The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is stric...The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.)展开更多
In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped i...In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.展开更多
This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself propos...This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blueprint of the brain’s OS. A first addition to the book (see Chapters 5 to 10 below) concerns the relation between the afore-mentioned blueprint and the more than 2000-year-old so-called fundamental laws of thought of logic and philosophy, which came to be viewed as being three (3) in number, namely the laws of 1) Identity, 2) Contradiction, and 3) the Excluded Middle. The blueprint and the laws cannot both be the final foundation of the brain’s OS. The design of the present paper is to interpret the laws in strictly mathematical terms in light of the blueprint. This addition constitutes the bulk of the present article. Chapters 5 to 8 set the stage. Chapters 9 and 10 present a detailed mathematical analysis of the laws. A second addition to the book (Chapter 11) concerns the distinction between the laws and the axioms of the brain’s OS. Laws are part of physics. Axioms are part of mathematics. Since the theory of the brain’s OS involves both physics and mathematics, it exhibits both laws and axioms. A third addition (Chapter 12) to the book involves an additional flavor of digitality in the brain’s OS. In the book, there are five (5). But brain chemistry requires a sixth. It will be called Existence Digitality. A fourth addition (Chapter 13) concerns reflections on the role of imagination in theories of physics in light of the ignorance of deeper causes. Chapters 1 to 4 present preliminary matter, for the most part a brief survey of general concepts derived from what is in the book [1]. Some historical notes are gathered at the end in Chapter 14.展开更多
人们通常将智能革命与以往多次科技革命并列,但这不能反映智能革命的特质和影响。以往的科技革命都是专能(专门能力)革命,智能革命是首次发生的通能革命,引发社会前所未有的巨变。人工智能风险与伦理治理收效甚微,其首要原因是公众和学...人们通常将智能革命与以往多次科技革命并列,但这不能反映智能革命的特质和影响。以往的科技革命都是专能(专门能力)革命,智能革命是首次发生的通能革命,引发社会前所未有的巨变。人工智能风险与伦理治理收效甚微,其首要原因是公众和学术界深陷十大认识误区。深度信息化、数字化导致人类边际收益递减,AI机器人因不受生理限制而收益越来越大,远超人类的收益,直到反客为主,危害人类,可谓“数字反噬”。人工智能造成“短期失业、长期增业”论不能成立,通能革命势必引发大规模失业,可谓“通能塔诅咒”。“奇点到来还很遥远”这一判断是错误的,人工智能“还没有超过人类智能”“还没有自主意识”,并不等同于AI没有威胁人类安全。只要AI或利用AI可造成毁灭性灾难,即可认为“奇点”来临,至少广义的“奇点”——“畸点”已临。AI for Science导致的最大风险是辅助或自主生产“致毁知识”,对它而言,科技伦理形同虚设。初探科技风险剧增理论,指出人工智能等高科技带来的好处越来越多,却终将毁于一旦,可谓“全押归零的人工智能赌局”。因此急需发展以提高助人能力为目标的人工辅能(AAI),尽快实现从以提高智慧能力为目标的人工智能A模式向以提高辅助能力为目标的人工智能B模式(人工辅能模式)的转变。展开更多
The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The ma...The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.展开更多
文摘The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.)
文摘In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.
文摘This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blueprint of the brain’s OS. A first addition to the book (see Chapters 5 to 10 below) concerns the relation between the afore-mentioned blueprint and the more than 2000-year-old so-called fundamental laws of thought of logic and philosophy, which came to be viewed as being three (3) in number, namely the laws of 1) Identity, 2) Contradiction, and 3) the Excluded Middle. The blueprint and the laws cannot both be the final foundation of the brain’s OS. The design of the present paper is to interpret the laws in strictly mathematical terms in light of the blueprint. This addition constitutes the bulk of the present article. Chapters 5 to 8 set the stage. Chapters 9 and 10 present a detailed mathematical analysis of the laws. A second addition to the book (Chapter 11) concerns the distinction between the laws and the axioms of the brain’s OS. Laws are part of physics. Axioms are part of mathematics. Since the theory of the brain’s OS involves both physics and mathematics, it exhibits both laws and axioms. A third addition (Chapter 12) to the book involves an additional flavor of digitality in the brain’s OS. In the book, there are five (5). But brain chemistry requires a sixth. It will be called Existence Digitality. A fourth addition (Chapter 13) concerns reflections on the role of imagination in theories of physics in light of the ignorance of deeper causes. Chapters 1 to 4 present preliminary matter, for the most part a brief survey of general concepts derived from what is in the book [1]. Some historical notes are gathered at the end in Chapter 14.
文摘人们通常将智能革命与以往多次科技革命并列,但这不能反映智能革命的特质和影响。以往的科技革命都是专能(专门能力)革命,智能革命是首次发生的通能革命,引发社会前所未有的巨变。人工智能风险与伦理治理收效甚微,其首要原因是公众和学术界深陷十大认识误区。深度信息化、数字化导致人类边际收益递减,AI机器人因不受生理限制而收益越来越大,远超人类的收益,直到反客为主,危害人类,可谓“数字反噬”。人工智能造成“短期失业、长期增业”论不能成立,通能革命势必引发大规模失业,可谓“通能塔诅咒”。“奇点到来还很遥远”这一判断是错误的,人工智能“还没有超过人类智能”“还没有自主意识”,并不等同于AI没有威胁人类安全。只要AI或利用AI可造成毁灭性灾难,即可认为“奇点”来临,至少广义的“奇点”——“畸点”已临。AI for Science导致的最大风险是辅助或自主生产“致毁知识”,对它而言,科技伦理形同虚设。初探科技风险剧增理论,指出人工智能等高科技带来的好处越来越多,却终将毁于一旦,可谓“全押归零的人工智能赌局”。因此急需发展以提高助人能力为目标的人工辅能(AAI),尽快实现从以提高智慧能力为目标的人工智能A模式向以提高辅助能力为目标的人工智能B模式(人工辅能模式)的转变。
文摘The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.
