Highlights
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Everyone has a basic understanding of how the physical world works. We learn about physics and chemistry in school, letting us explain the world around us in terms of concepts like force, acceleration, and gravity—the Laws of Nature. But we don’t have the same fluency with the concepts needed to understand the world inside us—the Laws of Thought.
El psicoanálisis tiene bastante bagaje al respecto.
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The first success in using mathematics to analyze thought wouldn’t appear until the middle of the nineteenth century, when George Boole cracked the problem that Leibniz hadn’t been able to solve by coming up with a new kind of algebra. That first success had far-reaching consequences, leading to the development of formal logic and computers. The first attempts to evaluate mathematical theories of thought by comparing them to human behavior wouldn’t appear until the middle of the twentieth century, in the Cognitive Revolution that launched the field of cognitive science—the interdisciplinary science of the mind. Cognitive scientists have since come to recognize the limits of formal logic as a model of human cognition, and have developed completely new mathematical approaches—artificial neural networks, which illustrate the power of continuous representations and statistical learning, and Bayesian models, which reveal how to capture prior knowledge and deal with uncertainty. Each has something to offer for understanding the mind.
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Cognitive scientists still don’t agree on how the mind works. Instead, we have developed a set of theoretical frameworks that each capture important parts of human cognition. However, over the last few years the insights offered by these different frameworks have begun to converge on a more complete picture. After three hundred years of effort, we may finally be able to sketch out the Laws of Thought.
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Cognitive scientists face a unique problem: How can we apply the methods of science to thought, something that we can’t see or touch? Psychologists in the first half of the twentieth century had a solution to this problem: We don’t. Instead, we apply the methods of science to what we can see and touch, namely external behaviors and the environmental stimuli that produce them. The dominant theoretical position, behaviorism, was that a rigorous science of the mind shouldn’t mention the mind at all.
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Artificial neural networks combine continuous representations with powerful general-purpose methods for learning from data. This approach could capture many of the regularities that had led people to favor rule-based accounts of language, without needing to postulate that people use explicit rules. It also solved the problem of learning: Provided with enough data, a neural network could potentially learn to do anything.
Redes neuronales artificiales como alternativa a una visión cognitivista basada en la lógica.
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The weakness of artificial neural networks is that the power to learn anything comes at a cost: Learning can require a significant amount of data. By contrast, learning from small amounts of data is one of the key characteristics of human intelligence: A child can learn a new word after hearing it used just once. Bayesian models of cognition, our third theoretical framework, offer a way to understand this.
Modelo Bayesianos ofrecen un framework para explicar la eficiencia del aprendizaje humano.
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These three frameworks—rules and symbols, neural networks, and Bayesian models—offer complementary perspectives on the mind. Each framework highlights a different kind of mathematics that is ultimately going to be critical to understanding the Laws of Thought.
Hay gente en el mundo psicoanalítico que esté actualizando los modelos de la disciplina en función del segundo y tercer framework?
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one of the major theoretical approaches in cognitive science: trying to explain the mind as a system of rules and symbols.
Cognitivismo clásico
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Descartes, Wilkins, and Leibniz proposed ideas that we will see being repeatedly reinvented in the following pages, such as assigning numbers to concepts and organizing those concepts into hierarchies. But more fundamentally, they were suggesting that a mysterious process—thought—could be reduced to a more familiar one—arithmetic. In doing so, they were arguing that the mind can be understood as what modern cognitive scientists would call a “formal system.” A formal system is simply a more precise way to specify what we might intuitively describe as a system of rules and symbols. To use a popular definition, a formal system has three properties: It is a token manipulation system, it is digital, and it is medium independent. Even though this might sound fairly abstract, I am willing to bet that you are intimately familiar with a variety of formal systems. In fact, if you have ever played a board game, you have interacted with a formal system. A token manipulation system can be described using three things: a set of tokens, initial positions for those tokens, and a set of rules that indicates how the tokens can be manipulated. That’s basically just the rules of a board game.
Sistema formal, tal como es entendido desde la psicología cognitiva.
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A lot of what we do in science involves establishing correspondences between particular formal systems and the world around us. For example, Newton’s physics was successful because it created a new link between the formal system of Euclidean geometry and the behavior of objects like planets and comets. In your calculus class, x is just a token to be manipulated. But when you go down the hall for your physics class, x becomes a symbol denoting the location of a planet.
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This is what is exciting about logic: It reduces a semantic question, about what is true in the world we live in, to a syntactic procedure, defined purely by the formulas we use to describe that world. Just as Descartes and Leibniz had imagined, we can use a formal system—a token manipulation system—to determine what to believe. Identifying the truth or falsehood of a statement is just a matter of following the rules of a game, where the pieces are P, Q, ˄, ˅, and so on, and the moves involve applying inference rules like modus ponens.
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As I mentioned in the introduction, psychology is an unusual science in that its subject can neither be seen nor touched. Physics deals with things that are very far away or very small, but we can still see them using telescopes and microscopes and touch them with space probes and particle accelerators. No matter how good our telescopes and particle accelerators get, they will never let us see a thought or touch a feeling. The first psychologists got around this problem by measuring behavior—the downstream consequence of thoughts and feelings—and then making inferences back to the thoughts and feelings behind it. For example, Wilhelm Wundt studied how long it takes people to react to sounds, with the goal of measuring how information is transmitted through the nervous system. An experimental participant would sit in a quiet room in front of a special device with a button on it. An electrical signal would trigger a sound and start a timer, which would be stopped by the participant pushing the button. Using this device, reaction time—the time between the sound and the button press—could be measured very precisely.
La psicología no tiene biomarcadores.
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Making inferences about consciousness and attention from how long it takes people to push a button after hearing a sound might seem like a stretch. To some psychologists, concerned about the scientific rigor of their discipline, it was a stretch too far. This was the start of the behaviorist movement, founded on the idea that the subject of psychology should be just those things we can see and touch: the environments that people occupy and the behaviors they produce. Some behaviorists would go even farther, seeing consciousness and attention not just as troublesome concepts to be eliminated from scientific discourse but as illusions that would be replaced by a more complete understanding of psychology.
conductismo
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Psychology as the behaviorist views it is a purely objective experimental branch of natural science. Its theoretical goal is the prediction and control of behavior. Introspection forms no essential part of its methods, nor is the scientific value of its data dependent upon the readiness with which they lend themselves to interpretation in terms of consciousness. The behaviorist, in his efforts to get a unitary scheme of animal response, recognizes no dividing line between man and brute. The behavior of man, with all of its refinement and complexity, forms only a part of the behaviorist’s total scheme of investigation.
conductismo cita de Watson en Columbia 1913
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Skinner’s primary subject was animal behavior, and in particular the study of learning. Skinner made breakthroughs in the methods used to study animals. For example, he helped to standardize studies of learning by developing the “operant conditioning chamber”—later dubbed the “Skinner box”—a carefully designed cage in which animals could perform behaviors and receive rewards or punishments. Using these methods, he launched a detailed study of operant conditioning, in which animals learn to produce a behavior in order to receive a reward or avoid a punishment, developing techniques that are still used to train animals today.
condicionamiento operante No sabía que Skinner mismo había desarrollado el paradigma experimental.
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Skinner also introduced the idea of radical behaviorism, which aims to extend behaviorism to the world of thoughts and feelings. Watson denied that thoughts and feelings need to be a part of psychology, but Skinner acknowledged their existence. He just believed that thoughts and feelings should never be used to explain behavior. Rather, thoughts and feelings should be considered a kind of behavior that could itself be explained. And those explanations should appeal to the same basic principles of learning that we use to explain other kinds of behavior in animals.
Skinner pensaba que los pensamientos podian ser explicados bajo los mismos principios que la conducta. No sabía esto. Lo pone en una posición más compatible con el cognitivismo.
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At the heart of this study, and a series of others conducted by Bruner and his colleagues in the late 1940s, was the radical idea that not everybody experiences the environment in the same way. That’s a challenge for behaviorism, as it means that our perception of the stimuli to which we respond might differ in ways that cannot be measured externally.
El conductismo supone y requiere que los aparatos perceptuales de las personas sean homogables, porque si no el condicionamiento depende de factores que no se puede medir.
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But as much as literature could reveal the richness of internal experience, it didn’t solve the fundamental problem posed by the behaviorists: developing a scientifically sound way of studying the mind. For that, Bruner would require a different muse. He found one in the form of John von Neumann, a mathematician who was creating a thinking machine.
Los comienzos del cognitivismo se nutren del encuentro entre la subjetividad y las máquinas pensantes.
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This idea—the universal machine, changing its behavior when provided with different instructions—lays the foundation for all of computer science. It’s the distinction between hardware and software, the physical substrate on which a program runs and the program itself.
Fundamento de las computadoras y diferencia entre hardware y software. .nota Máquina de Turing
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Shannon had taken a class in mathematical logic at the University of Michigan. He spent the summer after his first year at MIT visiting the Bell Telephone Laboratories in New Jersey. While he was there he began to realize that there might be a connection between switching circuits and logic: A switch is either on or off. A proposition is either true or false. Perhaps there was a way to build circuits that corresponded to logical formulas? Shannon discovered a way to wire up circuits that corresponded to the basic components of propositional logic. Imagine the simplest possible circuit—a lamp connected to a battery. The current flows to the lamp along one wire, with a second wire from the lamp back to the battery completing the circuit. The lamp won’t light up if either wire is cut. Inserting a switch along one of the wires is a way to cut and reconnect that wire as needed. When the switch is in the “on” position, the lamp lights. When it is in the “off” position, it stays dark. Now imagine inserting a second switch along the same wire. What happens? In order for the lamp to light, both connections need to be made. Both switches need to be in the “on” position. If either of them is “off,” the circuit is not completed and the lamp doesn’t light.
Shannon fue el primero que hizo esta relación entre números binarios y lógica Booleana?
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If we replace the lamp in our logical circuits with a relay switch, we can begin building more complex circuits. If the original switches represent P and Q, the relay switch represents P ˄ Q or P ˅ Q, depending on whether the original switches are in series or parallel. Using the relay switch to control another circuit lets us build up more complex circuits, just as we can build more complex logical formulas by combining together simpler formulas.
Contar con interruptores de relé, activados por corriente, permite combinar circuitos y desarrollar operaciones complejas
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In the next few years, both Turing and Shannon would spend time in Princeton, New Jersey. Turing completed a PhD in mathematics at Princeton University in 1938, while Shannon became a National Research Fellow at the Institute for Advanced Study in 1940. They were drawn into the orbit of Princeton’s mathematical luminaries—Alonzo Church, Kurt Gödel, Hermann Weyl. And, shining particularly brightly, John von Neumann.
Tremenda reunión de genios en princeton
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The ENIAC was an impressive machine, filling an entire room. It had grown directly out of the shortcomings of the analog computer that Shannon had worked on—the Moore School had one of these devices and engineers had been speeding it up by adding more electronic components before realizing that the solution was to build a fully electronic computer. However, the ENIAC had some serious limitations: Every time it was used to carry out a different computation, it had to be physically rewired by connecting or disconnecting an array of cables linked up to plugboards. This work was carried out by a team of highly skilled women, the “ENIAC Six”: Kathleen McNulty, Betty Jean Jennings, Elizabeth Snyder, Marlyn Wescoff, Frances Bilas, and Ruth Lichterman. However, it could still take weeks to set up the machine to perform a new calculation. To overcome this limitation, von Neumann worked with the team at the Moore School to come up with the design for a computing machine that would have a stored program. Just as a universal Turing machine can emulate any other Turing machine by reading a set of instructions on its tape, a computer with a stored program could be quickly set up to carry out any computation by simply changing the instructions in its memory. No rewiring required! The machine would be called the Electronic Discrete Variable Automatic Computer, or EDVAC. Von Neumann wrote up these ideas in a document titled “First Draft of a Report on the EDVAC,” laying out the logical design of the new computer. The report was dated June 30, 1945, just a few months before the end of the war.
La primera vez que se construyó una máquina Turing universal.
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Von Neumann had designed a practical way to build something like a universal Turing machine. The memory acts like the infinite tape, storing the program and recording the intermediate results of computations. Information would be read into the memory from punch cards and included both the program and the data. The control unit would follow the steps in the program while the arithmetic unit executed them, together making up the central processing unit of the system. At the end, the results of these computations—the output—could be returned to the user. After the war, von Neumann returned to the Institute for Advanced Study, where he began to build such a device.
Implementación concreta de la máquina de Turing universal en el esquema de un computador diseñado por Von Neumann.
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While working on building his computer, John von Neumann unwittingly provided the spark for the Cognitive Revolution. Jerome Bruner visited the Institute for Advanced Study from 1951 to 1952, mixing with classicists and physicists at the invitation of Robert Oppenheimer. Bruner knew Oppenheimer from the war, when they both stayed with the same friends when visiting Washington, D.C., although he had no idea at the time that Oppenheimer was the head of the Los Alamos Laboratory and responsible for the development of the atomic bomb. Following the war, Oppenheimer became the director of the Institute for Advanced Study, where he tried to cultivate new insights by bringing together researchers from different disciplines. One of the great successes of this effort was that Bruner, a psychologist eager to expand the scope of his discipline, spent time with von Neumann. In the period when Bruner visited, von Neumann was designing a system to store and recover information from memory—something that required specifying how facts should be represented and how to search for them. Bruner was inspired. Upon returning to Harvard, he asked the dean for space to set up a new “Cognition Project” and started on a line of work that would illustrate how psychologists could study thought, not just perception. And at the heart of this project was … logic.
Sobre la importancia de la interdisciplina. Un ejemplo similar se dio con las conferencias Macy en la cibernética. Bateson tiene una cita al respecto que no recuerdo, sobre cómo los encuentros entre ecosistemas son los lugares más biodiversos.
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Bruner saw how logic could be used to precisely characterize thought and set out to run experiments to test just how well it worked.
A diferencia de los intentos anteriores, en los que sólo se trabajaba desde la abstracción, Brunner estaba entrenado para contrastar estar hipótesis con la evidencia experimental de la psicología.
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Goodnow completed her PhD in just over two years, working with Bruner to explore how people’s choices are influenced by their perception of the task. For example, in one experiment she showed that people act differently when they think they are trying to solve a tricky problem than when they think they are gambling, even if the chance they get rewarded for their choices is exactly the same. Same environment, different behavior—another blow against behaviorism!
Lo cual es una instanciación experimental de la amenaza potencial del cognitivismo al conductismo: que el condicionamiento y la conducta dependan de variables que no son observables externamente.
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When people performed this task, it was immediately clear that they were doing something quite different from what a behaviorist might expect. Rather than gradually learning associations between the features of the cards and obtaining a positive response, people explicitly formed and tested hypotheses. They pursued various strategies for testing these hypotheses, exploring along specific dimensions or trying variations around cards that they knew belonged to the category.
Esta estrategia es característica del razonamiento humano desde la temprana infancia y es lo que fue documentado y estudiado por Piaget.
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As Bruner described it, “A Study of Thinking was a ‘protest’ book. We were trying to break out of the anti-intellectual corset by having recourse as much to rigorous logic as to psychology. Ours was in some ways more a logician’s than a psychologist’s approach.”
El cognitivismo emerge explícitamente como una protesta frente al conductismo.
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The symposium closed with a sequence of talks on perception and memory. Here, it was Miller himself who was the star. Miller presented a paper on “Human Memory and the Storage of Information,” in which he used ideas from information theory to study the capacity of human memory. The ideas he presented were one of the ingredients that went into Miller’s most famous paper—in fact, one of the most famous papers in all of psychology—“The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information.”
Paper publicado en la misma génesis del cognitivismo, por uno de sus parteros.
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What these talks had in common was a new strategy for answering questions about the mind: using mathematics to express precise hypotheses about how thought and language work, and then using information about human behavior to evaluate those hypotheses. This new strategy provided a response to the concerns about scientific rigor that had motivated behaviorism: We can formulate and test theories about the mind in a rigorous way. We just have to express those theories mathematically.
La estrategia investigativa que superaba la crítica fundamental del conductismo respecto del estudio de la mente.
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1956 was a banner year for the idea that we can describe human thought as a system of rules and symbols—a formal system—based on logic.
La idea central del primer cognitivismo.
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Inference rules, like modus ponens, tell us how to take a set of statements and infer what other statements are true. By stringing together sequences of inference rules we can develop longer proofs that establish perhaps unexpected consequences of our current knowledge. The fact that this procedure depends only on the syntax of the statements involved opened the door to automating logic—to developing digital computers. But it also offers a way of thinking about the structure of thought: Maybe thinking is just applying inference rules to the statements inside our heads, figuring out what new statements follow? Bruner had started down this path, looking at how people changed their logical hypotheses when provided with new information. Newell and Simon would go much farther, using inference rules as the basis for an entire theory of human problem-solving.
El origen de la metáfora computacionalista de la mente. A diferencia de lo que pensaba, no es que se propone una vez que aparecen los computadores, sino que el desarrollo de los cumputadores fue una consecuencia del intento de formalizar el pensamiento humano, ejercicio que comenzó al menos desde Leibniz de manera seria. Ese ejercicio se realizó de manera inductiva, intentando aplicar la lógica para describir el pensamiento, en lugar de caracterizar el pensamiento y evaluar en qué medida es congruente (o no) con la lógica. Esto último justamente es el programa de investigación del cognitivismo.
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In 1940, a distinguished professor of psychiatry at the University of Illinois, Warren McCulloch, met a homeless teenage polymath, Walter Pitts, who had devoured books on mathematical logic since the age of twelve. Three years later they published a paper together that presented a mathematical theory of the functioning of neurons called “A Logical Calculus of the Ideas Immanent in Nervous Activity.” The paper suggested that neurons—brain cells—could be used to build logical circuits. In their model, neurons could be connected to other neurons in ways that “excited” or “inhibited” those neurons. An excitatory connection would send a positive signal, an inhibitory one a negative signal. If a neuron received signals that, when added together, exceeded a threshold, the neuron would “fire” and send a signal to all the neurons it was connected to. By connecting these simplified neurons together in different ways, circuits could be built that would fire if either of two inputs fired (a logical or, ˅), or only if both inputs fired (a logical and, ˄). By using inhibitory connections, a neuron could be prevented from firing (a logical not, ¬).
El paper que presenta la idea de que las neuronas pueden entenderse como implementando circuitos que implementan operadores lógicos. .nota
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When Simon made this declaration, the “machine” part of the thinking machine was still a few months away from being a reality. The first run of the Logic Theorist program was a model made of card stock, flesh, and blood. Simon gathered his family—his wife and their nine-, eleven-, and thirteen-year-old children—and some graduate students in a room and gave each of them part of the program written on a card. By working together, following the rules of the program, they were able to successfully prove theorems in logic.
MVP Un excelente ejemplo de prototipo o producto mínimo viable. Las startups suelen utilizar estrategias como esta para validar una solución antes de invertir los recursos necesarios para implementarla realmente.
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All this work came together over the summer of 1956. Newell and Simon presented a description of the program at the first workshop on artificial intelligence—the place where the term “artificial intelligence” (and its abbreviation, AI) was coined—in June. The fully automated Logic Theorist produced its first complete proof of a theorem on August 9—just a month before it was presented at the Symposium on Information Theory.
IA Primer uso del concepto tan solo meses antes de las conferencias que gestaron el cognitivismo.
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The Dani lived in a different world—they used primarily wood and stone tools to cultivate sweet potatoes and raise pigs, wore little clothing, and lived in huts with grass roofs. But the aspect of their culture that was most relevant to Rosch was their language: The Dani primarily used just two words to name colors: “mola” and “mili.” Roughly, mola referred to light colors and mili to dark, but mola also included warm shades such as yellow and red and mili included cool colors like green and blue. Mola and mili provided the perfect testing ground for understanding the relationship between language and memory. Rosch recruited members of the Dani to participate in the color memory experiment that had been run with Harvard undergraduates. Surprisingly, she found very similar results: The colors that were a good match for the names of colors in English were easier for the Dani to remember, even though they didn’t have names for those colors. The fact that those particular colors were memorable seemed to be more about human perception and memory than about language and culture.
Evidencia de que las palabras para los colores no afecta nuestra percepción de los mismos. Los colores son categorías naturales… qué más podría serlo ?
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Wittgenstein argued that we should think about categories in terms of a kind of family resemblance structure. Members of a family tend to have some features in common but no set of features that defines them. One member of the family might have a long nose and small ears, another has small ears and brown hair, another brown hair and a long nose. Nobody has all three features, but they all resemble one another. Likewise, cats tend to have features like being small, furry, domestic, and carnivorous, but none of those features are necessary to be a cat. This kind of family resemblance structure captured what Rosch had seen in her studies. Categories—whether color names or everyday concepts like furniture—had some core cases that everyone agreed on, and other cases were evaluated based on their similarity to that core. Chairs, tables, and chests of drawers are all similar to one another in various ways, and quite different from ashtrays, fans, and telephones. The things that we identify as furniture share a family resemblance, and those that we don’t would stand out at any furniture family reunion.
Las categorías naturales tienen límites difusos. se asemejan más a un campo gravitacional que a orbitales atómicos.