is veridical under natural conditions. How-
ever, this is generally the result of combining many probabilistic sources
of information (optic flow, shading, shadows, texture gradients, binocular


4
The Interface Theory of Perception

disparity, and so on). Bayesian ideal observer theory specifies how, in prin-
ciple, to combine the different sources of information in an optimal manner
in order to achieve an effectively deterministic outcome” (p. 397).
Lehar [24] endorses faithful depiction:
“The perceptual modeling ap-
proach reveals the primary function of perception as that of generating a
fully spatial virtual-reality replica of the external world in an internal rep-
resentation.” (p. 375).
Hoffman [15] endorsed faithful depiction, arguing that to understand per-
ception we must ask, “First, why does the visual system need to organize
and interpret the images formed on the retinas? Second, how does it remain
true to the real world in the process? Third, what rules of inference does it
follow?” (p. 154).
No¨e and Regan [25] endorse a version of faithful depiction that is sensitive
to issues of attention and embodied perception, proposing that “Perceivers
are right to take themselves to have access to environmental detail and to
learn that the environment is detailed” (p. 576) and that “the environmental
detail is present, lodged, as it is, right there before individuals and that they
therefore have access to that detail by the mere movement of their eyes or
bodies” (p. 578).
Purves and Lotto [29] endorse a version of faithful depiction that is di-
achronic rather than synchronic, i.e., that includes an appropriate history of
the world, contending that “what observers actually experience in response
to any visual stimulus is its accumulated statistical meaning (i.e., what the
stimulus has turned out to signify in the past) rather than the structure of
the stimulus in the image plane or its actual source in the present” (p. 287).
Proponents of faithful depiction will, of course, grant that there are obvi-
ous limits. Unaided vision, for instance, sees electromagnetic radiation only
through a chink between 400 and 700 nm, and it fails to be veridical for
objects that are too large or too small. But these proponents maintain that,
for middle-sized objects to which vision is adapted, our visual perceptions
are in general veridical.

1.3 The Conventional Evolutionary Argument

Proponents of faithful depiction offer an evolutionary argument for their po-
sition, albeit an argument different than the one sketched above for the prin-
ciple of satisficing categories. Their argument is spelled out, for instance, by
Palmer [27](p. 6) in his textbook Vision Science, as follows: “Evolutionarily
speaking, visual perception is useful only if it is reasonably accurate. . . . In-
deed, vision is useful precisely because it is so accurate. By and large, what


1.4 Bayes’ Circle
5

you see is what you get. When this is true, we have what is called veridi-
cal perception . . . perception that is consistent with the actual state of
affairs in the environment. This is almost always the case with vision . . .”
[emphases his].
The error in this argument is fundamental: Natural selection optimizes
fitness, not veridicality. The two are distinct and, indeed, can be at odds. In
evolution, where the race is often to the swift, a quick and dirty category can
easily trump one more complex and veridical. The jewel beetle’s desirable
female is a case in point. Such cases are ubiquitous in nature and central to
understanding evolutionary competition between organisms. This competi-
tion is predicated, in large part, on exploiting the nonveridical perceptions
of predators, prey and conspecifics, using techniques such as mimicry and
camouflage.
Moreover, as noted by Trivers [40], there are reasons other than greater
speed and less complexity for natural selection to spurn the veridical: “If
deceit is fundamental to animal communication, then there must be strong
selection to spot deception and this ought, in turn, to select for a degree
of self-deception, rendering some facts and motives unconscious so as not
to betray—by the subtle signs of self-knowledge—the deception being prac-
ticed.
Thus, the conventional view that natural selection favors nervous
systems which produce ever more accurate images of the world must be a
very na¨ıve view of mental evolution.”
So the claim that “vision is useful precisely because it is so accurate” gets
evolution wrong by conflating fitness and accuracy; they are not the same
and, as we shall see with simulations and examples, they are not highly cor-
related. This conflation is not a peripheral error with trivial consequences:
Fitness, not accuracy, is the objective function optimized by evolution. (This
way of saying it doesn’t mean that evolution tries to optimize anything. It
just means that what matters in evolution is raising more kids, not seeing
more truth.) Theories of perception based on optimizing the wrong func-
tion can’t help but be radically misguided. Rethinking perception with the
correct function leads to a theory strikingly different from the conventional.
But first, we examine a vicious circle in the conventional theory.

1.4 Bayes’ Circle

According to the conventional theory, a great way to estimate true proper-
ties of the world is via Bayes’ theorem. If one’s visual system receives some
images, I, and one wishes to estimate the probabilities of various world
properties, W, given these images, then one needs to compute the condi-


6
The Interface Theory of Perception

tional probabilities P(W|I). For instance, I might be a movie of some dots
moving in two dimensions, and W might be various rigid and nonrigid in-
terpretations of those dots moving in three dimensions. According to Bayes’
theorem, one can compute

P(W|I) = P(I|W)P(W)/P(I).

P(W) is the prior probability. According to the conventional theory, this
prior models the assumptions that human vision makes about the world, e.g.,
that it has three spatial dimensions, one temporal dimension, and contains
three-dimensional objects, many of which are rigid. P(I|W) is the likelihood.
According to the conventional theory, this likelihood models the assumptions
that human vision makes about how the world maps to images; it’s like a
rendering function of a graphics engine, which maps a pre-specified three-
dimensional world onto a two-dimensional image using techniques like ray
tracing with Gaussian dispersion. P(I) is just a scale factor to normalize the
probabilities. P(W|I) is the posterior, the estimate human vision computes
about the properties of the world given the images I. So the posterior, which
determines what we see, depends crucially on the quality of our priors and
likelihoods.
How can we check if our priors and likelihoods are correct? According to
the conventional theory, we can simply go out and measure the true priors
and likelihoods in the world. Geisler & Diehl [8], for instance, tell us, “In
these cases, the prior probability and likelihood distributions are based on
measurements of physical and statistical properties of natural environments.
For example, if the task in a given environment is to detect edible fruit in
background foliage, then the prior probability and likelihood distributions
are estimated by measuring representative spectral illumination functions
for the environment and spectral reflectance functions for the fruits and
foliage” (p. 380).
The conventional procedure, then, is to measure the true values in the
world for the priors and likelihoods, and use these to compute, via Bayes,
the desired posteriors. What the visual system ends up seeing is a function
of these posteriors and its utility functions.
The problem with this conventional approach is that it entails a vicious
circle, which we can call

Bayes’ Circle: We can only see the world through our posteriors. When
we measure priors and likelihoods in the world, our measurements are nec-
essarily filtered through our posteriors. Using our measurements of priors
and likelihoods to justify our posteriors thus leads to a vicious circle.


1.4 Bayes’ Circle
7

Suppose, for instance, that we build a robot with a vision system that com-
putes shape from motion using a prior assumption that the world contains
many rigid objects [41]. The system takes inputs from a video camera, does
some initial processing to find two-dimensional features in the video images,
and then uses an algorithm based on rigidity to compute three-dimensional
shape. It seems to work well, but we decide to double-check that the prior
assumption about rigid objects that we built into the system is in fact true
of the world. So we send our robot out into the world to look around. To our
relief, it comes back with the good news that it has indeed found numerous
rigid objects. Of course it did; that’s what we programmed it to do. If,
based on the robot’s good news, we conclude that our prior on rigid objects
is justified, we’ve just been bagged by Bayes’ Circle.
This example is a howler, but precisely the same mistake prompts the
conventional claim that we can validate our priors by measuring properties
of the objective world. The conventionalist can reply that the robot example
fails because it ignores the possibility of cross checking results with other
senses, other observers, and scientific instruments. But such a reply hides
the same howler, because other senses, other observers, and scientific instru-
ments all have built in priors. None is a filter-free window on an objective
(i.e., observation independent) world. Consensus among them entails, at
most, agreement among their priors; it entails nothing about properties or
statistical structures of an objective world.
It is, of course, possible to pursue a Bayesian approach to perception with-
out getting mired in Bayes’ circle. Indeed, Bayesian approaches are among
the most promising in the field. Conditional probabilities turn up every-
where in perception, because perception is often about determining what
is the best description of the world, or the best action to take, given (i.e.,
conditioned on) the current state of the sensoria. Bayes is simply the right
way to compute conditional probabilities using prior beliefs, and Bayesian
decision theory, more generally, is a powerful way to model the utilities and
actions of an organism in its computation of perceptual descriptions.
But it is possible to use the sophisticated tools of Bayesian decision theory,
to fully appreciate the importance of utilities and the perception-action loop,
and still to fall prey to Bayes’ circle—to conclude, as quoted from Palmer
above, that “Evolutionarily speaking, visual perception is useful only if it is
reasonably accurate.”


8
The Interface Theory of Perception

1.5 The Interface Theory of Perception

The conventional theory of perception gets evolution fundamentally wrong
by conflating fitness and accuracy. This leads the conventional theory to
the false claim that a primary goal of perception is faithful depiction of the
world. A standard way to state this claim is the

Reconstruction Thesis: Perception reconstructs certain properties and
categories of the objective world.

This claim is too strong. It must be weakened, on evolutionary grounds, to
a less tendentious claim, the

Construction Thesis: Perception constructs the properties and categories
of an organism’s perceptual world.

The construction thesis is clearly much weaker than the reconstruction the-
sis. One can, for instance, obtain the reconstruction thesis by starting with
the construction thesis and adding the claim that the organism’s constructs
are, at least in certain respects, roughly isomorphic to the properties or
categories of the objective world, thus qualifying them to be deemed recon-
structions.
But the range of possible relations between perceptual constructs and
the objective world is infinite; isomorphism is just one relation out of this
infinity and, on evolutionary grounds, an unlikely one. Thus the reconstruc-
tion thesis is a conceptual straightjacket that constrains us to think only
of improbable isomorphisms, and impedes us from exploring the full range
of possible relations between perception and the world. Once we dispense
with the straightjacket we’re free to explore all possible relations that are
compatible with evolution [23].
To this end we note that, to the extent that perceptual properties and
categories are satisficing solutions to adaptive problems, they admit a func-
tional description. Admittedly, a conceivable, though unlikely, function of
perception is faithful depiction of the world. That’s the function favored by
the reconstruction thesis of the conventionalist. But once we repair the con-
flation of fitness and accuracy, we can consider other perceptual functions
with greater evolutionary plausibility. To do so properly requires a serious
study of the functional role of perception in various evolutionary settings.
Beetles falling for bottles is one instructive example; in the next section we
consider a few more.
But here it’s useful to introduce a model of perception that can help us
study its function without relapse into conventionalism. The model is the


1.5 The Interface Theory of Perception
9

Interface Theory of Perception: The perceptions of an organism are a
user interface between that organism and the objective world [16, 17, 20].

This theory addresses the natural question, “If our perceptions are not ac-
curate, then what good are they?” The answer becomes obvious for user
interfaces. The colour, for instance, of an icon on a computer screen does
not estimate, or reconstruct, the true colour of the file that it represents in
the computer. If an icon is, say, green, it would be ludicrous to conclude that
this green must be an accurate reconstruction of the true colour of the file
it represents. It would be equally ludicrous to conclude that, if the colour of
the icon doesn’t accurately reconstruct the true colour of the file, then the
icon’s colour is useless, or a blatant deception. This is simply a na¨ıve mis-
understanding of the point of a user interface. The conventionalist theory
that our perceptions are reconstructions is, in precisely the same manner,
equally na¨ıve.
Colour is, of course, just one example among many: The shape of an
icon doesn’t reconstruct the true shape of the file; the position of an icon
doesn’t reconstruct the true position of the file in the computer. A user
interface reconstructs nothing. Its predicates and the predicates required
for a reconstruction can be entirely disjoint: Files, for instance, have no
colour.
And yet a user interface is useful despite the fact that it’s not a recon-
struction.
Indeed, it’s useful because it’s not a reconstruction.
We pay
good money for user interfaces because we don’t want to deal with the over-
whelming complexity of software and hardware in a PC. A user interface
that slavishly reconstructed all the diodes, resistors, voltages and magnetic
fields in the computer would probably not be a best seller. The user inter-
face is there to facilitate our interactions with the computer by hiding its
causal and structural complexity, and by displaying useful information in a
format that is tailored to our specific projects, such as painting or writing.
Our perceptions are a species-specific user interface. Space, time, position
and momentum are among the properties and categories of the interface of
H. sapiens that, in all likelihood, resemble nothing in the objective world.
Different species have different interfaces. And, due to the variation that
is normal in evolution, there are differences in interfaces among humans.
To the extent that our perceptions are satisficing solutions to evolutionary
problems, our interfaces are designed to guide adaptive behavior in our niche;
accuracy of reconstruction is irrelevant. To understand the properties and
categories of our interface we must understand the evolutionary problems,
both phylogenetic and ontogenetic, that it solves.


10
The Interface Theory of Perception

1.6 User Interfaces in Nature

The interface theory of perception predicts that (1) each species has its
own interface (with some variations among conspecifics and some similari-
ties across phylogenetically related species), (2) almost surely, no interface
performs reconstructions, (3) each interface is tailored to guide adaptive
behavior in the relevant niche, (4) much of the competition between and
within species exploits strengths and limitations of interfaces, and (5) such
competition can lead to arms races between interfaces that critically influ-
ence their adaptive evolution. In short, the theory predicts that interfaces
are essential to understanding the evolution and competition of organisms;
the reconstruction theory makes such understanding impossible. Evidence
of interfaces should be ubiquitous in nature.
The jewel beetle is a case in point. Its perceptual category desirable fe-
male works well in its niche. However, its soft spot for stubbies reveals that
its perceptions are not reconstructions. They are, instead, quick guides to
adaptive behavior in a stubbie-free niche. The stubbie is a so-called super-
normal stimulus, i.e., a stimulus that engages the interface and behavior of
the organism more forcefully than the normal stimuli to which the organ-
ism has been adapted. The bottle is shiny, dimpled, and the right colour
of brown. But what makes it a supernormal stimulus is apparently its su-
pernormal size. If so, then, contrary to the reconstruction thesis, the jewel
beetle’s perceptual category desirable female does not incorporate a statisti-
cal estimate of the true sizes of the most fertile females. Instead its category
satisfices with “bigger is better.” In its niche this solution is fit enough. A
stubbie, however, plunges it into an infinite loop.
Supernormal stimuli have been found for many species, and all such dis-
coveries are evidence against the claim of the reconstruction theory that our
perceptual categories estimate the statistical structure of the world; all are
evidence for species-specific interfaces that are satisficing solutions to adap-
tive problems. Herring gulls (Larus argentatus) provide a famous example.
Chicks peck a red spot near the tip of the lower mandible of an adult to
prompt the adult to regurgitate food. Tinbergen and Perdeck [38] found
that an artificial stimulus that is longer and thinner than a normal beak,
and whose red spot is more salient than normal, serves as a supernormal
stimulus for the chick’s pecking behaviors. The colour of the artificial beak
and head matter little. The chick’s perceptual category food bearer, or per-
haps food-bearing parent, is not a statistical estimate of the true properties of
food-bearing parents, but a satisficing solution in which longer and thinner
is better and in which greater salience of the red spot is better. Its inter-


1.6 User Interfaces in Nature
11

face employs simplified symbols that effectively guide behavior in its niche.
Only when its niche is invaded by pesky ethologists is this simplification
unmasked, and the chick sent seeking what can never satisfy.
Simplified does not mean simple. Every interface of every organism dra-
matically simplifies the complexity of the world, but not every interface is
considered by H. sapiens to be simple.
Selective sophistication in inter-
faces is the result, in part, of competition between organisms in which the
strengths in the interface of one’s nemesis or next meal are avoided and its
weaknesses exploited. Dueling between interfaces hones them and the strate-
gies used to exploit them. This is the genesis of mimicry and camouflage,
and of complex strategies to defeat them.
A striking example, despite brains the size of a pinhead, are jumping spi-
ders of the genus Portia [13]. Portia is araneophagic, preferring to dine on
other spiders. Such dining can be dangerous; if the interface of the intended
dinner detects Portia, dinner could be diner. So Portia has evolved coun-
termeasures. Its hair and colouration mimic detritus found in webs and on
the forest floor; its gait mimics the flickering of detritus—a stealth technol-
ogy cleverly adapted to defeat the interfaces of predators and prey. If Portia
happens on a dragline (a trail of silk) left by the jumping spider Jacksonoides
queenslandicus, odors from the dragline prompt Portia to use its eight eyes
to hunt for J. queenslandicus. But J. queenslandicus is well camouflaged
and, if motionless, invisible to Portia.
So Portia makes a quick vertical
leap, tickling the visual motion detectors of J. queenslandicus and trigger-
ing it to orient to the motion. By the time J. queenslandicus has oriented,
Portia is already down, motionless, and invisible to J. queenslandicus; but
it has seen the movement of J. queenslandicus. Once the eyes of J. queens-
landicus are safely turned away, Portia slowly stalks, leaps, and strikes with
its fangs, delivering a paralyzing dose of venom. Portia’s victory exploits
strengths of its interface and weaknesses in that of J. queenslandicus.
Jewel beetles, herring gulls and jumping spiders illustrate the ubiquitous
role in evolution of species-specific user interfaces.
Perception is not re-
construction, it is construction of a niche-specific, problem-specific, fitness-
enhancing interface, which the biologist Jakob von Uexk¨ull [42, 43] called
an Umwelt or “self-world” [34]. Perceptual categories are endogenous con-
structs of a subjective Umwelt, not exogenous mirrors of an objective world.
The conventionalist might object that these examples are self-refuting,
since they require comparison between the perceptions of an organism and
the objective reality that those perceptions get wrong. Only by knowing,
for instance, the objective differences between beetle and bottle can we un-
derstand a perceptual flaw of J. backewelli. So the very examples adduced


12
The Interface Theory of Perception

in support of the interface theory actually support the conclusion that per-
ceptual reconstruction of the objective world in fact occurs, in contradiction
to the predictions of that theory.
This objection is misguided. The examples discussed here, and all others
that might be unearthed by H. sapiens, are necessarily filtered through
the interface of H. sapiens, an interface whose properties and categories are
adapted for fitness, not accuracy. What we observe in these examples is not,
therefore, mismatches between perception and a reality to which H. sapiens
has direct access. Instead, because the interface of H. sapiens differs from
that of other species, H. sapiens can, in some cases, see flaws of others
that they miss themselves. In other cases, we can safely assume, H. sapiens
misses flaws of others due to flaws of its own. And, in yet other cases, flaws
of H. sapiens might be obvious to other species.
The conventionalist might further object, saying, “If you think that the
wild tiger over there is just a perceptual category of your interface, then
why don’t you go pet it? When it attacks, you’ll find out it’s more than an
Umwelt category, it’s an objective reality.”
This objection is also misguided.
I don’t pet wild tigers for the same
reason I don’t carelessly drag a file icon to the trash bin. I don’t take the
icon literally, as though it resembles the real file. But I do take it seriously.
My actions on the icon have repercussions for the file. Similarly, I don’t
take my tiger icon literally but I do take it seriously. Aeons of evolution
of my interface have shaped it to the point where I had better take its
icons seriously or risk harm. So the conventionalist objection fails because
it conflates taking icons seriously and taking them literally.
This conventionalist argument is not new.
Samuel Johnson famously
raised it in 1763 when, in response to the idealism of Berkeley, he kicked
a stone and exclaimed “I refute it thus” [4] (1, p. 134). Johnson thus con-
flated taking a stone seriously and taking it literally. Nevertheless Johnson’s
argument, one must admit, has strong psychological appeal despite the non
sequitur, and it is natural to ask why. Perhaps the answer lies in the evolu-
tion of our interface. There was, naturally enough, selective pressure to take
its icons seriously; those who didn’t take their tiger icons seriously came to
early harm. But were there selective pressures not to take its icons literally?
Did reproductive advantages accrue to those of our Pleistocene ancestors
who happened not to conflate the serious and the literal? Apparently not,
given the widespread conflation of the two in the modern population of H.
sapiens. Hence, the very evolutionary processes that endowed us with our
interfaces might also have saddled us with the penchant to mistake their
contents for objective reality. This mistake spawned sweeping commitments


1.7 Interface and World
13

to a flat earth and a geocentric universe, and prompted the persecution of
those who disagreed. Today it spawns reconstructionist theories of percep-
tion. Flat earth and geocentrism were difficult for H. sapiens to scrap; some
unfortunates were tortured or burned in the process.
Reconstructionism
will, sans the torture, prove even more difficult to scrap; it’s not just this
or that percept that must be recognized as an icon, but rather perception
itself that must be so recognized. The selection pressures on Pleistocene
hunter-gatherers clearly didn’t do the trick, but social pressures on modern
H. sapiens, arising in the conduct of science, just might.
The conventionalist might object that death is a counterexample:
it
should be taken seriously and literally. It is not just shuffling of icons.
This objection is not misguided. In death, one’s body icon ceases to func-
tion and, in due course, decays. The question this raises can be compared to
the following: When a file icon is dragged to the trash and disappears from
the screen, is the file itself destroyed, or is it still intact and just inaccessible
to the user interface? Knowledge of the interface itself might not license a
definitive answer. If not, then to answer the question one must add to the
interface a theory of the objective world it hides. How this might proceed
is the topic of the next section.
The conventionalist might persist, arguing that agreement between ob-
servers entails reconstruction and provides important reality checks on per-
ception. This argument also fails. First, agreement between observers may
only be apparent: It is straightforward to prove that two observers can be
functionally identical and yet differ in their conscious perceptual experi-
ences [18, 19]; reductive functionalism is false. Second, even if observers
agree, this doesn’t entail the reconstruction thesis.
The observers might
simply employ the same constructive (but not reconstructive) perceptual
processes. If two PC’s have the same icons on their screens, this doesn’t en-
tail that the icons reconstruct their innards. Agreement provides subjective
consistency checks—not objective reality checks—between observers.

1.7 Interface and World

The interface theory claims that perceptual properties and categories no
more resemble the objective world than Windows icons resemble the diodes
and resistors of a computer.
The conventionalist might object that this
makes the world unknowable and is, therefore, inimical to science.
This misses a fundamental point in the philosophy of science: Data never
determine theories.
This under-determination makes the construction of
scientific theories a creative enterprise. The contents of our perceptual in-


14
The Interface Theory of Perception

terfaces don’t determine a true theory of the objective world, but this in
no way precludes us from creating theories and testing their implications.
One such theory, in fact the conventionalist’s theory, is that the relation
between interface and world is, on appropriately restricted domains, an iso-
morphism. This theory is, as we have discussed, improbable on evolutionary
grounds and serves as an intellectual straightjacket, hindering the field from
considering more plausible options.
What might those options be? That depends on which constraints one
postulates between interface and world.
Suppose, for instance, that one
wants a minimal constraint that allows probabilities of interface events to
be informative about probabilities of world events. Then, following stan-
dard probability theory, one would represent the world by a measurable
space, i.e., by a pair (W, ΣW ), where W is a set and ΣW is a σ-algebra of
measurable events. One would represent the user interface by a measurable
space (U, ΣU), and the relation between interface and world by a measurable
function f: W → U. The function f could be many-to-one, and the features
represented by W disjoint from those represented by U. The probabilities
of events in the interface (U, ΣU) would be distributions of the probabilities
in the world (W, ΣW ), i.e., if the probability of events in the world is µ,
then the probability of any interface event A ∈ ΣU is µ(f−1(A)). Using
this terminology, the problem of Bayes’ circle, scouted above, can be stated
quite simply: It is conflating U with W, and assuming that f: W → U is
approximately 1 to 1, when in fact it’s probably infinite to 1. This mistake
can be made even while using all the sophisticated tools of Bayesian decision
theory and machine learning theory.
The measurable-space proposal could be weakened if, for instance, one
wished to accommodate quantum systems with noncommuting observables.
In this case the event structures would not be σ-algebras but instead σ-
additive classes, which are closed under countable disjoint union rather than
under countable union [10], and f would be measurable with respect to these
classes. This would still allow probabilities of events in the interface to be
distributions of probabilities of events in the world. It would explain why
science succeeds in uncovering statistical laws governing events in space-
time, even though these events, and space-time itself, in no way resemble
objective reality.
This proposal could be weakened further. One could give up the measura-
bility of f, thereby giving up any quantitative relation between probabilities
in the interface and the world. The algebra or class structure of events in
the interface would still reflect an isomorphic subalgebra or subclass struc-
ture of events in the world. This is a nontrivial constraint: Subset relations


1.7 Interface and World
15

in the interface, for instance, would genuinely reflect subset relations of the
corresponding events in the world.
Further consideration of the interface might prompt us, in some cases,
to weaken the proposal even further. Multistable percepts, for instance, in
which the percept switches while the stimulus remains unchanged, may force
us to reconsider whether the relation between interface and world is even a
function: Two or more states of the interface might be associated to a single
state of the world.
These proposals all assume, of course, that mathematics, which has proved
useful in studying the interface, will also prove useful in modeling the world.
We shall see.
The discussion here is not intended, of course, to settle the issue of the
relation between interface and world, but to sketch how investigation of the
relation may proceed in the normal scientific fashion. This investigation is
challenging because we see the world through our interface, and it can there-
fore be difficult to discern the limitations of that interface. We are naturally
blind to our own blindness. The best remedy at hand for such blindness
is the systematic interplay of theory and experiment that constitutes the
scientific method.
The discussion here should, however, help place the interface theory of
perception within the philosophical landscape. It is not classical relativism,
which claims that there is no objective reality, only metaphor; it claims
instead that there is an objective reality that can be explored in the normal
scientific manner. It is not na¨ıve realism, which claims that we directly see
middle-sized objects; nor is it indirect realism, or representationalism, which
says that we see sensory representations, or sense data, of real middle-sized
objects, and do not directly see the objects themselves. It claims instead that
the physicalist ontology underlying both na¨ıve realism and indirect realism
is almost surely false: A rock is an interface icon, not a constituent of
objective reality. Although the interface theory is compatible with idealism,
it is not idealism, because it proposes no specific model of objective reality,
but leaves the nature of objective reality as an open scientific problem.
It is not a scientific physicalism that rejects the objectivity of middle-sized
objects in favor of the objectivity of atomic and subatomic particles; instead
it claims that such particles, and the space-time they inhabit, are among the
properties and categories of the interface of H. sapiens. Finally, it differs
from the utilitarian theory of perception [5, 30, 31], which claims that vision
uses a bag of tricks (rather than sophisticated general principles) to recover
useful information about the physical world; interface theory (1) rejects the
physicalist ontology of the utilitarian theory, (2) asserts instead that space


16
The Interface Theory of Perception

and time, and all objects that reside within them, are properties or icons of
our species-specific user interface, and therefore (3) rejects the claim of the
utilitarian theory that vision recovers information about preexisting physical
objects in space-time. It agrees, however, with the utilitarian theory that
evolution is central to understanding perception.
A conventionalist might object, saying, “These proposals about the rela-
tion of interface and world are fine as theoretical possibilities. But, in the
end, a rock is still a rock.” In other words, all the intellectual arguments
in the world won’t make the physical world—always obstinate and always
irrepressible—conveniently disappear. The interface theorist, no less than
the physicalist, must take care not to stub a toe on a rock.
Indeed. But in the same sense a trash-can icon is still a trash-can icon.
Any file whose icon stubs its frame on the trash can will suffer deletion. The
trash can is, in this way, as obstinate and irrepressible as a rock. But both
are simplifying icons. Both usefully hide a world that is far more complex.
Space and time do the same.
The conventionalist might further object, saying, “The proposed dissimi-
larity between interface and world is contradicted by the user-interface ex-
ample itself. The icons of a computer interface perhaps don’t resemble the
innards of a computer, but they do resemble real objects in the physical
world. Moreover, when using a computer to manipulate 3D objects, as in
computer aided design, the computer interface is most useful if its symbols
really resemble the actual 3D objects to be manipulated.”
Certainly. These arguments show that an interface can sometimes resem-
ble what it represents. And that is no surprise at all. But user interfaces can
also not resemble what they represent, and can be quite effective precisely
because they don’t resemble what they represent. So the real question is
whether the user interface of H. sapiens does in fact resemble what it rep-
resents. Here, I claim, the smart money says No.

1.8 Future Research on Perceptual Categorization

So what?
So what if perception is a user-interface construction, not an
objective-world reconstruction? How will this affect concrete research on
perceptual categorization?
Here are some possibilities. First, as discussed already, current attempts
to verify priors are misguided. This doesn’t mean we must abandon such
attempts. It does mean that our attempts must be more sophisticated; at a
minimum they must not founder on Bayes’ circle.
But that is at a minimum. Real progress in understanding the relation


1.8 Future Research on Perceptual Categorization
17

between perception and the world requires careful theory building.
The
conventional theory that perception approximates the world is hopelessly
simplistic.
Once we reject this facile theory, once we recognize that our
perceptions are to the world as a user interface is to a computer, we can
begin serious work. We must postulate, and then try to justify and confirm,
possible structures for the world and possible mappings between world and
interface. Clinging to approximate isomorphisms is a natural, but thus far
fruitless, response to this daunting task.
It’s now time to develop more
plausible theories. Some elementary considerations toward this end were
presented in the previous section.
Our efforts should be informed by relevant advances in modern physics.
Experiments by Alain Aspect [1, 2], building on the work of Bell [3], persuade
most physicists to reject local realism, viz., the doctrine that (1) distant
objects cannot directly influence each other (locality) and (2) all objects have
pre-existing values for all possible measurements, before any measurements
are made (realism). Aspect’s experiments demonstrate that distant objects,
say two electrons, can be entangled, such that measurement of a property
of one immediately affects the value of that property of the other. Such
entanglement is not just an abstract possibility, it is an empirical fact now
being exploited in quantum computation to give substantial improvements
over classical computation [6, 21]. Our untutored categories of space, time
and objects would lead us to expect that two electrons a billion light years
apart are separate entities; in fact, because of entanglement, they are a
single entity with a unity that transcends space and time. This is a puzzle
for proponents of faithful depiction, but not for interface theory.
Space,
time and separate objects are useful fictions of our interface, not faithful
depictions of objective reality.
Our theories of perceptual categorization must be informed by explicit
dynamical models of perceptual evolution, models such as those studied in
evolutionary game theory [14, 26, 33]. Our perceptual categories are shaped
inter alia by factors such as predators, prey, sexual selection, distribution of
resources, and social interactions. We won’t understand categorization un-
til we understand how categories emerge from dynamical systems in which
these factors interact.
There are promising leads.
Geisler and Diehl [8]
simulate interactions between simplified predators and prey, and show how
these might shape the spectral sensitivities of both. Komarova, Jameson
and Narens [22] show how colour categories can evolve from a minimal per-
ceptual psychology of discrimination together with simple learning rules and
simple constraints on social communication. Some researchers are explor-
ing perceptual evolution in foraging contexts [9, 32, 35]. These papers are


18
The Interface Theory of Perception

useful pointers to the kind of research required to construct theories of cat-
egorization that are evolutionarily plausible. As a concrete example of such
research, consider the following class of evolutionary games.

1.9 Interface Games

In the simplest interface game, two animals compete over three territories.
Each territory has a food value and a water value, each value ranging from,
say, 0 to 100. The first animal to choose a territory obtains its food and water
values; the second animal then chooses one of the remaining two territories,
and obtains its food and water values. The animals can adopt one of two
perceptual strategies. The truth interface strategy perceives the exact values
of food and of water for each territory. Thus the total information that truth
obtains is IT = 3 [territories] × 2 [resources per territory] × log2 101 [bits
per resource] ≈ 39.95 bits. The simple interface strategy perceives only one
bit of information per territory: if the food value of a territory is greater
than some fixed value (say 50), simple perceives that territory as green,
otherwise simple perceives that territory as red. Thus the total information
that simple obtains is IS = 3 bits.
It costs energy to obtain perceptual information. Let the energy cost per
bit be denoted by ce. Since the truth strategy obtains IT bits, the total
energy cost to truth is IT ce, which is subtracted from the sum of food and
water values that truth obtains from the territory it chooses. Similarly, the
total energy cost to simple is ISce.
It takes t units of time to obtain one bit of perceptual information. If
t > 0, then simple acquires all of its perceptual information before truth
does, allowing simple to be first to choose a territory.
Assuming, for simplicity, that the food and water values are independent,
identically distributed random variables with, say, a uniform distribution on
the integers from 0 to 100, we can compute a matrix of expected payoffs:

Truth
Simple

Truth:
a
b
Simple:
c
d

Here a is the expected payoff to truth if it competes against truth, b is the
expected payoff to truth if it competes against simple, c is the expected
payoff to simple if it competes against truth, and d is the expected payoff to
simple if it competes against simple.
As is standard in evolutionary game theory, we consider a population of
truth and simple players and equate payoff with fitness.
Let xT denote


1.9 Interface Games
19

the frequency of truth players and xS the frequency of simple players; the
population is thus ⃗x = (xT , xS). Then, assuming players meet at random,
the expected payoffs for truth and simple are, respectively, fT (⃗x) = axT +bxS
and fS(⃗x) = cxT + dxS. The selection dynamics is then x′
T = xT [fT (⃗x) −
F]; x′
S = xS[fS(⃗x) − F], where primes denote temporal derivatives and F is
the average fitness, F = xT fT (⃗x) + xSfS(⃗x).

If a > c and b > d, then truth drives simple to extinction. If a < c and
b < d then simple drives truth to extinction. If a > c and b < d, then
truth and simple are bistable; which goes extinct depends on the initial
frequencies, ⃗x(0), at time 0. If a < c and b > d then truth and simple stably
coexist, with the truth frequency given by (d−b)/(a−b−c+d). If a = c and
b = d, then selection does not change the frequencies of truth and simple.

The entries in the payoff matrix described above will vary, of course, with
the correlation between food and water values, with the specific value of
food that is used by simple as the boundary between green and red, and
with the cost ce per bit of information obtained.

boundary

0
100

0
100

cost per bit

0.2

0.4

0.6

0.2

0.4

0.6

1.0

1.2
r = 0

r = 1

Fig 1.1. Asymptotic behavior of the interface game as a function of the cost per
bit of information and the choice of the red-green boundary in the simple strategy.
Light gray indicates that simple drives truth to extinction, intermediate gray that
the two strategies coexist, and dark gray that truth drives simple to extinction. The


20
The Interface Theory of Perception

upper plot is for uncorrelated food and water, the lower for perfectly correlated food
and water.

And here is the punchline. Simple drives truth to extinction for most
values of the red-green boundary, even when the cost per bit of information is
small and the correlation between food and water is small. This is illustrated
in Figure 1.1, which shows the results of Matlab simulations. Evolutionary
pressures do not select for veridical perception; instead they drive it, should
it arise, to extinction.

The interface game just described might seem too simple to be useful. One
can, however, expand on the simple game just described in several ways, in-
cluding (1) increasing the number of territories at stake, (2) increasing the
number of resources per territory, (3) having dangers as well as resources in
the territories, (4) considering distributions other than uniform (e.g., Gaus-
sian) for the resources and dangers, (5) considering two-boundary, three-
boundary, n-boundary interface strategies, and more general categorization
algorithms that don’t rely on such boundaries, (6) considering populations
with three or more interface strategies, (7) considering more sophisticated
maps from resources to interfaces, including probabilistic maps, (8) consid-
ering time and energy costs that vary with architecture (e.g., serial versus
parallel) and that are probabilistic functions of the amount of information
gleaned and (9) extending the replicator dynamics, e.g., to include commu-
nication between players and to include a spatial dimension in which players
only interact with nearby players (as has been done with stag hunt and Lewis
signaling games [36, 37, 45]). Interface games, in all these varieties, allow
us to explore the complex evolutionary pressures that shape perception and
perceptual categorization, and to do so as realistically as our imaginations
and computational resources will allow.

They will also allow us to address a natural question: As an organism’s
perceptions and behaviors become more complex, shouldn’t it be the case
that the goal of perception approaches that of recovering the properties of
the environment?

Using simulations of interface games, one can ask for what environments
(including what kinds of competitors) will the reproductive pressures push
an organism to true perceptions of the environment, so that perceptual truth
is an evolutionarily stable strategy. My bet: None of interest.


1.10 Conclusion
21

1.10 Conclusion

Most experts assume that perception estimates true properties of an objec-
tive world. They justify this assumption with an argument from evolution:
Natural selection rewards true perceptions. I propose instead that if true
perceptions crop up, then natural selection mows them down; natural se-
lection fosters perceptions that act as simplified user interfaces, expediting
adaptive behavior while shrouding the causal and structural complexity of
the objective world. In support of this proposal, I discussed mimicry and
mating errors in nature, and presented simulations of an evolutionary game.
Old habits die hard.
I suspect that few experts will be persuaded by
these arguments to adopt the interface theory of perception. Most will still
harbor the long-standing conviction that, although we see reality through
small portals, nevertheless what we see is, in general, veridical. To such
experts I offer one final claim, and one final challenge. I claim that natural
selection drives true perception to swift extinction: Nowhere in evolution,
even among the most complex of organisms, will you find that natural selec-
tion drives truth to fixation, i.e., so that the predicates of perception (e.g.,
space, time, shape and color) approximate the predicates of the objective
world (whatever they might be). Natural selection rewards fecundity, not
factuality, so it shapes interfaces, not telescopes on truth [28] (p. 571). The
challenge is clear: Provide a compelling counterexample to this claim.

Acknowledgements.
Justin Mark collaborated in developing the interface
games, and wrote the simulations presented in Figure 1.1. For helpful com-
ments on previous drafts, I thank Ori Amir, Mike D’Zmura, Geoff Iverson,
Carol Skrenes, Duncan Luce, Larry Maloney, Brian Marion, Justin Mark,
Louis Narens, Steve Pinker, Kim Romney, John Serences, Brian Skyrms, and
Joyce Wu. For helpful discussions I thank Mike Braunstein, Larry Maloney,
Jon Merzel, Chetan Prakash, Rosie Sedghi, and Phat Vu.


References

1. Aspect, A., Grangier, P. and Roger, G. (1982a). Experimental realization of
Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bells
inequalities. Physical Review Letters 49, 91–94.
2. Aspect, A., Dalibard, J. and Roger, G. (1982b). Experimental test of Bells in-
equalities using time-varying analyzers. Physical Review Letters 49, 1804–1807.
3. Bell. J.S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200.
4. Boswell, J. (1791). The life of Samuel Johnson.
5. Braunstein, M.L. (1983). Contrasts between human and machine vision: Should
technology recapitulate phylogeny?, in Human and machine vision, ed. J. Beck,
B. Hope, and A. Rosenfeld (Academic Press, New York).
6. Nielsen, M.A. and Chuang, I.L. (2000). Quantum computation and quantum
information. (Cambridge University Press, Cambridge).
7. Daly, M. and Wilson, M. (1978). Sex, evolution, and behavior. (Duxbury Press,
Massachusetts).
8. Geisler, W.S. and Diehl, R.L. (2003). A Bayesian approach to the evolution of
perceptual and cognitive systems. Cognitive Science 27, 379–402.
9. Goldstone, R.L., Ashpole, B.C., and Roberts, M.E. (2005). Knowledge of re-
sources and competitors in human foraging. Psychonomic Bulletin & Review
12, 81–87.
10. Gudder, S. (1988). Quantum probability. (Academic Press, San Diego).
11. Gwynne, D.T. & Rentz, D.C.F. (1983). Beetles on the Bottle: Male Buprestids
Make Stubbies for Females. Journal of Australian Entomological Society 22,
79–80.
12.
Gwynne,
D.T.
(2003).
Mating
mistakes,
in
Encyclopedia
of
insects,
ed.V.H. Resh and R.T. Carde (Academic Press: San Diego).
13. Harland, D.P. & Jackson, R.R. (2004). Portia perceptions: The Umwelt of an
Araneophagic jumping spider, in Complex worlds from simpler nervous sys-
tems, ed. F.R. Prete (MIT Press, Cambridge, MA).
14. Hofbauer, J. & Sigmund, K. Evolutionary games and population dynamics.
(Cambridge University Press, Cambridge).
15. Hoffman, D. D. (1983). The interpretation of visual illusions. Scientific Ameri-
can 249, 154–162.
16. Hoffman, D. D. (1998). Visual intelligence: How we create what we see. (W.W.
Norton, New York).
17. Hoffman, D. D. (2006a). Mimesis and its perceptual reflections, in A View in

22


References
23

the Rear-Mirror: Romantic Aesthetics, Culture, and Science Seen from Today.
Festschrift for Frederick Burwick on the Occasion of His Seventieth Birthday,
ed. W. Pape (WVT, Wissenschaftlicher Verlag Trier: Trier) (Studien zur En-
glischen Romantik 3).
18. Hoffman, D.D. (2006b). The scrambling theorem: A simple proof of the logical
possibility of spectrum inversion. Consciousness and Cognition 15, 31–45.
19. Hoffman, D.D. (2006c). The scrambling theorem unscrambled: A response to
commentaries. Consciousness and Cognition 15, 51–53.
20. Hoffman, D.D. (2008, in press). Conscious realism and the mind-body problem.
Mind & Matter.
21. Kaye, P., Laflamme, R. and Mosca, M. (2007). An introduction to quantum
computing. (Oxford University Press: Oxford).
22. Komarova, N.L., Jameson, K.A. and Narens, L. (2007). Evolutionary models
of color categorization based on discrimination. Journal of Mathematical Psy-
chology 51, 359–382.
23. Mausfeld, R. (2002). The physicalist trap in perception theory, in Perception
and the physical world, ed. D. Heyer and R. Mausfeld (Wiley, New York).
24. Lehar, S. (2003). Gestalt isomorphism and the primacy of subjective conscious
experience: A Gestalt Bubble model. Behavioral and Brain Sciences 26, 375–
444.
25. No¨e, A, and Regan, J.K. (2002). On the brain-basis of visual consciousness: A
sensorimotor account, in Vision and mind: Selected readings in the philosophy
of perception, ed. A. No¨e and E. Thompson (MIT Press, Cambridge, MA).
26. Nowak, M.A. (2006). Evolutionary dynamics: Exploring the equations of life.
(Belknap/Harvard University Press, Cambridge, MA).
27. Palmer, S.E. (1999). Vision science: Photons to phenomenology. (MIT Press,
Cambridge, MA).
28. Pinker, S. (1997). How the mind works. (W.W. Norton, New York).
29. Purves, D., and Lotto, R. B. (2003). Why we see what we do: An empirical
theory of vision. (Sinauer, Sunderland, MA).
30. Ramachandran, V.S. (1985). The neurobiology of perception. Perception 14,
97–103.
31. Ramachandran, V.S. (1990). Interactions between motion, depth, color and
form: The utilitarian theory of perception, in Vision: Coding and efficiency,
ed. C. Blakemore (Cambridge University Press, Cambridge).
32. Roberts, M.E. and Goldstone, R.L. (2006). EPICURE: Spatial and knowledge
limitations in group foraging. Adaptive Behavior 14, 291–313.
33. Samuelson, L. (1997). Evolutionary games and equilibrium selection. (MIT
Press, Cambridge, MA).
34. Schiller, C.H. (1957). Instinctive behavior: Development of a modern concept.
(Hallmark Press, New York).
35. Sernland, E., Olsson, O., and Holmgren, N.M.A. (2003). Does information
sharing promote group foraging? Proceedings of the Royal Society of London
270, 1137–1141.
36. Skyrms, B. (2002). Signals, evolution, and the explanatory power of transient
information. Philosophy of Science 69, 407–428.
37. Skyrms, B. (2004). The stag hunt and the evolution of social structure. (Cam-
bridge University Press, Cambridge).
38. Tinbergen, N., and A. C. Perdeck. (1950). On the stimulus situation releasing
the begging response in the newly hatched Herring Gull chick (Larus argentatus


24
References

argentatus Pont.). Behaviour 3, 1–39.
39. Trivers, R.L. (1972). Parental investment and sexual selection, in Sexual se-
lection and the descent of man, 1871-1971,
ed. B. Campbell (Aldine Press,
Chicago).
40. Trivers, R.L. (1976). Foreword, in R. Dawkins, The selfish gene. (Oxford Uni-
versity Press: New York).
41. Ullman, S. (1979). The interpretation of visual motion. (MIT Press, Cambridge,
MA).
42. Von Uexk¨ull, J. (1909). Umwelt und Innenwelt der Tiere. (Springer-Verlag,
Berlin).
43. Von Uexk¨ull, J. (1934). A stroll through the worlds of animals and men: A
picture book of invisible worlds, reprinted in Instinctive behavior: Development
of a modern concept, C.H. Schiller (1957) (Hallmark Press, New York).
44. Yuille, A., and B¨ulthoff, H. (1996). Bayesian decision theory and psychophysics,
in Perception as Bayesian inference, ed. D. Knill and W. Richards (Cambridge
University Press, Cambridge).
45. Zollman, K. (2005). Talking to neighbors: The evolution of regional meaning.
Philosophy of Science 72, 69–85.