People usually cite Postmodernity as having begun "sometime in the early 1930s" or in 1945. By citing the beginning of the era, a person isn't really doing any sort of historical analysis, they are just making an argument as to whether or not people should be optimistic or pessimistic about the era. My theory is that neither of the citations really make all that good of an argument. You should either state that Postmodernity began in 1883 when Sir Francis Galton coined the term, "Eugenics", or on the 10th of December in 1948 when the Universal Declaration of Human Rights was adopted. I'd prefer to remain optimistic, but, given the number of genocides that have occurred in modern history, I think that you just kind of have to call it and wait for the next era. As technological progress accelerates the progression of history, it will hopefully not only come soon, but, also, not surpass our era in terms of human catastrophe, or even involve that at all, really. It could even already be beginning. Though I do sort of ascribe to a kind of, though I only mind obscurantism so much and am sort of a relativist, post-postmodernism, I think that we should just call the next era "The New Age".