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Mathematics

 

Review Essays of Academic, Professional & Technical Books in the Humanities & Sciences

 

AI: Artificial Intelligence

Artificial Intelligence with Uncertainty by Deyi Li, Yi Du (Chapman & Hall/CRC) The information deluge currently assaulting us in the 21st century is having profound impact on our lifestyles and how we work. We must constantly separate trustworthy and required information from the massive amount of data we encounter each day. Through mathematical theories, models, and experiment. computations, Artificial Intelligence with Uncertainty explores the uncertainties of knowledge and intelligence that occur during the cognitive processes of human beings. The authors focus on the importance of natural language—the carrier of knowledge and intelligence—for artificial intelligence (Al) study.

This book develops a framework that shows how uncertainty in Al expand and generalizes traditional Al. It describes the cloud model, its uncertainties of randomness and fuzziness, and the correlation between them. The book also centers on other physical methods for data mining, such as the data field am knowledge discovery state space. In addition, it presents an inverted pendulum example to discuss reasoning and control with uncertain knowledge as well a' provides a cognitive physics model to visualize human thinking with hierarchy.

  • With in-depth discussions on the fundamentals, methodologies, and uncertainties in Al, this book explains and simulates human thinking, leading to a better understanding of cognitive processes.
  • Covers the mathematical foundations of Al uncertainty, including probability theory, rough set theory, kernel functions, and principal curves
  • Presents the cloud model, a qualitative-quantitative model that illustrates the uncertain mechanism during the transformation between qualitative concepts and quantitative values
  • Demonstrates how the data field can be used in the classification and clustering of data mining
  • Describes the extended cloud model, which can simulate plant variations
  • Provides numerous algorithms to facilitate the development of application programs

It is said that there are three hard scientific questions that have not yet been well answered: the original source of life, the original source of the world, and the working mechanism of the human brain. This book is related to the third question by studying and exploring uncertainties of knowledge and intelligence during the human being's cognitive process. The authors pay particular attention to setting up models and exper­imental computations to deal with such uncertainties as well.

Why do humans have intelligence? How does the human brain work in daily life? As a result of human evolution, which may have taken billions of years for biology and hundreds of millions of years for humankind, the brain runs well in dealing with all kinds of uncertainty in sensation, perception, learning, reasoning, thinking, under­standing, and action. Mysteries of the brain are studied by brain science, having achieved great success on molecule-level and cell-level research. However, there is still a long way to go to understand the cognitive functions of a brain as a whole. How can we understand the nonlinear function of a brain? How does the left brain (with the priority of logic thinking) cooperate with the right brain (with the priority of visual thinking)? We know very little about the working principles and scientific mechanisms of a brain today. A new direction for cognitive science is the interdisciplinary study by a diverse group of scientists, including biologists, psychologists, mathematicians, physicists, and computer scientists.

Knowledge representation is a fundamental issue in artificial intelligence (AI) study. Over the 50-year history of AI, it seems that people paid more attention to using symbolic representation and problem solving for simulation of human thinking. However, natural language is an essential tool for thinking in a brain. Human civili­zation comes from the history of humankind. Only because of the written natural language can human beings record the accumulation or knowledge of human history. The most important difference in intelligence between human beings and other life forms might be language. One of the most influential scientists in the past century, the so-called "father of the modern electronic computer," Dr. Von Neumann, after an in-depth study on the differences and similarities between the electronic computer and the human brain, asserted in his posthumous book The Computer and the Brain, "the thinking language for human beings is not mathematic language-like at all." We emphasize that one of the important perspectives for AI study should be directed to natural language, which is the carrier of knowledge and intelligence. A language concept expressed by the cloud model in this book contains uncertainty, and in particular, randomness and fuzziness and the correlation between them. With such a perspective, we are going to explore the AI with uncertainty in detail.

In the twenty-first century, information is becoming the leading industry in the global economy, and fast-developing information technology is drastically changing the global world, including the working mode and lifestyle of human beings. It is claimed that the knowledge age dominated by information technology is coming. While enjoying the

Internet technology and World Wide Web culture, we are also suffering from an infor­mation deluge. It is a good wish to mine the trustful and required information from such huge data, and mine the knowledge at multi-scales we have not discovered. From this perspective, we concentrate on the physical methods for data mining by use of the tools of cloud model, data field, and knowledge discovery state space in this book. Reasoning and control with uncertain knowledge are also given in an inverted pendulum example. What we have done in our research seems to develop a satisfying framework to show how the uncertainty AI expands and generalizes the traditional AI.

"Seeking unknown knowledge" and "seeking beauty" are the natural desires of human beings. How to understand the cognitive process of human beings, and how to explain and simulate human thinking with a "beautiful" theory is a challenging topic indeed. Due to the limit of the authors' academic and practical capabilities, the book is an exploration that inevitably contains some flaws and your help in pointing these out will be sincerely appreciated.

Readers of this book could be scholar researchers in the fields of cognitive science, brain science, artificial intelligence, computer science, or control theory, in particular research and development (R&D) personnel for natural language under­standing, intelligent searching, knowledge engineering, data mining, and intelligent control. The book can also be used as a textbook or reference book for graduate students of relevant majors in colleges and universities.

How to Build a Mind: Toward Machines With Imagination by Igor Aleksander (Maps of the Mind: Columbia University Press)
Igor Aleksander heads a major British team that has applied engineering principles to the understanding of the human brain and has built several pioneering machines, culminating in "Magnus," which he calls a machine with imagination. When he asks it (in words) to produce an image of a banana that is blue with red spots, the image appears on the screen in seconds. The idea of such an apparently imaginative, even conscious machine seems heretical and its advocates are often accused of sensationalism, arrogance, or philosophical ignorance. Part of the problem, according to Aleksander, is that consciousness remains ill defined. Interweaving anecdotes from his own life and research with imagined dialogues between historical figures - including Descartes, Locke, Hume, Kant, Wittgenstein, Francis Crick, and Steven Pinker - Aleksander leads readers toward an understanding of consciousness. He shows not only how the latest work with artificial neural systems suggests that an artificial form of consciousness is possible but also that its design would clarify many of the puzzles surrounding the murky concept of consciousness itself. The book also looks at the presentation of "self" in robots, the learning of language, and the nature of emotion, will, instinct, and feelings.

Igor Aleksander heads a major British team that has applied engineering principles to the understanding of the human brain and has built several pioneering machines, culminating in MAGNUS, which he calls a machine with imagination. When he asks it (in words) to pro­duce an image of a banana that is blue with red spots, the image appears on the screen in seconds.

Excerpt:

The idea of such an apparently imaginative, even conscious, machine seems heretical, and its advocates are often accused of sensational­ism, arrogance, or philosophical ignorance. Part of the problem, according to Aleksander, is that consciousness remains ill defined. Interweaving anecdotes from his own life and research with imagined dialogues between historical figures-including Descartes, Locke, Hume, Kant, Wittgenstein, Francis Crick, and Steven Pinker-Aleksander leads readers toward an understanding of conscious­ness. He shows not only how the latest work with artificial neural systems suggests that an artificial form of consciousness is possible but also that its design would clarify many of the puzzles surrounding the murky concept of consciousness itself. How to Build a Mind also examines the presentation of "self' in robots, the learning of language, and the nature of emotion, will, instinct, and feelings.

Igor Aleksander is professor of neural sys­tems engineering and head of Intelligent and Interactive Systems at the Imperial College of Science, Technology, and Medicine in London. He has studied artificial intelligence for more than thirty years and has published over 200 papers and ten books on the subject, including Reinventing Man, Thinking Machines, Impossible Minds, Introduction to Neural Computing, Designing Intelligent Systems, and Neurons and Symbols. In 2000 he received the Outstanding Achievement Medal for Informatics from the Institution of Electrical Engineers.

My own exploration of machinery with internal states capable of imagination is one strand of this book. The other, as trailed earlier, is that I am encroaching on territory conventionally trodden by philosophers. I therefore felt the need to understand why my ideas might be running against conventional culture. Why do some feel uneasy about my mechanistic approach? Understanding the pas­sions and opinions that are stimulated by the idea of artificial minds is almost as important as designing such artificial systems in the first place. Such passions are often quite explicit. I am labeled as a re­ductionist. I am often told that I am flouting philosophical areas of agreement. These views come from deeply held beliefs that have their roots in many millennia not only of philosophy but also of cultural evolution. It is vital that I should not ignore this existing wisdom.

But I am a visitor in the land of philosophy, and a visitor I need to stay. I would not dare to attempt a critical essay. So I have imag­ined being able to talk to, or just to hear, the influential philoso­phers of Western civilization on topics that relate to mind and its origins. In chapter 2, I imagine being a castaway in 540 B.C. in the region of Miletus where, by many accounts, philosophy began. The concern of Thales, Anaximenes, and Anaximander for answering deep questions about "what are things made of" does not stop at material things. The notion of a soul emerges. Does it survive the body? It is destined that our human sense of the enduring self will be central to the discourses of those who follow in the footsteps of the Miletians for thousands of years to come. The Miletians spoke of machines, but autonomous motion was for them what defined life. How valid was this as an idea at the time?

For me, the great era of Greek philosophy reached a peak with Aristotle. Here was a giant not only in the history of philosophy but also in the history of humankind. Through Saint Thomas Aquinas and Saint Augustine, he influenced the Christian culture that molds much of the way in which mind and soul feature in Western thought. But what might Aristotle have been like at the decline of his influence in his own time? In chapter 4, I imagine being a fly on the wall during Aristotle's trial for impiety that led to his flight from Athens. This fictional segment of the book lets me imagine how Aristotle may have viewed his own accomplishments, from the tutelage of Alexander the Great to his thoughts on the soul and minds of mortals.

Undoubtedly, another hugely influential figure in the history of philosophy was Ren6 Descartes, who is now more often criticized than followed for his division of mind from body. But, purely per­sonally, I have been fascinated by the immediate effect that Descartes had on the philosophers who followed him after the end of the seventeenth century. Known as the empiricists, John Locke, David Hume, and Immanuel Kant were concerned not so much with how minds work but with what kind of objects they contain. How does an imagined idea differ from an experienced one? To imagine their reactions to the idea of an imagining machine, chap­ter 6 is a dream about these thinkers being subjected to the brash­ness of a television interview: an experience which many modern thinkers are forced to experience.

Hopping from giant to giant, in chapter 8 we meet Ludwig Wittgenstein on a train to Cambridge. I find him enigmatic but enormously stimulating. He was aware of the debate that was be­ginning to surround Alan Turing's idea that computers might be able to think. During the train journey I imagine that he has the opportunity of telling me how misguided I am for looking for the mechanisms of imagination in anything but the world of human beings.

The "expose it in the media theme, started in chapter 6, is re­vived in chapter 10. "Consciousness" is the basis of many popular programs on TV and a vast number of popular books, and a source of robust public debate. I imagine being part of a millennial radio discussion program chaired by British media personality Melvyn Bragg. I am caught in the crossfire between scientists, philosophers, and mathematicians, all of

whom have seen fit to pronounce on the nature of consciousness during the last decade of the twentieth cen­tury. What chance do I as a machine-builder stand in this array of eloquent dissonance? Does the imagining machine become the common anathema for the others? At least, I get a word in edgewise on how working with machines might throw light on opposing opinions.

It would not only be thoroughly unprofessional for me to give away at this stage what I think to be the answer, but the answer itself would not make much sense without taking the journey that I de­scribe in this book. It took me that length of time to begin to see some of the "Lights" that are the "Intelligences in our minds" so imaginatively expressed in Antonia Byatt's poetry. So I leave it until chapter 12 to approach the flimsy beginnings of an answer, while here I wish to focus a little on the exact nature of the question that needs to be answered. In doing this I recognize that whatever it is, it begs most of the questions posed by the puzzle of consciousness. I cannot avoid the word in my vocabulary, but I need to treat it carefully: it is capable of leading us back into culs-de-sac that have emerged over more than two thousand years.

To illustrate what might constitute an appropriate question, imagine that one day a robot arrives in town and everyone agrees that it is a conscious machine. We purposefully but temporarily put aside the question of how anybody knows that it is conscious. The designer of the machine proposes to tell us how its consciousness works. In what sense are we better off? This clearly depends crucially on how the designer expresses herself. Should the explanation be couched in a series of quantum-theoretical equations, we would have a situation where the quantum physicist says to the rest of the world, "I know how consciousness works but no one else can, un­less they learn quantum physics." Similarly, a computational expla­nation might mean something only to the computer scientist, and a neural one only to the neural network expert.

Clearly, it is important that the explanation should make sense to common experience in the way that most of us can grasp what happens when water freezes, when a light bulb lights up, when a baby is born, or when the earth goes around the sun. So what is it that puzzles all of us about those inner feelings we call our imagi­nation, our consciousness? I suggest there is one key question that dictates the underlying agenda for this book:

What is there in my brain that allows me to feel that I, as an in­dividual, live in a real world, can imagine without perception, know who I am, and am able to decide what I want to do?

This is the question that has motivated my work for a long time and now motivates the writing of this book

It Can't Be Done! Some readers may have read this far with a mounting degree of in­credulity. Have I not heard that American philosopher John Searle has said that computers, because they are programmed to use sym­bols, can never have the imagination necessary to understand nat­ural language?' Imagining my rustic table is just what they cannot do: they can only manipulate "rustic" and "table" as meaningless symbols. Have I not heard that another American philosopher, David Chalmers, has shown that modeling the neural structure of the brain (as I do) can only get to grips with some easy side of the problem, leaving the hard part (the stuff of feelings and imagination) untouched? Have I not heard that the brilliant British math­ematician Roger Penrose has argued that consciousness is noncom­putable? Indeed, he has written that the answer lies in some form of quantum processing in the microtubules of the brain. Micro­tubules are those parts of the structure (cytoskeleton) of the brain that keep the neural networks of the brain in place.

It Might Be Done!

I have no quarrel with Searle, Chalmers, or Penrose. But I do warn the reader against believing that anyone, including myself, who presents their ideas on how consciousness works, has the last, defi­nite word. The arguments used by Penrose are elegantly illustrated by showing that consciousness involves "insight." An example he quotes is the insight needed to decide how to prove a mathematical theorem. He rightly worries about the limitations of computation as we know it from our laptops. The point I shall make is that ma­chines are not all like my laptop, and that some might well perform computations in other ways-ways that include insight, conscious­ness, and imagination. I argue for the existence of such machines while Penrose recognizes the limitations of current computational powers. Both are beliefs, but they are not contradictory and neither is the last word.

David Chalmers, on the other hand, may be importing an error from the philosophical deliberations of several millennia. For this reason, some of the great Greek philosophers appear in this book: they had few scientific facts at their disposal, and some believed that the philosophy of the mind should be based on the power of the mind turned on itself rather than its physical character. Anticipat­ing subsequent discussions a little, the "hard problem" is this: It may well be that, put in a suitable magnetic resonance imaging (MRI) apparatus (a brain-scanner), the thoughts of a subject could be found to correlate exactly with the broad activity of the brain that the experimenter can see on the screen. The "easy problem" is to construct theories of how such brain activity is generated, learned, and modified. The "hard problem" is to work out how this activity causes anything the subject might feel internally. Some philosophers object to those who say that the two are the same thing, and call them "reductionists." The latter retaliate by calling the former "dualists" (there are many "-ists" in between, which need not concern us for the time being). However, as the relation of brain activity to sensation is becoming progressively better under­stood, it seems to be a tiny bit perverse to relegate for eternity such findings to some "easy" category, believing that the "hard" unyield­ingly shifts further afield.

For most, such distinctions are pretty distant. But on the whole, the instinct of many would lean toward dualism rather than reduc­tionism, for purely cultural or historical reasons. For the moment, it is worth saying that studies in imagining machines suggest a soft boundary between the easy and the hard. The easy problem turns out to be harder than Chalmers suggests, while the hard problem may be waning in importance.

Finally, much time has passed since Searle expressed his perfectly justified attacks on the exaggerated claims of the artificial intelli­gence practitioners of the 1970s. Indeed, in a much more recent publications he clearly suggests that non-biological machines may be of interest:

When I say that the brain is a biological organ and conscious­ness is a biological process, I do not, of course, say or imply that it would be impossible to produce an artificial brain out of non-­biological materials that could also cause and sustain conscious­ness.

However, he goes on to say that a biological understanding of how the living brain causes mind must be achieved before such machines might be designed. I believe this to be an unhelpful constraint. When I say that the heart is like a mechanical pump, I say this be­ cause I believe that the heart and the pump have some key princi­ples in common. These principles are reached through an under­standing of both the biological and the mechanical at the same time. The great advantage of doing both is that principles in me­chanics may not be so well known to biologists, and vice versa. In this book I play the roles of the naive neurobiologist and the naive philosopher but also of someone who brings an advancing knowl­edge of brain like machinery into the argument.

My agenda is to show in the simplest possible way that attempting to design such non-biological systems gives us some additional un­derstanding of how any machinery, biological or otherwise, can sus­tain conscious imagination and in this way takes us forward in at­tempting to answer the key question posed above. I do this without losing sight of the fact that the two will always be different: the liv­ing brain will have a consciousness that largely reflects its biological nature; the artificially conscious machine will have a consciousness which, by comparison, may be a rum thing, and perhaps may not merit the appellative at all. But it is the mechanism common to the two that constitutes the "additional understanding." While I am not proposing silicon transplants for the brain, I do reflect on the fact that the patient with the plastic heart survives on the basis of the properties common to the biological and the artificial heart. In the same way, I shall be looking at what I know about the artificial that may be common to the real, as we begin the journey toward trying to understand imagination and consciousness.

 

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