From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that...From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.展开更多
Paul B. Baltes于1981年在马普人类发展研究所成立的毕生发展心理研究中心已经使毕生发展心理学成为了发展心理学中的一个重要的概念分支2004年以来,中心已经将研究项目扩展到了发展行为神经科学。中心主要在三个主题上开展研究工作:(1...Paul B. Baltes于1981年在马普人类发展研究所成立的毕生发展心理研究中心已经使毕生发展心理学成为了发展心理学中的一个重要的概念分支2004年以来,中心已经将研究项目扩展到了发展行为神经科学。中心主要在三个主题上开展研究工作:(1)研究作为成熟、学习和衰老的交互作用的结果,毕生的不同发展阶段中人类行为变化的规律:(2)发展能够整合来自于自身机能、时间序列、以及行为和神经层面分析等领域实证证据的理论和方法体系。(3)通过探索不同年龄可塑性上的差异寻找发展的机制。中心继续重点关注成人晚期和老年期,这为理论和实践上的创新提供了独特的机遇。同时,中心加强了对包括婴儿期和儿童早期在内的个体发展早期阶段的研究。本文报告了来自四项从行为和神经层面分析感觉和认知发展的研究的最新发现。展开更多
文摘From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.
文摘Paul B. Baltes于1981年在马普人类发展研究所成立的毕生发展心理研究中心已经使毕生发展心理学成为了发展心理学中的一个重要的概念分支2004年以来,中心已经将研究项目扩展到了发展行为神经科学。中心主要在三个主题上开展研究工作:(1)研究作为成熟、学习和衰老的交互作用的结果,毕生的不同发展阶段中人类行为变化的规律:(2)发展能够整合来自于自身机能、时间序列、以及行为和神经层面分析等领域实证证据的理论和方法体系。(3)通过探索不同年龄可塑性上的差异寻找发展的机制。中心继续重点关注成人晚期和老年期,这为理论和实践上的创新提供了独特的机遇。同时,中心加强了对包括婴儿期和儿童早期在内的个体发展早期阶段的研究。本文报告了来自四项从行为和神经层面分析感觉和认知发展的研究的最新发现。
