Biology and Computation: A Physicists Choice (Advanced Series in Neuroscience, Vol. 3)
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Obeying the instructions requires no special ingenuity or creativity. For example, the familiar grade-school algorithms describe how to compute addition, multiplication, and division. Until the early twentieth century, mathematicians relied upon informal notions of computation and algorithm without attempting anything like a formal analysis. Developments in the foundations of mathematics eventually impelled logicians to pursue a more systematic treatment. A Turing machine is an abstract model of an idealized computing device with unlimited time and storage space at its disposal.
The device manipulates symbols , much as a human computing agent manipulates pencil marks on paper during arithmetical computation. Turing says very little about the nature of symbols. He assumes that primitive symbols are drawn from a finite alphabet. Turing translates this informal description into a rigorous mathematical model. For more details, see the entry on Turing machines. Turing motivates his approach by reflecting on idealized human computing agents. Citing finitary limits on our perceptual and cognitive apparatus, he argues that any symbolic algorithm executed by a human can be replicated by a suitable Turing machine.
He concludes that the Turing machine formalism, despite its extreme simplicity, is powerful enough to capture all humanly executable mechanical procedures over symbolic configurations. Subsequent discussants have almost universally agreed. Turing computation is often described as digital rather than analog. What this means is not always so clear, but the basic idea is usually that computation operates over discrete configurations. By comparison, many historically important algorithms operate over continuously variable configurations. For example, Euclidean geometry assigns a large role to ruler-and-compass constructions , which manipulate geometric shapes.
For any shape, one can find another that differs to an arbitrarily small extent. Symbolic configurations manipulated by a Turing machine do not differ to arbitrarily small extent. Turing machines operate over discrete strings of elements digits drawn from a finite alphabet. One recurring controversy concerns whether the digital paradigm is well-suited to model mental activity or whether an analog paradigm would instead be more fitting MacLennan ; Piccinini and Bahar Besides introducing Turing machines, Turing proved several seminal mathematical results involving them.
In particular, he proved the existence of a universal Turing machine UTM. In that sense, the UTM is a programmable general purpose computer. To a first approximation, all personal computers are also general purpose: they can mimic any Turing machine, when suitably programmed. The main caveat is that physical computers have finite memory, whereas a Turing machine has unlimited memory. More accurately, then, a personal computer can mimic any Turing machine until it exhausts its limited memory supply.
As we know, computer scientists can now build extremely sophisticated computing machines. Rapid progress in computer science prompted many, including Turing, to contemplate whether we could build a computer capable of thought. More precisely, it aims to construct computing machines that execute core mental tasks such as reasoning, decision-making, problem solving, and so on.
During the s and s, this goal came to seem increasingly realistic Haugeland Early AI research emphasized logic. A famous example was the Logic Theorist computer program Newell and Simon , which proved 38 of the first 52 theorems from Principia Mathematica Whitehead and Russell Early success of this kind stimulated enormous interest inside and outside the academy.
Many researchers predicted that intelligent machines were only a few years away. Obviously, these predictions have not been fulfilled. Intelligent robots do not yet walk among us. Even relatively low-level mental processes such as perception vastly exceed the capacities of current computer programs. Nevertheless, the decades have witnessed gradual progress.
Another major success was the driverless car Stanley Thrun, Montemerlo, Dahlkamp, et al. A less flashy success story is the vast improvement in speech recognition algorithms. One problem that dogged early work in AI is uncertainty. Nearly all reasoning and decision-making operates under conditions of uncertainty.
For example, you may need to decide whether to go on a picnic while being uncertain whether it will rain. Bayesian decision theory is the standard mathematical model of decision-making under uncertainty. Uncertainty is codified through probability. Precise rules dictate how to update probabilities in light of new evidence and how to select actions in light of probabilities and utilities. In the s and s, technological and conceptual developments enabled efficient computer programs that implement or approximate Bayesian inference in realistic scenarios. An explosion of Bayesian AI ensued Thrun, Burgard, and Fox , including the aforementioned advances in speech recognition and driverless vehicles.
Tractable algorithms that handle uncertainty are a major achievement of contemporary AI, and possibly a harbinger of more impressive future progress. Some philosophers insist that computers, no matter how sophisticated they become, will at best mimic rather than replicate thought.
A computer simulation of the weather does not really rain. A computer simulation of flight does not really fly. Even if a computing system could simulate mental activity, why suspect that it would constitute the genuine article? Turing anticipated these worries and tried to defuse them. He proposed a scenario, now called the Turing Test , where one evaluates whether an unseen interlocutor is a computer or a human. A computer passes the Turing test if one cannot determine that it is a computer.
Ned Block offers an influential critique. He argues that certain possible machines pass the Turing test even though these machines do not come close to genuine thought or intelligence. For more on AI, see the entry logic and artificial intelligence. For much more detail, see Russell and Norvig Warren McCulloch and Walter Pitts first suggested that something resembling the Turing machine might provide a good model for the mind.
In the s, Turing computation became central to the emerging interdisciplinary initiative cognitive science , which studies the mind by drawing upon psychology, computer science especially AI , linguistics, philosophy, economics especially game theory and behavioral economics , anthropology, and neuroscience.
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The label classical computational theory of mind which we will abbreviate as CCTM is now fairly standard. According to CCTM, the mind is a computational system similar in important respects to a Turing machine, and core mental processes e.
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These formulations are imprecise. CCTM is best seen as a family of views, rather than a single well-defined view. This description is doubly misleading.
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As Chalmers also notes, one need not claim that the mind is programmable simply because one regards it as a Turing-style computational system. Most Turing machines are not programmable. The point here is not just terminological. Since classical computationalists need not claim and usually do not claim that the mind is a programmable general purpose computer, the objection is misdirected. Second, CCTM is not intended metaphorically.
CCTM does not simply hold that the mind is like a computing system. CCTM holds that the mind literally is a computing system. Of course, the most familiar artificial computing systems are made from silicon chips or similar materials, whereas the human body is made from flesh and blood. But CCTM holds that this difference disguises a more fundamental similarity, which we can capture through a Turing-style computational model.
In offering such a model, we prescind from physical details. We attain an abstract computational description that could be physically implemented in diverse ways e. CCTM holds that a suitable abstract computational model offers a literally true description of core mental processes. The formalism seems too restrictive in several ways:. He contrasted his position with logical behaviorism and type-identity theory.
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Each position purports to reveal the nature of mental states, including propositional attitudes e. According to logical behaviorism, mental states are behavioral dispositions.
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According to type-identity theory, mental states are brain states. Putnam advances an opposing functionalist view, on which mental states are functional states. According to functionalism, a system has a mind when the system has a suitable functional organization. Each mental state is individuated by its interactions with sensory input, motor output, and other mental states.
Putnam defends a brand of functionalism now called machine functionalism. He emphasizes probabilistic automata , which are similar to Turing machines except that transitions between computational states are stochastic. The machine table specifies an appropriate functional organization, and it also specifies the role that individual mental states play within that functional organization. Machine functionalism faces several problems. One problem, highlighted by Ned Block and Jerry Fodor , concerns the productivity of thought.
A normal human can entertain a potential infinity of propositions.
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Machine functionalism identifies mental states with machine states of a probabilistic automaton. Since there are only finitely many machine states, there are not enough machine states to pair one-one with possible mental states of a normal human. Of course, an actual human will only ever entertain finitely many propositions. However, Block and Fodor contend that this limitation reflects limits on lifespan and memory, rather than say some psychological law that restricts the class of humanly entertainable propositions.