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Hypercomputation: computing more than the Turing machine
, 2002
"... In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which al ..."
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Cited by 31 (5 self)
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In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines. I begin with a succinct introduction to the classical theory of computation and its place amongst some of the negative results of the 20 th Century. I then explain how the ChurchTuring Thesis is commonly misunderstood and present new theses which better describe the possible limits on computability. Following this, I introduce ten different hypermachines (including three of my own) and discuss in some depth the manners in which they attain their power and the physical plausibility of each method. I then compare the powers of the different models using a device from recursion theory. Finally, I examine the implications of hypercomputation to mathematics, physics, computer science and philosophy. Perhaps the most important of these implications is that the negative mathematical results of Gödel, Turing and Chaitin are each dependent upon the nature of physics. This both weakens these results and provides strong links between mathematics and physics. I conclude that hypercomputation is of serious academic interest within many disciplines, opening new possibilities that were previously ignored because of long held misconceptions about the limits of computation.
1 Pluralistic Modeling of Complex Systems
, 1007
"... The modeling of complex systems such as ecological or socioeconomic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not allow one to decide what model is the right one, the best one, ..."
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Cited by 2 (1 self)
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The modeling of complex systems such as ecological or socioeconomic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not allow one to decide what model is the right one, the best one, or most appropriate one. Moreover, as the recent financial and economic crisis shows, relying on a single, idealized model can be very costly. This contribution tries to shed new light on problems that arise when complex systems are modeled. While the arguments can be transferred to many different systems, the related scientific challenges are illustrated for social, economic, and traffic systems. The contribution discusses issues that are sometimes overlooked and tries to overcome some frequent misunderstandings and controversies of the past. At the same time, it is highlighted how some longstanding scientific puzzles may be solved by considering nonlinear models of heterogeneous agents with spatiotemporal interactions. As a result of the analysis, it is concluded that a paradigm shift towards a pluralistic or possibilistic modeling approach, which integrates multiple world views, is overdue. In this connection, it is argued that it can be useful to combine many different approaches to obtain a good picture of reality, even though they may be inconsistent. Finally, it is identified what would be profitable areas of collaboration between the socioeconomic, natural, and engineering sciences. 1
MeaningBased Natural Intelligence Vs. InformationBased Artificial Intelligence By
"... In this chapter, we reflect on the concept of MeaningBased Natural Intelligence a fundamental trait of Life shared by all organisms, from bacteria to humans, associated with: semantic and pragmatic communication, assignment and generation of meaning, formation of selfidentity and of associated id ..."
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In this chapter, we reflect on the concept of MeaningBased Natural Intelligence a fundamental trait of Life shared by all organisms, from bacteria to humans, associated with: semantic and pragmatic communication, assignment and generation of meaning, formation of selfidentity and of associated identity (i.e., of the group the individual belongs to), identification of natural intelligence, intentional behavior, decisionmaking and intentionally designed selfalterations. These features place the MeaningBased natural Intelligence beyond the realm of Informationbased Artificial Intelligence. Hence, organisms are beyond manmade predesigned machinery and are distinguishable from nonliving systems. Our chain of reasoning begins with the simple distinction between intrinsic and extrinsic contextual causations for acquiring intelligence. The first, associated with natural intelligence, is required for the survival of the organism (the biotic system) that generates it. In contrast, artificial intelligence is implemented externally to fulfill a purpose for the benefit of the organism that engineered the “Intelligent Machinery”. We explicitly propose that the ability to assign contextual meaning to externally gathered information is an essential
focus modeldriven development What Models Mean
"... If today’s software developers use models at all, they use them mostly as simple sketches of design ideas, often discarding them once they’ve written the code. This is sufficient for traditional codecentric development. With a modeldriven approach, however, the models themselves become the primary ..."
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If today’s software developers use models at all, they use them mostly as simple sketches of design ideas, often discarding them once they’ve written the code. This is sufficient for traditional codecentric development. With a modeldriven approach, however, the models themselves become the primary artifacts in the development of software. In this case, a clear, common understanding of the semantics of our modeling languages is at least as important as a clear, common understanding of the semantics of our programming languages. There has been, and continues to be, a great deal of discussion within the software community on modeling and metamodeling and the relationships between modeling languages and metamodeling languages. Such relationships’ circular nature makes them particularly
Gödel's incompleteness theorems and artificial life
, 1997
"... In this paper I discuss whether Gödel's incompleteness theorems have any implications for studies in Artificial Life (AL). Since Gödel's incompleteness theorems have been used to argue against certain mechanistic theories of the mind, it seems natural to attempt to apply the theorems to certain stro ..."
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In this paper I discuss whether Gödel's incompleteness theorems have any implications for studies in Artificial Life (AL). Since Gödel's incompleteness theorems have been used to argue against certain mechanistic theories of the mind, it seems natural to attempt to apply the theorems to certain strong mechanistic arguments postulated by some AL theorists. We find that an argument using the incompleteness theorems can not be constructed that will block the hard AL claim, specifically in the field of robotics. However, we will see that the beginnings of an argument casting doubt on our ability to create living systems entirely resident in a computer environment might be suggested by looking at the incompleteness theorems from the point of view of Gödel's belief in mathematical realism.
Gödel's Incompleteness Theorems: A Revolutionary View of the Nature of Mathematical Pursuits
"... The work of the mathematician Kurt Gödel changed the face of mathematics forever. His famous incompleteness theorem proved that any formalized system of mathematics would always contain statements that were undecidable, showing that there are certain inherent limitations to the way many mathematicia ..."
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The work of the mathematician Kurt Gödel changed the face of mathematics forever. His famous incompleteness theorem proved that any formalized system of mathematics would always contain statements that were undecidable, showing that there are certain inherent limitations to the way many mathematicians studies mathematics. This paper provides a history of the mathematical developments that laid the foundation for Gödel's work, describes the unique method used by Gödel to prove his famous incompleteness theorem, and discusses the farreaching mathematical implications thereof. 2 I.
“Common Grace Social Capital ” Investments for Sustaining Ethical Conduct in New and Emerging Economies” replaces original title below: Synergistic Development of Sustainable Ethical Processes when Pursuing Opportunities with Unpredictable Emerging Econom
"... Ten “common grace ” social capital investments are developed as normative propositions for sustaining ethical conduct with a variety of new economy and emerging economy challenges. Drawing primarily upon Clay Christensen and Geoff Moore’s findings regarding adoption risks with “disruptive technologi ..."
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Ten “common grace ” social capital investments are developed as normative propositions for sustaining ethical conduct with a variety of new economy and emerging economy challenges. Drawing primarily upon Clay Christensen and Geoff Moore’s findings regarding adoption risks with “disruptive technologies ” authenticity/integrity and competence issues are explored within the larger perspectives of true excellence and goodness derived from Morris ’ “If Aristotle Ran G.M.”. The cognitive psychological limits to moral development such as the illusion of ethical superiority and inoculation effects attending legalistic judgmentalism constitute some of the more serious impediments that suggest the need for a combination of trust and gratitude resolutions. When practical applications of trust and gratitudebased mentoring are synthesized with the “social capital ” guidelines from Prusak & Cohen we begin to see the desirability of a “common grace ” social capital construct workedout in terms of five trust and five gratitude guidelines for sustainable ethical conduct robust enough to handle extraordinary pressures from “new economy pathologies ” and emerging economies.
unknown title
"... Discuss the advantages and disadvantages of adopting a multiparadigm or multirationality approach to management and decision making This paper shall examine the consequences of a conscious adoption of a multiparadigm or multirationality approach. Firstly the limits of formal logic are examined, a ..."
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Discuss the advantages and disadvantages of adopting a multiparadigm or multirationality approach to management and decision making This paper shall examine the consequences of a conscious adoption of a multiparadigm or multirationality approach. Firstly the limits of formal logic are examined, and thus those of rationality, and what logic itself suggests should be done about it. Management is supposed to direct organisations through highlevel decision making, but this paper suggests its true purpose is actually to manage uncertainty 1 i.e.; organisations exist to manage uncertainty, usually through conversion into risk. The paper then concludes with case examples of how pathological the fear of uncertainty can become, but also how paradoxically the exact same mechanism can save us from the same morass. The Limits of Rationality More than anything else, the age of reason defines the modern age 2, and nothing is of more importance to rational thought than the systematic application of logic and mathematics. However, with the publication of Principia Mathematica in 19111913, the terrible reality that logic has limits reared its head 3. With Kurt Gödel’s 1931 paper on Principia Mathematica, the incompleteness of formal logical systems became incontrovertible truth. Put simply, Gödel’s Incompleteness Theorem means that for any consistent formal theory that proves basic arithmetical truths, one can construct an arithmetical statement that is true but not 1 Uncertainty throughout this paper is used as a technical term for the future.
Our Prediction of the Near Future for the West.................... 8
, 2009
"... A very short pamphlet overviewing our principles and proposals which offer a highgrowth future for our civilisation in a time of ..."
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A very short pamphlet overviewing our principles and proposals which offer a highgrowth future for our civilisation in a time of
Connected Mathematics  Building . . . with Mathematical Knowledge
, 1993
"... The context for this thesis is the conflict between two prevalent ways of viewing mathematics. The first way is to see mathematics as primarily a formal enterprise, concerned with working out the syntactic/formal consequences of its definitions. In the second view, mathematics is a creative enterpri ..."
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The context for this thesis is the conflict between two prevalent ways of viewing mathematics. The first way is to see mathematics as primarily a formal enterprise, concerned with working out the syntactic/formal consequences of its definitions. In the second view, mathematics is a creative enterprise concerned primarily with the construction of new entities and the negotiation of their meaning and value. Among teachers of mathematics the formal view dominates. The consequence for learners is a shallow brittle understanding of the mathematics they learn. Even for mathematics that they can do, in the sense of calculating an answer, they often can't explain why they're doing what they're doing, relate it to other mathematical ideas or operations, or connect the mathematics to any idea or problem they may encounter in their lives. The aim of this thesis is to develop alternative ways of teaching mathematics which strengthen the informal, intuitive and creative in mathematics. This research develops an approach to learning mathematics called "connected mathematics" which emphasizes learners’ negotiation of mathematical meaning. I have