"Let it be remarked [...] that an important difference between the way in which we use the brain and the machine is that the machine is intended for many successive runs, either with no reference to each other, or with a minimal, limited reference, and that it can be cleared between such runs; while the brain, in the course of nature, never even approximately clears out its past records. Thus the brain, under normal circumstances, is not the complete analogue of the computing machine but rather the analogue of a single run on such a machine." (Norbert Wiener, "Cybernetics: Or Control and Communication in the Animal and the Machine", 1948)
"A computer would deserve to be called intelligent if it could deceive a human into believing that it was human." (Alan Turing, "Computing Machinery and Intelligence" , Mind Vol. 59, 1950)
"It is interesting to consider what a thinking machine will be like. It seems clear that as soon as the machines become able to solve intellectual problems of the highest difficulty which can be solved by humans they will be able to solve most of the problems enormously faster than a human." (John F Nash, "Parallel Control", 1954)
"We could define the intelligence of a machine in terms of the time needed to do a typical problem and the time needed for the programmer to instruct the machine to do it."
"A computer is a person or machine that is able to take in information (problems and data), perform reasonable operations on the iformation, and put out answers. A computer is identified by the fact that it (or he) handles information reasonably." (Edmund C Berkeley & Lawrence Wainwright, Computers: Their Operation and Applications", 1956)
"An information retrieval system is therefore defined here as any device which aids access to documents specified by subject, and the operations associated with it. The documents can be books, journals, reports, atlases, or other records of thought, or any parts of such records - articles, chapters, sections, tables, diagrams, or even particular words. The retrieval devices can range from a bare list of contents to a large digital computer and its accessories. The operations can range from simple visual scanning to the most detailed programming." (Brian C Vickery, "The Structure of Information Retrieval Systems", 1959)
"Computers do not decrease the need for mathematical analysis, but rather greatly increase this need. They actually extend the use of analysis into the fields of computers and computation, the former area being almost unknown until recently, the latter never having been as intensively investigated as its importance warrants. Finally, it is up to the user of computational equipment to define his needs in terms of his problems, In any case, computers can never eliminate the need for problem-solving through human ingenuity and intelligence." (Richard E Bellman & Paul Brock, "On the Concepts of a Problem and Problem-Solving", American Mathematical Monthly 67, 1960)
"There is the very real danger that a number of problems which could profitably be subjected to analysis, and so treated by simpler and more revealing techniques. will instead be routinely shunted to the computing machines [...] The role of computing machines as a mathematical tool is not that of a panacea for all computational ills." (Richard E Bellman & Paul Brock, "On the Concepts of a Problem and Problem-Solving", American Mathematical Monthly 67, 1960)
"These machines have no common sense; they have not yet learned to 'think', and they do exactly as they are told, no more and no less. This fact is the hardest concept to grasp when one first tries to use a computer." (Donald Knuth, "The Art of Computer Programming, Volume 1: Fundamental Algorithms", 1968)
"Because the subject matter of cybernetics is the propositional or informational aspect of the events and objects in the natural world, this science is forced to procedures rather different from those of the other sciences. The differentiation, for example, between map and territory, which the semanticists insist that scientists shall respect in their writings must, in cybernetics, be watched for in the very phenomena about which the scientist writes. Expectably, communicating organisms and badly programmed computers will mistake map for territory; and the language of the scientist must be able to cope with such anomalies." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)
"Computers can do better than ever what needn't be done at all. Making sense is still a human monopoly." (Marshall McLuhan, "Take Today: The Executive as Dropout", 1972)
"Everything we think we know about the world is a model. Every word and every language is a model. All maps and statistics, books and databases, equations and computer programs are models. So are the ways I picture the world in my head - my mental models. None of these is or ever will be the real world. […] Our models usually have a strong congruence with the world. That is why we are such a successful species in the biosphere. Especially complex and sophisticated are the mental models we develop from direct, intimate experience of nature, people, and organizations immediately around us." (Donella Meadows, "Limits to Growth", 1972)
"It follows from this that man's most urgent and pre-emptive need is maximally to utilize cybernetic science and computer technology within a general systems framework, to build a meta-systemic reality which is now only dimly envisaged. Intelligent and purposeful application of rapidly developing telecommunications and teleprocessing technology should make possible a degree of worldwide value consensus heretofore unrealizable." (Richard F Ericson, "Visions of Cybernetic Organizations", 1972)
"The mind is defined as the sum total of all the programs and the metaprograms of a given human computer, whether or not they are immediately elicitable, detectable, and visibly operational to the self or to others." (John C Lilly "Programming and Metaprogramming in the Human Biocomputer" 2nd Ed., 1972)
"The pseudo approach to uncertainty modeling refers to the use of an uncertainty model instead of using a deterministic model which is actually (or at least theoretically) available. The uncertainty model may be desired because it results in a simpler analysis, because it is too difficult (expensive) to gather all the data necessary for an exact model, or because the exact model is too complex to be included in the computer."
"Computers make possible an entirely new relationship between theories and models. I have already said that theories are texts. Texts are written in a language. Computer languages are languages too, and theories may be written in them. Indeed, for the present purpose we need not restrict our attention to machine languages or even to the kinds of 'higher-level' languages we have discussed. We may include all languages, specifically also natural languages, that computers may be able to interpret. The point is precisely that computers do interpret texts given to them, in other words, that texts determine computers' behavior. Theories written in the form of computer programs are ordinary theories as seen from one point of view." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)
"Man is not a machine, [...] although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. [...] No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. [...] However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns." (Joesph Weizenbaum, Computer Power and Human Reason: From Judgment to Calculation, 1976)
"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicitly states or which may be derived from it. [...] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)
"It is essential to realize that a computer is not a mere 'number cruncher', or supercalculating arithmetic machine, although this is how computers are commonly regarded by people having no familiarity with artificial intelligence. Computers do not crunch numbers; they manipulate symbols. [...] Digital computers originally developed with mathematical problems in mind, are in fact general purpose symbol manipulating machines." (Margaret A Boden, "Minds and mechanisms", 1981)
"The basic idea of cognitive science is that intelligent beings are semantic engines - in other words, automatic formal systems with interpretations under which they consistently make sense. We can now see why this includes psychology and artificial intelligence on a more or less equal footing: people and intelligent computers (if and when there are any) turn out to be merely different manifestations of the same underlying phenomenon. Moreover, with universal hardware, any semantic engine can in principle be formally imitated by a computer if only the right program can be found." (John Haugeland, "Semantic Engines: An introduction to mind design", 1981)
"Computers and robots replace humans in the exercise of mental functions in the same way as mechanical power replaced them in the performance of physical tasks. As time goes on, more and more complex mental functions will be performed by machines. Any worker who now performs his task by following specific instructions can, in principle, be replaced by a machine. This means that the role of humans as the most important factor of production is bound to diminish - in the same way that the role of horses in agricultural production was first diminished and then eliminated by the introduction of tractors." (Wassily Leontief, National perspective: The definition of problem and opportunity, 1983)
"If arithmetical skill is the measure of intelligence, then computers have been more intelligent than all human beings all along. If the ability to play chess is the measure, then there are computers now in existence that are more intelligent than any but a very few human beings. However, if insight, intuition, creativity, the ability to view a problem as a whole and guess the answer by the “feel” of the situation, is a measure of intelligence, computers are very unintelligent indeed. Nor can we see right now how this deficiency in computers can be easily remedied, since human beings cannot program a computer to be intuitive or creative for the very good reason that we do not know what we ourselves do when we exercise these qualities." (Isaac Asimov, "Machines That Think", 1983)
"The digital-computer field defined computers as machines that manipulated numbers. The great thing was, adherents said, that everything could be encoded into numbers, even instructions. In contrast, scientists in AI [artificial intelligence] saw computers as machines that manipulated symbols. The great thing was, they said, that everything could be encoded into symbols, even numbers." (Allen Newell, "Intellectual Issues in the History of Artificial Intelligence", 1983)
"Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)
"Let us change our traditional attitude to the construction of programs: Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do." (Donald E Knuth, "Literate Programming", 1984)
"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)
"The trouble with an analog computer is that one begins to construct mathematical models which can be treated using an analog computer. In many cases this is not realistic." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Under pressure from the computer, the question of mind in relation to machine is becoming a central cultural preoccupation." (Sherry Turkle, "The Second Self: Computers and the Human Spirit", 1984)
"A computer is an interpreted automatic formal system - that is to say, a symbol-manipulating machine." (John Haugeland, "Artificial intelligence: The very idea", 1985)
"Computers are the first thing to come along since books that will sit there and interact with you endlessly, without judgment." (Steve Jobs, Playboy, 1985)
"Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped onto the other (the computer)." (George Johnson, Machinery of the Mind: Inside the New Science of Artificial Intelligence, 1986)
"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases." (Stephen Hawking, "A Brief History of Time", 1988)
"Cybernetics is simultaneously the most important science of the age and the least recognized and understood. It is neither robotics nor freezing dead people. It is not limited to computer applications and it has as much to say about human interactions as it does about machine intelligence. Today’s cybernetics is at the root of major revolutions in biology, artificial intelligence, neural modeling, psychology, education, and mathematics. At last there is a unifying framework that suspends long-held differences between science and art, and between external reality and internal belief." (Paul Pangaro, "New Order From Old: The Rise of Second-Order Cybernetics and Its Implications for Machine Intelligence", 1988)
"A popular myth says that the invention of the computer diminishes our sense of ourselves, because it shows that rational thought is not special to human beings, but can be carried on by a mere machine. It is a short stop from there to the conclusion that intelligence is mechanical, which many people find to be an affront to all that is most precious and singular about their humanness." (Jeremy Campbell, "The improbable machine", 1989)
"Fuzziness, then, is a concomitant of complexity. This implies that as the complexity of a task, or of a system for performing that task, exceeds a certain threshold, the system must necessarily become fuzzy in nature. Thus, with the rapid increase in the complexity of the information processing tasks which the computers are called upon to perform, we are reaching a point where computers will have to be designed for processing of information in fuzzy form. In fact, it is the capability to manipulate fuzzy concepts that distinguishes human intelligence from the machine intelligence of current generation computers. Without such capability we cannot build machines that can summarize written text, translate well from one natural language to another, or perform many other tasks that humans can do with ease because of their ability to manipulate fuzzy concepts." (Lotfi A Zadeh, "The Birth and Evolution of Fuzzy Logic", 1989)
"Looking at ourselves from the computer viewpoint, we cannot avoid seeing that natural language is our most important 'programming language'. This means that a vast portion of our knowledge and activity is, for us, best communicated and understood in our natural language. [...] One could say that natural language was our first great original artifact and, since, as we increasingly realize, languages are machines, so natural language, with our brains to run it, was our primal invention of the universal computer. One could say this except for the sneaking suspicion that language isn’t something we invented but something we became, not something we constructed but something in which we created, and recreated, ourselves. (Justin Leiber, "Invitation to cognitive science", 1991)
"The cybernetics phase of cognitive science produced an amazing array of concrete results, in addition to its long-term (often underground) influence: the use of mathematical logic to understand the operation of the nervous system; the invention of information processing machines (as digital computers), thus laying the basis for artificial intelligence; the establishment of the metadiscipline of system theory, which has had an imprint in many branches of science, such as engineering (systems analysis, control theory), biology (regulatory physiology, ecology), social sciences (family therapy, structural anthropology, management, urban studies), and economics (game theory); information theory as a statistical theory of signal and communication channels; the first examples of self-organizing systems. This list is impressive: we tend to consider many of these notions and tools an integrative part of our life […]" (Francisco Varela, "The Embodied Mind", 1991)
"What a computer is to me is the most remarkable tool that we have ever come up with. It’s the equivalent of a bicycle for our minds." (Steve Jobs, "Memory and Imagination: New Pathways to the Library of Congress", 1991)
"A computer terminal is not some clunky old television with a typewriter in front of it. It is an interface where the mind and body can connect with the universe and move bits of it about." (Douglas N Adams, "Mostly Harmless", 1992)
"Finite Nature is a hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities. [...] We take the position that Finite Nature implies that the basic substrate of physics operates in a manner similar to the workings of certain specialized computers called cellular automata." (Edward Fredkin, "A New Cosmogony", PhysComp ’92: Proceedings of the Workshop on Physics and Computation, 1993)
"The insight at the root of artificial intelligence was that these 'bits' (manipulated by computers) could just as well stand as symbols for concepts that the machine would combine by the strict rules of logic or the looser associations of psychology." (Daniel Crevier, "AI: The tumultuous history of the search for artificial intelligence", 1993)
"At first glance the theory of numbers is deprived of any geometricity. But this is actually not the case. At the contemporary stage of development of computers it has become possible to explain to a wide range of readers that visual geometry helps not only to illustrate some abstract situations from the number theory, but sometimes also to solve new problems."
"On the other hand, those who design and build computers know exactly how the machines are working down in the hidden depths of their semiconductors. Computers can be taken apart, scrutinized, and put back together. Their activities can be tracked, analyzed, measured, and thus clearly understood - which is far from possible with the brain. This gives rise to the tempting assumption on the part of the builders and designers that computers can tell us something about brains, indeed, that the computer can serve as a model of the mind, which then comes to be seen as some manner of information processing machine, and possibly not as good at the job as the machine. (Theodore Roszak, "The Cult of Information", 1994)
"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems. […] Self-organization provides a paradigm for behavior and cognition, as well as the structure and function of the nervous system. In contrast to a computer, which requires particular programs to produce particular results, the tendency for self-organization is intrinsic to natural systems under certain conditions." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)
"Representation is the process of transforming existing problem knowledge to some of the known knowledge-engineering schemes in order to process it by applying knowledge-engineering methods. The result of the representation process is the problem knowledge base in a computer format."
"Shearing away detail is the very essence of model building. Whatever else we require, a model must be simpler than the thing modeled. In certain kinds of fiction, a model that is identical with the thing modeled provides an interesting device, but it never happens in reality. Even with virtual reality, which may come close to this literary identity one day, the underlying model obeys laws which have a compact description in the computer - a description that generates the details of the artificial world." (John H Holland, "Emergence" , Philosophica 59, 1997)
"Modelling techniques on powerful computers allow us to simulate the behaviour of complex systems without having to understand them. We can do with technology what we cannot do with science. […] The rise of powerful technology is not an unconditional blessing. We have to deal with what we do not understand, and that demands new ways of thinking."
"For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed." (Lynn A Steen,"Twenty Questions about Mathematical Reasoning", 1999)
"Once a computer achieves human intelligence it will necessarily roar past it." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999)
"The classic example of chaos at work is in the weather. If you could measure the positions and motions of all the atoms in the air at once, you could predict the weather perfectly. But computer simulations show that tiny differences in starting conditions build up over about a week to give wildly different forecasts. So weather predicting will never be any good for forecasts more than a few days ahead, no matter how big (in terms of memory) and fast computers get to be in the future. The only computer that can simulate the weather is the weather; and the only computer that can simulate the Universe is the Universe." (John Gribbin, "The Little Book of Science", 1999)
"Conventional wisdom, fooled by our misleading 'physical intuition', is that the real world is continuous, and that discrete models are necessary evils for approximating the 'real' world, due to the innate discreteness of the digital computer." (Doron Zeilberger, "'Real' Analysis is a Degenerate Case of Discrete Analysis", 2001)
"The randomness of the card-shuffle is of course caused by our lack of knowledge of the precise procedure used to shuffle the cards. But that is outside the chosen system, so in our practical sense it is not admissible. If we were to change the system to include information about the shuffling rule – for example, that it is given by some particular computer code for pseudo-random numbers, starting with a given ‘seed value’ – then the system would look deterministic. Two computers of the same make running the same ‘random shuffle’ program would actually produce the identical sequence of top cards."(Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)
"There are endless examples of elaborate structures and apparently complex processes being generated through simple repetitive rules, all of which can be easily simulated on a computer. It is therefore tempting to believe that, because many complex patterns can be generated out of a simple algorithmic rule, all complexity is created in this way." (F David Peat, "From Certainty to Uncertainty", 2002)
"We build models to increase productivity, under the justified assumption that it's cheaper to manipulate the model than the real thing. Models then enable cheaper exploration and reasoning about some universe of discourse. One important application of models is to understand a real, abstract, or hypothetical problem domain that a computer system will reflect. This is done by abstraction, classification, and generalization of subject-matter entities into an appropriate set of classes and their behavior." (Stephen J Mellor, "Executable UML: A Foundation for Model-Driven Architecture", 2002)
"Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algorithms are more scalable than statisticians ever thought possible. Formal statistical theory is more pervasive than computer scientists had realized."
"Computers bootstrap their own offspring, grow so wise and incomprehensible that their communiqués assume the hallmarks of dementia: unfocused and irrelevant to the barely-intelligent creatures left behind. And when your surpassing creations find the answers you asked for, you can't understand their analysis and you can't verify their answers. You have to take their word on faith." (Peter Watts, "Blindsight", 2006)
"In specific cases, we think by applying mental rules, which are similar to rules in computer programs. In most of the cases, however, we reason by constructing, inspecting, and manipulating mental models. These models and the processes that manipulate them are the basis of our competence to reason. In general, it is believed that humans have the competence to perform such inferences error-free. Errors do occur, however, because reasoning performance is limited by capacities of the cognitive system, misunderstanding of the premises, ambiguity of problems, and motivational factors. Moreover, background knowledge can significantly influence our reasoning performance. This influence can either be facilitation or an impedance of the reasoning process." (Carsten Held et al, "Mental Models and the Mind", 2006)
"A neural network is a particular kind of computer program, originally developed to try to mimic the way the human brain works. It is essentially a computer simulation of a complex circuit through which electric current flows." (Keith J Devlin & Gary Lorden, "The Numbers behind NUMB3RS: Solving crime with mathematics", 2007)
"The burgeoning field of computer science has shifted our view of the physical world from that of a collection of interacting material particles to one of a seething network of information. In this way of looking at nature, the laws of physics are a form of software, or algorithm, while the material world - the hardware - plays the role of a gigantic computer." (Paul C W Davies, "Laying Down the Laws", New Scientist, 2007)
"We tend to form mental models that are simpler than reality; so if we create represented models that are simpler than the actual implementation model, we help the user achieve a better understanding. […] Understanding how software actually works always helps someone to use it, but this understanding usually comes at a significant cost. One of the most significant ways in which computers can assist human beings is by putting a simple face on complex processes and situations. As a result, user interfaces that are consistent with users’ mental models are vastly superior to those that are merely reflections of the implementation model." (Alan Cooper et al, "About Face 3: The Essentials of Interaction Design", 2007)
"An algorithm refers to a successive and finite procedure by which it is possible to solve a certain problem. Algorithms are the operational base for most computer programs. They consist of a series of instructions that, thanks to programmers’ prior knowledge about the essential characteristics of a problem that must be solved, allow a step-by-step path to the solution." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"We evolved to be good at learning and using rules of thumb, not at searching for ultimate causes and making fine distinctions. Still less did we evolve to spin out long chains of calculation that connect fundamental laws to observable consequences. Computers are much better at it!" (Frank Wilczek,"The Lightness of Being – Mass, Ether and the Unification of Forces", 2008)
"Chess, as a game of zero sum and total information is, theoretically, a game that can be solved. The problem is the immensity of the search tree: the total number of positions surpasses the number of atoms in our galaxy. When there are few pieces on the board, the search space is greatly reduced, and the problem becomes trivial for computers’ calculation capacity." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Generally, these programs fall within the techniques of reinforcement learning and the majority use an algorithm of temporal difference learning. In essence, this computer learning paradigm approximates the future state of the system as a function of the present state. To reach that future state, it uses a neural network that changes the weight of its parameters as it learns." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"From a historical viewpoint, computationalism is a sophisticated version of behaviorism, for it only interpolates the computer program between stimulus and response, and does not regard novel programs as brain creations. [...] The root of computationalism is of course the actual similarity between brains and computers, and correspondingly between natural and artificial intelligence. The two are indeed similar because the artifacts in question have been designed to perform analogs of certain brain functions. And the computationalist program is an example of the strategy of treating similars as identicals." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)
"[...] we also distinguish knowledge from information, because some pieces of information, such as questions, orders, and absurdities do not constitute knowledge. And also because computers process information but, since they lack minds, they cannot be said to know anything." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)
"System dynamics models have little impact unless they change the way people perceive a situation. A model must help to organize information in a more understandable way. A model should link the past to the present by showing how present conditions arose, and extend the present into persuasive alternative futures under a variety of scenarios determined by policy alternatives. In other words, a system dynamics model, if it is to be effective, must communicate with and modify the prior mental models. Only people's beliefs - that is, their mental models - will determine action. Computer models must relate to and improve mental models if the computer models are to fill an effective role." (Jay W Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"Now think about the prospect of competition from computers instead of competition from human workers. On the supply side, computers are far more different from people than any two people are different from each other: men and machines are good at fundamentally different things. People have intentionality - we form plans and make decisions in complicated situations. We’re less good at making sense of enormous amounts of data. Computers are exactly the opposite: they excel at efficient data processing, but they struggle to make basic judgments that would be simple for any human." (Peter Thiel & Blake Masters, "Zero to One: Notes on Startups, or How to Build the Future", 2014)
"With fast computers and plentiful data, finding statistical significance is trivial. If you look hard enough, it can even be found in tables of random numbers."
"Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense - or deciding whether the method is the right one to use in the first place - requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel." (Jordan Ellenberg, "How Not to Be Wrong: The Power of Mathematical Thinking", 2014)
"The term data, unlike the related terms facts and evidence, does not connote truth. Data is descriptive, but data can be erroneous. We tend to distinguish data from information. Data is a primitive or atomic state (as in ‘raw data’). It becomes information only when it is presented in context, in a way that informs. This progression from data to information is not the only direction in which the relationship flows, however; information can also be broken down into pieces, stripped of context, and stored as data. This is the case with most of the data that’s stored in computer systems. Data that’s collected and stored directly by machines, such as sensors, becomes information only when it’s reconnected to its context." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)
"[…] the usefulness of mathematics is by no means limited to finite objects or to those that can be represented with a computer. Mathematical concepts depending on the idea of infinity, like real numbers and differential calculus, are useful models for certain aspects of physical reality." (Alfred S Posamentier & Bernd Thaller, "Numbers: Their tales, types, and treasures", 2015)
"The human mind isn’t a computer; it cannot progress in an orderly fashion down a list of candidate moves and rank them by a score down to the hundredth of a pawn the way a chess machine does. Even the most disciplined human mind wanders in the heat of competition. This is both a weakness and a strength of human cognition. Sometimes these undisciplined wanderings only weaken your analysis. Other times they lead to inspiration, to beautiful or paradoxical moves that were not on your initial list of candidates." (Garry Kasparov, "Deep Thinking", 2017)
"There are other problems with Big Data. In any large data set, there are bound to be inconsistencies, misclassifications, missing data - in other words, errors, blunders, and possibly lies. These problems with individual items occur in any data set, but they are often hidden in a large mass of numbers even when these numbers are generated out of computer interactions." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)
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