万物的数学理论
Algorithmic Theories of Everything
摘要：
概率分布P代表了一种万物理论或TOE，我们的宇宙历史就是从概率分布P中取样的。我们假设P是形式上可描述的。由于大多数（不可数的）分布不是，这强加了一个强烈的归纳偏差。我们表明，P（x）是小的任何宇宙x缺乏一个简短的描述，并研究了频谱的TOE跨越两个P，一个反映了最紧凑的建设性的描述，其他最快的方式计算一切。前者来自传统可计算性的推广，Solomonoff的算法概率，Kolmogorov复杂性，以及比Chaitin的Omega更随机的对象，后者来自Levin的通用搜索和自然资源导向的假设：在时间t内所有x的累积先验概率通过这个最佳算法应该是1/t。在两个P之间，我们发现一个普遍的累积可计数测度，它支配着传统的可计数测度;任何这样的CEM都必须为任何缺乏短枚举程序的宇宙分配低概率。我们得出P-特定的后果，不断发展的观察者，归纳推理，量子物理学，哲学，和我们的宇宙的预期持续时间。
英文摘要：
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong inductive bias. We show that P(x) is small for any universe x lacking a short description, and study the spectrum of TOEs spanned by two Ps, one reflecting the most compact constructive descriptions, the other the fastest way of computing everything. The former derives from generalizations of traditional computability, Solomonoff's algorithmic probability, Kolmogorov complexity, and objects more random than Chaitin's Omega, the latter from Levin's universal search and a natural resource-oriented postulate: the cumulative prior probability of all x incomputable within time t by this optimal algorithm should be 1/t. Between both Ps we find a universal cumulatively enumerable measure that dominates traditional enumerable measures; any such CEM must assign low probability to any universe lacking a short enumerating program. We derive P-specific consequences for evolving observers, inductive reasoning, quantum physics, philosophy, and the expected duration of our universe.
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