1253 lines
171 KiB
Markdown
1253 lines
171 KiB
Markdown
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ORIGINAL RESEARCHARTICLE
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published: 17 June 2014
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doi: 10.3389/fpsyg.2014.00577
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Objects of consciousness
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DonaldD.Hoffman1*andChetanPrakash2
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1 Department of Cognitive Sciences, University of California, Irvine, CA, USA
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2 Department of Mathematics, California State University, San Bernardino, CA, USA
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Edited by: Current models of visual perception typically assume that human vision estimates true
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Chris Fields, New Mexico State properties of physical objects, properties that exist even if unperceived. However, recent
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University, USA (retired) studies of perceptual evolution, using evolutionary games and genetic algorithms, reveal
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Reviewedby: that natural selection often drives true perceptions to extinction when they compete
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John Serences, University of with perceptions tuned to fitness rather than truth: Perception guides adaptive behavior;
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California San Diego, USA
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David Marcus Appleby, University of it does not estimate a preexisting physical truth. Moreover, shifting from evolutionary
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Sydney, Australia biology to quantum physics, there is reason to disbelieve in preexisting physical truths:
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*Correspondence: Certain interpretations of quantum theory deny that dynamical properties of physical
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Donald D. Hoffman, Department of objects have definite values when unobserved. In some of these interpretations the
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Cognitive Sciences, University of observer is fundamental, and wave functions are compendia of subjective probabilities,
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California, Irvine, CA 92697, USA
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e-mail: ddhoff@uci.edu not preexisting elements of physical reality. These two considerations, from evolutionary
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biology and quantum physics, suggest that current models of object perception require
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fundamental reformulation. Here we begin such a reformulation, starting with a formal
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model of consciousness that we call a “conscious agent.” We develop the dynamics of
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interacting conscious agents, and study how the perception of objects and space-time
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can emerge from such dynamics. We show that one particular object, the quantum free
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particle, has a wave function that is identical in form to the harmonic functions that
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characterize the asymptotic dynamics of conscious agents; particles are vibrations not of
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stringsbutofinteractingconsciousagents.Thisallowsustoreinterpretphysicalproperties
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such as position, momentum, and energy as properties of interacting conscious agents,
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rather than as preexisting physical truths. We sketch how this approach might extend to
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the perception of relativistic quantum objects, and to classical objects of macroscopic
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scale.
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Keywords: consciousness, quantum theory, Markov chains, combination problem, geometric algebra
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INTRODUCTION brain exists when unperceived (Edelman, 2004). When Francis
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The human mind is predisposed to believe that physical objects, Crick asserted the “astonishing hypothesis” that “You’re noth-
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when unperceived, still exist with definite shapes and locations ing but a pack of neurons” he assumed that neurons exist when
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in space. The psychologist Piaget proposed that children start to unperceived (Crick, 1994).
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develop this belief in “object permanence” around 9 months of Object permanence underlies the standard account of evo-
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age, and have it firmly entrenched just 9 months later (Piaget, lution by natural selection. As James memorably put it, “The
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1954). Further studies suggest that object permanence starts as point which as evolutionists we are bound to hold fast to is
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early as 3 months of age (Bower, 1974; Baillargeon and DeVos, that all the new forms of being that make their appearance are
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1991). reallynothingmorethanresultsoftheredistributionofthe
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Belief in object permanence remains firmly entrenched into original and unchanging materials. The self-same atoms which,
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adulthood, even in the brightest of minds. Abraham Pais said of chaotically dispersed, made the nebula, now, jammed and tem-
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Einstein, “We often discussed his notions on objective reality. I porarily caught in peculiar positions, form our brains” (James,
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recall that on one walk Einstein suddenly stopped, turned to me 1890).Evolutionarytheory,inthestandardaccount,assumesthat
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and asked whether I really believed that the moon exists only atoms, and the replicating molecules that they form, exist when
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when I look at it” (Pais, 1979). Einstein was troubled by inter- unperceived.
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pretations of quantum theory that entail that the moon does not Object permanence underlies computational models of the
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exist when unperceived. visual perception of objects. David Marr, for instance, claimed
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Belief in object permanence underlies physicalist theories of “We ... very definitely do compute explicit properties of the
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the mind-body problem. When Gerald Edelman claimed, for real visible surfaces out there, and one interesting aspect of the
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instance, that “There is now a vast amount of empirical evi- evolution of visual systems is the gradual movement toward the
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dence to support the idea that consciousness emerges from the difficult task of representing progressively more objective aspects
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organization and operation of the brain” he assumed that the of the visual world” (Marr, 1982). For Marr, objects and their
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www.frontiersin.org June 2014 | Volume 5 | Article 577 | 1
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Hoffman and Prakash Objects of consciousness
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surfaces exist when unperceived, and human vision has evolved perceptual representations that are genuine insights into the true
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to describe their objective properties. nature of the objective world.
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Bayesian theories of vision assume object permanence. They Evaluating object permanence on evolutionary grounds might
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model object perception as a process of statistical estimation of seem quixotic, or at least unfair, given that we just noted that
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object properties, such as surface shape and reflectance, that exist evolutionary theory, as it’s standardly described, assumes object
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when unperceived. As Alan Yuille and Heinrich Bülthoff put it, permanence(e.g., of DNA and the physical bodies of organisms).
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“Wedefinevisionasperceptualinference,theestimationofscene Howthencouldonepossiblyuseevolutionarytheorytotestwhat
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properties from an image or sequence of images ...”(Yuille and it assumes to be true?
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Bülthoff, 1996). However, Richard Dawkins and others have observed that the
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There is a long and interesting history of debate about which core of evolution by natural selection is an abstract algorithm
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properties of objects exist when unperceived. Shape, size, and with three key components: variation, selection, and retention
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position usually make the list. Others, such as taste and color, (Dennett, 1995; Blackmore, 1999). This abstract algorithm con-
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often do not. Democritus, a contemporary of Socrates, famously stitutes a “universal Darwinism” that need not assume object
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claimed, “by convention sweet and by convention bitter, by con- permanence and can be profitably applied in many contexts
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vention hot, by convention cold, by convention color; but in beyond biological evolution. Thus, it is possible, without beg-
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reality atoms and void” (Taylor, 1999). ging the question, to use formal models of evolution by natural
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Locke proposed that “primary qualities” of objects, such as selection to explore whether object permanence is an insight
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“bulk, figure, or motion” exist when unperceived, but that “sec- or not.
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ondaryproperties” of objects, such as “colors and smells” do not. Jerry Fodor has criticized the theory of natural selection itself,
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He then claimed that “...the ideas of primary qualities of bod- arguing, for instance, that it impales itself with an intensional fal-
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ies are resemblances of them, and their patterns do really exist lacy, viz., inferring from the premise that “evolution is a process
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in the bodies themselves, but the ideas produced in us by these inwhichcreatureswithadaptivetraitsareselected”totheconclu-
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secondary qualities have no resemblance of them at all” (Locke, sion that “evolution is a process in which creatures are selected
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1690). for their adaptive traits” (Fodor and Piattelli-Palmarini, 2010).
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Philosophical and scientific debate continues to this day on However, Fodor’s critique seems wide of the mark (Futuyma,
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whether properties such as color exist when unperceived (Byrne 2010) and the evidence for evolution by natural selection is
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and Hilbert, 2003; Hoffman, 2006). But object permanence, cer- overwhelming(Coyne,2009;Dawkins,2009).
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tainly regarding shape and position, is so deeply assumed by the What,then,dowefindwhenweexploretheevolutionof
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scientific literature in the fields of psychophysics and computa- perception using evolutionary games and genetic algorithms?
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tional perception that it is rarely discussed. The standard answer, at least among vision scientists, is that we
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It is also assumed in the scientific study of consciousness and should find that natural selection favors veridical perceptions,
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the mind-body problem. Here the widely acknowledged failure i.e., perceptions that accurately represent objective properties of
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to create a plausible theory forces reflection on basic assump- the external world that exist when unperceived. Steven Palmer,
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tions, including object permanence. But few researchers in fact for instance, in a standard graduate-level textbook, states that
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give it up. To the contrary, the accepted view is that aspects “Evolutionarily speaking, visual perception is useful only if it is
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of neural dynamics—from quantum-gravity induced collapses reasonablyaccurate...Indeed,visionisusefulpreciselybecauseit
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of wavefunctions at microtubules (Hameroff, 1998)toinforma- is so accurate. By andlarge,whatyouseeiswhatyouget.Whenthis
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tional properties of re-entrant thalamo-cortical loops (Tononi, is true, we have what is called veridicalperception ...perception
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2004)—cause, or give rise to, or are identical to, conscious- that is consistent with the actual state of affairs in the environ-
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ness.AsColinMcGinnputsit,“weknowthatbrainsarethe ment. This is almost always the case with vision ...”(Palmer,
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de facto causal basis of consciousness, but we have, it seems, 1999).
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no understanding whatever of how this can be so” (McGinn, Theargument,roughly,isthatthoseofourpredecessorswhose
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1989). perceptions were more veridical had a competitive advantage
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over those whose perceptions were less veridical. Thus, the genes
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EVOLUTIONANDPERCEPTION that coded for more veridical perceptions were more likely to
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Thehumanmindispredisposedfromearlychildhoodtoassume propagate to the next generation. We are, with good probability,
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object permanence, to assume that objects have shapes and posi- the offspring of those who, in each succeeding generation, per-
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tions in space even when the objects and space are unperceived. It ceived more truly, and thus we can be confident that our own
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is reasonable to ask whether this assumption is a genuine insight perceptions are, in the normal case, veridical.
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into the nature of objective reality, or simply a habit that is The conclusion that natural selection favors veridical percep-
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perhaps useful but not necessarily insightful. tionsiscentraltocurrentBayesianmodelsofperception,inwhich
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We can look to evolution for an answer. If we assume that perceptual systems use Bayesian inference to estimate true prop-
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ourperceptual and cognitive capacities have been shaped, at least erties of the objective world, properties such as shape, position,
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in part, by natural selection, then we can use formal models of motion, and reflectance (Knill and Richards, 1996; Geisler and
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evolution, such as evolutionary game theory (Lieberman et al., Diehl,2003).Objectsexistandhavethesepropertieswhenunper-
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2005; Nowak, 2006) and genetic algorithms (Mitchell, 1998), to ceived, and the function of perception is to accurately estimate
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exploreif, and under whatcircumstances,naturalselectionfavors pre-existing properties.
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Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 2
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Hoffman and Prakash Objects of consciousness
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However, when we actually study the evolution of perception THEINTERFACETHEORYOFPERCEPTION
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usingMonteCarlosimulationsofevolutionarygamesandgenetic Natural selection favors perceptions that are useful though not
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algorithms, we find that natural selection does not, in general, true. This might seemcounterintuitive, even to experts in percep-
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favor perceptions that are true reports of objective properties of tion. Palmer, for instance, in the quote above, makes the plausible
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the environment. Instead, it generally favors perceptual strategies claim that “vision is useful precisely because it is so accurate”
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that are tuned to fitness (Mark et al., 2010; Hoffman et al., 2013; (Palmer, 1999). Geisler and Diehl agree, taking it as obvious that
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Marion,2013;Mark,2013). “In general, (perceptual) estimates that are nearer the truth have
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Why? Several principles emerge from the simulations. First, greater utility than those that are wide of the mark” (Geisler and
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there is no free information. For every bit of information one Diehl, 2002). Feldman also takes it as obvious that “it is clearly
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obtains about the external world, one must pay a price in energy, desirable (say from an evolutionary point of view) for an organ-
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e.g., in calories expended to obtain, process and retain that infor- ism to achieve veridical percepts of the world” (Feldman, 2013).
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mation. And for every calorie expended in perception, one must Knill and Richards concur that vision “... involves the evolu-
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go out and kill something and eat it to get that calorie. So tion of an organism’s visual system to match the structure of the
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natural selection tends to favor perceptual systems that, ceteris world ...”(Knill and Richards, 1996).
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paribus, use fewer calories. One way to use fewer calories is This assumption that perceptions are useful to the extent that
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to see less truth, especially truth that is not informative about theyaretrueisprimafacieplausible,anditcomportswellwiththe
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fitness. assumption of object permanence. For if our perceptions report
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Second, for every bit of information one obtains about the to us a three-dimensional world containing objects with specific
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external world, one must pay a price in time. More information shapes and positions, and if these perceptual reports have been
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requires, in general, more time to obtain and process. But in the shaped by evolution to be true, then we can be confident that
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real world where predators are on the prowl and prey must be those objects really do, in the normal case, exist and have their
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wary, the race is often to the swift. It is the slower gazelle that positions and shapes even when unperceived.
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becomes lunch for the swifter cheetah. So natural selection tends So we find it plausible that perceptions are useful only if true,
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to favor perceptual systems that, ceteris paribus, take less time. and we find it deeply counterintuitive to think otherwise. But
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One way to take less time is, again, to see less truth, especially studies with evolutionary games and genetic algorithms flatly
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truth that is not informative about fitness. contradict this deeply held assumption. Clearly our intuitions
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Third, in a world where organisms are adapted to niches and needalittle help here. How can we try to understand perceptions
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require homeostatic mechanisms, the fitness functions guiding that are useful but not true?
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their evolution are generally not monotonic functions of struc- Fortunately, developments in computer technology have pro-
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tures or quantities in the world. Too much salt or too little can vided a convenient and helpful metaphor: the desktop of a win-
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be devastating; something in between is just right for fitness. The dowsinterface(Hoffman,1998,2009,2011,2012,2013;Mausfeld,
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same goldilocks principle can hold for water, altitude, humidity, 2002; Koenderink, 2011a; Hoffman and Singh, 2012; Singh and
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andsoon.Inthesecases,perceptions that are tuned to fitness are Hoffman, 2013). Suppose you are editing a text file and that the
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ipso facto not tuned to the true structure of the world, because the icon for that file is a blue rectangle sitting in the lower left corner
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two are not monotonically related; knowing the truth is not just of the desktop. If you click on that icon you can open the file and
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irrelevant, it can be inimical, to fitness. revise its text. If you drag that icon to the trash, you can delete the
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Fourth, in the generic case where noise and uncertainty are file.Ifyoudragittotheiconforanexternalharddrive,youcan
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endemictotheperceptualprocess,astrategythatestimatesatrue create a backup of the file. So the icon is quite useful.
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state of the world and then uses the utility associated to that state Butisittrue?Well,theonlyvisiblepropertiesoftheiconareits
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to govern its decisions must throw away valuable information position, shape, and color. Do these properties of the icon resem-
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aboututility. It will in general be driven to extinction by a strategy ble the true properties of the file? Clearly not. The file is not blue
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that does not estimate the true state of the world, and instead uses orrectangular, and it’s probably not in the lower left corner of the
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all the information about utility (Marion, 2013). computer. Indeed, files don’t have a color or shape, and needn’t
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Fifth, more complex perceptual systems are more difficult to have a well-defined position (e.g., the bits of the file could be
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evolve. Monte Carlo simulations of genetic algorithms show that spread widely over memory). So to even ask if the properties of
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there is a combinatorial explosion in the complexity of the search the icon are true is to make a category error, and to completely
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required to evolve more complex perceptual systems. This com- misunderstand the purpose of the interface. One can reasonably
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binatorial explosion itself is a selection pressure toward simpler askwhethertheiconisusefullyrelatedtothefile,butnotwhether
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perceptual systems. it truly resembles the file.
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In short, natural selection does not favor perceptual systems Indeed, a critical function of the interface is to hide the truth.
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that see the truth in whole or in part. Instead, it favors per- Mostcomputerusersdon’twanttoseethecomplexityoftheinte-
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ceptions that are fast, cheap, and tailored to guide behaviors grated circuits, voltages, and magnetic fields that are busy behind
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needed to survive and reproduce. Perception is not about truth, the scenes when they edit a file. If they had to deal with that
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it’s about having kids. Genes coding for perceptual systems that complexity, they might never finish their work on the file. So
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increase the probability of having kids are ipso facto the genes the interface is designed to allow the user to interact effectively
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that are more likely to code for perceptual systems in the next with the computer while remaining largely ignorant of its true
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generation. architecture.
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www.frontiersin.org June 2014 | Volume 5 | Article 577 | 3
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Hoffman and Prakash Objects of consciousness
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Ignorant, also, of its true causal structure. When a user drags perception, our perceptions primarily resonate to “affordances,”
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a file icon to an icon of an external drive, it looks obvious that those aspects of the objective world that have important con-
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themovementofthefileicontothedriveiconcauses the file to sequences for fitness (Gibson, 1979). While we disagree with
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be copied. But this is just a useful fiction. The movement of the Gibon’s direct realism and denial of information processing in
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file icon causes nothing in the computer. It simply serves to guide perception, we agree with his emphasis on the tuning of percep-
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the user’s operation of a mouse, triggering a complex chain of tion to fitness.
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causal events inside the computer, completely hidden from the So we must clarify the relationship between truth and fitness.
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user. Forcing the user to see the true causal chain would be an In evolutionary theory it is as follows. If W denotes the objec-
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impediment,notahelp. tive world then, for a fixed organism, state, and action, we can
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Turning now to apply the interface metaphor to human per- think of a fitness function to be a function f:W → [0,1], which
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ception, the idea is that natural selection has not shaped our per- assigns to each state w of W a fitness value f(w). If, for instance,
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ceptions to be insights into the true structure and causal nature the organism is a hungry cheetah and the action is eating, then f
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of objective reality, but has instead shaped our perceptions to be might assign a high fitness value to world state w in which fresh
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a species-specific user interface, fashioned to guide the behav- raw meat is available; but if the organism is a hungry cow then f
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iors that we need to survive and reproduce. Space and time are mightassign a low fitness value to the same state w.
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the desktop of our perceptual interface, and three-dimensional If the true probabilities of states in the world are given by a
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objects are icons on that desktop. probability measuremonW,thenonecandefineanewprobabil-
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Ourinterfacegivestheimpressionthatitrevealstruecauseand ity measuremf onW,whereforanyeventAofW,mf(A)issimply
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effect relations. When one billiard ball hits a second, it certainly the integral of f over A with respect to m; mf must of course be
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looksasthoughthefirstcausesthesecondtocareenaway.Butthis normalized so that mf(W) = 1.
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appearance of cause and effect is simply a useful fiction, just as it And here is the key point. A perceptual system that is tuned
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is for the icons on the computer desktop. to maximize the mutual information with m will not, in gen-
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Thereisanobviousrejoinder:“Ifthatcobraisjustaniconof eral,maximizemutualinformationwithmf (CoverandThomas,
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yourinterfacewithnocausalpowers,whydon’tyougrabitbythe 2006). Being tuned to truth, i.e., maximizing mutual information
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tail?” The answer is straightforward: “I don’t grab the cobra for with m, is not the same as being tuned to fitness, i.e., maximiz-
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thesamereasonIdon’tcarelesslydragmyfileicontothetrash—I ingmutualinformationwithmf.Indeed,dependingonthefitness
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could lose a lot of work. I don’t take my icons literally:Thefile, functionf, a perceptual system tuned to truth might carry little or
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unlike its icon, is not literally blue or rectangular. But I do take noinformationaboutfitness,andviceversa.Itisinthissensethat
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myiconsseriously.” the interface theory of perception claims that our perceptions are
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Similarly, evolution has shaped us with a species-specific inter- tunedtofitnessratherthantruth.
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face whose icons we must take seriously. If there is a cliff, don’t There is another rejoinder: “The interface metaphor is noth-
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stepover.Ifthereisacobra,don’tgrabitstail.Naturalselection ingnew.Physicistshavetoldusformorethanacenturythat
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has endowed us with perceptions that function to guide adaptive solid objects are really mostly empty space. So an apparently solid
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behaviors, and we ignore them at our own peril. stone isn’t the true reality, but its atoms and subatomic particles
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But, given that we must take our perceptions seriously, it does are.” Physicists have indeed said this since Rutherford published
|
|||
|
|
not follow that we must take them literally. Such an inference is his theory of the atomic nucleus in 1911 (Rutherford, 1911). But
|
|||
|
|
natural, in the sense that most of us, even the brightest, make it the interface metaphor says something more radical. It says that
|
|||
|
|
automatically.WhenSamuelJohnsonheardBerkeley’stheorythat space and time themselves are just a desktop, and that anything
|
|||
|
|
“To be is to be perceived” he kicked a stone and said, “I refute it in space and time, including atoms and subatomic particles, are
|
|||
|
|
thus!” (Boswell, 1986) Johnson observed that one must take the themselves simply icons. It’s not just the moon that isn’t there
|
|||
|
|
stone seriously or risk injury. From this Johnson concluded that when one doesn’t look, it’s the atoms, leptons and quarks them-
|
|||
|
|
onemusttakethestoneliterally. But this inference is fallacious. selves that aren’t there. Object permanence fails for microscopic
|
|||
|
|
Onemightobjectthattherestillisanimportantsenseinwhich objects just as it does for macroscopic.
|
|||
|
|
our perceptual icon of, say, a cobra does resemble the true objec- This claim is, to contemporary sensibilities, radical. But there
|
|||
|
|
tive reality: The consequences for an observer of grabbing the tail is a perspective on the intellectual evolution of humanity over the
|
|||
|
|
of the cobra are precisely the consequences that would obtain if last few centuries for which the interface theory seems a natural
|
|||
|
|
the objective reality were in fact a cobra. Perceptions and internal next step. According to this perspective, humanity has gradually
|
|||
|
|
information-bearing structures are useful for fitness-preserving been letting go of the false belief that the way H. sapiens sees the
|
|||
|
|
orenhancingbehaviorbecausethereissomemutualinformation worldisaninsightintoobjectivereality.
|
|||
|
|
between the predicted utility of a behavior (like escaping) and its Many ancient cultures, including the pre-Socratic Greeks,
|
|||
|
|
actualutility. If there’s no mutual information and no mechanism believed the world was flat, for the obvious reason that it looks
|
|||
|
|
for increasing mutual information, fitness is low and stays that that way. Aristotle became persuaded, on empirical grounds, that
|
|||
|
|
way. Here we use mutual information in the sense of standard the earth is spherical, and this view gradually spread to other cul-
|
|||
|
|
information theory (Cover and Thomas, 2006). tures. Reality, we learned, departed in important respects from
|
|||
|
|
This point is well-taken. Our perceptual icons do give us gen- someofourperceptions.
|
|||
|
|
uine information about fitness, and fitness can be considered an Butthenageocentricmodeloftheuniverse,inwhichtheearth
|
|||
|
|
aspect of objective reality. Indeed, in Gibson’s ecological theory of is at the center and everything revolves around it, still held sway.
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 4
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
Why? Because that’s the way things look to our unaided percep- halt states, and (7) a finite set of simple transition rules (Hopcroft
|
|||
|
|
tions. The earth looks like it’s not moving, and the sun, moon, et al., 2006).
|
|||
|
|
planets, and stars look like they circle a stationary earth. Not until Turingandothersthenconjecturedthatafunctionisalgorith-
|
|||
|
|
the work of Copernicus and Kepler did we recognize that once mically computable if and only if it is computable by a Turing
|
|||
|
|
again reality differs, in important respects, from our perceptions. machine. This “Church-Turing Thesis” can’t be proven, but it
|
|||
|
|
This was difficult to swallow. Galileo was forced to recant in the could in principle be falsified by a counterexample, e.g., by some
|
|||
|
|
Vatican basement, and Giordano Bruno was burned at the stake. exampleofaprocedurethateveryoneagreedwascomputablebut
|
|||
|
|
Butwefinally, and painfully, accepted the mismatch between our for which no Turing machine existed. No counterexample has yet
|
|||
|
|
perceptions and certain aspects of reality. been found, and the Church-Turing thesis is considered secure,
|
|||
|
|
Theinterfacetheoryentailsthatthesefirsttwostepsweremere even definitional.
|
|||
|
|
warmup.Thenextstepintheintellectual history of H. sapiens is Similarly, to construct a theory of consciousness we propose a
|
|||
|
|
a big one. We must recognize that all of our perceptions of space, simplebutrigorousformalismcalledaconsciousagent,consisting
|
|||
|
|
time and objects no more reflect reality than does our perception ofsixcomponents.Wethenstatetheconsciousagentthesis,which
|
|||
|
|
ofaflatearth.It’snotjustthisorthataspectofourperceptions claims that every property of consciousness can be represented
|
|||
|
|
that must be corrected, it is the entire framework of a space-time by some property of a conscious agent or system of interacting
|
|||
|
|
containing objects, the fundamental organization of our percep- conscious agents. The hope is to start with a small and simple
|
|||
|
|
tual systems, that must be recognized as a mere species-specific set of definitions and assumptions, and then to have a complete
|
|||
|
|
modeofperceptionratherthananinsightintoobjectivereality. theory of consciousness arise as a series of theorems and proofs
|
|||
|
|
Bythistimeitshouldbeclearthat,iftheargumentsgivenhere (or simulations, when complexity precludes proof). We want a
|
|||
|
|
are sound, then the current Bayesian models of object perception theory of consciousness qua consciousness, i.e., of consciousness
|
|||
|
|
needmorethantinkeringaroundtheedges,theyneedfundamen- onitsownterms,notassomethingderivativeoremergentfroma
|
|||
|
|
tal transformation. And this transformation will necessarily have prior physical world.
|
|||
|
|
ramifications for scientific questions well-beyond the confines of Nodoubtthisapproachwillstrikemanyasprimafacieabsurd.
|
|||
|
|
computational models of object perception. It is a commonplace in cognitive neuroscience, for instance, that
|
|||
|
|
One example is the mind-body problem. A theory in which most of our mental processes are unconscious processes (Bargh
|
|||
|
|
objects and space-time do not exist unperceived and do not have and Morsella, 2008). The standard account holds that well more
|
|||
|
|
causal powers, cannot propose that neurons—which by hypoth- than 90% of mental processes proceed without conscious aware-
|
|||
|
|
esis do not exist unperceived and do not have causal powers— ness. Therefore, the proposal that consciousness is fundamental
|
|||
|
|
cause any of our behaviors or conscious experiences. This is so is, to contemporary thought, an amusing anachronism not worth
|
|||
|
|
contrary to contemporary thought in this field that it is likely to serious consideration.
|
|||
|
|
be taken as a reductio of the view rather than as an alternative Thiscritique is apt. It’s clear from many experiments that each
|
|||
|
|
direction of inquiry for a field that has yet to construct a plausible of us is indeed unaware of most of the mental processes underly-
|
|||
|
|
theory. ingouractionsandconsciousperceptions.Butthisisnosurprise,
|
|||
|
|
given the interface theory of perception. Our perceptual inter-
|
|||
|
|
DEFINITIONOFCONSCIOUSAGENTS faces have been shaped by natural selection to guide, quickly and
|
|||
|
|
If our reasoning has been sound, then space-time and three- cheaply, behaviors that are adaptive in our niche. They have not
|
|||
|
|
dimensional objects have no causal powers and do not exist been shaped to provide exhaustive insights into truth. In con-
|
|||
|
|
unperceived.Therefore,weneedafundamentallynewfoundation sequence, our perceptions have endogenous limits to the range
|
|||
|
|
from which to construct a theory of objects. Here we explore the andcomplexityoftheir representations. It was not adaptive to be
|
|||
|
|
possibility that consciousness is that new foundation, and seek a awareofmostofourmentalprocessing,justasitwasnotadaptive
|
|||
|
|
mathematicallyprecise theory. The idea is that a theory of objects tobeawareofhowourkidneysfilterblood.
|
|||
|
|
requires, first, a theory of subjects. We must be careful not to assume that limitations of our
|
|||
|
|
Thisis, of course, a non-trivial endeavor. Frank Wilczek, when species-specific perceptions are insights into the true nature of
|
|||
|
|
discussing the interpretation of quantum theory, said, “The rel- reality. My friend’s mind is not directly conscious to me, but that
|
|||
|
|
evant literature is famously contentious and obscure. I believe it does not entail that my friend is unconscious. Similarly, most of
|
|||
|
|
will remain so until someone constructs, within the formalism of my mental processes are not directly conscious to me, but that
|
|||
|
|
quantummechanics, an “observer,” that is, a model entity whose does not entail that they are unconscious. Our perceptual sys-
|
|||
|
|
states correspondtoarecognizablecaricatureofconsciousaware- tems have finite capacity, and will therefore inevitably simplify
|
|||
|
|
ness ...Thatisaformidableproject,extendingwell-beyondwhat and omit. We are well-advised not to mistake our omissions and
|
|||
|
|
is conventionally considered physics” (Wilczek, 2006). simplifications for insights into reality.
|
|||
|
|
The approach we take toward constructing a theory of con- There are of course many other critiques of an approach
|
|||
|
|
sciousness is similar to the approach Alan Turing took toward that takes consciousness to be fundamental: How can such an
|
|||
|
|
constructing a theory of computation. Turing proposed a simple approach explain matter, the fundamental forces, the Big Bang,
|
|||
|
|
but rigorous formalism, now called the Turing machine (Turing, the genesis and structure of space-time, the laws of physics,
|
|||
|
|
1937; Herken, 1988). It consists of six components: (1) a finite evolution by natural selection, and the many neural correlates
|
|||
|
|
set of states, (2) a finite set of symbols, (3) a special blank sym- of consciousness? These are non-trivial challenges that must be
|
|||
|
|
bol, (4) a finite set of input symbols, (5) a start state, (6) a set of faced by the theory of conscious agents. But for the moment we
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 5
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
will postpone them and develop the theory of conscious agents output alphabet Y and a probability transition matrix p(x|y)that
|
|||
|
|
itself. expresses the probability of observing the output symbol y given
|
|||
|
|
Conscious agent is a technical term, with a precise mathemat- that we send the symbol x”(Cover and Thomas, 2006). Thus, a
|
|||
|
|
ical definition that will be presented shortly. To understand the discrete channel is simply a Markovian kernel.
|
|||
|
|
technicalterm,itcanbehelpfultohavesomeintuitionsthatmoti- So, each time a conscious agent interacts with the world and,
|
|||
|
|
vate the definition. The intuitions are just intuitions, and if they in consequence, has a conscious experience, we can think of this
|
|||
|
|
don’t help they can be dropped. What does the heavy lifting is the interaction as a message being passed from the world to the con-
|
|||
|
|
definition itself. scious agent over a channel. Similarly, each time the conscious
|
|||
|
|
Akeyintuition is that consciousness involves three processes: agent has a conscious experience and, in consequence, decides on
|
|||
|
|
perception, decision,andaction. anactiontotake,wecanthinkofthisdecisionasamessagebeing
|
|||
|
|
In the process of perception, a conscious agent interacts with passedoverachannelwithintheconsciousagentitself.Andwhen
|
|||
|
|
the world and, in consequence, has conscious experiences. the conscious agent then takes the action and, in consequence,
|
|||
|
|
In the process of decision, a conscious agent chooses what alters the state of the world, we can think of this as a message
|
|||
|
|
actions to take based on the conscious experiences it has. being passed from the conscious agent to the world over a chan-
|
|||
|
|
In the process of action, the conscious agent interacts with the nel. In the discrete case, we can keep track of the number of times
|
|||
|
|
world in light of the decision it has taken, and affects the state of each channel is used. That is, we can count the number of mes-
|
|||
|
|
the world. sages that are passed over each channel. Assuming that all three
|
|||
|
|
Another intuition is that we want to avoid unnecessarily channels (perception, decision, action) all work in lock step, we
|
|||
|
|
restrictive assumptions in constructing a theory of consciousness. can use one counter, N,tokeeptrackofthenumberofmessages
|
|||
|
|
Our conscious visual experience of nearby space, for instance, that are passed.
|
|||
|
|
is approximately Euclidean. But it would be an unnecessary These are some of the intuitions that underlie the definition
|
|||
|
|
restriction to require that all of our perceptual experiences be of conscious agent that we will present. These intuitions can be
|
|||
|
|
represented by Euclidean spaces. represented pictorially in a diagram, as shown in Figure1.The
|
|||
|
|
However it does seem necessary to discuss the probability of channel P transmits messages from the world W, leading to con-
|
|||
|
|
having a conscious experience, of making a particular decision, scious experiences X. The channel D transmits messages from X,
|
|||
|
|
and of making a particular change in the world through action. leading to actions G. The channel A transmits messages from G
|
|||
|
|
Thus, it seems necessary to assume that we can represent the that are received as new states of W. The counter N is an inte-
|
|||
|
|
world, our conscious experiences, and our possible actions with ger that keeps track of the number of messages that are passed on
|
|||
|
|
probability spaces. each channel.
|
|||
|
|
We also want to avoid unnecessarily restrictive assumptions In what follows we will be using the notion of a measurable
|
|||
|
|
about the processes of perception, decision, and action. We might space. Recall that a measurable space, (X, X), is a set X together
|
|||
|
|
find, for instance, that a particular decision process maximizes withacollectionXofsubsetsofX,calledevents,thatsatisfiesthree
|
|||
|
|
expected utility, or minimizes expected risk, or builds an explicit properties: (1) X is in X;(2)X is closed under complement(i.e., if
|
|||
|
|
model of the self. But it would be an unnecessary restriction to asetAisinXthenthecomplementofAisalsoinX);and(3)Xis
|
|||
|
|
require this of all decisions. closed under countable union. The collection of events X is a σ-
|
|||
|
|
However, when considering the processes of perception, deci- algebra (Athreya and Lahiri, 2006). A probability measure assigns
|
|||
|
|
sion and action, it does seem necessary to discuss conditional a probability to each event in X.
|
|||
|
|
probability. It seems necessary, for instance, to discuss the con- Withtheseintuitions, we now present the formal definition of
|
|||
|
|
ditional probability of deciding to take a specific action given a a conscious agent where, for the moment, we simply assume that
|
|||
|
|
specificconsciousexperience,theconditionalprobabilityofapar- the world is a measurable space (W, W).
|
|||
|
|
ticular change in the world given that a specific action is taken, Definition1.Aconsciousagent,C,isasix-tuple
|
|||
|
|
andtheconditionalprobability of a specific conscious experience
|
|||
|
|
given a specific state of the world. C=((X,X),(G,G),P,D,A,N)), (1)
|
|||
|
|
A general way to model such conditional probabilities is by
|
|||
|
|
the mathematicalformalismofMarkoviankernels(Revuz,1984). where:
|
|||
|
|
One can think of a Markovian kernel as simply an indexed list
|
|||
|
|
of probability measures. In the case of perception, for instance, (1) (X, X)and(G,G)aremeasurablespaces;
|
|||
|
|
a Markovian kernel might specify that if the state of the world is (2) P : W ×X→[0,1],D:X ×G→[0,1],A:G×W→[0,1]
|
|||
|
|
w1,thenhereisalistoftheprobabilitiesforthevariousconscious are Markovian kernels; and
|
|||
|
|
experiencesthatmightresult,butifthestateoftheworldisw2, (3) N is an integer.
|
|||
|
|
thenhereisadifferentlistoftheprobabilitiesforthevariouscon-
|
|||
|
|
scious experiences that might result, and so on for all the possible
|
|||
|
|
states of the world. A Markovian kernel onafinitesetofstatescan For convenience we will often write a conscious agent C as
|
|||
|
|
bewritten as matrix in which the entries in each row sum to 1.
|
|||
|
|
A Markovian kernel can also be thought of as an informa- C=(X,G,P,D,A,N), (2)
|
|||
|
|
tion channel. Cover and Thomas, for instance, define “a discrete
|
|||
|
|
channel to be a system consisting of an input alphabet X and omitting the σ-algebras.
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 6
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
FIGURE2|Twoconsciousagents,C andC .EachispartoftheworldW
|
|||
|
|
1 2
|
|||
|
|
for the other conscious agent. The lower part of the diagram represents C
|
|||
|
|
1
|
|||
|
|
and the upper part represents C2. This creates an undirected combination
|
|||
|
|
of C1 and C2, a concept we define in section The Combination Problem.
|
|||
|
|
existing data and theories, and make predictions that are novel,
|
|||
|
|
FIGURE1|Adiagramofaconsciousagent.Aconsciousagenthassix interesting and testable.
|
|||
|
|
components as illustrated here. The maps P, D,andA can be thought of as
|
|||
|
|
communication channels.
|
|||
|
|
TWOCONSCIOUSAGENTS
|
|||
|
|
Conscious realism can be expressed mathematically in a simple
|
|||
|
|
Given that P, D,andA are channels, each has a channel form.Considertheelementarycase,inwhichtheworldW ofone
|
|||
|
|
capacity, viz., a highest rate of bits per channel use, at which conscious agent,
|
|||
|
|
information can be sent across the channel with arbitrarily low C =(X ,G ,P ,D ,A ,N ), (3)
|
|||
|
|
chance of error (Cover and Thomas, 2006). 1 1 1 1 1 1 1
|
|||
|
|
Theformalstructureofaconsciousagent,likethatofaTuring
|
|||
|
|
machine,issimple.Nevertheless,wewillpropose,inthenextsec- contains just C1 and one other agent,
|
|||
|
|
tion, a “conscious-agent thesis” which, like the Church-Turing
|
|||
|
|
C =(X ,G ,P ,D ,A ,N ), (4)
|
|||
|
|
thesis, claims wide application for the formalism. 2 2 2 2 2 2 2
|
|||
|
|
CONSCIOUSREALISM andviceversa. This is illustrated in Figure 2.
|
|||
|
|
One glaring feature of the definition of a conscious agent is that Observe that although W is the world it cannot properly be
|
|||
|
|
it involves the world, W. This is not an arbitrary choice; W is called, in this example, the external world of C1 or of C2 because
|
|||
|
|
required to define the perceptual map P andactionmapA of the C1andC2areeachpartofW.ThisconstructionofW requiresthe
|
|||
|
|
conscious agent. compatibility conditions
|
|||
|
|
This raises the question: What is the world? If we take it to be
|
|||
|
|
P =A , (5)
|
|||
|
|
the space-time world of physics, then the formalism of conscious 1 2
|
|||
|
|
agents is dualistic, with some components (e.g., X and G) refer- P =A , (6)
|
|||
|
|
ring to consciousness and another, viz., W, referring to a physical 2 1
|
|||
|
|
world. N =N . (7)
|
|||
|
|
1 2
|
|||
|
|
We want a non-dualistic theory. Indeed, the monism we
|
|||
|
|
want takes consciousness to be fundamental. The formal- These conditions mean that the perceptions of one conscious
|
|||
|
|
ism of conscious agents provides a precise way to state this agentareidenticaltotheactionsoftheother,andthattheircoun-
|
|||
|
|
monism. ters are synchronized. To understand this, recall that we can think
|
|||
|
|
Hypothesis1.Consciousrealism:TheworldW consistsentirely of P , P , A ,andA asinformationchannels.Sointerpreted,con-
|
|||
|
|
1 2 1 2
|
|||
|
|
of conscious agents. ditions (5) and (6) state that the action channel of one agent is
|
|||
|
|
Consciousrealismisaprecisehypothesisthat,ofcourse,might the same information channel as the perception channel of the
|
|||
|
|
be precisely wrong. We can explore its theoretical implications other agent. Condition (7) states that the channels of both agents
|
|||
|
|
in the normal scientific manner to see if they comport well with operate in synchrony.
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 7
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
FIGURE3|Twoadjacentconsciousagents,C andC .Eachagent
|
|||
|
|
1 2
|
|||
|
|
receives messages from the other (indicated by the concave receivers) and
|
|||
|
|
sends messages to the other (indicated by the semicircular transmitters).
|
|||
|
|
Arrows show the direction of information flow.
|
|||
|
|
If two conscious agents C1 and C2 satisfy the commuting dia-
|
|||
|
|
gramofFigure2,thenwesaythattheyarejoinedoradjacent:the
|
|||
|
|
experiences and actions of C1 affect the probabilities of experi-
|
|||
|
|
ences and actions for C2 andviceversa.Figure3 illustrates the
|
|||
|
|
ideassofar.
|
|||
|
|
WecansimplifythediagramsfurtherandsimplywriteC1—C2
|
|||
|
|
to represent two adjacent conscious agents.
|
|||
|
|
THREECONSCIOUSAGENTS
|
|||
|
|
Anynumberofconsciousagentscanbejoined.Considerthecase
|
|||
|
|
of three conscious agents,
|
|||
|
|
C =(X,G,P,D,A,N),i=1,2,3. (8)
|
|||
|
|
i i i i i i i
|
|||
|
|
This is illustrated in Figure 4,andcompactlyinFigure5.
|
|||
|
|
Because C1 interacts with C2 and C3, its perceptions are
|
|||
|
|
affected by both C2 and C3. Thus, its perception kernel,
|
|||
|
|
P , must reflect the inputs of C and C .Wewriteitas
|
|||
|
|
1 2 3
|
|||
|
|
follows:
|
|||
|
|
P =P ⊗P :(G ×G )×X →[0,1], (9) FIGURE4|Threeadjacentconsciousagents.Thethirdagentis
|
|||
|
|
1 12 13 2 3 1 replicated at the top and bottom of the diagram for visual simplicity.
|
|||
|
|
where
|
|||
|
|
X =σ(X ×X ), (10) receive from C2 need not be the same as the kinds of perceptions
|
|||
|
|
1 12 13 that C1 can receive from C3.
|
|||
|
|
(X , X ) is the measurable space of perceptions that C can Because C1 interacts with C2 and C3, its actions affect both.
|
|||
|
|
12 12 1 However, the way C1 acts on C2 might differ from how it acts on
|
|||
|
|
receive from C ,and(X , X ) is the measurable space of
|
|||
|
|
2 13 13 C3, and the definition of its action kernel, A1, must allow for this
|
|||
|
|
perceptions that C1 can receive from C3,andσ(X12 × X13) difference of action. Therefore, we define the action kernel, A1,to
|
|||
|
|
denotes the σ-algebra generated by the Cartesian product of bethetensorproduct
|
|||
|
|
X and X . The tensor product P of (9) is given by the
|
|||
|
|
12 13 1
|
|||
|
|
formula A =A ⊗A :G ×σ(X ×X )→[0,1], (12)
|
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|
|
1 12 13 1 2 3
|
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|
|||
|
|
P (g ,g ),(x ,x ) = P (g ,x )P (g ,x ), (11)
|
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|
|
1 2 3 12 13 12 2 12 13 3 13 where
|
|||
|
|
whereg ∈ G ,g ∈ G ,x ∈X ,andx ∈X .Notethat(11) G =G ×G , (13)
|
|||
|
|
2 2 3 3 12 12 13 13 1 12 13
|
|||
|
|
allows that the perceptions that C1 gets from C2 could be entirely
|
|||
|
|
different from those it gets from C3, and expresses the probabilis- (G12, G12) is the measurable space of actions that C1 can take on
|
|||
|
|
tic independence of these perceptual inputs. In general, X need C ,and(G ,G )isthemeasurablespaceofactionsthatC can
|
|||
|
|
12 2 13 13 1
|
|||
|
|
not be identical to X13, since the kinds of perceptions that C1 can take on C3.
|
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|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 8
|
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Hoffman and Prakash Objects of consciousness
|
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|
|
FIGURE7|Threeconsciousagentswithdirectedjoins.Herewe
|
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|
|
assumeA =P ,A =P ,andA =P .
|
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|
|
1 2 2 3 3 1
|
|||
|
|
FIGURE5|Threeadjacentconsciousagents.Thisisacompact
|
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|
|
representation of the diagram in Figure 4.
|
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FIGURE8|Simplifiedgraphofthreeconsciousagentswithdirected
|
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joins.
|
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FIGURE6|Threeconsciousagentswhosegraphiscomplete.
|
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message from C2 and sends no message to C3. Similar remarks
|
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|
|
hold, mutatis mutandis,forC2 and C3.
|
|||
|
|
In this situation, the three conscious agents have the property Figure7canbesimplifiedasshowninFigure8.
|
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|
|
thateverypairisadjacent;wesaythatthegraphofthethreeagents Directed joins can model the standard situation in visual
|
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|
is complete.ThisisillustratedinFigure6. perception, in which there are multiple levels of visual represen-
|
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Sofarwehaveconsideredjoinsthatareundirected,inthe tations,onelevelbuildingonothersbelowit.Forinstance,atone
|
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sense that if C1 sends a message to C2 then C2 sends a message level there could be the construction of 2D motions based on a
|
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to C1. However, it is also possible for conscious agents to have solution to the correspondence problem; at the next level there
|
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|
|
directed joins.ThisisillustratedinFigure7.Inthiscase,C1 sends could be a computation of 3D structure from motion, based on
|
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|
|
amessagetoC2 and receives a message from C3, but receives no the 2D motions computed at the earlier level (Marr, 1982). So
|
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|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 9
|
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|
|
Hoffman and Prakash Objects of consciousness
|
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|
|
anagentC1 mightsolvethecorrespondenceproblemandpassits There are total of 24 = 16 possible states for the dynamics of
|
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|
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solution to C2, which solves the structure-from-motion problem, the two agents, which we can write as |0000, |0001, |0010, ...
|
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|
|
andthenpassesitssolution to C3, which does object recognition. |1111, where the leftmost digit is the state of X1, the next digit
|
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|
|
Wecan join any number of conscious agents into any multi- the state of G1,thenextofX2, and the rightmost of G2.
|
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|
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graph, where nodes denote agents and edges denote directed or The asymptotic (i.e., long-term) dynamics of these two con-
|
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|
undirectedjoinsbetweenagents(ChartrandandPing,2012).The scious agents can be characterized by its absorbing sets and their
|
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|
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nodes can have any finite degree, i.e., any finite number of edges. periods. Recall that an absorbing set for such a dynamics is
|
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|
|
As a special case, conscious agents can be joined to form deter- a smallest set of states that acts like a roach motel: once the
|
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|
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ministic or non-deterministic cellular automata (Ceccherini- dynamics enters the absorbing set it never leaves, and it forever
|
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|
|
Silberstein and Coornaert, 2010) and universal Turing machines cycles periodically through the states within that absorbing set.
|
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|
|
(Cook,2004). It is straightforward to verify that for the simple dynamics of
|
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|
|
DYNAMICSOFTWOCONSCIOUSAGENTS conscious agents just described, the asymptotic behavior is as
|
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|
|
follows:
|
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|
|
Twoconsciousagents
|
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|
|
C =(X ,G ,P ,D ,A ,N ), (14) (1) {|0000} is absorbing with period 1;
|
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|
|
1 1 1 1 1 1 1 (2) {|1111} is absorbing with period 1;
|
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|
|
and (3) {|0101, |1010}isabsorbingwithperiod2;
|
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|
|
(4) {|0001, |1000, |0100, |0010} is absorbing with period 4,
|
|||
|
|
andcycles in that order;
|
|||
|
|
C =(X ,G ,P ,D A ,N ), (15)
|
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|
|
2 2 2 2 2, 2 2 (5) {|0011, |1001, |1100, |0110} is absorbing with period 4,
|
|||
|
|
andcycles in that order;
|
|||
|
|
can be joined, as illustrated in Figure2, to form a dynamical (6) {|0111, |1011, |1101, |1110} is absorbing with period 4,
|
|||
|
|
system. Here we discuss basic properties of this dynamics. andcycles in that order.
|
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|
|
Thestatespace,E,ofthedynamicsisE = X ×G ×X ×G ,
|
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|
|
1 1 2 2
|
|||
|
|
with product σ-algebra E. The idea is that for the current step, SECONDEXAMPLEOFASYMPTOTICBEHAVIOR
|
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|
|
t ∈ N, of the dynamics, the state can be described by the vec- If we alter this dynamics by simply changing the kernel D1 from
|
|||
|
|
tor (x (t),g (t),x (t),g (t)), and based on this state four actions
|
|||
|
|
1 1 2 2 an identity matrix to the matrix D1 = ((0,1),(1,0)), then the
|
|||
|
|
happen simultaneously: (1) agent C1 experiences the perception asymptotic behavior changes to the following:
|
|||
|
|
x (t) ∈ X and decides, according to D , on a specific action
|
|||
|
|
1 1 1
|
|||
|
|
g (t) ∈ G to take at step t + 1; (2) agent C , using A , takes
|
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|
|
1 1 1 1 (1) {|0000, |0100, |0110, |0111, |1111, |1011, |1001, |1000}
|
|||
|
|
the action g1(t) ∈ G1;(3)agentC2 experiences the perception is absorbing with period 8, and cycles in that order;
|
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|
|
x (t) ∈ X and decides, according to D , on a specific action
|
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|
|
2 2 2 (2) {|0001, |1100, |0010, |0101, |1110, |0011, |1101, |1010}
|
|||
|
|
g (t) ∈ G to take at step t + 1; (4) agent C , using A , takes the
|
|||
|
|
2 2 2 2 is absorbing with period 8, and cycles in that order.
|
|||
|
|
action g2(t) ∈ G2.
|
|||
|
|
Thus, the state evolves by a kernel If instead of changing D we changed D (or A or A )to
|
|||
|
|
1 2 1 2
|
|||
|
|
L : E × E →[0,1], (16) ((0,1),(1,0)), we would get the same asymptotic behavior. Thus,
|
|||
|
|
in general, an asymptotic behavior corresponds to an equivalence
|
|||
|
|
whichisgiven,forstatee = (x (t),g (t),x (t),g (t)) ∈ E at time class of interacting conscious agents.
|
|||
|
|
1 1 2 2 The range of possible dynamics of pairs of conscious agents
|
|||
|
|
t and event B ∈ E, comprised of a measurable set of states of the is huge, and grows as one increases the richness of the state
|
|||
|
|
form(x (t +1),g (t +1),x (t +1),g (t +1)),by
|
|||
|
|
1 1 2 2 space E and, therefore, the set of possible kernels. The possibil-
|
|||
|
|
ities increase as one considers dynamical systems of three or more
|
|||
|
|
L(e,B) = A (g (t),dx (t + 1))D (x (t),dg (t + 1))A (g (t), conscious agents, with all the possible directed and undirected
|
|||
|
|
2 2 1 1 1 1 1 1
|
|||
|
|
B joins among them, forming countless connected multi-graphs or
|
|||
|
|
dx (t + 1))D (x (t),dg (t + 1)). (17) amenablegroups.
|
|||
|
|
2 2 2 2
|
|||
|
|
With this brief introduction to the dynamics of conscious
|
|||
|
|
This is not kernel composition; it is simply multiplication of the agents we are now in a position to state another key hypothesis.
|
|||
|
|
four kernel values. The idea is that at each step of the dynamics Hypothesis 2. Conscious-agent thesis. Every property of con-
|
|||
|
|
eachofthefourkernelsactssimultaneouslyandindependentlyof sciousness can be represented by some property of a dynamical
|
|||
|
|
the others to transition the state (x (t),g (t),x (t),g (t)) to the system of conscious agents.
|
|||
|
|
1 1 2 2
|
|||
|
|
next state (dx (t + 1), dg (t + 1), dx (t + 1), dg (t + 1)).
|
|||
|
|
1 1 2 2 THECOMBINATIONPROBLEM
|
|||
|
|
FIRSTEXAMPLEOFASYMPTOTICBEHAVIOR Conscious realism and the conscious-agent thesis are strong
|
|||
|
|
For concreteness, consider the simplest possible case where (1) claims, and face a tough challenge: Any theory that claims con-
|
|||
|
|
X , G , X ,andG each have only two states which, using Dirac sciousness is fundamental must solve the combination problem
|
|||
|
|
1 1 2 2
|
|||
|
|
notation, we denote |0 and |1,and(2)eachofthekernelsA2, (Seager, 1995; Goff, 2009; Blamauer, 2011; Coleman, 2014).
|
|||
|
|
D , A ,andD isa2×2identitymatrix. William Seager describes this as “the problem of explaining how
|
|||
|
|
1 1 2
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 10
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
the myriad elements of ‘atomic consciousness’ can be combined Theorem1.(Undirected Join Theorem.) An undirected join of
|
|||
|
|
into a new, complex and rich consciousness such as that we twoconsciousagentscreates a new conscious agent.
|
|||
|
|
possess” (Seager, 1995). Proof.(By construction.) Let two conscious agents
|
|||
|
|
William James saw the problem back in 1890: “Where the ele-
|
|||
|
|
mental units are supposed to be feelings, the case is in no wise C =((X ,X ),(G ,G ),P ,D ,A ,N ), (18)
|
|||
|
|
1 1 1 1 1 1 1 1 1
|
|||
|
|
altered. Take a hundred of them, shuffle them and pack them as
|
|||
|
|
close together as you can (whatever that may mean); still each and
|
|||
|
|
remains the same feeling it always was, shut in its own skin, win-
|
|||
|
|
dowless, ignorant of what the other feelings are and mean. There C =((X ,X ),(G ,G ),P ,D ,A ,N ), (19)
|
|||
|
|
would be a hundred-and-first feeling there, if, when a group or 2 2 2 2 2 2 2 2 2
|
|||
|
|
series of such feelings were set up, a consciousness belonging to have an undirected join. Let
|
|||
|
|
the group as such should emerge. And this 101st feeling would
|
|||
|
|
be a totally new fact; the 100 original feelings might, by a curious
|
|||
|
|
physical law, be a signal for its creation, when they came together; C=((X,X),(G,G),P,D,A,N)) (20)
|
|||
|
|
but they would have no substantial identity with it, nor it with
|
|||
|
|
them, and one could never deduce the one from the others, or where
|
|||
|
|
(in any intelligible sense) say that they evolved it. ... The pri-
|
|||
|
|
vate minds do not agglomerate into a higher compound mind” X = X ×X , (21)
|
|||
|
|
1 2
|
|||
|
|
(James, 1890/2007). G=G ×G, (22)
|
|||
|
|
There are really two combination problems. The first is 1 2
|
|||
|
|
the combination of phenomenal experiences, i.e., of qualia. For T
|
|||
|
|
P = P ⊗P :G ×X→[0,1], (23)
|
|||
|
|
1 2
|
|||
|
|
instance, one’s taste experiences of salt, garlic, onion, basil and D=D ⊗D :X×G→[0,1], (24)
|
|||
|
|
tomato are somehow combined into the novel taste experience 1 2
|
|||
|
|
of a delicious pasta sauce. What is the relationship between one’s T
|
|||
|
|
A=A ⊗A :G×X →[0,1], (25)
|
|||
|
|
experiences of the ingredients and one’s experience of the sauce? 1 2
|
|||
|
|
N =N =N , (26)
|
|||
|
|
The second problem is the combination of subjects of expe- 1 2
|
|||
|
|
riences. In the sauce example, a single subject experiences the
|
|||
|
|
ingredients and the sauce, so the problem is to combine experi- where superscript T indicates transpose, e.g., XT = X ×X ;
|
|||
|
|
2 1
|
|||
|
|
ences within a single subject. But how can we combine subjects where X is the σ-algebra generated by the Cartesian product of
|
|||
|
|
themselves to create a new unified subject? Each subject has its X1andX2;whereGistheσ-algebragenerated by G1and G2;and
|
|||
|
|
point of view. How can different points of view be combined to where the Markovian kernels P, D,andA are given explicitly, in
|
|||
|
|
give a new, single, point of view? the discrete case, by
|
|||
|
|
No rigorous theory has been given for combining phenome-
|
|||
|
|
nal experiences, but there is hope. Sam Coleman, for instance, P((g ,g ),(x ,x )) = P ⊗P ((g ,g ),(x ,x ))
|
|||
|
|
2 1 1 2 1 2 2 1 1 2
|
|||
|
|
is optimistic but notes that “there will have to be some sort of =P (g ,x )P (g ,x ), (27)
|
|||
|
|
qualitative blending or pooling among the qualities carried by 1 2 1 2 1 2
|
|||
|
|
each ultimate: if each ultimate’s quality showed up as such in the D((x ,x ),(g ,g )) = D ⊗D ((x ,x ),(g ,g ))
|
|||
|
|
1 2 1 2 1 2 1 2 1 2
|
|||
|
|
macro-experience,itwouldlackthenotablehomogeneityof(e.g., =D(x ,g )D (x ,g ), (28)
|
|||
|
|
color experience, and plausibly some mixing of basic qualities is 1 1 1 2 2 2
|
|||
|
|
required to obtain the qualities of macro-experience” (Coleman, A((g ,g ),(x ,x )) = A ⊗A ((g ,g ),(x ,x ))
|
|||
|
|
1 2 2 1 1 2 1 2 2 1
|
|||
|
|
2014). =A(g ,x )A (g ,x ), (29)
|
|||
|
|
Likewise, no rigorous theory has been given for combining 1 1 2 2 2 1
|
|||
|
|
subjects. But here there is little hope. Thomas Nagel, for instance,
|
|||
|
|
where g ∈ G , g ∈ G , x ∈ X ,andx ∈ X .ThenC satisfies
|
|||
|
|
says “Presumably the components out of which a point of view 1 1 2 2 1 1 2 2
|
|||
|
|
is constructed would not themselves have to have points of view” the definition of a conscious agent.
|
|||
|
|
(Nagel, 1979). Coleman goes further, saying, “it is impossible to Thus, the undirected join of two conscious agents (illustrated
|
|||
|
|
explainthegenerationofamacro-subject(likeoneofus)interms in Figure2) creates a single new conscious agent that we call
|
|||
|
|
of the assembly of micro-subjects, for, as I show, subjects cannot their undirected combination. It is straightforward to extend the
|
|||
|
|
combine”(Coleman,2014). construction in Theorem 1 to the case in which more than
|
|||
|
|
So at present there is the hopeful, but unsolved, problem of two conscious agents have an undirected join. In this case the
|
|||
|
|
combining experiences and the hopeless problem of combining joined agents create a single new agent that is their undirected
|
|||
|
|
subjects. combination.
|
|||
|
|
Thetheory of conscious agents provides two ways to combine Theorem 2.(Directed Join Theorem.) A directed join of two
|
|||
|
|
conscious agents: undirected combinations and directed combi- conscious agents creates a new conscious agent.
|
|||
|
|
nations. We prove this, and then consider the implications for Proof.(By construction.) Let two conscious agents
|
|||
|
|
solving the problems of combining experiences and combining
|
|||
|
|
subjects. C =((X ,X ),(G ,G ),P ,D ,A ,N ), (30)
|
|||
|
|
1 1 1 1 1 1 1 1 1
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 11
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
and the phenomenology of decision making is intimately connected
|
|||
|
|
with the spaces of perceptual experiences that are integrated in
|
|||
|
|
C =((X ,X ),(G ,G ),P ,D ,A ,N ), (31) the decision process. This is an interesting prediction of the for-
|
|||
|
|
2 2 2 2 2 2 2 2 2
|
|||
|
|
malism of conscious agents, and suggests that solution of the
|
|||
|
|
have the directed join C1 → C2.Let combination problem for experience will necessarily involve the
|
|||
|
|
integration of experience with decision-making.
|
|||
|
|
C=((X,X),(G,G),P,D,A,N)) (32) We turn now to the combination of subjects. Coleman
|
|||
|
|
describes subjects as follows: “The idea of being a subject goes
|
|||
|
|
where with being an experiential entity, something conscious of phe-
|
|||
|
|
nomenal qualities. That a given subject has a particular phe-
|
|||
|
|
X = X , (33)
|
|||
|
|
1 nomenological point of view can be taken as saying that there
|
|||
|
|
G=G2, (34) exists a discrete ‘sphere’ of conscious-experiential goings-on cor-
|
|||
|
|
P = P , (35) respondingtothissubject,withregardtowhichothersubjectsare
|
|||
|
|
1 distinct in respect of the phenomenal qualities they experience,
|
|||
|
|
D=DAD :X ×G →[0,1], (36) andtheyhavenodirect(i.e.,experiential)accesstothequalitative
|
|||
|
|
1 1 2 1 2
|
|||
|
|
A=A, (37) fieldenjoyedbythefirstsubject.Asubject,then,canbethoughtof
|
|||
|
|
2 asapointofviewannexedtoaprivatequalitativefield”(Coleman,
|
|||
|
|
N =N =N , (38) 2014).
|
|||
|
|
1 2
|
|||
|
|
A conscious agent Ci is a subject in the sense described by
|
|||
|
|
where D A D denotes kernel composition. Then C satisfies the Coleman. It has a distinct sphere, X , of “conscious-experiential
|
|||
|
|
1 1 2 i
|
|||
|
|
definition of a conscious agent. goings-on”andhasnodirectexperientialaccesstothesphere,Xj,
|
|||
|
|
Thus,thedirectedjoinoftwoconsciousagentscreatesasingle of experiences of any other conscious agent Cj. Moreover, a con-
|
|||
|
|
new conscious agent that we call their directed combination.Itis scious agent is a subject in the further sense of being an agent, i.e.,
|
|||
|
|
straightforward to extend the construction in Theorem 2 to the makingdecisions and taking actions on its own. Thus, according
|
|||
|
|
case in which more than one conscious agent has a directed join to the theory being explored here a subject, a point of view, is a
|
|||
|
|
to C2. In this case, all such agents, together with C2,createanew six-tuple that satisfies the definition of a conscious agent.
|
|||
|
|
agent that is their directed combination. The problem with combining subjects is, according to Goff,
|
|||
|
|
GivenTheorems1and2,wemakethefollowing that “It is never the case that the existence of a number (one or
|
|||
|
|
Conjecture 3:(Combination Conjecture.) Given any pseu- more) of subjects of experience with certain phenomenal char-
|
|||
|
|
dograph of conscious agents, with any mix of directed and acters a priori entails the existence of some other subject of
|
|||
|
|
undirected edges, then any subset of conscious agents from the experience” (Goff, 2009).
|
|||
|
|
pseudograph, adjacent to each other or not, can be combined to Coleman goes further, saying that “The combination of sub-
|
|||
|
|
create a new conscious agent. jects is a demonstrablyincoherentnotion,notjustonelackingina
|
|||
|
|
How do these theorems address the problems of combining prioriintelligibility...”(Coleman,2014).Heexplainswhy:“...a
|
|||
|
|
experiences and subjects? We consider first the combination of set of points of view have nothingtocontributeassuchtoasingle,
|
|||
|
|
experiences. unified successor point of view. Their essential property defines
|
|||
|
|
Suppose C1 has a space of possible perceptual experiences X1, themagainst it: in so far as they are points of view they are expe-
|
|||
|
|
and C2 has a space of possible perceptual experiences X2.Then rientially distinct and isolated—they have different streams of
|
|||
|
|
their undirected join creates a new conscious agent C that has consciousness. The diversity of the subject-set, of course, derives
|
|||
|
|
a space of possible perceptual experiences X = X × X .Inthis from the essential oneness of any given member: since each sub-
|
|||
|
|
1 2
|
|||
|
|
case, C has possible experiences that are not possible for C1 or ject is essentially a oneness, a set of subjects are essentially diverse,
|
|||
|
|
C2. If, for instance, C1 can see only achromatic brightness, and for they must be a set of onenesses. Essential unity from essential
|
|||
|
|
C2 canseeonlyvariationsinhue,thenC can see hues of varying diversity ...is thus a case of emergence ...”
|
|||
|
|
brightness. Although C’s possible experiences X are the Cartesian Thetheoryofconsciousagentsproposesthatasubject,apoint
|
|||
|
|
product of X and X ,neverthelessC might exhibit perceptual of view, is a six-tuple that satisfies the definition of conscious
|
|||
|
|
1 2
|
|||
|
|
dependence between X and X , due to feedback inherent in an agent. The directed and undirected join theorems give construc-
|
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|
1 2
|
|||
|
|
undirected join (Maddox and Ashby, 1996; Ashby, 2000). tive proofs of how conscious agents and, therefore, points of view,
|
|||
|
|
For a directed join C1 → C2, the directed-combination agent can be combined to create a new conscious agent, and thus a
|
|||
|
|
C has a space of possible perceptual experiences X = X1.This new point of view. The original agents, the original subjects, are
|
|||
|
|
might suggest that no combination of experiences takes place. not destroyed in the creation of the new agent, the new sub-
|
|||
|
|
However, C has a decision kernel D that is given by the kernel ject. Instead the original subjects structurally contribute in an
|
|||
|
|
product D A D . This product integrates (in the literal sense of understandable, indeed mathematically definable, fashion to the
|
|||
|
|
1 1 2
|
|||
|
|
integral calculus) over the entire space of perceptual experiences structureandpropertiesofthenewagent.Theoriginalagentsare,
|
|||
|
|
X , making these perceptual experiences an integral part of the indeed, influenced in the process, because they interact with each
|
|||
|
|
2
|
|||
|
|
decision process. This comports well with evidence that there is other. But they retain their identities. And the new agent has new
|
|||
|
|
something it is like to make a decision (Nahmias et al., 2004; properties not enjoyed by the constituent agents, but which are
|
|||
|
|
BayneandLevy,2006),andsuggeststheintriguingpossibilitythat intelligible from the structure and interactions of the constituent
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 12
|
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|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
agents. In the case of undirected combination, for instance, we • Eachinvariant event ρ is partitioned into a finite number dρof
|
|||
|
|
have seen that the new agent can have periodic asymptotic prop- “asymptotic” events, indexed by ρ and by δ = 1, ..., dρ,so
|
|||
|
|
erties that are not possessed by the constituent agents but that are that once the chain enters the asymptotic event δ,itwillthen
|
|||
|
|
intelligible—and thus not emergent in a brute sense—from the proceed, with certainty, to δ + 1, δ + 2, and so on, cyclically
|
|||
|
|
structures and interactions of the constituent agents. aroundthesetofasymptoticeventsfortheinvarianteventρ.
|
|||
|
|
Thus,inshort,thetheoryofconsciousagentsprovidesthefirst
|
|||
|
|
rigorous theoretical account of the combination of subjects. The Then there is a correspondence between eigenfunctions of
|
|||
|
|
formalismisrichwithdeductiveimplicationstobeexplored.The L and harmonic functions of Q (Revuz, 1984, p. 210)
|
|||
|
|
discussion here is just a start. But one hint is the following. The Welet
|
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|
|
undirected combination of two conscious agents is a single con-
|
|||
|
|
λ =exp(2iπk/dρ), (41)
|
|||
|
|
scious agent whose world, W, is itself. This appears to be a model ρ,k
|
|||
|
|
of introspection, in which introspection emerges, in an intelligible
|
|||
|
|
fashion, from the combination of conscious agents. and
|
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|
|
MICROPHYSICALOBJECTS dρ
|
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|
|
f =(λ )δU (42)
|
|||
|
|
Wehavesketched a theory of subjects. Now we use it to sketch a ρ,k ρ,k ρ,δ
|
|||
|
|
theoryofobjects,beginningwiththemicroscopicandproceeding δ=1
|
|||
|
|
to the macroscopic. whereρistheindexovertheinvariantevents(i.e.,absorbingsets),
|
|||
|
|
The idea is that space-time and objects are among the sym- the variable k is an integer modulo d ,andU is the indicator
|
|||
|
|
bols that conscious agents employ to represent the properties and ρ ρ,δ
|
|||
|
|
interactions of conscious agents. Because each agent is finite, but function of the asymptotic event with index ρ, δ. For instance,
|
|||
|
|
the realm of interacting agents is infinite, the representations of in the example of section First Example of Asymptotic Behavior,
|
|||
|
|
each agent, in terms of space-time and objects, must omit and there are 6 absorbing sets, so ρ = 1,2,...,6. The first absorbing
|
|||
|
|
simplify. Hence the perceptions of each agent must serve as an set has only one state, so d1 = 1. Similarly, d2 = 1, d3 = 2, d4 =
|
|||
|
|
interface to that infinite realm, not as an isomorphic map. d5 = d6 = 4.ThefunctionU1,1 hasthevalue1onthestate|0000
|
|||
|
|
Interacting conscious agents form dynamical systems, with and 0 for all other states; U5,3 has the value 1 on the state |1100
|
|||
|
|
asymptotic (i.e., long-term) behaviors. We propose that micro- and0forallotherstates.
|
|||
|
|
physical objects represent asymptotic properties of the dynamics Thenitisatheoremthat
|
|||
|
|
of conscious agents, and that space-time is simply a convenient Lf =λ f , (43)
|
|||
|
|
framework for this representation. Specifically, we observe that ρ,k ρ,k ρ,k
|
|||
|
|
the harmonic functions of the space-time chain that is associated
|
|||
|
|
withthedynamicsofasystemofconsciousagentsareidenticalto i.e., that fρ,k is an eigenfunction of L with eigenvalue λρ,k,and
|
|||
|
|
the wave function of a free particle; particles are vibrations not of that
|
|||
|
|
strings but of interacting conscious agents. −n
|
|||
|
|
Consider, for concreteness, the system of two conscious agents g (· , n) = (λ ) f , (44)
|
|||
|
|
ρ,k ρ,k ρ,k
|
|||
|
|
of section Dynamics of Two Conscious Agents, whose dynam-
|
|||
|
|
icsisgovernedbythekernelL of (17). This dynamics is clearly is Q-harmonic (Revuz, 1984). Then, using (41–42), we have
|
|||
|
|
Markovian, because the change in state depends only on the cur-
|
|||
|
|
rent state. The space-time chain associated to L has, by definition, dρ
|
|||
|
|
the kernel g (·,n) = exp(2iπk/d )−n exp(2iπk/d )δU
|
|||
|
|
ρ,k ρ ρ ρ,δ
|
|||
|
|
Q:(E×N)×(E⊗2N)→[0,1], (39) δ=1
|
|||
|
|
dρ
|
|||
|
|
given by =exp(2iπk δ −2iπk n )Uρ,δ
|
|||
|
|
δ=1 dρ dρ
|
|||
|
|
dρ
|
|||
|
|
L e, A if m = n +1,
|
|||
|
|
Q((e, n), A×{m}) = ( ) (40) kδ kn
|
|||
|
|
= cis(2π −2π )U
|
|||
|
|
0, otherwise, d d ρ,δ
|
|||
|
|
δ=1 ρ ρ
|
|||
|
|
wheree∈E,n,m∈N,andA∈E(Revuz,1984). dρ
|
|||
|
|
Thenit is a theorem (Revuz, 1984) that, if Q is quasi-compact =cis(2π δ −2π n )U (45)
|
|||
|
|
d d ρ,δ
|
|||
|
|
(this is true when the state space is finite, as here), the asymptotic δ=1 ρ,k ρ,k
|
|||
|
|
dynamicsoftheMarkovchaintakesonacyclicalcharacter:
|
|||
|
|
where dρ,k = dρ/k. This is identical in form to the wavefunction
|
|||
|
|
• Thereareafinitenumberofinvarianteventsorabsorbingsets: of the free particle (Allday, 2009, §7.2.3):
|
|||
|
|
once the chain lands in any of these, it stays there forever. And
|
|||
|
|
the union of these events exhausts the state space E.Wewill ψ(x,t) = A cis(2π x − 2π t )|x (46)
|
|||
|
|
index these events with the letter ρ. x λ T
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 13
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
ThisleadsustoidentifyA 1, Uρ,δ |x, δ x, n t,and OBJECTIONSANDREPLIES
|
|||
|
|
dρ,k λ = T.Thenthemomentumoftheparticleisp = h/dρ,k Here we summarize helpful feedback from readers of earlier
|
|||
|
|
and its energy is E = hc/dρ,k,whereh is Planck’s constant and c drafts, in the form of objections and replies.
|
|||
|
|
is the speed of light.
|
|||
|
|
Thus, we are identifying (1) a wavefunction ψ of the free par- (1) Your definition of conscious agents could equally well-apply
|
|||
|
|
ticle with a harmonic function g of a space-time Markov chain to unconscious agents. Thus, your theory says nothing about
|
|||
|
|
of interacting conscious agents, (2) the position basis |x of the consciousness.
|
|||
|
|
particle with indicator functions Uρ,δ of asymptotic events of the
|
|||
|
|
agentdynamics,(3)thepositionindexxwiththeasymptoticstate Even if the definition could apply to unconscious agents, that
|
|||
|
|
index δ, (4) the time parameter t with the step parameter n,(5) would not preclude it from applying to consciousness, any more
|
|||
|
|
the wavelength λ and period T with the number of asymptotic than using the integers to count apples would preclude using
|
|||
|
|
events dρ,k in the asymptotic behavior of the agents, and (6) the themtocountoranges.
|
|||
|
|
momentum p and energy E as functions inversely proportional
|
|||
|
|
to dρ,k.
|
|||
|
|
Note that wavelength and period are identical here: in these (2) Howcanconsciousness be cast in a mathematical formalism
|
|||
|
|
units, the speed of the wave is 1. without losing something essential?
|
|||
|
|
This identification is for non-relativistic particles. For the rel-
|
|||
|
|
ativistic case we sketch a promising direction to explore, starting The mathematics does lose something essential, viz., conscious-
|
|||
|
|
with the dynamics of two conscious agents in an undirected join. ness itself. Similarly, mathematical models of weather also lose
|
|||
|
|
In this case, the state of the dynamics has six components: N1, somethingessential, viz., weather itself. A mathematical model of
|
|||
|
|
N , X , X , G , G .Weidentifythesewiththegeneratingvectors hurricanes won’t create rain, and a mathematical model of con-
|
|||
|
|
2 1 2 1 2
|
|||
|
|
of a geometric algebra (2, 4) (Doran and Lasenby, 2003). The sciousness won’t create consciousness. The math is not the terri-
|
|||
|
|
components N and N have positive signature, and the remain- tory. But, properly constructed, mathematicsrevealsthestructure
|
|||
|
|
1 2
|
|||
|
|
ing have negative signature. (2, 4) is the conformal geometric of the territory.
|
|||
|
|
algebra for a space-time with signature (1, 3), i.e., the Minkowski
|
|||
|
|
space of special relativity. The conformal group includes as a (3) WhydoyourepresentqualiabyaprobabilityspaceX?
|
|||
|
|
subgroupthePoincaregroupofspace-timetranslationsandrota-
|
|||
|
|
tions; but the full conformal group is needed for most massless Probability spaces can be used, of course, to represent a diverse
|
|||
|
|
relativistic theories, and appears in theories of supersymmetry range of content domains, from the outcomes of coin-flips to the
|
|||
|
|
and supergravity. The Lie group SU(2, 2) is isomorphic to the long-term behavior of equity markets. But this does not preclude
|
|||
|
|
rotor group of (2, 4), which provides a connection to the usingprobabilityspacestorepresentqualia.Aprobabilityspaceis
|
|||
|
|
twistor program of Roger Penrose for quantum gravity (Penrose, notitself identical to qualia (or to coin flips or equity markets). To
|
|||
|
|
2004). proposethatwerepresentthepossiblequaliaofaconsciousagent
|
|||
|
|
Thus,theideaistoconstructageometricalgebra (2,4)from by a probability space is to propose that qualia convey informa-
|
|||
|
|
the dynamics of two conscious agents, and from this to con- tion, since probability and information are (as Shannon showed)
|
|||
|
|
struct space-time and massless particles. Each time we take an transforms of each other. It is also to propose that qualia need
|
|||
|
|
undirected join of two conscious agents, we get a new geometric not,ingeneral,exhibitotherstructures,suchasmetricsordimen-
|
|||
|
|
algebra (2, 4) with new basis vectors as described above. Thus, sions. Nowcertainqualiaspaces,suchasthespaceofphenomenal
|
|||
|
|
weget a nested hierarchy of such geometric algebras from which colors, do exhibit metrical and dimensional properties. These
|
|||
|
|
wecanbuildspace-timefromthePlanckscaleuptomacroscopic properties are not precluded. They are allowed but not required.
|
|||
|
|
scales. The metric would arise from the channel capacity of the All that is required is that we can meaningfully talk about the
|
|||
|
|
joined agents. information content of qualia.
|
|||
|
|
Themassivecaseinvolvessymmetrybreaking,andapromising The qualia X of a conscious agent C are private, in the sense
|
|||
|
|
direction to explore here involves hierarchies of stopping times that no other conscious agent C can directly experience X.
|
|||
|
|
in the Markovian dynamics of conscious agents. The idea is that i
|
|||
|
|
one system of conscious agents might infrequently interact with Instead each Ci experiences its own qualia Xi. Thus, the qualia
|
|||
|
|
another system, an interaction that can be modeled using stop- Xare“inside”theconsciousagentC.The“outside”forC isW,or
|
|||
|
|
ping times. Such interactions can create new conscious agents, moreprecisely, W-C.
|
|||
|
|
using the combination theorems presented earlier, whose “time”
|
|||
|
|
is moving more slowly than that of the original systems of agents (4) A conscious agent should have free will. Where is this mod-
|
|||
|
|
involved in the combination. This hierarchy of stopping times eled in your definition?
|
|||
|
|
proceeds all the way up to the slow times of our own con-
|
|||
|
|
sciousexperiencesashumanobservers(roughly1040 timesslower The kernel D represents the free will choices of the conscious
|
|||
|
|
than the Planck time). The hierarchy of stopping times is linked agentC.ForanyparticularqualexinX,thekernelDgivesaprob-
|
|||
|
|
to a hierarchy of combinations of conscious agents, leading up ability measure on possible actions in the set G that the conscious
|
|||
|
|
to the highest level of conscious agents that constitute us, and agent might choose to perform. We take this probability measure
|
|||
|
|
beyond. to represent the free will choice of the conscious agent. Thus, we
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 14
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
interpret the probabilities as objective probabilities, i.e., as rep- defeater for belief in natural selection. See Alvin Plantinga’s
|
|||
|
|
resenting a true nondeterminism in nature. We are inclined to argumentonthis(Plantinga,2002).
|
|||
|
|
interpret all the other probabilities as subjective, i.e., as reflections
|
|||
|
|
of ignorance and degrees of belief. Evolutionarygamesandgeneticalgorithmsdemonstratethatnat-
|
|||
|
|
ural selection does not, in general, favor true perceptions. But
|
|||
|
|
(5) Aconsciousagentshouldhavegoalsandgoal-directedbehav- this entails nothing about the reliability of our cognitive facul-
|
|||
|
|
iors. Where are these modeled in your definition? ties more generally. Indeed, selection pressures might favor more
|
|||
|
|
accurate logic and mathematics, since these are critical for the
|
|||
|
|
Goals and goal-directed behaviors are not in the definition of proper estimation of the fitness consequences of actions. The
|
|||
|
|
conscious agent. This allows the possibility of goal-free conscious selection pressures on each cognitive faculty must be studied
|
|||
|
|
agents, and reflects the view that goals are not a definitional prop- individually before conclusions about reliability are drawn.
|
|||
|
|
erty of consciousness. However, since one can construct universal
|
|||
|
|
Turing machines from dynamical systems of conscious agents, (10) The undirected join of conscious agents doesn’t really solve
|
|||
|
|
it follows that one can create systems of conscious agents that the problem of combining subjects, because the decision
|
|||
|
|
exhibit goal-directed behaviors. Goals experienced as conscious kernel of the combination is just the product of the deci-
|
|||
|
|
desires can be represented as elements of a qualia space X. sion kernels of the two conscious agents that are combined.
|
|||
|
|
This product only models two separate agents making sep-
|
|||
|
|
(6) Your theory doesn’t reject object permanence, because con- arate decisions, not two subjects combined into a single
|
|||
|
|
scious agents are the “objects” that give rise to our percep- decision-making subject.
|
|||
|
|
tions of size and shape, and those agents are permanent even
|
|||
|
|
whenwe’renotlooking. It’s true that the decision kernel, D, of the combination starts
|
|||
|
|
out as a product, indicating independent decisions. But as the
|
|||
|
|
Conscious realism proposes that conscious agents are there even conscious agents in the combination continue to interact, the
|
|||
|
|
when one is not looking, and thus rejects solipsism. But it also decisions become less and less independent. In the asymptotic
|
|||
|
|
rejects object permanence, viz., the doctrine that 3D space and n
|
|||
|
|
physical objects exist when they are not perceived. To claim that limit, the decision kernel D as n →∞of the combination
|
|||
|
|
cannot, in general, be written as a product. In this limit, the
|
|||
|
|
conscious agents exist unperceived differs from the claim that combinationnowhasasingleunifieddecisionkernel,notdecom-
|
|||
|
|
unconscious objects and space-time exist unperceived. posable as a product of the original decision kernels. And yet the
|
|||
|
|
two conscious agents in the combination still retain their iden-
|
|||
|
|
(7) If our perceptions of space-time and objects don’t resem- tities. Thus, the undirected join models a combination process
|
|||
|
|
ble objective reality, if they’re just a species-specific interface, which starts off as little more than the product of the constituent
|
|||
|
|
then science is not possible. agents but ends up with those agents fully entangled to form a
|
|||
|
|
newconsciousagentwithagenuinelynewandintegrateddecision
|
|||
|
|
The interface theory of perception poses no special problems for kernel.
|
|||
|
|
science. The normal process of creating theories and testing pre-
|
|||
|
|
dictions continues as always. A particularly simple theory, viz., (11) IfIhaveanobjectionitisthattheauthors’proposalismaybe
|
|||
|
|
that our perceptions resemble reality, happens to be false. Fine. notcrazyenough.Iamwiththem100%whentheycompare
|
|||
|
|
Wecandevelop other theories of perception and reality, and test neuronstoiconsonacomputerscreen.But(ifIhaveunder-
|
|||
|
|
them. Science always faces the problem, well-known to philoso- stood them correctly) they then go on to attribute absolute
|
|||
|
|
phers of science, that no collection of data uniquely determines existencetoconsciousness.Myowninclinationistopropose
|
|||
|
|
the correct theory. But that makes science a creative and engaging that consciousness is also just an icon on a computer screen.
|
|||
|
|
process.
|
|||
|
|
Conscious realism is the hypothesis that the objective world W
|
|||
|
|
(8) Your proposal that consciousness, rather than physics, is consists of conscious agents. The theory of conscious agents
|
|||
|
|
fundamentalplaces consciousness outside of science. is a mathematical theory of consciousness that quantifies over
|
|||
|
|
qualia that it assumes really exist. So this theory does assume the
|
|||
|
|
Absolutely not. The onus is on us to provide a mathematically existence of consciousness.
|
|||
|
|
rigorous theory of consciousness, to show how current physics However,itdoesnotassumeincorrigibilityofqualia(tobelieve
|
|||
|
|
falls out as a special case, and to make new testable predictions one has a quale is to have one) or infallibility about the con-
|
|||
|
|
beyondthoseofcurrentphysics.Todismissthephysicalisttheory tents of one’s consciousness. Psychophysical studies provide clear
|
|||
|
|
that space-time and objects are fundamental is not to reject the evidence against incorrigibility and infallibility [see, e.g., the lit-
|
|||
|
|
methodologyofscience. It is just to dismiss a specific theory that erature on change blindness (Simons and Rensink, 2005)]. Nor
|
|||
|
|
is false. does it assume that the mathematics of conscious agents is itself
|
|||
|
|
identical to consciousness; a theory is just a theory.
|
|||
|
|
(9) You argue that natural selection does not favor true per- One might try to interpret the theory of conscious agents as
|
|||
|
|
ceptions. But this entails that the reliability of our cognitive describing a psychophysical monism, in which matter and con-
|
|||
|
|
faculties is low or inscrutable, and therefore constitutes a sciousness are two aspects of a more abstract reality. Such an
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 15
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
interpretation,ifpossible,mightstillbeunpalatabletomostphys- that triggers the organism to perceive a lion, but whatever that
|
|||
|
|
icalists since it entails that dynamical physical properties, such as something is, it almost surely doesn’t resemble a lion. A lion is
|
|||
|
|
position, momentum and spin, have definite values only when simply a species-specific adaptive symbol, not an insight into
|
|||
|
|
they are observed. objective reality.
|
|||
|
|
(12) One problem with section Evolution and Perception is that (13) In section Evolution and Perception, the authors’ argument
|
|||
|
|
theauthorsneverdefineeithertheirnotionofTruth,ortheir seemstobe:Argument1:(1)Naturalselectionfavorsfitness
|
|||
|
|
notionofPerception.Theyseemtobelievethatifyoustartle inperceptualsystems.(2)Fitnessisincompatiblewithtruth.
|
|||
|
|
at anysoundofrustlingleaves(asasortofsensitivepredator (3) Therefore, natural selection favors perceptions that do
|
|||
|
|
avoidance system), then when you run from a real predator, not see truth in whole or in part.
|
|||
|
|
you are not in any way in touch with the truth. But this is With some minor tweaking, Argument 1 can be made
|
|||
|
|
incorrect. valid. But premise 2 is completely implausible. If a tiger is
|
|||
|
|
charging you with lunch on his mind, truth works in the
|
|||
|
|
Forsakeofbrevity,weomittedourdefinitionsoftruthandper- service of fitness. (The authors’ treatment here raises the
|
|||
|
|
ception from this paper. But they are defined precisely in papers question of why we have perceptual systems at all and not
|
|||
|
|
thatstudytheevolutionofperceptioninMonteCarlosimulations just kaleidoscope eyes. They never address this.)
|
|||
|
|
of evolutionary games and genetic algorithms (Mark et al., 2010; The authors would object that premise 2 is too strong.
|
|||
|
|
Hoffmanetal.,2013;Marion,2013;Mark,2013). They don’t subscribe to premise 2, they would say. They
|
|||
|
|
Briefly, we define a perceptual strategy as a measurable func- wouldperhapsholdoutforArgument2:
|
|||
|
|
tion (or, more generally, a Markovian kernel) p : W → X,where Argument 2: (1) Natural selection favors fitness in per-
|
|||
|
|
Wis a measurable space denoting the objective world and X is ceptual systems. (2) Fitness need not always coincide with
|
|||
|
|
a measurable space denoting an organism’s possible perceptions. truth. (3) Therefore, natural selection favors perceptions
|
|||
|
|
If X = W and p is an isomorphism that preserves all structures that do not see truth in whole or in part.
|
|||
|
|
on W,thenp is a naïve realist perceptual strategy. If X ⊂ W and But Argument 2 is not valid and not tweakable into a
|
|||
|
|
p is structure preserving on this subset, then p is a strong critical valid argument. The conclusion is a lot stronger than the
|
|||
|
|
realist strategy. If X need not be a subset of W and p is structure premises.
|
|||
|
|
preserving, then p is a weak critical realist strategy. If X need not Worse, any weaker premise doesn’t give the authors their
|
|||
|
|
be a subset of W and p need not be structure preserving, then p needed/wantedradicalthesis: Perception is not about truth,
|
|||
|
|
is an interface strategy. These strategies form a nested hierarchy: it is about havingkids.Whichtheyinsistmustbeinterpreted
|
|||
|
|
naïve realist strategies are a subset of strong critical realist, which as Perception is never about truth, but about having kids.
|
|||
|
|
are a subset of weak critical realist, which are a subset of interface. Butthisinterpretationisobviouslyfalse.Foronething,ifan
|
|||
|
|
Naïve realist strategies see all and only the truth. Strong criti- ancientancestorofours(callher,Ug)issuccessfulinhaving
|
|||
|
|
cal realist strategies see some, but in general not all, of the truth. kids, she needs to know the truth: that she has kids! Why?
|
|||
|
|
Weakcriticalrealist strategies in general see none of the truth, but Because Ug needs to take care of them!
|
|||
|
|
the relationships among their perceptions genuinely reflect true
|
|||
|
|
relationships in the structure of the objective world W.Interface Wedonotuseeitherargument.WesimplyuseMonteCarlosim-
|
|||
|
|
strategies in general see none of the truth, and none of the true ulations of evolutionary games and genetic algorithms to study
|
|||
|
|
relationships in the structure of W. Thus, our mathematical for- the evolution of perceptual strategies (as discussed in Objection
|
|||
|
|
mulationofperceptualstrategies allows a nuanced exploration of 12). We find, empirically, that strategies tuned to truth almost
|
|||
|
|
the role of truth in perception. always go extinct, or never even arise, in hundreds of thousands
|
|||
|
|
We let these perceptual strategies compete in hundreds of of randomly chosen worlds.
|
|||
|
|
thousands of evolutionary games in hundreds of thousands of The key to understanding this finding is the distinction
|
|||
|
|
randomlychosenworlds, and find that strategies which see some between fitness and truth. If W denotes the objective world (i.e.,
|
|||
|
|
or all of the truth have a pathetic tendency to go extinct when the truth), O denotes an organism, S the state of that organ-
|
|||
|
|
competing against interface strategies that are tuned to fitness ism, and A an action of that organism, then one can describe
|
|||
|
|
rather than truth. The various truth strategies don’t even get a fitness as a function f : W × O × S × A → R.Inotherwords,
|
|||
|
|
chancetocompeteinthegeneticalgorithms,becausetheyarenot fitness depends not only on the objective truth W,butalso
|
|||
|
|
fit enough even to get on the playing field. on the organism, its state and the action. Thus, fitness and
|
|||
|
|
Thus, natural selection favors interface strategies that are truth are quite distinct. Only if the fitness function happens
|
|||
|
|
tuned to fitness, rather than truth. If an organism with an to be a monotonic function of some structure in W, i.e., so
|
|||
|
|
interface perceptual strategy perceives, say, a predatory lion, then that truth and fitness happen to coincide, will natural selection
|
|||
|
|
it really does perceive a lion in the same sense that someone allow a truth strategy to survive. In the generic case, where truth
|
|||
|
|
having a headache really does have a headache. However, this and fitness diverge, natural selection sends truth strategies to
|
|||
|
|
does not entail that the objective world, W, contains an observer- extinction.
|
|||
|
|
independentlion,anymorethanabluerectangulariconona Tophrasethisasanargumentofthekindgivenintheobjection
|
|||
|
|
computer desktop entails that there is a blue rectangular file we would have Argument 3: (1) Natural selection favors fitness
|
|||
|
|
inthecomputer.ThereissomethingintheobjectiveworldW in perceptual systems. (2) Truth generically diverges from fitness.
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 16
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
(3)Therefore,naturalselectiongenerically favorsperceptionsthat properties when they are not observed. These predictions are in
|
|||
|
|
diverge from the truth. factcompatiblewithquantumtheory,andarepartofthestandard
|
|||
|
|
The word generically here is a technical term. Some property interpretation of quantum theory.
|
|||
|
|
holdsgenerically if it holds everywhere except on a set of measure SupposeEisfalse.Thenourperceptionsdidnotevolvebynat-
|
|||
|
|
zero. So, for instance, the cartesian coordinates (x, y)ofapoint ural selection. At present, science has no other theory on offer
|
|||
|
|
in the plane generically have a non-zero y coordinate. Here we are for the development of our perceptual systems. So, in this case,
|
|||
|
|
assuming an unbiased (i.e., uniform) measure on the plane, in science cannot at present make an informed prediction about
|
|||
|
|
whichthemeasureofasetisproportionaltoitsarea.Sincetheset whether our perceptions are true or not. But this is not a logical
|
|||
|
|
of points with a zero y coordinate is the x-axis line, and since lines contradiction.
|
|||
|
|
have no area, it follows that generically a point in the plane has So there is no liar paradox. And there’d better not be. Science
|
|||
|
|
a non-zero y coordinate. Note, however, that there are infinitely cannot be precluded apriorifrom questioning the veridicality
|
|||
|
|
manypoints with a zero y coordinate, even though this property of the perceptions of H. sapiens, any more than it can be pre-
|
|||
|
|
is non-generic. cluded from questioning the veridicality of the perceptions of
|
|||
|
|
Soourargumentisthat,foranappropriateunbiasedmeasure, other species. David Marr, for instance, argues that “... it is
|
|||
|
|
fitness functions generically diverge from truth, and thus natural extremely unlikely that the fly has any explicit representation of
|
|||
|
|
selection generically favors perceptions that diverge from truth. thevisualworldaroundhim—notrueconceptionofasurface,for
|
|||
|
|
This does not entail the stronger conclusion that natural selec- example, but just a few triggers and some specifically fly-centered
|
|||
|
|
tion never favors truth. That conclusion is indeed stronger than parameters ...” and that the fly’s perceptual information “...is
|
|||
|
|
our premises and stronger than required for the interface theory all very subjective” (Marr, 1982, p. 34). Science has no trouble
|
|||
|
|
of perception. Perhaps H. sapiens is lucky and certain aspects of investigating the veridicality of the perceptions of other species
|
|||
|
|
our perceptual evolution has been shaped by a non-generic fit- and concluding, e.g., in the case of the fly, that they fail to be
|
|||
|
|
nessfunctionthatdoesnotdivergefromtruth.Inthiscasesome veridical. Its methods apply equally well to evaluating the veridi-
|
|||
|
|
aspects of our perceptions might be shaped to accurately report cality of the perceptions of H. sapiens (Koenderink et al., 2010;
|
|||
|
|
the truth, in the same sense that your lottery ticket might be the Koenderink, 2011b, 2013).
|
|||
|
|
winner. But the smart money would bet long odds against it.
|
|||
|
|
That’s what non-generic means. (15) Section The Interface Theory of Perception fares no better.
|
|||
|
|
The account of the interface theory about Ug’s perception of Here they say Reality, we learned, departed in important
|
|||
|
|
herkidsisthesameastheaccountinObjection12forthepercep- respects from some of our perceptions. This is true. But it
|
|||
|
|
tion of lions. There are no public physical objects. Lions and kids is true because other perceptions of ours won out because
|
|||
|
|
arenomorepublicandobserverindependentthanareheadaches. they were true. E.g., the Earth is not a flat disk or plane.
|
|||
|
|
Lions and kids (and space-time itself) are useful species-specific Otherperceptionsindeedwonout—notbecausetheyaretruebut
|
|||
|
|
perceptions that have been shaped by natural selection not to becausetheyareadaptiveinawiderrangeofcontexts.Flatearthis
|
|||
|
|
report the truth but simply to guide adaptive behavior. We must adequateformanyeverydayactivities,butifonewantstocircum-
|
|||
|
|
take them seriously, but it is a logical error to conclude that we navigate the earth by boat then a spherical earth is more adaptive.
|
|||
|
|
musttakethemliterally. If one wants to control satellites in orbit or navigate strategic sub-
|
|||
|
|
Although our eyes do not report the truth, they are not marines then a spherical earth is inadequate and a more complex
|
|||
|
|
kaleidoscope eyes because they do report what matters: fitness. modelisrequired.
|
|||
|
|
(14) We see then that the authors are caught in version of the Perceived 3D space is simply a species-specific perceptual
|
|||
|
|
Liar: Science shows that perception never cares about truth. interface, not an insight into objective reality; we have argued
|
|||
|
|
Let this statement be L. L is derived via perception. So is L for this on evolutionary grounds, and researchers in embod-
|
|||
|
|
(together with its perceptual base) true or false? If it is one, ied cognition have arrived at a similar conclusion (Laflaquiere
|
|||
|
|
then it is the other. Contradiction. et al., 2013; Terekhov and O’Regan, 2013). Space as modeled in
|
|||
|
|
physics extends perceived space via the action of groups, e.g., the
|
|||
|
|
This is not our argument. We claim that perception evolved by Euclideangroup,Poincaregroup,orarbitrarydifferentiablecoor-
|
|||
|
|
naturalselection. Call this statement E.NowE isindeedinformed dinate transformations (Singh and Hoffman, 2013). Any objects
|
|||
|
|
by the results of experiments, and thus by our perceptions. We embedded in space, including earth and its 3D shape, are thus
|
|||
|
|
observe, from evolutionary game theory, that one mathematical descriptions in a species-specific vocabulary, not insights into
|
|||
|
|
predictionofEisthatnaturalselectiongenericallydrivestrueper- objective reality.
|
|||
|
|
ceptionstoextinctionwhentheycompetewithperceptionstuned (16) Also, I don’t understand their interface theory of percep-
|
|||
|
|
to fitness. tion. I not only take my icons seriously, but literally: they
|
|||
|
|
Suppose E is true. Then our perceptions evolved by natural are icons. I’m prepared to wager the farm on this: they are
|
|||
|
|
selection. This logically entails that our perceptions are generi- indeed icons.
|
|||
|
|
cally about fitness rather than truth. Is this a contradiction? Not
|
|||
|
|
at all. It is a scientific hypothesis that makes testable predic- We would agree that icons are indeed icons. When I open my
|
|||
|
|
tions. For instance, it predicts that (1) physical objects have no eyes and see a red apple, that red apple is indeed an icon of my
|
|||
|
|
causalpowersand(2)physicalobjectshavenodynamicalphysical perceptual interface. When I close my eyes that icon disappears; I
|
|||
|
|
www.frontiersin.org June 2014 | Volume 5 | Article 577 | 17
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
see just a mottled gray field. Now some physicalists would like to their model, they discuss this very objection (objection 10).
|
|||
|
|
claim that even when my eyes are closed, an objective red apple Unfortunately, their resolution to this objection is mere
|
|||
|
|
still exists, indeed the very red apple that triggered my perceptual handwaving:Butastheconsciousagentsinthecombination
|
|||
|
|
interface to have a red apple icon. It is this claim that is generically continuetointeract,thedecisionsbecomelessandlessinde-
|
|||
|
|
incorrect, if our perceptual systems evolved by natural selection. pendent.Thisismerewishfulthinking.Theauthorshaveno
|
|||
|
|
reasontobelievethislessandlessbusinessandthey’vegiven
|
|||
|
|
(17) The authors make too much of the Humean idea that the the reader no reason to think this either. In fact, if this less
|
|||
|
|
appearance of cause and effect is simply a useful fiction andlessbusinessweretrue,theirmodelwouldn’trequirethe
|
|||
|
|
(section The Interface Theory of Perception). They like all Cartesianproductinthefirstplace.Frankly,thisobjection
|
|||
|
|
mammalsandperhapsmostanimalscannotfailtoseecau- and their failure to handle it guts their model. In this same
|
|||
|
|
sation in the deepest aspects of their lives. The authors paragraph, in the next couple of sentences, the authors just
|
|||
|
|
believe in causation as deeply as anyone in the world. Why? assert (using proof by blatant assertion) that in some unde-
|
|||
|
|
Becauseweareallhardwiredtoseecausation.Andwhileitis finedlimit,atruenewconsciousentityemerges.Thismakes
|
|||
|
|
true that causation goes away at the quantum level, we have the complex presentation of their model otiose. Why not
|
|||
|
|
no reason to believe that it doesn’t really exist at the macro just write a haiku asserting that the combination problem
|
|||
|
|
level. These two levels don’t live well together, but pretend- isnotaproblem?
|
|||
|
|
ing that there’s no such thing as causation is silly, at least it
|
|||
|
|
is silly without a lot of argument. Even Hume admitted that The limit we speak of (for the emergence of a new combined
|
|||
|
|
causation was perfectly real when he had left his study and conscious agent) is the asymptotic limit. Asymptotic behavior
|
|||
|
|
wenttoplaybackgammonwithhisfriends. is a precise technical concept in the theory of Markov chains
|
|||
|
|
(see, e.g., Revuz, 1984, chapter 6). We have given, in sections
|
|||
|
|
There is indeed good evidence that belief in causation is either First Example of Asymptotic Behavior and Second Example of
|
|||
|
|
innate or learned early in life (Carey, 2009; Keil, 2011). And of Asymptotic Behavior, concrete examples of undirected joins for
|
|||
|
|
course we, the authors, are no exception; we, no less than oth- which,asymptotically,anewcombinedconsciousagentiscreated
|
|||
|
|
ers, have a psychological penchant toward causal reasoning about that is not just a Cartesian product of the original agents.
|
|||
|
|
the physical world. But, equally, we no less than others have a Intuitively, the reason that the undirected combination of two
|
|||
|
|
psychological penchant toward assuming that space, time and agents creates a new agent that is not just a product is that there is
|
|||
|
|
physical objects are not merely icons of a species-specific percep- feedback between the two agents (this is illustrated in Figure 2).
|
|||
|
|
tual interface, but are instead real insights into the true nature Thus, the decisions and actions of one agent influence those of
|
|||
|
|
ofobjectivereality.Sciencehasahabitofcorrectingourpen- the other. This influence is not fully felt in the first step of the
|
|||
|
|
chants, even those deeply held. Evolutionary games and genetic dynamics, but in the asymptotic limit of the dynamics it com-
|
|||
|
|
algorithms convinced us, against our deeply held convictions to pletely dominates, carving the state space of the dynamics into
|
|||
|
|
the contrary, that perceptions are, almost surely, interfaces not various absorbing sets with their own periodic behaviors, in a
|
|||
|
|
insights; they also convinced us that the appearance of causality fashion that is not reducible to a simple product of the original
|
|||
|
|
amongphysicalobjectsis a useful fiction. twoagents.
|
|||
|
|
Perceptual icons do, we propose, inform thebehaviorofthe The degree to which the new conscious agent is not reducible
|
|||
|
|
perceiver, and in this sense might be claimed to have causal pow- to a simple product of the original agents can be precisely quan-
|
|||
|
|
ers. This sense of causality, however, differs from that typically tifiedusing,forinstance,themeasureofintegrated information
|
|||
|
|
attributed to physical objects. developed by Tononi and others (Tononi and Edelman, 1998;
|
|||
|
|
Hume’s ideas on causation had little influence on us, in part TononiandSpoorns,2003;Tononi,2008;TononiandKoch,2008;
|
|||
|
|
because exegesis of his ideas is controversial, including projec- Barrett and Seth, 2011). It is straightforward to compute, for
|
|||
|
|
tivist, reductionist and realist interpretations (Garrett, 2009). instance, that the new agent in Second Example of Asymptotic
|
|||
|
|
Our views on causality are consistent with interpretations of Behavior has 2 bits of integrated information, i.e., of new infor-
|
|||
|
|
quantum theory that abandon microphysical causality, such as mation that is not reducible to that of the two original agents.
|
|||
|
|
the Copenhagen,quantumBayesianand(arguably)many-worlds Thus, there is a precise and quantifiable sense in which the undi-
|
|||
|
|
interpretations, (Allday, 2009; Fuchs, 2010; Tegmark, 2014). The rected combination of conscious agents creates a new conscious
|
|||
|
|
burdenofproofissurelyononewhowouldabandonmicrophys- agent with its own new information.
|
|||
|
|
ical causation but still cling to macrophysical causation. Weshould note, however, that our use here of Tononi’s mea-
|
|||
|
|
sure of integrated information does not imply that we endorse
|
|||
|
|
(18) Their treatment of the combination problem is worth read- his theory of consciousness. Tononi is a reductive functionalist,
|
|||
|
|
ing. Thereishoweveraverylargeproblemwiththeirmodel: proposing that consciousness is identical to integrated infor-
|
|||
|
|
It relies on the Cartesian product of X and X (this is right mation and that qualia are identical to specific informational
|
|||
|
|
1 2
|
|||
|
|
after Conjecture 3). The Cartesian product is not conducive relationships (Tononi, 2008). Consistent with this view he asserts,
|
|||
|
|
to real combination (this problem is all over mathematics, for instance, that spectrum inversion is impossible (Tononi, 2008,
|
|||
|
|
by the way—mathematicians don’t care about it because footnote 8). However, a recent theorem proves that all reductive
|
|||
|
|
they only care about high level abstractions). In section functionalist theories of consciousness are false (Hoffman, 2006).
|
|||
|
|
Objections and Replies, where they discuss objections to A fortiori, Tononi’s theory is false. His measure of integrated
|
|||
|
|
Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 18
|
|||
|
|
Hoffman and Prakash Objects of consciousness
|
|||
|
|
information and his analyses of informational relationships are evolutionarytheorytobetrue,butinsteadtobea“boundarycon-
|
|||
|
|
valuable. But his next move, of identifying consciousness with dition” on the new evolutionary theory. Standard evolutionary
|
|||
|
|
integrated information, is provably false. He could fix this by theory is simply how the new evolutionary theory appears when
|
|||
|
|
makingtheweakerclaimthatconsciousnessiscausedbyorresults it is shoehorned into the perceptual framework that H. sapiens
|
|||
|
|
from integrated information. His theory would no longer be nec- happenstohave.
|
|||
|
|
essarily false. But then he would need to offer a scientific theory The process we are describing here is standard procedure in
|
|||
|
|
about how integrated information causes or gives rise to con- science. Wealwaysuseourcurrentbesttheoryasaladdertoabet-
|
|||
|
|
sciousness. No such theory is currently on offer and, we suspect, ter theory, whereupon we can, if necessary, kick away the ladder.
|
|||
|
|
nosuchtheoryispossible. However, we needn’t take our best theory to be true. It’s simply
|
|||
|
|
the best ladder we have to our next theory. We are here adopting
|
|||
|
|
(19) The paper explicitly commits a fallacy: it privileges the a philosophy of instrumentalism in regards to scientific theories.
|
|||
|
|
authors’ take on reality while denying that there is any such The development of a new generalized theory of evolution is
|
|||
|
|
thing as reality. For example: The authors say “There are no not just an abstract possibility, but is in fact one of our current
|
|||
|
|
public physical objects. Lions and kids are no more pub- projects. We are investigating the possibility of keeping the core
|
|||
|
|
lic and observer independent than are headaches. Lions and ideas of standard evolutionary theory that are sometimes referred
|
|||
|
|
kids (and space-time itself) are useful species-specific per- to as “Universal Darwinism,” ideas that include abstract notions
|
|||
|
|
ceptions that have been shaped by natural selection not to of variation, selection and retention. We plan to apply Universal
|
|||
|
|
report the truth but simply to guide adaptive behavior. We Darwinismtointeractingsystemsofconsciousagentstomodel
|
|||
|
|
musttakethemseriously,butitisalogicalerrortoconclude their evolution.
|
|||
|
|
that we must take them literally.” The new limited resource that is the source of competition
|
|||
|
|
Natural selection, which the authors clearly think is the would be information, which is the measure we use to quantify
|
|||
|
|
truth, is just as susceptible to their arguments as headaches the channel capacity of conscious agents. This is a promising
|
|||
|
|
or truth itself. So by their own reasoning, natural selection direction, since information is equivalent to energy, and informa-
|
|||
|
|
is not true; neither are their computer programs/models. tion can be converted into energy (Toyabe et al., 2010). Limited
|
|||
|
|
So the reader doesn’t have to take natural selection or their energy resources, e.g., in the form of food, are a clear source of
|
|||
|
|
models either seriously or literally. So their paper is now competition in standard evolutionary theory.
|
|||
|
|
exposedasself-refuting. Thenewevolutionarytheorythatweconstructshouldexplain
|
|||
|
|
why the standard evolutionary theory was a good ladder to the
|
|||
|
|
If we indeed proposed a “take on reality while denying that there newtheory,andwhywearejustifiedinkickingawaythatladder.
|
|||
|
|
is any such thing as reality,” we would of course be self-refuting.
|
|||
|
|
However, we do not deny that there is any such thing as real- (20) The authors say, “In short, natural selection does not favor
|
|||
|
|
ity. We cheerfully admit that there is a reality. We simply inquire perceptual systems that see the truth in whole or in part.
|
|||
|
|
into the relationship between reality and the perceptions of a Instead, it favors perceptions that are fast, cheap, and tai-
|
|||
|
|
particular species, H. sapiens. Such inquiry is surely within the lored to guide behaviors needed to survive and reproduce.
|
|||
|
|
purview of science. Moreover all currently accepted theories in Perception is not about truth, it’s about having kids.” This is
|
|||
|
|
science, including evolutionary theory, are appropriate tools for afalsedichotomy.
|
|||
|
|
such inquiry.
|
|||
|
|
Wefindthatevolutionarytheoryentails a low probability that The distinction between truth and fitness, between truth and
|
|||
|
|
our perceptions are veridical, and thus a high probability that having more kids, is not a false dichotomy to evolutionary biol-
|
|||
|
|
reality is not isomorphictoourperceptions,e.g.,ofspacetimeand ogists. It is a distinction that is central to their theory. The same
|
|||
|
|
objects. This promptsustoproposeanewtheoryofreality,which objectively true world can have an infinite variety of different fit-
|
|||
|
|
we have done by defining conscious agents and proposing con- ness functions, corresponding to the variety of organisms, states
|
|||
|
|
scious realism, viz., that reality consists of interacting conscious and actions. A steak that conveys substantial fitness benefits to
|
|||
|
|
agents. a hungry lion conveys no benefits to a cow. Each distinct fitness
|
|||
|
|
This proposal invites us to revisit evolutionary theory itself. function drives natural selection in a different direction.
|
|||
|
|
The standard formulation of evolutionary theory, i.e., the neo-
|
|||
|
|
Darwiniansynthesis,iscouchedintermsofspacetimeandobjects (21) In response to the claim that “Your definition of conscious
|
|||
|
|
(suchasorganismsandgenes),whichwenowtaketobeaspecies- agentscouldequallywell-applytounconsciousagents;thus,
|
|||
|
|
specific perceptual representation, not an insight into reality. But your theory says nothing about consciousness.” the authors
|
|||
|
|
we are not forced into self-refutation at this point. It is open to reply that “Even if the definition could apply to unconscious
|
|||
|
|
us to formulate a new generalized theory of evolution that oper- agents,thatwouldnotprecludeitfromapplyingtocon-
|
|||
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ates on what we now take to be reality, viz., interacting systems of sciousness, any morethanusingtheintegerstocountapples
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conscious agents. wouldprecludeusingthemtocountoranges.”
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Akeyconstraintonournewevolutionarytheoryisthis:When However, the very fact that the integers can be used to
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the new evolutionary theory is projected onto the spacetime count apples and oranges and peace treaties, etc., is pre-
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perceptual interface of H. sapiens wemustgetbackthestan- cisely WHY the integers are not a theory of either apples or
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dard evolutionary theory. Thus, we do not take the standard orangesorpeacetreaties,etc.Thesameistrueofdefinitions.
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www.frontiersin.org June 2014 | Volume 5 | Article 577 | 19
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Hoffman and Prakash Objects of consciousness
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If my definition of integer applies equally well to the com- is, of course, a tall order. We have taken some first steps by
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plex numbers as well as to the integers, then I do not have (1) proposing the formalism of conscious agents, (2) using that
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a definition of integers. Instead I have a definition of com- formalism to find solutions to the combination problem of con-
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plex numbers. So their definition is useless; all they’ve done sciousness, and (3) sketching how the asymptotic dynamics of
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is define an agent. Consciousness is not present, except conscious agents might lead to particles and space-time itself.
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accidentally. Much work remains to flesh out this account. But if it succeeds,
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H. sapiens might just replace object permanence with objects of
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Theintegers are not considered a theory of peace treaties because consciousness.
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they don’t have the appropriate mathematical structure to model
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peace treaties—not because they can be used to count apples and ACKNOWLEDGMENTS
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peace treaties. For helpful discussions and comments on previous drafts we
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If one has a mathematical structure that is rich enough to pro- thank Marcus Appleby, Wolfgang Baer, Deepak Chopra, Federico
|
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vide a useful theory of some subject, this does not entail that Faggin, Pete Foley, Stuart Hameroff, David Hoffman, Menas
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the same structure cannot be a useful theory of a different sub- Kafatos, Joachim Keppler, Brian Marion, Justin Mark, Jeanric
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ject. The group SU(3), for instance, models an exact symmetry of Meller, Julia Mossbridge, Darren Peshek, Manish Singh, Kyle
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quark colors and an approximate symmetry of flavors. No physi- Stephens, and an anonymous reviewer.
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cist would insist that because SU(3) is a useful theory of quark
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NY:CambridgeUniversityPress),123–162. The use, distribution or reproduction in other forums is permitted, provided
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the original author(s) or licensor are credited and that the original publica-
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Conflict of Interest Statement: The authors declare that the research was con- tion in this journal is cited, in accordance with accepted academic practice. No
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ducted in the absence of any commercial or financial relationships that could be use, distribution or reproduction is permitted which does not comply with these
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construed as a potential conflict of interest. terms.
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