Artificial Intelligence by Anthony J. Bell Essay
The second theme is based around the observation thata computer is an intrinsically dualistic entity, with its physical set-up designed so as not to interfere ith its logical set-up, which executes the computation. The brain Is dlierent. When analysed empirically at several dlierent levels (cellular, molecularl It appears that there Is no satisfactory way to separate a physical brain model (or algorithm, or representation), from a physical implementational substrate.
When program and implementation are inseparable and thus interfere with each other, a dualistic point- of-view is impossible. Forced by empiricism into a monistic perspective, the brainAmind appears as neither embodied by or embedded in physical reality, but rather as Identical to physical reality. This perspective has Implications for the future of science and society. I will approach these from a negative point-of-view, by critiquing some of our millennial culture’s popular projected futures.
Keywords: arti Ccial intelligence; neuroscience; cyclic systems; dualism; science Cction The ‘Net- heads’ will have been passed on the way by the ‘Worldbots’, digital mechanical life- forms which will Crst ease human life by performing all mundane tasks, but will shortly after become so much more intelligent than the unenhanced us that they will practically become ‘spiritual machines’, which may or may not use selCsh altruism to ecide to be benign towards the human animals. and If we are lucky. they will continue to serve us, something like digital Bodhisattvas.
Back in the cyberworld, boundaries between individuals will break down, and transhuman life-forms will appear, analogously to the emergence of multicellular life in the ocean. Implanted into robot spaceships, these life-forms will lumber into space like the Crst amphibious Csh lumbered onto the land. A long time after this, perhaps after a few galactic wars (In which the ‘ Dark Side’ may be brleEy Elrted with but not Joined foreverh the universe will be one huge Internet, matter everywhere drawn into the rocess of computational living. The extremum of this is called the Omega Point. A Cnal twist is that since the Omega Point does not join the Dark Side, again possibly using game theoretic reasoning, it will decide to be benign and resurrect everyone who ever lived and give them what they most desire. This is called the Judeo- Christian heaven by Tipler (1995). Other references used in constructing this version of future history are Gibson (1986), Moravec (1990) and Kurzweil (1999),) 1. INTRODUCTION In this paper I will survey the recent history, current status and future prospects of rtiCclal intelligence (A1) and neuroscience.
I will attempt to relate the social motivations and potential Impact of the Gelds concerned on society at large. 2. THE Formalities over, and given that the Millennium is a signiCcant enough social phenomenon that it colours popular impressions of the future of science, it is worth looking at what impressions a person of the year 2000 might have formed from late twentieth century popular science books, science Cction books and Clms, and even from the science pages of newspapers. Such a person might be forgiven for thinking that the future will be something like this.
Nano-robots will perform all molecular repairs in our bodies, making us eiectively immortal. Highly engineered drugs, perhaps the descendants of Prozac and Ecstasy, will take care of emotional disorders, as a side-eiect solving all social problems, so everyone will be happy (Cnally). That’s for the nostalgic minority who cling to living in the primitive biological form. More cyber-aware individuals will have downloaded themselves into the ‘Net’ and will exist like a William Gibson character in a global computer network which is capable of providing all protagonists with the most fantastic entertainment.
Many global problems will be solved with the demographic move to the ‘Net’, problems such as population, food, transportation and energy. Phil. T rans. R. Soc. Lond. B (1999) 354, 201 “2020 These amazing developments are the almost inevitable consequences of the merging of the digital and the organic worlds, on the threshold of which we are now standing. Cellphones and laptop computers are only the beginning. We might call this future the bio-informational age, in keeping with its millennial timing, and the smoothness with which it mixes in with elements of NewAge philosophy. 013 & 1999 The Royal Society 2014 A. J. sell Levels and loops: the future of artiCcial intelligence and neuroscience side is statistics and signal processing. This is perhaps what makes it such a great Geld to work in. Symbolic A1 was thus subverted by a shift to statistical learning theories. It was also subverted in two other directions by the emergence of the Gelds of artiCcial life (Langton 1997) and behaviour-based robotics (Arkin 1998) (or situated agents).
ArtiCcial life (or alife) is subsymbolic in that it implicitly assumes that intelligence is just the complex end of a simulatable life process. A living system and its environment are typically simulated together, often using genetic algorithms and population dynamics to simulate evolution. Behaviour-based robotics attempts bravely to deal with the perceptual-motor loop of a robot in a real environment, rejecting both the alife simulated worlds and the mainstream A1 notion of a representation of the world.
Echoing Gibson (1979) in his famous debate with Marr (1982) (Bruce & Green 1990), the ‘agents’-literature focuses on complex behaviour coming from simple mechanisms operating in tight coupling with a complex nvironment, in contrast to Marr’s emphasis on the feedforward computation of a structural foundation such as that given to neural networks and statistical machine learning by mathematics. This makes it hard to Judge progress or assess methodology in these Gelds.
However, on the other side, neural networks that learn both sensory perceptions and motor actions in an environment are extremely rare, and for a good reason: it is dizcult to build a statistical model of an environment when the system’s perceptions are transformed into actions that arct the statistics of the input. Furthermore, what should such an acting system do? There is an obvious goal for a feed-forward perceptual system: build a probability distribution of what happens.
The hidden symmetries (dependencies, redundancies) in this distribution are the hidden structure of the world. But in this cyclic case, when the world is at least partly constructed by the actions of the system, the shape of this distribution is action dependent ¶ the system gets to partly choose what symmetries exist, and the notion of a hidden set of privileged symmetries is under threat. This is post-modernism for statisticians.
At this point, most people would abandon informational, or unsupervised, goals and appeal to one of the many speciCc goals which a robot system might have, such as to Cnd food or recharge the batteries. While these are no doubt important, they do have an air of arbitrariness about them that makes us uneasy: we are familiar enough with the Eux of goals in our personal experiences to desire something more invariant to underly action selection. 5. QUESTIONS CURRENTLY LATENT IN ARTIFICIAL INTELLIGENCE 3. THE CURRENT JOB OF SCIENCE It’s a giddy picture indeed, but how much of it, if any, will come true ?
If none of it is going to happen, it would be very helpful if science could tell us why, so that we could get on with living our real future. The dizculty for science is that the prospect of a bioinformational future, with its cyborg, transpersonal themes causes us to ask questions concerning individuality, consciousness, mind and machine, exactly those questions which science has had least success in framing. A1 and neuroscience are the Gelds that come closest in engineering and biology to framing such questions.
Scratch the surface of many A1 researchers and neuroscientists (perhaps quite igorously) and you may Gnd someone who started Oi by asking ‘What are we The answers to this question are not that numerous. Either we are machines, in which case A1 should be possible and neuroscience should be able to work out the algorithm (or algorithms) that the brain is running, or we are something else, in which case both projects will fail in their ultimate goals, which is not to say they will not achieve great things along the way. One of the great things that they might achieve is an exact picture of their own limits. ) Either way, by examining the history nd current state of A1 and neuroscience and by identifying the issues beneath the surface of these Gelds, we may gather some sense of what are the important themes playing along science’s internal frontier (disregarding for now how diierent this frontier looks from outside). 4. HISTORY AND STATE OF ARTIFICIAL INTELLIGENCE A1’s ultimate purpose is to build a robot that lives in the world with a computer for a be captured in digital computation.
The Crst attempts to produce A1 in the 1960s involved writing facts and rules into the machine using various quasi-logical languages. In the 1980s this became less popular. Rule-based systems were seen as non-robust: they could not adapt well to small changes in circumstances. Also, every fact had to be programmed in by a human. This led people to think that real- numbered, ‘subsymbolic’ systems were needed, and these systems had to be able to learn facts (or learn something) themselves, Just by observing data. Historically, this view carried within it the cybernetics view of the 1950s.
It was one short step from this shift to statistical theories. The short step was called neural networks (Haykin 999); it started in 1984 (Rummelhart & McClelland 1986) and it is not over yet. An interdisciplinary Geld with a higher than average tolerance for speculation and free- wheeling enquiry, neural networks were popular with students and military funders, and often regarded with frustration by other disciplines that shared a border. As the Geld became more rigorous, it reestablished its connections with mainstream A1, through common interests in statistical machine learning.
T echnically speaking, the Geld of neural networks is contentless. The empirical side is neuroscience; the theoretical Phil. T rans. R. Soc. Lond. B (1999) Here we have identiCed two questions which lie beneath the surface of the pluralistic A1 of today. The Crst question, to rephrase, asks why we do not have a mathematical theory of the perceptionAaction cycle. Of course there is work on active perception, on sensorpmotor coordinate systems, and engineering Levels and loops: the future of artiCcial intelligence and neuroscience A. J. Bell department robotics is full of mathematics.
But the kind of theory I mean is one that is as universally useful for characterizing cyclic systems as Shannon’s information heory is for characterizing communications channels, i. e. feed-forward systems). (Incidentally, maximizing the channel capacity involves Cnding those hidden symmetries we mentioned that exist in the probability distribution of the input. This forms the basic goal of my own favoured area of neural networks¶unsupervised learning (Hinton & SeJnowski 1999). ) Implicit in this is the second question. What would we want such a post-Shannon system to do?
What quantity should a perceptionAaction cycle system maximize, as a feed-forward channel might maximize its capacity? A third question was directed at A1 researchers by Penrose (1989), and by the hostility and controversy it caused, you knew he had hit a weak spot in A1. Penrose wondered if the fact that the physical substrate of the world, of which relativity and quantum mechanics are our best accounts, might be suzciently diierent from the digital substrate of computers that it would render A1 impossible. Is there something in the quantum that is necessary for mind?
Scozng A1-philosophers characterized Penrose’s position as ‘we dont understand quantum mechanics and we don’t understand consciousness, so they must be the same thing’. The derision increased when Penrose, to make his hypothesis more speciCc, proposed, with Stuart Hameroi, that quantum consciousness manifests itself through coherent quantum eiects in a network of proteins called microtubules which form the structural skeleton proposals (which are not crucial to his argument), may miss the validity of Penrose’s general doubt about the computer: that it is a particularly unusual artifact, being deterministic, discrete time and discrete state.
The whole state of the machine at the digital level may be written down. No natural objects seem to be of this nature. The omputer is really a physical instantiation of a model. We know a model can compute, but can it live or think ? Functionalism (the philosophy of A1) was based on using the computer metaphor for mind, arguing that the brain was the hardware implementation of the ‘mental program’. But Penrose’s arguments were really designed to raise doubts about this separation of physical and mental processes. Could the brain be separated from a supposedly Cnitely describable mental process running on ” it ?
Since Rene Descartes, the conceptual separation has been there in our language, but is it scientiCcally really there? Either there is a physical level at which the separation can be performed (analogous to the level of logic gates in computers) or functionalists have to admit that the brain is not a machine. But the failure to detecta ‘logic gate level’ halfway up the brain’s reductionist hierarchy may not be the end of the argument for the functionalist, who could still argue that if there is a computer at the bottom, A1 would be possible, at the very least with a computer with the resources of the universe.
The ‘universe-ascomputer’ is a popular fringe-topic in physics, lying behind an eiort to Cnd a Cnite discrete process such as a ellular automaton that might underly the known laws of Phil. T rans. R. Soc. Lond. B (1999) 2015 physics. But until someone succeeds in showing this, we might be wiser to stick with R. F. Feynman, who noted that quantum processes are not in general simulatable, even by Turing machines (and who in the process gave rise to the mysterious and unformed Geld known today as quantum computing). The luck (or skill) of scientists is that sometimes they do not have to philosophize to Cnd the answer.
They can ask questions of Nature directly. So perhaps this is a good point to survey the history and urrent state of neuroscience, because this is the discipline whose empirical project is exactly the Cnite description of brain processes. 6. HISTORY AND STATE OF NEUROSCIENCE The early landmarks in post-war neuroscience were the Nobel prize winning work of Hubel & Wiesel (1968) for their studies of the receptive Gelds of monkey visual cortical cells, and that of Hodgkin & Huxley (1952) for their uncovering of the mechanism and mathematics of spiking in neurons.
It has grown into a huge Geld with the annual Society of Neurosciences meeting in the USA attracting 30 000 people. The two early Nobel prizes refect perhaps a natural split in the Geld between those working above or below the level of the cell. Many of the great successes of the 1970s and 1980s were at the subcellular level, as the molecular biology revolution progressed, and as a result this part of neurobiology was highly empirical and essentially continuous with mainstream cellular, molecular and developmental biology. In this period, the uncovered.
A bewildering array of ion channels, neurotransmitters and neuromodulators were found to be engaged in the processes of sculpting neural response properties and controlling communication between neurons. From the chemistry of photon absorption by photoreceptors, to the chemistry of muscle contraction, the nervous system apparently performed an astonishingly complicated and coordinated series of molecular actions not qualitatively diierent from those in other living cells, but somehow in the brain this molecular dance constituted percept, thought and action.
At and above the level of the spiking neuron, things were slightly diierent. Lacking the formal structural basis of molecular biology, neuron-level neuroscience focused on the spike trains as signals representing neural information. The discreteness of the spike as an information-carrying unit was matched in biology only by the genetic code. This led to early attempts to characterize the ‘neural code’, attempts that were revived by Bialek and co-workers in the 1990s (Rieke et al. 1997). Notably, inevitably, these eiorts attempt to characterize neurons as feed-forward information channels. ) Behind these eiorts is a faith in the neuron level, certainly as a useful descriptive level, but also as a ‘computing level’ which molecular and biophysical processes exist to implement. Does the goop that we see in the electron icrographs merely exist to implement ‘the spiking computer’? This is the neuroscience analogue of the functionalist debate in A1, and I will return to it in h 7(c), after addressing the issue of cycles in neuroscience. 016 Levels and loops: the future of artiCcial intelligence and neuroscience we may measure their Joint probability distribution p(X, Y), and we could do so by observing X and Y under normal operating conditions, observing a peak in the distribution at equilibrium, and some trajectories corresponding to the stereotypical dynamics of the variables. But in trying to estimate whether X controls Y, experiments often take he form of measuring the conditional distribution p(YJX) and constructing the Joint distribution through the formula p(X, Y) 0 p(YJX)p(X).
This latter strategy gives the wrong answer for p(X, Y) because (i) rather than the system controlling p(X), we are controlling it, thus cutting the system at X, and we have, through our choice of independent and dependent variables, imposed on the system a direction (X ! Y) of dependency, with an implied direction of causality that does not exist in nature. There is no doubt that such experiments can still be useful in teasing out dynamic cyclic behaviour.
The kinetics of ion channels can be identiCed with the aid of voltage and current clamping techniques, but there is a recognition in such experiments that the clamped cell is a frozen picture of the true process. This recognition often seems to go missing as the feedback loops get wider ( ‘out of sight, out of mind’) and particularly as biology becomes technology. Examples that spring to mind are the widespread prescription of drugs that combat depression by controlling seratonin levels, or attempts to control ecosystems by introducing new species, or, for that industrial model of agriculture.
Anyone seriously studying or modelling metabolism or ecosystems knows the extent to which they are dealing with cycles, but somehow, when the results reach into the area of medicine or its macroscopic equivalent ‘ planet management’, the causal, feed-forward style of thinking is what is presented, particularly to the news media and commercial interests. Anything which does not Ct the feed-forward model is linguistically demoted to the status ofa ‘side-eiect’, to be eliminated if possible. But sideeiects are nature’s way of telling the scientist that all processes are cyclic.
I cannot resist, at this point, discussing the role of biology’s master control node, the genome. Although it is somewhat Oi the subject of A1 and neuroscience, arguments pointing back to the genome as the causal factor behind animal behaviour and intelligence are so universal in our culture, that to allow the genome special status outside feedback cycles would be to endorse a control-node mysticism rivalled in shape and form only by that of the monotheistic Anglican bishops who debated so famously with T. H. Huxley. When science became a greater authority on human origins than the church, the transition hid the fact that it was a hange of government without a change in policy. Furthermore, aiording the genome special status allows the present-day church of evolutionary psychology to rampage unchecked and, in my opinion, the wrong lessons are then drawn from biology. ) The genome’s grand cycle with other genomes, mediated through populations of phenotypes is the king of all biological feedback loops. It is a trans-individual (b) Interlude: biology’s master control node 7.
QUESTIONS CURRENTLY LATENT IN NEUROSCIENCE The same problem with cycles presents itself in neuroscience as in A1, but whereas he primary cycle of concern in A1 was the perceptionAaction cycle, in neuroscience, the cycles are everywhere. It is interesting that the clearest stories in neuroscience are those which at Crst glance most closely resemble feedforward systems. One example is the synapse. The spike arrives at the presynaptic bouton, causing vesicles of neurotransmitter to be released, which in turn cause ion channels in the postsynaptic site to open and change the postsynaptic electrical potential.
Another example is the early visual system, starting with the retina and moving through thalamus into early visual cortex. The treatment of this system as a feed-forward channel, despite massive corticothalamic and corticocortical feedback, has enabled information theoretic learning models the modest success of producing qualitatively correct predictions for the form of the static (Bell & SeJnowski 1997) and dynamic (Van Hateren & Van der Schaaf 1998) cortical receptive Gelds that were Crst observed by Hubel & Wiesel (1968).
However, feed-forward processing in the nervous system is the exception rather than the rule, and often what looks feed-forward contains complicated feedback systems at a diierent level of analysis. For example, the spikes of a cortical neuron have now been seen to extend far into the dendritic tree, aiecting, through voltagedependent channels, the integration of signals from synapses. This destroys the illusion that the neuron works like a directional ‘neural network’ neuron, performing a weighted sum of its input signals.
Even in the synapse inputs from the brain, the brain controls gaze direction which determines what the retina sees. Although neurotransmitter does not travel backwards across synapses in most neurons, many other molecular signals do, as the extensive and controversial ttempts to Cnd synaptic Hebbian learning mechanisms in long-term potentiation have revealed. In abstract, the lack of a theory of cycles in biology can be seen by considering an experiment in which some variable X is changed and some other variable Y is monitored. What is published are the relatively rare cases where some correlation in X and Y is observed.
The temptation then is to say that ‘X controls Y’ and from this to build a model of feed-forward neural information processing (or if X is a chemical, we may market it as a drug to control Y). In nature, things happen diierently from in the experiment. X may rise, causing Y to rise, but then increased Y usually causes X to diminish, directly or through some other variables Z. These cycles of positive and negative feedback are universal in biology and cause equilibrium values of X and Y, or stereotypical dynamic behaviour to occur.
A neural spike is one example of a transient dynamic caused by positive and negative feedback, where X is the sodium current and Y the potassium current. Slipping into the language of probability theory, if we desire to discover the relationship in nature, of X and Y, Phil. T rans. R. soc. Lond. B (1999) a) Cycles in neuroscience molecular regulation loop, qualitatively similar to those occurring within cells, with cooperation (or symbiosis; Margulis & Sagan 1995) corresponding to the positive feedback loop and competition for resources corresponding to the negative feedback loop.
Neo-Darwinists, stuck on the negative pole, like to interpret cooperative behaviour as ‘selCsh’ altruism (I’ll scratch your back if you scratch mine). The inverse position, on the positive pole, is to interpret competition for resources as selEess greediness (I’ll eat you, but honestly, this is not about me). Y might consider both positions absurd, or you ou might use the latter point of view as an antidote to the dominance of the former in our culture.
The point here is that competition and cooperation have equal status and the process of ‘natural selection’ in which we are judged by an external environment (more biblical parallels) is better viewed as a complex molecular regulation loop like any other. The regulation loop is mediated through phenotypic success, which brings up another loop-denying habit of neo- Darwinists, which is to see the genome as a controller for all aspects of the henotype, right down to its speciCc behaviour: DNA as the determining code for an organism.
There must be a particular attraction in this idea for certain authors, because they take great pleasure in outraging people’s common sense by portraying organisms as the helpless puppets of their genes (Dawkins 1990). I will not duplicate the eiort of the many authors who have attacked the social or behavioural versions of this notion (for example, the preposterous notion that there could be a gene for homelessness, which was actually considered in an editorial in Science), because this would be to attack it at its weakest point. I’d like to attack the notion in its strongest proteins, and not the other way round’.
The central dogma of molecular biology is wrong! Sequences of DNA code for strings of amino acids ¶ true ¶ but how these amino acids are assembled into functioning proteins and which parts of the DNA are read in the Crst place are both controlled by proteins, and depend on the state of the cell and its type. It’s as if there was a bookish town (a cell) with a central library (the genome) and people (proteins) who came in to read short sections here and there, share with each other what they had read, and use the knowledge to build and hange the town. Who is controlling here ¶ the townsfolk or the library? Answer: neither. ) Where did the people in the town come from? If ‘genes make proteins’, then the library made them, but the truth is that they were there all along. The functioning networks of enzymes that set to work on your DNA when you were conceived were already in place in the salty water of your mother’s egg cell. They were Just the latest instalment in a continuous epigenetic lineage that stretches back to your primordial metabolic ancestor, a droplet of seawater that accidentally got stuck inside a lipid embrane with a fortuitous set of amino acids.
It is harder to make more unsubstantiated assertions in biology than in the area known as ‘origin of life’. But if the ‘genes makes proteins’ debate really comes down to whether there was RNA (code) before proteins Phil. T rans. R. Soc. Lond. B (1999) 2017 (metabolism) or proteins before RNA in the Crst protocells (De Duve 1991), then two factors should be considered: (i) amino-acid chains form much more readily than nucleic-acid chains, and (it) it is more likely that the Crst people wrote the Crst books, than that the Crst books wrote the Crst people.
It is noteworthy that both neoDarwinists and New T estament theologians believe that ‘in the beginning was the word (logos)’. ) Of course, now it is claimed there were ribozymes (RNA with the ability to catalyse reactions), but was this metabolism evolving a code, or a code evolving metabolism? The outcome of this debate is not crucial. The intent here is merely to weaken the notion of DNA as a kind of controller of the phenotype. An equally valid (and equally invalid) perspective has the phenotype choosing what is read from the gene and what is done with it.
In reality, the organism and its genes re caught in a cyclic dynamic, and if the organism decides to spend its afternoon in a (real) library, instead of attempting to father children, then you can be sure that the pattern of gene expression will alter accordingly. This argument Cts with our Crst general theme of critiquing feed-forward thinking in A1 and neuroscience. Returning now to the second theme we touched on when discussing A1, h 5 ended with a consideration of levels of a system and functionalism.
There was a challenge to the functionalist to empirically investigate the brain and identify a level at which the rain could be Cnitely ‘written down’, a level analogous to logic gates in computers. The obvious candidate is the neuron level. If we wrote down the sequence of all spikes of all neurons, would that be enough to specify the ‘neural computation’? Do molecular and biophysical processes exist to implement a ‘spiking computer’ at the neuron level ? I believe the answer to these questions is no.
While no speciCc operation of the computer (unless something goes wrong), this cannot be said at the neuron level of the brain. Molecular and biophysical processes control the sensitivity f neurons to incoming spikes (both synaptic ezciency and postsynaptic responsivity), the excitability of the neuron to produce spikes, the patterns of spikes it can produce and the likelihood of new synapses forming (dynamic rewiring), to list only four of the most obvious interferences from the subneural level.
Furthermore, transneural volume eiects such as local electric Gelds and the transmembrane diiusion of nitric oxide have been seen to inEuence, respectively, coherent neural Cring, and the delivery of energy (blood Eow) to cells, the latter of which directly correlates with eural activity. The list could go on. I believe that anyone who seriously studies neuromodulators, ion channels or synaptic mechanism and is honest, would have to reject the neuron level as a separate computing level, even while Cnding it to be a useful descriptive level.
Perhaps a physicist or a neural-network theorist, in looking for an easy theory, would still argue that the molecular level is mere implementational detail, but in most cases this is more a result of prejudice, supported by laziness and ignorance. If the molecular level is unimportant for an (c) Levels in neuroscience 2018 Levels and loops: the future of artiCcial intelligence and neuroscience nature may be diierent. In fact, it is. There are submolecular interferences that violate the separateness of the ‘molecular machine’ level, and they are quantum eiects.
Two examples of this are electron transfer in photosynthesis and the energetics of enzyme interactions (Welch 1986). In both cases, quantum coherences are necessary to explain the ezciency of the reactions. But we don’t even need to go as far down as quantum eiects, because proteins do not end at the edges of the black and red balls of which ball-and-stick molecular models are constructed. Their electrical Gelds extend into the surrounding water molecules, orientating them to form what is called structured water. Structured water is also important in determining how enzyme reactions occur, and how ion channels are selective to certain ions.
T argue that one piece of structured water or one o quantum coherence is a necessary detail in the functional description of the brain would clearly be ludicrous. But if, in every cell, molecules derive systematic functionality from these submolecular processes, if these processes are used all the time, all over the brain, to reEect, record and ropagate spatio-temporal correlations of molecular Euctuations, to enhance or diminish the probabilities and speciCcities of reactions, then we have a situation qualitatively diierent from the logic gate.
The variables lying beneath the level of a molecular ‘gate’ can arct the behaviour of the gate, so the functionalist is again frustrated, and the notion of the brain as a molecular ‘computer’ can be viewed as no more than an analogy, and an inaccurate one.