Interdisciplinary Research Workshop on Future Trends in Hypercomputation

我们打算于2006年9月在谢菲尔德举办一个为期3天、30人参加的关于超计算未来趋势的跨学科研究研讨会。超计算是一个新的研究领域，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、智力理论和哲学。超计算的工作可以分为5个主题：哲学一直是现代超计算理论背后的主要驱动力；实际上，他们创造了这个词。特别相关的是计算主义的问题--将大脑视为计算机，将人类行为视为计算机的行为是否合理。许多哲学家不这么认为，因此他们认为生物系统可以表现出超级计算的行为。霍加斯在90年代初表明，宇宙学奇点可以通过这种方式加以利用，最近，Kieu提出，量子绝热定理为超级计算主义提供了空间。超级计算在纯粹的牛顿环境下也是可能的；根据夏教授的说法，n体系统中的一个物体可以在有限的时间内被弹射到无限大--这种系统的可行性需要实施超级计算的“超级任务”。根据威尔斯的数学和计算机科学，著名数学家塔尔斯基假设存在一个“可决定的”但不是“递归的”系统--换句话说，一个其行为违反丘奇-图灵命题的数学系统。同样，在计算机科学中，经常提出行为超过标准图灵机的模型；例如，摩尔展示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。研究问题到目前为止，研究界一直满足于确定具有超级计算能力的特别数学、物理或生物系统--但如果我们要创建一个基于超级计算的行业，我们将需要开始编码和设计超级计算机。这样做将带来该领域独有的一些问题。例如，我们显然不能通过给出一个‘算法’来描述一个超级计算行为，因为超级计算从定义上来说是非算法的--那么我们该怎么做呢？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试图解决这些问题和其他问题作为其任务。反对尽管人们对超级计算和超级计算系统越来越感兴趣，但一小群研究人员强烈认为超级计算不是一个有效的研究领域。我们认为，将这些研究人员纳入辩论是很重要的，因为预计他们会提出一些棘手的问题，这将引发重要的研究主题。通过将争论的双方都包括在内，我们可以确保超级计算的理论建议始终得到物理审计。

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.