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I don't think it naturally follows that smart people have big egos.

ego /ˈi:ɡəʊ; ˈeɡəʊ; US / noun [countable] (pl. egos) the (good) opinion that you have of yourself It was a blow to her ego when she lost her job. ▶ poczucie własnej wartości

We are moving toward a dictatorship of relativism which does not recognize anything as definitive and has as its highest value one's own ego and one's own desires.