diff --git a/hoffman_archive/markdown/Objects_of_Consciousness.md b/hoffman_archive/markdown/Objects_of_Consciousness.md new file mode 100644 index 00000000..88f4dd5e --- /dev/null +++ b/hoffman_archive/markdown/Objects_of_Consciousness.md @@ -0,0 +1,1252 @@ + ORIGINAL RESEARCHARTICLE + published: 17 June 2014 + doi: 10.3389/fpsyg.2014.00577 + Objects of consciousness + DonaldD.Hoffman1*andChetanPrakash2 + 1 Department of Cognitive Sciences, University of California, Irvine, CA, USA + 2 Department of Mathematics, California State University, San Bernardino, CA, USA + Edited by: Current models of visual perception typically assume that human vision estimates true + Chris Fields, New Mexico State properties of physical objects, properties that exist even if unperceived. However, recent + University, USA (retired) studies of perceptual evolution, using evolutionary games and genetic algorithms, reveal + Reviewedby: that natural selection often drives true perceptions to extinction when they compete + John Serences, University of with perceptions tuned to fitness rather than truth: Perception guides adaptive behavior; + California San Diego, USA + David Marcus Appleby, University of it does not estimate a preexisting physical truth. Moreover, shifting from evolutionary + Sydney, Australia biology to quantum physics, there is reason to disbelieve in preexisting physical truths: + *Correspondence: Certain interpretations of quantum theory deny that dynamical properties of physical + Donald D. Hoffman, Department of objects have definite values when unobserved. In some of these interpretations the + Cognitive Sciences, University of observer is fundamental, and wave functions are compendia of subjective probabilities, + California, Irvine, CA 92697, USA + e-mail: ddhoff@uci.edu not preexisting elements of physical reality. These two considerations, from evolutionary + biology and quantum physics, suggest that current models of object perception require + fundamental reformulation. Here we begin such a reformulation, starting with a formal + model of consciousness that we call a “conscious agent.” We develop the dynamics of + interacting conscious agents, and study how the perception of objects and space-time + can emerge from such dynamics. We show that one particular object, the quantum free + particle, has a wave function that is identical in form to the harmonic functions that + characterize the asymptotic dynamics of conscious agents; particles are vibrations not of + stringsbutofinteractingconsciousagents.Thisallowsustoreinterpretphysicalproperties + such as position, momentum, and energy as properties of interacting conscious agents, + rather than as preexisting physical truths. We sketch how this approach might extend to + the perception of relativistic quantum objects, and to classical objects of macroscopic + scale. + Keywords: consciousness, quantum theory, Markov chains, combination problem, geometric algebra + INTRODUCTION brain exists when unperceived (Edelman, 2004). When Francis + The human mind is predisposed to believe that physical objects, Crick asserted the “astonishing hypothesis” that “You’re noth- + when unperceived, still exist with definite shapes and locations ing but a pack of neurons” he assumed that neurons exist when + in space. The psychologist Piaget proposed that children start to unperceived (Crick, 1994). + develop this belief in “object permanence” around 9 months of Object permanence underlies the standard account of evo- + age, and have it firmly entrenched just 9 months later (Piaget, lution by natural selection. As James memorably put it, “The + 1954). Further studies suggest that object permanence starts as point which as evolutionists we are bound to hold fast to is + early as 3 months of age (Bower, 1974; Baillargeon and DeVos, that all the new forms of being that make their appearance are + 1991). reallynothingmorethanresultsoftheredistributionofthe + Belief in object permanence remains firmly entrenched into original and unchanging materials. The self-same atoms which, + adulthood, even in the brightest of minds. Abraham Pais said of chaotically dispersed, made the nebula, now, jammed and tem- + Einstein, “We often discussed his notions on objective reality. I porarily caught in peculiar positions, form our brains” (James, + recall that on one walk Einstein suddenly stopped, turned to me 1890).Evolutionarytheory,inthestandardaccount,assumesthat + and asked whether I really believed that the moon exists only atoms, and the replicating molecules that they form, exist when + when I look at it” (Pais, 1979). Einstein was troubled by inter- unperceived. + pretations of quantum theory that entail that the moon does not Object permanence underlies computational models of the + exist when unperceived. visual perception of objects. David Marr, for instance, claimed + Belief in object permanence underlies physicalist theories of “We ... very definitely do compute explicit properties of the + the mind-body problem. When Gerald Edelman claimed, for real visible surfaces out there, and one interesting aspect of the + instance, that “There is now a vast amount of empirical evi- evolution of visual systems is the gradual movement toward the + dence to support the idea that consciousness emerges from the difficult task of representing progressively more objective aspects + organization and operation of the brain” he assumed that the of the visual world” (Marr, 1982). For Marr, objects and their + www.frontiersin.org June 2014 | Volume 5 | Article 577 | 1 + Hoffman and Prakash Objects of consciousness + surfaces exist when unperceived, and human vision has evolved perceptual representations that are genuine insights into the true + to describe their objective properties. nature of the objective world. + Bayesian theories of vision assume object permanence. They Evaluating object permanence on evolutionary grounds might + model object perception as a process of statistical estimation of seem quixotic, or at least unfair, given that we just noted that + object properties, such as surface shape and reflectance, that exist evolutionary theory, as it’s standardly described, assumes object + when unperceived. As Alan Yuille and Heinrich Bülthoff put it, permanence(e.g., of DNA and the physical bodies of organisms). + “Wedefinevisionasperceptualinference,theestimationofscene Howthencouldonepossiblyuseevolutionarytheorytotestwhat + properties from an image or sequence of images ...”(Yuille and it assumes to be true? + Bülthoff, 1996). However, Richard Dawkins and others have observed that the + There is a long and interesting history of debate about which core of evolution by natural selection is an abstract algorithm + properties of objects exist when unperceived. Shape, size, and with three key components: variation, selection, and retention + position usually make the list. Others, such as taste and color, (Dennett, 1995; Blackmore, 1999). This abstract algorithm con- + often do not. Democritus, a contemporary of Socrates, famously stitutes a “universal Darwinism” that need not assume object + claimed, “by convention sweet and by convention bitter, by con- permanence and can be profitably applied in many contexts + vention hot, by convention cold, by convention color; but in beyond biological evolution. Thus, it is possible, without beg- + reality atoms and void” (Taylor, 1999). ging the question, to use formal models of evolution by natural + Locke proposed that “primary qualities” of objects, such as selection to explore whether object permanence is an insight + “bulk, figure, or motion” exist when unperceived, but that “sec- or not. + ondaryproperties” of objects, such as “colors and smells” do not. Jerry Fodor has criticized the theory of natural selection itself, + He then claimed that “...the ideas of primary qualities of bod- arguing, for instance, that it impales itself with an intensional fal- + ies are resemblances of them, and their patterns do really exist lacy, viz., inferring from the premise that “evolution is a process + in the bodies themselves, but the ideas produced in us by these inwhichcreatureswithadaptivetraitsareselected”totheconclu- + secondary qualities have no resemblance of them at all” (Locke, sion that “evolution is a process in which creatures are selected + 1690). for their adaptive traits” (Fodor and Piattelli-Palmarini, 2010). + Philosophical and scientific debate continues to this day on However, Fodor’s critique seems wide of the mark (Futuyma, + whether properties such as color exist when unperceived (Byrne 2010) and the evidence for evolution by natural selection is + and Hilbert, 2003; Hoffman, 2006). But object permanence, cer- overwhelming(Coyne,2009;Dawkins,2009). + tainly regarding shape and position, is so deeply assumed by the What,then,dowefindwhenweexploretheevolutionof + scientific literature in the fields of psychophysics and computa- perception using evolutionary games and genetic algorithms? + tional perception that it is rarely discussed. The standard answer, at least among vision scientists, is that we + It is also assumed in the scientific study of consciousness and should find that natural selection favors veridical perceptions, + the mind-body problem. Here the widely acknowledged failure i.e., perceptions that accurately represent objective properties of + to create a plausible theory forces reflection on basic assump- the external world that exist when unperceived. Steven Palmer, + tions, including object permanence. But few researchers in fact for instance, in a standard graduate-level textbook, states that + give it up. To the contrary, the accepted view is that aspects “Evolutionarily speaking, visual perception is useful only if it is + of neural dynamics—from quantum-gravity induced collapses reasonablyaccurate...Indeed,visionisusefulpreciselybecauseit + of wavefunctions at microtubules (Hameroff, 1998)toinforma- is so accurate. By andlarge,whatyouseeiswhatyouget.Whenthis + tional properties of re-entrant thalamo-cortical loops (Tononi, is true, we have what is called veridicalperception ...perception + 2004)—cause, or give rise to, or are identical to, conscious- that is consistent with the actual state of affairs in the environ- + ness.AsColinMcGinnputsit,“weknowthatbrainsarethe ment. This is almost always the case with vision ...”(Palmer, + de facto causal basis of consciousness, but we have, it seems, 1999). + no understanding whatever of how this can be so” (McGinn, Theargument,roughly,isthatthoseofourpredecessorswhose + 1989). perceptions were more veridical had a competitive advantage + over those whose perceptions were less veridical. Thus, the genes + EVOLUTIONANDPERCEPTION that coded for more veridical perceptions were more likely to + Thehumanmindispredisposedfromearlychildhoodtoassume propagate to the next generation. We are, with good probability, + object permanence, to assume that objects have shapes and posi- the offspring of those who, in each succeeding generation, per- + tions in space even when the objects and space are unperceived. It ceived more truly, and thus we can be confident that our own + is reasonable to ask whether this assumption is a genuine insight perceptions are, in the normal case, veridical. + into the nature of objective reality, or simply a habit that is The conclusion that natural selection favors veridical percep- + perhaps useful but not necessarily insightful. tionsiscentraltocurrentBayesianmodelsofperception,inwhich + We can look to evolution for an answer. If we assume that perceptual systems use Bayesian inference to estimate true prop- + ourperceptual and cognitive capacities have been shaped, at least erties of the objective world, properties such as shape, position, + in part, by natural selection, then we can use formal models of motion, and reflectance (Knill and Richards, 1996; Geisler and + evolution, such as evolutionary game theory (Lieberman et al., Diehl,2003).Objectsexistandhavethesepropertieswhenunper- + 2005; Nowak, 2006) and genetic algorithms (Mitchell, 1998), to ceived, and the function of perception is to accurately estimate + exploreif, and under whatcircumstances,naturalselectionfavors pre-existing properties. + Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 2 + Hoffman and Prakash Objects of consciousness + However, when we actually study the evolution of perception THEINTERFACETHEORYOFPERCEPTION + usingMonteCarlosimulationsofevolutionarygamesandgenetic Natural selection favors perceptions that are useful though not + algorithms, we find that natural selection does not, in general, true. This might seemcounterintuitive, even to experts in percep- + favor perceptions that are true reports of objective properties of tion. Palmer, for instance, in the quote above, makes the plausible + the environment. Instead, it generally favors perceptual strategies claim that “vision is useful precisely because it is so accurate” + that are tuned to fitness (Mark et al., 2010; Hoffman et al., 2013; (Palmer, 1999). Geisler and Diehl agree, taking it as obvious that + Marion,2013;Mark,2013). “In general, (perceptual) estimates that are nearer the truth have + Why? Several principles emerge from the simulations. First, greater utility than those that are wide of the mark” (Geisler and + there is no free information. For every bit of information one Diehl, 2002). Feldman also takes it as obvious that “it is clearly + obtains about the external world, one must pay a price in energy, desirable (say from an evolutionary point of view) for an organ- + e.g., in calories expended to obtain, process and retain that infor- ism to achieve veridical percepts of the world” (Feldman, 2013). + mation. And for every calorie expended in perception, one must Knill and Richards concur that vision “... involves the evolu- + 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 + natural selection tends to favor perceptual systems that, ceteris world ...”(Knill and Richards, 1996). + paribus, use fewer calories. One way to use fewer calories is This assumption that perceptions are useful to the extent that + to see less truth, especially truth that is not informative about theyaretrueisprimafacieplausible,anditcomportswellwiththe + fitness. assumption of object permanence. For if our perceptions report + Second, for every bit of information one obtains about the to us a three-dimensional world containing objects with specific + external world, one must pay a price in time. More information shapes and positions, and if these perceptual reports have been + requires, in general, more time to obtain and process. But in the shaped by evolution to be true, then we can be confident that + real world where predators are on the prowl and prey must be those objects really do, in the normal case, exist and have their + wary, the race is often to the swift. It is the slower gazelle that positions and shapes even when unperceived. + becomes lunch for the swifter cheetah. So natural selection tends So we find it plausible that perceptions are useful only if true, + to favor perceptual systems that, ceteris paribus, take less time. and we find it deeply counterintuitive to think otherwise. But + One way to take less time is, again, to see less truth, especially studies with evolutionary games and genetic algorithms flatly + truth that is not informative about fitness. contradict this deeply held assumption. Clearly our intuitions + Third, in a world where organisms are adapted to niches and needalittle help here. How can we try to understand perceptions + require homeostatic mechanisms, the fitness functions guiding that are useful but not true? + their evolution are generally not monotonic functions of struc- Fortunately, developments in computer technology have pro- + tures or quantities in the world. Too much salt or too little can vided a convenient and helpful metaphor: the desktop of a win- + be devastating; something in between is just right for fitness. The dowsinterface(Hoffman,1998,2009,2011,2012,2013;Mausfeld, + same goldilocks principle can hold for water, altitude, humidity, 2002; Koenderink, 2011a; Hoffman and Singh, 2012; Singh and + andsoon.Inthesecases,perceptions that are tuned to fitness are Hoffman, 2013). Suppose you are editing a text file and that the + 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 + 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 + irrelevant, it can be inimical, to fitness. revise its text. If you drag that icon to the trash, you can delete the + Fourth, in the generic case where noise and uncertainty are file.Ifyoudragittotheiconforanexternalharddrive,youcan + endemictotheperceptualprocess,astrategythatestimatesatrue create a backup of the file. So the icon is quite useful. + state of the world and then uses the utility associated to that state Butisittrue?Well,theonlyvisiblepropertiesoftheiconareits + to govern its decisions must throw away valuable information position, shape, and color. Do these properties of the icon resem- + 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 + 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 + all the information about utility (Marion, 2013). computer. Indeed, files don’t have a color or shape, and needn’t + Fifth, more complex perceptual systems are more difficult to have a well-defined position (e.g., the bits of the file could be + evolve. Monte Carlo simulations of genetic algorithms show that spread widely over memory). So to even ask if the properties of + there is a combinatorial explosion in the complexity of the search the icon are true is to make a category error, and to completely + required to evolve more complex perceptual systems. This com- misunderstand the purpose of the interface. One can reasonably + binatorial explosion itself is a selection pressure toward simpler askwhethertheiconisusefullyrelatedtothefile,butnotwhether + perceptual systems. it truly resembles the file. + In short, natural selection does not favor perceptual systems Indeed, a critical function of the interface is to hide the truth. + that see the truth in whole or in part. Instead, it favors per- Mostcomputerusersdon’twanttoseethecomplexityoftheinte- + ceptions that are fast, cheap, and tailored to guide behaviors grated circuits, voltages, and magnetic fields that are busy behind + needed to survive and reproduce. Perception is not about truth, the scenes when they edit a file. If they had to deal with that + it’s about having kids. Genes coding for perceptual systems that complexity, they might never finish their work on the file. So + increase the probability of having kids are ipso facto the genes the interface is designed to allow the user to interact effectively + that are more likely to code for perceptual systems in the next with the computer while remaining largely ignorant of its true + generation. architecture. + www.frontiersin.org June 2014 | Volume 5 | Article 577 | 3 + Hoffman and Prakash Objects of consciousness + Ignorant, also, of its true causal structure. When a user drags perception, our perceptions primarily resonate to “affordances,” + a file icon to an icon of an external drive, it looks obvious that those aspects of the objective world that have important con- + themovementofthefileicontothedriveiconcauses the file to sequences for fitness (Gibson, 1979). While we disagree with + be copied. But this is just a useful fiction. The movement of the Gibon’s direct realism and denial of information processing in + file icon causes nothing in the computer. It simply serves to guide perception, we agree with his emphasis on the tuning of percep- + the user’s operation of a mouse, triggering a complex chain of tion to fitness. + causal events inside the computer, completely hidden from the So we must clarify the relationship between truth and fitness. + 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- + impediment,notahelp. tive world then, for a fixed organism, state, and action, we can + Turning now to apply the interface metaphor to human per- think of a fitness function to be a function f:W → [0,1], which + 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, + ceptions to be insights into the true structure and causal nature the organism is a hungry cheetah and the action is eating, then f + of objective reality, but has instead shaped our perceptions to be might assign a high fitness value to world state w in which fresh + a species-specific user interface, fashioned to guide the behav- raw meat is available; but if the organism is a hungry cow then f + iors that we need to survive and reproduce. Space and time are mightassign a low fitness value to the same state w. + the desktop of our perceptual interface, and three-dimensional If the true probabilities of states in the world are given by a + objects are icons on that desktop. probability measuremonW,thenonecandefineanewprobabil- + Ourinterfacegivestheimpressionthatitrevealstruecauseand ity measuremf onW,whereforanyeventAofW,mf(A)issimply + 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 + looksasthoughthefirstcausesthesecondtocareenaway.Butthis normalized so that mf(W) = 1. + 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 + is for the icons on the computer desktop. to maximize the mutual information with m will not, in gen- + Thereisanobviousrejoinder:“Ifthatcobraisjustaniconof eral,maximizemutualinformationwithmf (CoverandThomas, + yourinterfacewithnocausalpowers,whydon’tyougrabitbythe 2006). Being tuned to truth, i.e., maximizing mutual information + 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- + thesamereasonIdon’tcarelesslydragmyfileicontothetrash—I ingmutualinformationwithmf.Indeed,dependingonthefitness + 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 + unlike its icon, is not literally blue or rectangular. But I do take noinformationaboutfitness,andviceversa.Itisinthissensethat + myiconsseriously.” the interface theory of perception claims that our perceptions are + Similarly, evolution has shaped us with a species-specific inter- tunedtofitnessratherthantruth. + face whose icons we must take seriously. If there is a cliff, don’t There is another rejoinder: “The interface metaphor is noth- + stepover.Ifthereisacobra,don’tgrabitstail.Naturalselection ingnew.Physicistshavetoldusformorethanacenturythat + has endowed us with perceptions that function to guide adaptive solid objects are really mostly empty space. So an apparently solid + behaviors, and we ignore them at our own peril. stone isn’t the true reality, but its atoms and subatomic particles + 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) + 1 12 13 1 2 3 +   + P (g ,g ),(x ,x ) = P (g ,x )P (g ,x ), (11) + 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. + Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 8 + Hoffman and Prakash Objects of consciousness + FIGURE7|Threeconsciousagentswithdirectedjoins.Herewe + assumeA =P ,A =P ,andA =P . + 1 2 2 3 3 1 + FIGURE5|Threeadjacentconsciousagents.Thisisacompact + representation of the diagram in Figure 4. + FIGURE8|Simplifiedgraphofthreeconsciousagentswithdirected + joins. + FIGURE6|Threeconsciousagentswhosegraphiscomplete. + message from C2 and sends no message to C3. Similar remarks + hold, mutatis mutandis,forC2 and C3. + In this situation, the three conscious agents have the property Figure7canbesimplifiedasshowninFigure8. + thateverypairisadjacent;wesaythatthegraphofthethreeagents Directed joins can model the standard situation in visual + is complete.ThisisillustratedinFigure6. perception, in which there are multiple levels of visual represen- + Sofarwehaveconsideredjoinsthatareundirected,inthe tations,onelevelbuildingonothersbelowit.Forinstance,atone + 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 + to C1. However, it is also possible for conscious agents to have solution to the correspondence problem; at the next level there + directed joins.ThisisillustratedinFigure7.Inthiscase,C1 sends could be a computation of 3D structure from motion, based on + amessagetoC2 and receives a message from C3, but receives no the 2D motions computed at the earlier level (Marr, 1982). So + www.frontiersin.org June 2014 | Volume 5 | Article 577 | 9 + Hoffman and Prakash Objects of consciousness + anagentC1 mightsolvethecorrespondenceproblemandpassits There are total of 24 = 16 possible states for the dynamics of + solution to C2, which solves the structure-from-motion problem, the two agents, which we can write as |0000, |0001, |0010, ... + andthenpassesitssolution to C3, which does object recognition. |1111, where the leftmost digit is the state of X1, the next digit + Wecan join any number of conscious agents into any multi- the state of G1,thenextofX2, and the rightmost of G2. + graph, where nodes denote agents and edges denote directed or The asymptotic (i.e., long-term) dynamics of these two con- + undirectedjoinsbetweenagents(ChartrandandPing,2012).The scious agents can be characterized by its absorbing sets and their + nodes can have any finite degree, i.e., any finite number of edges. periods. Recall that an absorbing set for such a dynamics is + 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 + ministic or non-deterministic cellular automata (Ceccherini- dynamics enters the absorbing set it never leaves, and it forever + Silberstein and Coornaert, 2010) and universal Turing machines cycles periodically through the states within that absorbing set. + (Cook,2004). It is straightforward to verify that for the simple dynamics of + DYNAMICSOFTWOCONSCIOUSAGENTS conscious agents just described, the asymptotic behavior is as + follows: + Twoconsciousagents + C =(X ,G ,P ,D ,A ,N ), (14) (1) {|0000} is absorbing with period 1; + 1 1 1 1 1 1 1 (2) {|1111} is absorbing with period 1; + and (3) {|0101, |1010}isabsorbingwithperiod2; + (4) {|0001, |1000, |0100, |0010} is absorbing with period 4, + andcycles in that order; + C =(X ,G ,P ,D A ,N ), (15) + 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. + Thestatespace,E,ofthedynamicsisE = X ×G ×X ×G , + 1 1 2 2 + with product σ-algebra E. The idea is that for the current step, SECONDEXAMPLEOFASYMPTOTICBEHAVIOR + 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 + 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; + x (t) ∈ X and decides, according to D , on a specific action + 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- + 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 + 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 + 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 + MICROPHYSICALOBJECTS dρ + 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- + ates on what we now take to be reality, viz., interacting systems of sciousness, any morethanusingtheintegerstocountapples + conscious agents. wouldprecludeusingthemtocountoranges.” + Akeyconstraintonournewevolutionarytheoryisthis:When However, the very fact that the integers can be used to + the new evolutionary theory is projected onto the spacetime count apples and oranges and peace treaties, etc., is pre- + perceptual interface of H. sapiens wemustgetbackthestan- cisely WHY the integers are not a theory of either apples or + dard evolutionary theory. Thus, we do not take the standard orangesorpeacetreaties,etc.Thesameistrueofdefinitions. + www.frontiersin.org June 2014 | Volume 5 | Article 577 | 19 + Hoffman and Prakash Objects of consciousness + If my definition of integer applies equally well to the com- is, of course, a tall order. We have taken some first steps by + plex numbers as well as to the integers, then I do not have (1) proposing the formalism of conscious agents, (2) using that + a definition of integers. Instead I have a definition of com- formalism to find solutions to the combination problem of con- + plex numbers. So their definition is useless; all they’ve done sciousness, and (3) sketching how the asymptotic dynamics of + is define an agent. Consciousness is not present, except conscious agents might lead to particles and space-time itself. + accidentally. Much work remains to flesh out this account. But if it succeeds, + H. sapiens might just replace object permanence with objects of + Theintegers are not considered a theory of peace treaties because consciousness. + they don’t have the appropriate mathematical structure to model + peace treaties—not because they can be used to count apples and ACKNOWLEDGMENTS + peace treaties. For helpful discussions and comments on previous drafts we + If one has a mathematical structure that is rich enough to pro- thank Marcus Appleby, Wolfgang Baer, Deepak Chopra, Federico + vide a useful theory of some subject, this does not entail that Faggin, Pete Foley, Stuart Hameroff, David Hoffman, Menas + the same structure cannot be a useful theory of a different sub- Kafatos, Joachim Keppler, Brian Marion, Justin Mark, Jeanric + ject. The group SU(3), for instance, models an exact symmetry of Meller, Julia Mossbridge, Darren Peshek, Manish Singh, Kyle + quark colors and an approximate symmetry of flavors. 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Soc. 2, 42, 230–265. doi: Citation: HoffmanDDandPrakashC(2014)Objectsofconsciousness.Front.Psychol. + 10.1112/plms/s2-42.1.230 5:577. doi: 10.3389/fpsyg.2014.00577 + Wilczek, F. (2006). Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm. This article was submitted to Perception Science, a section of the journal Frontiers in + Singapore: World Scientific. Psychology. + Yuille, A., and Bülthoff, H. (1996). “Bayesian decision theory and psychophysics,” Copyright © 2014 Hoffman and Prakash. This is an open-access article dis- + in Perception as Bayesian inference, eds D. Knill and W. Richards (New York, tributed under the terms of the Creative Commons Attribution License (CC BY). + NY:CambridgeUniversityPress),123–162. The use, distribution or reproduction in other forums is permitted, provided + the original author(s) or licensor are credited and that the original publica- + 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 + 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 + construed as a potential conflict of interest. terms. + Frontiers in Psychology | Perception Science June 2014 | Volume 5 | Article 577 | 22 diff --git a/hoffman_archive/pdfs/Objects_of_Consciousness_Hoffman_Prakash_2014.pdf b/hoffman_archive/pdfs/Objects_of_Consciousness_Hoffman_Prakash_2014.pdf new file mode 100644 index 00000000..141ac0a2 --- /dev/null +++ b/hoffman_archive/pdfs/Objects_of_Consciousness_Hoffman_Prakash_2014.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:db73e744ff1dd9ca6fadc040ebf76fa570a1131693066aa2a57a3daf266c8e14 +size 1387594