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基础理论的自然美
热度 2 yqgu 2020-10-14 22:43
最近看到博文《自然的数学观》 , Penrose 认为 “ 自然的新数学模型并不是仅仅为了寻求符合事实的最佳理论而发明的人造物,更明白地说,数学纲 领其实已经在大自然的运行中发生作用了。这种数学的简单性(或简洁性或随你怎么形容它)是自然行为方式的真实部分,而不是我们的头脑习惯被数学美所感染。另一方面,当我们有心用数学美的准则去构建理论时,很容易被引向歧路。 ” 杨振宁先生最近也表达过类似的观点,认为数学不仅仅是研究物理的工具,而是基础理论的一部分。这也算是对他自己的 “ 数学和物理的双叶理论 ” 的一次重要改进。 我完全赞同这样的观点,而且一直在苦苦寻觅这套造物主的密码系统。如果看过我的新书《几何代数和统一场论》,应该会同意我可能已经找到了这套密码,这就是 Clifford 代数或几何代数。这个代数建立了一百多年,得到了很多数学和物理大师的深入研究,已有广泛的应用 。如果将有关概念稍作推广和重新解释,几何代数就是描述基础物理和量化数学的自然语言和工具,自然地统一了现有基础理论的大部分内容。这是因为几何代数的定义自动蕴含了向量、长度、角度、面积和体积等几何概念,将标量、旋量、向量、外积和张量等代数运算统一起来,忠实地描述几何和物理中内容,不多也不少。几何代数推广了实数、复数、四元数和向量代数,将复杂的关系和运算转化为独立于坐标系的矩阵代数。 通过引入微分算子和联络算子, Clifford 代数也包含了微分几何。几何代数运算类似于算术的加减乘除,每个一般智力的人都能很好地理解。这一特点对教学目的非常有用,如果在高中和大学推广几何代数,将大大提高学生学习数学和物理基础知识的效率。 学习现代数学的真正困难在于,为了理解一个很小的结果,我们需要掌握一长串微妙的概念。数学家习惯于在概念之上定义概念,如果学习概念的链条断裂,随后的内容将是不可理解的。除了专业人士外,普通读者不可能有那么多时间仔细检查和理解所有的概念。幸运的是, Clifford 代数可以避免这个问题,因为几何代数只依赖于一些简单的概念,并且同构于一些特殊的矩阵代数; Clifford 代数的规则是标准化的,适用于无脑操作。因此,可以预期克里福德代数将完成科学知识体系的一次大综合。 在我的印象中 Penrose 是个信奉繁琐哲学的人,所以我一直不是很欣赏他的东西,觉得他抓不住问题的要领。例如他和 Newman 搞的那套零标架表示: 瞟一眼都觉得浪费时间,真是佩服他们的耐心。自然规律怎么可能是这幅样子。现在 Penrose 的观念能有这样的转变实属难得。还有梁灿彬老先生,出国回来准备在国内推广 Penrose 等人开发的微分几何抽象记号系统 。形式上微妙易错,实质内容又没有表达清楚,很难掌握。经过二十多年的努力,最后老先生捧书感叹:微分几何推广起来怎么这么难! 大自然的书是用最简单但是最精美的数学写成的。看看我书中的内容,心情应该是完全不同的。 李咏,自然的数学观, http://blog.sciencenet.cn/home.php?mod=spaceuid=279992 Ying-Qiu Gu, Some Applications of Clifford Algebra in Geometry , https://www.researchgate.net/publication/338582922 https://doi.org/10.5772/intechopen.93444 梁灿彬,周彬,微分几何入门与广义相对论 ( 上中下 ) , 科学出版社,北京, 2006
3004 次阅读|3 个评论
[严肃内容] 狭义相对论“尺缩效应”Penrose 旋转的滤波器解释
热度 3 zlyang 2020-10-9 19:59
汉语是联合国官方正式使用的 6 种同等有效语言之一。请不要歧视汉语! Chinese is one of the six equally effective official languages of the United Nations. Not to discriminate against Chinese, please! 狭义相对论“尺缩效应” Penrose 旋转 的 滤波器 解释 爱因斯坦 说: “ 提出一个问题往往比解决一个问题更重要 ,因为解决问题也许仅能是一个数学上或实验室上的技能而已。 而提出新的问题、新的可能性, 从新的角度去看旧的问题, 都需要有创造性的想象力, 而且标志着科学的真正进步。 ” Roger Penrose 终于因为“黑洞”获得 2020年 诺贝尔物理奖 了。 恭喜! Roger Penrose: https://loff.it/wp-content/uploads/2014/08/loffit_roger-penrose_04-600x450-1596703657.jpg 蹭 Penrose 先生的热度,推广一下真傻的一个本科生课《电工学》教学创新:“ Lorentz Contraction 的 Penrose 旋转的 一阶高通滤波器解释 ”吧!爱因斯坦先生《狭义相对论》的“洛伦兹收缩/尺缩效应”的彭罗斯旋转的“一阶高通滤波器解释”。 这个么,虽然不是惊天动地的大事, 很可能又是一个“写进教材”级别的小小贡献。 详细的内容,请看: 2005-04-27,《Lorentz Contraction的矢量化表示和它的滤波器解释》, Vector Expression of Lorentz Contraction and Its Filter Interpretation . http://www.paper.edu.cn/releasepaper/content/200504-173 早一点的一个要点,请看: 电工教学中的“科学”发现与猜测(“Science” discoveries in electrical engineering teaching are guessed) ,《高教研究与探索》,1996,4: 10-13. 截图如下: 大约的确是 中国人 首先提出 了爱因斯坦狭义相对论里洛伦兹收缩(Lorentz Contraction)的 矢量化表示 和它的 一阶高通滤波器解释 。 这个狭义相对论“尺缩效应”的旋转解释, 美国人一般叫做“Terrell Rotation 特雷尔旋转”, 英国人一般叫做“Penrose Rotation 彭罗斯旋转”。 在遥远的青年时代,俺发现了“全人类不怎么懂爱因斯坦相对论”的谜底!是1959年前后彭罗斯旋转的“一阶高通滤波器”化解释:爱因斯坦的相对论,是个实数公式。该实数公式是“一阶高通滤波器”的模。Penrose、Terrell 旋转是该滤波器的相角!爱因斯坦自己明白,别人可是费劲了。 这就是俺教《电工学》课时的发现!您说俺爱不爱《电工学》? 参考资料: The Nobel Prize in Physics 2020 https://www.nobelprize.org/prizes/physics/2020/summary/ one half awarded to Roger Penrose for the discovery that black hole formation is a robust prediction of the general theory of relativity, R. Penrose. The apparent shape of a relativistically moving sphere . Proceedings of the Cambridge Philosophical Society, 1959, 55: 137-139. DOI: https://doi.org/10.1017/S0305004100033776 James Terrell. Invisibility of the Lorentz contraction . Physical Review, 1959, 116(4): 1041-1045. https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041 Victor Frederick Weisskopf. The visual appearance of rapidly moving objects . Physics Today, 1960, 13(9): 24-27. https://physicstoday.scitation.org/doi/10.1063/1.3057105 Anthony P. French. Special relativity . New York: W. W. Norton Company, Inc., 1968. 相关链接: 2019-06-26,俺在《中国科技论文在线》贴出的论文 http://blog.sciencenet.cn/blog-107667-1186935.html 电工教学中的“科学”发现与猜测 . 高教研究与探索,1996, (4): 10-13. 2013-01-25,真傻当选2012年度“中国科技论文在线”优秀评审专家 http://blog.sciencenet.cn/blog-107667-656443.html 2010-05-06,真傻被评为:2009年度“中国科技论文在线”优秀评审专家 http://blog.sciencenet.cn/blog-107667-320480.html 2020-03-04,首个世界工程日:重申俺的一项《电工学》教学创新优先权 http://blog.sciencenet.cn/blog-107667-1221742.html 2020-10-04, 中国人首先提出 SI 基本单位“安培”新定义? http://blog.sciencenet.cn/blog-107667-1253168.html 2020-10-08, 黑洞、电磁黑洞(静电黑洞)、联合黑洞(黑洞+电磁黑洞),统一场“黑洞” http://blog.sciencenet.cn/blog-107667-1253596.html 感谢您的指教! 感谢您指正以上任何错误! 感谢您提供更多的相关资料!
个人分类: 痛苦的人生|4891 次阅读|7 个评论
[转载]Roger Penrose on Physics and Consciousness
josh 2013-5-27 11:29
转自: http://en.wikipedia.org/wiki/Roger_Penrose ... Penrose has written books on the connection between fundamental physics and human (or animal) consciousness. In The Emperor's New Mind (1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity ). Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic . (E.g., imagine a system with only two states, ON and OFF. If the system's state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system's state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic yet non-algorithmic processes may come in play in the quantum mechanical wave function reduction , and may be harnessed by the brain. He argues that the present computer is unable to have intelligence because it is an algorithmically deterministic system. He argues against the viewpoint that the rational processes of the mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence , who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic because things such as the insolubility of the halting problem and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims were originally espoused by the philosopher John Lucas of Merton College , Oxford . The Penrose/Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been widely criticized by mathematicians, computer scientists and philosophers, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack. Marvin Minsky , a leading proponent of artificial intelligence, was particularly critical, stating that Penrose tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle. Minsky's position is exactly the opposite - he believes that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains that one can carry that quest too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness. Penrose responded to criticism of The Emperor's New Mind with his follow up 1994 book Shadows of the Mind , and in 1997 with The Large, the Small and the Human Mind . In those works, he also combined his observations with that of anesthesiologist Stuart Hameroff . Penrose and Hameroff have argued that consciousness is the result of quantum gravity effects in microtubules , which they dubbed Orch-OR (orchestrated objective reduction). Max Tegmark , in a paper in Physical Review E , calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence time by a factor of at least 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark's support: Physicists outside the fray, such as IBM's John A. Smolin , say the calculations confirm what they had suspected all along. 'We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior'. Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position. In their reply to Tegmark's paper, also published in Physical Review E , the physicists Scott Hagan, Jack Tuszynski and Hameroff claimed that Tegmark did not address the Orch-OR model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, but still well short of the 25 ms required if the quantum processing in the theory was to be linked to the 40 Hz gamma synchrony, as Orch-OR suggested. To bridge this gap, the group made a series of proposals. It was supposed that the interiors of neurons could alternate between liquid and gel states. In the gel state, it was further hypothesized that the water electrical dipoles are oriented in the same direction, along the outer edge of the microtubule tubulin subunits. Hameroff et al. proposed that this ordered water could screen any quantum coherence within the tubulin of the microtubules from the environment of the rest of the brain. Each tubulin also has a tail extending out from the microtubules, which is negatively charged, and therefore attracts positively charged ions. It is suggested that this could provide further screening. Further to this, there was a suggestion that the microtubules could be pumped into a coherent state by biochemical energy. Roger Penrose in the University of Santiago de Compostela to receive the Fonseca Prize . Finally, it is suggested that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of holding together quantum coherence in the face of environmental interaction. In the last decade, some researchers who are sympathetic to Penrose's ideas have proposed an alternative scheme for quantum processing in microtubules based on the interaction of tubulin tails with microtubule-associated proteins, motor proteins and presynaptic scaffold proteins. These proposed alternative processes have the advantage of taking place within Tegmark's time to decoherence. Hameroff, in a lecture in part of a Google Tech talks series exploring quantum biology , gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR model. In addition to this, a recent 2011 paper by Roger Penrose and Stuart Hameroff gives an updated model of their Orch-OR theory, in light of criticisms, and discusses the place of consciousness within the universe. Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are at present a minority view in scientific circles, citing Minsky's criticisms and quoting science journalist Charles Seife 's description of Penrose as one of a handful of scientists who believe that the nature of consciousness suggests a quantum process. ...
个人分类: 真真假假互联网|1681 次阅读|0 个评论

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