Interdisciplinary Research Workshop on Future Trends in Hypercomputation

我们计划于2006年9月在谢菲尔德举办一个为期3天、30人的关于超计算未来趋势的跨学科研究研讨会。超计算--对可证明具有超过标准图灵机能力的系统的研究--是一个新颖的研究领域，其工作涉及广泛的不同学科，包括计算机科学、数学、量子理论、生物学、神经网络、广义相对论、智能理论和哲学。超计算的工作可以分为5个主题：哲学哲学是现代超计算理论背后的主要驱动力;事实上，他们创造了这个词。特别相关的是计算主义的问题-把大脑看作计算机，把人类行为看作计算机的行为，这是否合理。许多哲学家不相信;因此，他们认为生物系统可以进行超计算。物理学许多物理系统可以进行超计算。霍加斯在90年代初表明，宇宙学奇点可以以这种方式被利用，最近，Kieu提出量子绝热定理为超计算主义提供了空间。超计算在纯牛顿环境下也是可能的;根据Xia的观点，n体系统中的一个物体可以在有限时间内被弹射到无穷远--这种系统的可行性需要实现超计算的“超级任务”。数学和计算机科学根据威尔斯的观点，著名的数学家塔斯基假设存在一个“可判定”但不是“递归”的系统--换句话说，一个行为违反丘奇-图灵命题的数学系统。同样，在计算机科学中，模型经常被提出，其行为超过标准图灵机的行为;例如，摩尔已经证明了一个行为良好的实时计算模型，具有明显的超级图灵潜力。物理或生物系统的超计算能力--但如果我们要创造一个基于超计算的产业，我们就需要开始编纂和设计超计算机。这样做会带来一些该领域特有的问题。例如，我们显然不能通过给出一个“算法”来描述超计算行为，因为超计算的定义是非算法的--那么我们怎么做呢？研讨会的一个重要主题将是确定关键的研究问题;随后的研究网络将把它作为其任务，试图解决这些问题，以及其他问题。反对的论点尽管超计算和超计算系统的兴趣越来越大，一小群研究人员热情地认为，超计算是不是一个有效的研究领域。我们认为将这些研究人员包括在辩论中是很重要的，因为他们可能会提出一些棘手的问题，从而推动重要的研究主题。通过包括争论的双方，我们可以确保超计算的理论建议始终受到物理性的审查。

We intend holding a 3-day, 30-person, Interdisciplinary Research Workshop on Future Trends in Hypercomputation, in Sheffield in September 2006.Hypercomputation -- the study of systems that are provably capable of more than the standard Turing machine -- is a novel research area, with work conducted across a wide range of disparate displines, including computer science, mathematics, quantum theory, biology, neural networks, general relativity, the theory of intelligence and philosophy.Work in hypercomputation can be divided into 5 main themes:PHILOSOPHY Philosophy has been a major driving force behind modern hypercomputation theory; indeed, they coined the word. Of particular relevance is the question of computationalism -- is it reasonable to regard the brain as a computer, and human behaviour as the behaviour of a computer. Many philosophers believe not; they therefore argue that biological systems can behave hypercomputationally.PHYSICS Many physical systems can behave hypercomputationally. Hogarth showed in the early 90s that cosmological singularities can be exploited in this way, and more recently, Kieu has suggested that the quantum adiabatic theorem offers scope for hypercomputationalism. Hypercomputation is also possible under purely Newtonian circumstances; according to Xia, a body in an n-body system can be ejected to infinity in finite time -- the feasibility of such systems entails the implementation of hypercomputational `supertasks'.MATHS AND COMPUTER SCIENCE According to Wells, the noted mathematician Tarski posited the existence of a system that was 'decidable' but not 'recursive' -- in other words, a mathematical system whose behaviour violates the Church-Turing thesis. Similarly in Computer Science, models have frequently been proposed with behaviours that exceed those of the standard Turing machine; Moore, for example, has demonstrated a well-behaved model of real-time computation with manifestly super-Turing potential.RESEARCH QUESTIONS To date, the research community has been content to identify ad-hoc mathematical, physical or biological systems with hypercomputational power -- but if we are ever to create an industry based on hypercomputation, we will need to start codifying and designing hypercomputers. Doing so will present a number of problems that are unique to the field. For example, we clearly cannot describe a hypercomputational behaviour by giving an 'algorithm', because hypercomputation is non-algorithmic by definition -- so how do we do it? An important theme of the Workshop will be the identification of key research questions; the ensuing Research Network will take it as its mandate to attempt a solution to these, and other, questions.ARGUMENTS AGAINST Despite the growing interest in hypercomputation and hypercomputational systems, a small group of researchers feels passionately that hypercomputation is not a valid research area. We feel it is important to include these researchers within the debate, as they can be expected to pose difficult questions that will prompt important research themes. By including both sides of the argument, we can ensure that theoretical proposals for hypercomputation are consistently audited for physicality.