210713704 2022-11-2 232314 10.pdf

2022 Blum&Blum 1 A Theory of Consciousness from a Theoretical Computer Science Perspective:Insights from the Conscious Turing Machine Lenore Blum and Manuel Blum Abstract The quest to understand consciousness,once the purview of philosophers and theologians,is now actively pursued by scientists of many stripes.We examine consciousness from the perspective of Theoretical Computer Science(TCS),a branch of mathematics concerned with understanding the underlying principles of computation and complexity,including the implications and surprising consequences of resource limitations.We are inspired by Alan Turings simple yet powerful definition of a computer,the Turing Machine(TM),and by the Global Workspace Theory(GWT)of consciousness originated by cognitive neuroscientist Bernard Baars and further developed by him,Stanislas Dehaene,Jean-Pierre Changeux,George Mashour and others.We are not looking for a complex model of the brain nor of cognition but for a simple substrate independent computational model of(the admittedly complex concept of)consciousness.We do this by defining the Conscious Turing Machine(CTM),also called a Conscious AI,and then we define consciousness and related notions in the CTM.While these are only mathematical TCS definitions,we suggest why the CTM has feelings of consciousness.The TCS perspective provides a simple framework to employ tools from computational complexity theory and machine learning to help us understand consciousness and related concepts.Previously we explored explanations for the feelings of pain and pleasure in the CTM.Here we consider additional phenomena generally associated with consciousness,again from the perspective of the CTM.We start with three examples related to vision(blindsight,inattentional blindness,and change blindness),then follow with a discussion of dreams,altered states,and free will.We give explanations derived from the model and draw confirmation from consistencies at a high level well above the level of neurons with the psychology and neuroscience literature.This paper is intended to be an introduction to a much-expanded monograph,in preparation.Key words:feelings of consciousness,theoretical computer science,substrate independent model,computational model,global workspace,multi-modal,model of the world,phenomenal consciousness,the hard problem.The work of Lenore Blum and Manuel Blum was supported in part by CMU,in part by a sabbatical year from CMU at the Simons Institute for the Theory of Computing,and in part by a gift from UniDT.Email addresses:lblumcs.cmu.edu and mblumcs.cmu.edu.The definition of the Conscious Turing Machine(CTM)first appeared in(Blum&Blum,2021).To be self-contained,a streamlined version of the basic definition of the model is presented here as well as amplification of key components and arguments for the“feeling of consciousness”.The sections in this paper on Blindsight,Inattentive Blindness,Change Blindness,Illusions,Dream Creation,Free Will,and Altered States of Consciousness in the CTM are new.2022 Blum&Blum 2 Introduction:Why a Theoretical Computer Science Perspective?Thanks to major advances in cognitive neuroscience,humanity is now on the brink of understanding how the brain achieves consciousness.In 1988,cognitive neuroscientist Bernard Baars proposed a Global Workspace Theory(GWT)of the brain,sketched its architecture,and outlined its implications for understanding consciousness.See(Baars B.J.,1988)2 and(Baars B.J.,2019).That,together with the invention of fMRI in 1990,and the seminal investigations by Francis Crick and Christof Koch(Crick&Koch,1990)into the neural correlates of consciousness,helped shake off the taboo on the scientific study of consciousness.As a consequence,the quest to understand consciousness is now actively pursued by scientists of many stripes.3 We study consciousness from the perspective of Theoretical Computer Science(TCS),a branch of mathematics concerned with understanding the underlying principles of computation.4 These principles largely include the complexity of computation,which deals with the consequences and unexpected usefulness of taking resource limitations into account.This perspective has provided not only a theoretical foundation for the computer revolution but also surprising new concepts and ingenious applications stemming from considerations of computational complexity.TCS is our principal tool.We claim that its perspective and unique insights add to the understanding of consciousness and related concepts such as qualia and free will.Demonstrating this is a major goal of our work.With this in mind,we give a simple abstract substrate-independent computational model of consciousness that we call the Conscious Turing Machine(CTM)(see Chapter 10).The CTM is inspired by Alan Turings simple yet powerful model of computation,the Turing Machine(TM),by Bernard Baars GWT,and by the Global Neuronal Workspace Theory(GNWT)of(Dehaene&Changeux,2011)and(Mashour,Roelfsema,Changeux,&Dehaene,2020).We are not looking to model the brain or suggest neural correlates of consciousness however interesting that may be.We are looking to understand consciousness and how a machine might experience feelings.Our intent is to come to terms,eventually,with the hard problem(Chalmers,1995).Our view is that consciousness is a property of all properly organized computing systems,whether made of flesh and blood or metal and silicon.Confirmation for explanations from the CTM come from consistencies at a high level well above the level of 2 Baars GWT is strongly influence by earlier work in cognitive science,much of which was done at Carnegie Mellon:(Simon,1969),(Reddy,1976),(Newell,1990)and(Anderson,1996).3 The various approaches to the study of consciousness include psychological(James,1890)and(Freud S.,1900);philosophical(Dennett D.C.,1991)and(Chalmers,1996);information theoretic measures of consciousness(Tononi,2004)and(Tononi&Koch,2015);structural(Baddeley&Hitch,1974);and neural correlates(Dehaene&Changeux,2011).Our approach to consciousness is architectural.It is informed by and close in spirit to(Baars B.J.,1997)and(Dehaene S.,2014).The architectural approach to the study of consciousness was inspired by the architectural models of cognition.These were developed largely at Carnegie Mellon University by Herb Simons Sciences of the Artificial(Simon,1969),Raj Reddys Blackboard Model(Reddy,1976),Allen Newells Unified Theories of Cognition(Newell,1990),and John Andersons ACT-R(Anderson,1996).The global workspace idea is due to Newell.An important more recent architectural model of cognition is LIDA(Baars&Franklin,2009).4(Sipser,2013)is a great introduction to TCS.2022 Blum&Blum 3 neurons with the psychology and neuroscience literature,5 and from agreement with aspects of other theories of consciousness(see Chapter 5).In this introduction,we present a brief overview of TCS and CTM using popular terms as they are typically informally understood.The perspective on TCS includes an example of the relevant seemingly paradoxical concept of pseudo-randomness that got defined and understood by TCS.In those same terms,we outline some of our understanding of consciousness from the CTM.These informal definitions and understandings from CTM are formalized after this introduction.The reader who wants the formal treatment straightaway can skip from here directly to Chapter 10.What is Theoretical Computer Science(TCS)?Alan Turings seminal paper“On computable numbers”(Turing A.M.,1937)is arguably the genesis of TCS.That paper presents a formal mathematical definition of a“computing machine”,now known as the Turing Machine(TM).In it,Turing defines a simple theoretical universal programmable computer6 that can compute any function computable by any computer or supercomputer,though of course it looks nothing like any modern-day computing machine.It was not until a decade later that Turing wrote the specs for a possible implementation.7 Theorems are the raison dtre of mathematical theories,and Turing proved what might be called the first theorem of TCS,namely the unsolvability of the Halting Problem.In modern parlance,this theorem proves there can be no universal(debugger)program for determining which computer programs halt and which do not:it is just not possible to construct one.This result is equivalent to the undecidability of elementary number theory(Church,1936),and it implies a weak form of Kurt Gdels First Incompleteness Theorem(Gdel,1931).8 After Gdel and Turing,mathematical logicians started categorizing which problems were solvable,which not,as well as investigating the esoteric hierarchy of unsolvable problems.With the advent and wider availability of computing machines in the 1960s,it soon became clear that a number of important problems that were solvable in principle could not in fact be solved,not even with the fastest conceivable computers,and that this was not a problem with the state of technology but something deeper.9 5 We note a historical synergy between theoretical computer science and neuroscience.Turings simple computer model led neuroscientist Warren S.McCulloch and mathematician Walter Pitts to define their formal neuron,itself a simple model of a neuron(McCulloch&Pitts,1943).Mathematics forced their model to have inhibition,not just excitation-because without inhibition,(loop-free)circuits of formal neurons can only compute monotonic functions-and these do not suffice to build a universal Turing Machine.The McCulloch-Pitts neuron also gave rise to the mathematical formalization of neural nets(Wikipedia,2022)and subsequent deep learning algorithms(Goodfellow,Bengio,&Courville,2016),further illustrating ongoing synergies.6 In the mathematical tradition going back to Euclid,of formulating axioms(basic premises)and proving theorems(deriving consequences),Turing identified fundamental principles(the Turing Machine)that lead to unexpected consequences(universal Turing Machine,the halting problem,etc.)and a deep understanding of computation.Many other models of discrete computation such as the lambda calculus of Alonzo Church(Church,1936)give rise to the same set of computable functions.This gives credence to the Church-Turing thesis that no reasonable model of computation can compute more than what a Turing Machine can compute.(See(Yao,2003)for implications to classical physics.)7 Although Turings 1937 paper was strictly a paper in mathematical logic there were no computers at the time Turing did intend to construct a practical programmable computing machine.In 1945,he brought with him to the British National Physical Laboratory an 86-page detailed blueprint for an Automatic Computing Engine(ACE),a universal programable computer,which he intended to build(Turing A.M.,1945).Politics intervened and it was never built,only the less ambitious PILOT ACE(Hodges,1992).8 Before Gdel and Turing,mathematicians had the unshakable belief that with enough knowledge and work,any mathematical problem could be solved.As the mathematician David Hilbert famously said in 1930 at his retirement address(Dawson,1997):“This conviction of the solvability of every mathematical problem is a powerful incentive to the worker.We hear within us the perpetual call:There is the problem.Seek its solution.You can find it by pure reason,for in mathematics there is no ignorabimus sic.”9 Suppose that when program P is run on computer C,on any input of length n,it has run time 2n.Let C+be the same computer except that C+runs twice as fast as C.Then program P,run on computer C+,on any input of length n+1,will have run time 2n+1/2=2n,which is 2022 Blum&Blum 4 Researchers in the emerging field of theoretical computer science10 realized that among natural finite(and therefore solvable)problems there appeared to be a dichotomy between those problems that were feasibly(efficiently)solvable and those that were not,mirroring the earlier dichotomy between solvable and unsolvable.Feasibly solvable became formalized mathematically as solvable(by some computer program)in polynomial time(P).Furthermore,the realization emerged that problems solvable in polynomial time and problems checkable in polynomial time(NP)might not be equivalent.11 Indeed,deciding the equivalence(or not)would answer the famous million-dollar P=?NP question,see(Goldreich,2010).Besides defining a hierarchy of serial fast(poly time)computational complexity classes,TCS defines a hierarchy of parallel superfast(polylog time)computational complexity classes.Both hierarchies inform the definitions and choices employed in our model.Understanding the dichotomy between easy and hard,quick and slow,and their implications launched a complexity revolution with a rich theory,reframing of ideas,novel concepts and stunning applications.Indeed,developments in computational complexity over the past 40 years have shown how to use hardness to our advantage,to deal with seemingly impossible problems.This has created a paradigm shift in mathematics,namely the ability to exploit the hardness of some problems to resolve others.12 We illustrate with the(relevant)concept of a computer-generated random sequence,called a pseudo-random sequence.On the face of it,the very idea of a pseudo-random sequence is so incongruous that von Neumann joked(von Neumann,1951),“Anyone who considers arithmetical methods of producing random digits is,of course,in a state of sin.”More precisely,a pseudo-random sequence generator is a feasible(polynomial time)computer program for generating sequences that cannot be distinguished from truly random sequences(generated by independent tosses of a fair coin)by any feasible computer program.Thus,in the polynomial time world in which we live,pseudo-random sequences are,for all intents and purposes,truly random.13 This understanding was impossible without the clarifications made by TCS and the distinctions between polynomial and superpolynomial complexity.(See(Yao,1982)and(Yao,2003).)An application of the above ideas is to replace the use of random sequences in the Conscious Turing Machine(CTM)by sequences produced by pseudo-random generators supplied with(short)random seeds.In particular,the same running time as C on any input of length n.TCS considers the increased speed of C+(and therefore C+,C+,)over that of C to be insignificant for running P when n is large.10 Early researchers in computational complexity included Jack Edmonds(Edmonds,1965),Stephen Cook(Cook,1971),Richard Karp(Karp,1972),and Leonid Levin(Levin,1973).11 Solvable in polynomial time(P)means it is possible to find a solution in time polynomial in the size of the problem instance.Checkable in polynomial time(NP)means that given a purported solution,its correctness can be checked in time that is polynomial in the size of the problem instance.On the face of it,finding a solution seems harder than checking it.Properly coloring the nodes of a graph with 3 colors is hard(NP-hard so likely not in P),while checking if a 3-coloring is proper