Again from the presidential dataset I am working with... I was interested to see if US presidents have become more self-centered/self-reverential over time (using the frequency of 'me', 'I', and 'my' in each address as a proxy). If anything (see below), the trend is in reverse; there seems to be a gradual decline in the use of the first person singular. Interestingly, only one president, Teddy Roosevelt, avoided use of both 'I' and 'me', all presidents used 'my' at least once, and Obama, Trump (shockingly), Bush Sr., Coolidge, and JFK avoided using 'me'.
In general, presidents' inaugural addresses have more in common with their recent predecessors and immediate successors. Given the rapidly changing human landscape, and the evolution of the English language, it is not surprising that mundane word choice, rather than left/right intellectual persuasion, wins out. Nonetheless, there are some interesting results within shorter time windows (for instance, Obama's inaugurals had more in common with Nixon's & Reagan's than Carter's) .The heat map below shows the cosine similarities of the speeches.
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