事实比文字少：沟通日益复杂
There Are Fewer Facts Than Words: Communication With A Growing Complexity
摘要：
我们提出了一个不可能的结果，称为关于事实和文字的定理，它适用于一般的通信系统。该定理指出，有限文本中使用的不同单词的数量大致大于同一文本中描述的独立基本持久事实的数量。特别是，这个定理可以与齐普夫定律，幂律缩放的互信息，和幂律尾学习曲线。该定理的假设是：一个有限的字母表，符号的线性序列，复杂度不会随着时间的推移而减少，熵率可以估计，以及逆复杂度率的有限性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
