Weinberger Edward D
Max Planck Institute for Biophysical Chemistry, Am Fassberg, D-3400 Göttingen, Germany.
Biosystems. 2002 Aug-Sep;66(3):105-19. doi: 10.1016/s0303-2647(02)00038-2.
'Standard' information theory says nothing about the semantic content of information. Nevertheless, applications such as evolutionary theory demand consideration of precisely this aspect of information, a need that has motivated a largely unsuccessful search for a suitable measure of an 'amount of meaning'. This paper represents an attempt to move beyond this impasse, based on the observation that the meaning of a message can only be understood relative to its receiver. Positing that the semantic value of information is its usefulness in making an informed decision, we define pragmatic information as the information gain in the probability distributions of the receiver's actions, both before and after receipt of a message in some pre-defined ensemble. We then prove rigorously that our definition is the only one that satisfies obvious desiderata, such as the additivity of information from logically independent messages. This definition, when applied to the information 'learned' by the time evolution of a process, defies the intuitions of the few previous researchers thinking along these lines by being monotonic in the uncertainty that remains after receipt of the message, but non-monotonic in the Shannon entropy of the input ensemble. It also follows that the pragmatic information of the genetic 'messages' in an evolving population is a global Lyapunov function for Eigen's quasi-species model of biological evolution. A concluding section argues that a theory such as ours must explicitly acknowledge purposeful action, or 'agency', in such diverse fields as evolutionary theory and finance.
“标准”信息论并未涉及信息的语义内容。然而，诸如进化论等应用恰恰需要考虑信息的这一方面，这一需求促使人们在很大程度上未能成功地寻找一种合适的“意义量”度量方法。本文基于这样一种观察展开尝试，即一条信息的意义只能相对于其接收者来理解。假定信息的语义价值在于其在做出明智决策时的有用性，我们将语用信息定义为在某个预定义集合中，接收者在收到消息前后行动概率分布中的信息增益。然后我们严格证明，我们的定义是唯一满足诸如来自逻辑独立消息的信息可加性等明显要求的定义。当将此定义应用于一个过程随时间演化“学到”的信息时，它违背了之前少数沿此思路思考的研究者的直觉，因为它在收到消息后剩余的不确定性方面是单调的，但在输入集合的香农熵方面是非单调的。由此还可得出，进化种群中遗传“信息”的语用信息是艾根生物进化准物种模型的一个全局李雅普诺夫函数。结论部分认为，像我们这样的理论必须在进化论和金融等不同领域中明确承认有目的的行动，即“能动性”。
