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Mathematical Intelligence

Author : Mubeen Junaid

Publisher : Simon and Schuster

Page : 215 pages

File Size : 26,81 MB

Release : 2022-11-01

Category : Mathematics

ISBN : 1639362576

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Book Description

A fresh exploration into the 'human nature versus technology’ argument, revealing an unexpected advantage that humans have over our future robot masters: we’re actually good at mathematics. There’s so much discussion about the threat posed by intelligent machines that it sometimes seems as though we should simply surrender to our robot overlords now. But Junaid Mubeen isn’t ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over computers, because of a remarkable system of thought that humans have developed over the millennia. It’s familiar to us all, but often badly taught in schools and misrepresented in popular discourse—math. Computers are, of course, brilliant at totting up sums, pattern-seeking, and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical talents. Just a few of the fascinating subjects covered in MATHEMATICAL INTELLIGENCE include: -Humans are endowed with a natural sense of numbers that is based on approximation rather than precise calculation. Our in-built estimation skills complement the precision of computers. Interpreting the real world depends on both. -What sets humans apart from other animals is language and abstraction. We have an extraordinary ability to create powerful representations of knowledge— more diverse than the binary language of computers. -Mathematics confers the most robust, logical framework for establishing permanent truths. Reasoning shields us from the dubious claims of pure pattern-recognition systems. -All mathematical truths are derived from a starting set of assumptions, or axioms. Unlike computers, humans have the freedom to break free of convention and examine the logical consequences of our choices. Mathematics rewards our imagination with fascinating and, on occasion, applicable concepts that originate from breaking the rules. -Computers can be tasked to solve a range of problems, but which problems are worth the effort? Questioning is as vital to our repertoire of thinking skills as problem-solving itself.



Artificial Mathematical Intelligence

Author : Danny A. J. Gómez Ramírez

Publisher : Springer Nature

Page : 268 pages

File Size : 46,88 MB

Release : 2020-10-23

Category : Mathematics

ISBN : 3030502732

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Book Description

This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.



Mathematical Structures of Natural Intelligence

Author : Yair Neuman

Publisher : Springer

Page : 179 pages

File Size : 30,42 MB

Release : 2017-12-01

Category : Mathematics

ISBN : 3319682466

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Book Description

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought. In this context, the book explores various topics and questions, such as the human representation of the number system, why our counting ability is different from that which is evident among non-human organisms, and why the idea of zero is so difficult to grasp. The book is organized into three parts: the first introduces the general reason for studying general structures underlying the human mind; the second part introduces category theory as a modeling language and use it for exposing the deep and fascinating structures underlying human cognition; and the third applies the general principles and ideas of the first two parts to reaching a better understanding of challenging aspects of the human mind such as our understanding of the number system, the metaphorical nature of our thinking and the logic of our unconscious dynamics.



The Mathematical Corporation

Author : Josh Sullivan

Publisher : PublicAffairs

Page : 289 pages

File Size : 42,69 MB

Release : 2017-06-06

Category : Business & Economics

ISBN : 1610397894

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Book Description

The most powerful weapon in business today is the alliance between the mathematical smarts of machines and the imaginative human intellect of great leaders. Together they make the mathematical corporation, the business model of the future. We are at a once-in-a-decade breaking point similar to the quality revolution of the 1980s and the dawn of the internet age in the 1990s: leaders must transform how they run their organizations, or competitors will bring them crashing to earth -- often overnight. Mathematical corporations -- the organizations that will master the future -- will outcompete high-flying rivals by merging the best of human ingenuity with machine intelligence. While smart machines are weapon number one for organizations, leaders are still the drivers of breakthroughs. Only they can ask crucial questions to capitalize on business opportunities newly discovered in oceans of data. This dynamic combination will make possible the fulfillment of missions that once seemed out of reach, even impossible to attain. Josh Sullivan and Angela Zutavern's extraordinary examples include the entrepreneur who upended preventive health care, the oceanographer who transformed fisheries management, and the pharmaceutical company that used algorithm-driven optimization to boost vaccine yields. Together they offer a profoundly optimistic vision for a dazzling new phase in business, and a playbook for how smart companies can manage the essential combination of human and machine.



Revolutionary Mathematics

Author : Justin Joque

Publisher : Verso Books

Page : 241 pages

File Size : 31,45 MB

Release : 2022-01-18

Category : Political Science

ISBN : 1788734009

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Book Description

Traces the revolution in statistics that gave rise to artificial intelligence and predictive algorithms refiguring contemporary capitalism. Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation.



Artificial and Mathematical Theory of Computation

Author : Vladimir Lifschitz

Publisher : Academic Press

Page : 488 pages

File Size : 47,94 MB

Release : 2012-12-02

Category : Computers

ISBN : 032314831X

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Book Description

Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project "proof checker for first-order logic" at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes.



Intelligence Reframed

Author : Howard E Gardner

Publisher : Basic Books

Page : 257 pages

File Size : 26,30 MB

Release : 2000-09-18

Category : Education

ISBN : 0465013147

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Book Description

Harvard psychologist Howard Gardner has been acclaimed as the most influential educational theorist since John Dewey. His ideas about intelligence and creativity - explicated in such bestselling books as Frames of Mind and Multiple Intelligences (over 200,000 copies in print combined) - have revolutionized our thinking. In his groundbreaking 1983 book Frames of Mind , Howard Gardner first introduced the theory of multiple intelligences, which posits that intelligence is more than a single property of the human mind. That theory has become widely accepted as one of the seminal ideas of the twentieth century and continues to attract attention all over the world. Now in Intelligence Reframed , Gardner provides a much-needed report on the theory, its evolution and revisions. He offers practical guidance on the educational uses of the theory and responds to the critiques leveled against him. He also introduces two new intelligences (existential intelligence and naturalist intelligence) and argues that the concept of intelligence should be broadened, but not so absurdly that it includes every human virtue and value. Ultimately, argues Gardner, possessing a basic set of seven or eight intelligences is not only a unique trademark of the human species, but also perhaps even a working definition of the species. Gardner also offers provocative ideas about creativity, leadership, and moral excellence, and speculates about the relationship between multiple intelligences and the world of work in the future.



The Structure of Intelligence

Author : Ben Goertzel

Publisher : Springer Science & Business Media

Page : 232 pages

File Size : 42,52 MB

Release : 2013-03-07

Category : Psychology

ISBN : 146124336X

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Book Description

0. 0 Psychology versus Complex Systems Science Over the last century, psychology has become much less of an art and much more of a science. Philosophical speculation is out; data collection is in. In many ways this has been a very positive trend. Cognitive science (Mandler, 1985) has given us scientific analyses of a variety of intelligent behaviors: short-term memory, language processing, vision processing, etc. And thanks to molecular psychology (Franklin, 1985), we now have a rudimentary understanding of the chemical processes underlying personality and mental illness. However, there is a growing feeling-particularly among non-psychologists (see e. g. Sommerhoff, 1990) - that, with the new emphasis on data collection, something important has been lost. Very little attention is paid to the question of how it all fits together. The early psychologists, and the classical philosophers of mind, were concerned with the general nature of mentality as much as with the mechanisms underlying specific phenomena. But the new, scientific psychology has made disappointingly little progress toward the resolution of these more general questions. One way to deal with this complaint is to dismiss the questions themselves. After all, one might argue, a scientific psychology cannot be expected to deal with fuzzy philosophical questions that probably have little empirical signifi cance. It is interesting that behaviorists and cognitive scientists tend to be in agreement regarding the question of the overall structure of the mind.



Applied Mathematics and Computational Intelligence

Author : Anna M. Gil-Lafuente

Publisher : Springer

Page : 439 pages

File Size : 27,76 MB

Release : 2018-03-06

Category : Technology & Engineering

ISBN : 331975792X

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Book Description

This book gathers selected papers presented at the conference of the Forum for Interdisciplinary Mathematics (FIM), held at Palau Macaya, Barcelona, on 18 to 20 November, 2015. The event was co-organized by the University of Barcelona (Spain), the Spanish Royal Academy of Economic and Financial Sciences (Spain) and the Forum for Interdisciplinary Mathematics (India). This instalment of the conference was presented with the title “Applied Mathematics and Computational Intelligence” and particularly focused on the use of Mathematics and Computational Intelligence techniques in a diverse range of scientific disciplines, as well as their applications in real-world problems. The book presents thirty peer-reviewed research papers, organised into four topical sections: on Mathematical Foundations; Computational Intelligence and Optimization Techniques; Modelling and Simulation Techniques; and Applications in Business and Engineering. This book will be of great interest to anyone working in the area of applied mathematics and computational intelligence and will be especially useful for scientists and graduate students pursuing research in these fields.



Mathematical Methods in Artificial Intelligence

Author : Edward A. Bender

Publisher : Wiley-IEEE Computer Society Press

Page : 0 pages

File Size : 25,84 MB

Release : 1996-02-10

Category : Technology & Engineering

ISBN : 9780818672002

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Book Description

Mathematical Methods in Artificial Intelligence introduces the student to the important mathematical foundations and tools in AI and describes their applications to the design of AI algorithms. This useful text presents an introductory AI course based on the most important mathematics and its applications. It focuses on important topics that are proven useful in AI and involve the most broadly applicable mathematics. The book explores AI from three different viewpoints: goals, methods or tools, and achievements and failures. Its goals of reasoning, planning, learning, or language understanding and use are centered around the expert system idea. The tools of AI are presented in terms of what can be incorporated in the data structures. The book looks into the concepts and tools of limited structure, mathematical logic, logic-like representation, numerical information, and nonsymbolic structures. The text emphasizes the main mathematical tools for representing and manipulating knowledge symbolically. These are various forms of logic for qualitative knowledge, and probability and related concepts for quantitative knowledge. The main tools for manipulating knowledge nonsymbolically, as neural nets, are optimization methods and statistics. This material is covered in the text by topics such as trees and search, classical mathematical logic, and uncertainty and reasoning. A solutions diskette is available, please call for more information.