论文标题
事实少于单词：与日益复杂的沟通
There Are Fewer Facts Than Words: Communication With A Growing Complexity
论文作者
论文摘要
我们提出了一个不可能的结果，称为事实和单词的定理，这与一般通信系统有关。该定理指出，有限文本中使用的不同单词的数量大约大于同一文本中描述的独立基本持久事实的数量。特别是，该定理可以与ZIPF定律，相互信息的幂律缩放和幂律尾学习曲线有关。定理的假设是：有限字母，符号的线性序列，不降低时间的复杂性，可以估计的熵率以及反复杂性速率的有限性。
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of independent elementary persistent facts described in the same text. In particular, this theorem can be related to Zipf's law, power-law scaling of mutual information, and power-law-tailed learning curves. The assumptions of the theorem are: a finite alphabet, linear sequence of symbols, complexity that does not decrease in time, entropy rate that can be estimated, and finiteness of the inverse complexity rate.
