What are some pre-19th or pre-20th century sources on information theory? Do they exist?

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    $\begingroup$ No. Information theory (in Shannon's sense) is a 20th century invention that could not even be formulated before Kolmogorov's formalization of probability in 1933. Etymonline says that the word started to be applied to broadcast signals from 1937, Shannon published in 1948. $\endgroup$ – Conifold Sep 12 '19 at 20:39
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    $\begingroup$ There is something in philosophy called semantic information theory that can, arguably, be traced to earlier times. But not by that name and it has little to do with Shannon's theory. $\endgroup$ – Conifold Sep 12 '19 at 20:53
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    $\begingroup$ Prior to Shannon, in a different context but still in the 20th C, Fisher, in his Theory of Statistical Estimation wrote about ""the whole of the information which a sample provides" in the 1920s. This is today called Fisher Information and the Fisher Information Metric. $\endgroup$ – Nick Sep 12 '19 at 22:02
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    $\begingroup$ @NickR Nyquist's 1924 "Certain Factors Affecting Telegraph Speed" is also prior to Shannon, but I'm looking for pre-20th cen., at least. $\endgroup$ – Geremia Sep 12 '19 at 22:50
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    $\begingroup$ Etaoin shrdlu and the Morse code perhaps? That is, letter frequency as a means for optimizing the composition of messages. $\endgroup$ – sand1 Sep 13 '19 at 13:46

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