In his Paradoxes in Probability Theory and Mathematical Statistics (1986), Gábor J. Székely shared a paradox learned from his professor, Alfréd Rényi:
Since I started to deal with information theory I have often meditated upon the conciseness of poems; how can a single line of verse contain far more ‘information’ than a highly concise telegram of the same length. The surprising richness of meaning of literary works seems to be in contradiction with the laws of information theory. The key to this paradox is, I think, the notion of ‘resonance.’ The writer does not merely give us information, but also plays on the strings of the language with such virtuosity, that our mind, and even the subconscious self resonate. A poet can recall chains of ideas, emotions and memories with a well-turned word. In this sense, writing is magic.
The paradox described above is also known as the Paradox of Information.
Thus, there is no “fixed” amount of information. The perceived quality and quantity of information depends upon the level of interaction between the sender and the receiver of the information. It is nugatory to only measure the amount of information from the information source.
Poetry is a special case. A single line of poetry can evoke powerful emotions. It can encapsulate an idea which could take a whole tome or more to explicate, and even then, it may not be enough. In addition, the information conveyed by a poem differs depending on who’s reading it. Even you would find a poem’s meaning changed based on your mood,
Revisiting a poem you read a while ago may prove to be enlightening since the new knowledge and experience you gained help you to look at the same poem from a different perspective.
So, in a way, a poem contains an infinite amount of information waiting to be unearthed.
As T. S. Eliot said, “Genuine poetry can communicate before it is understood.“