- “Based on the provided support, it is apparent then that it’s advantageous to be as random as possible for generation of ideas, but sticking with a particular response is predictive of creative originality. So next time your friends say that you are “sooo random,” hold your head up high and keep at it. But don’t forget to spot those brilliant ideas among the dis-order, and focus. Such is the recipe for creativity.”
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On the benefits of being random.
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.. - “Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a strictly convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex functions continue to satisfy such properties and as a result, they are the most well-understood functionals in the calculus of variations. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable.”
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That is from the Wikipedia article on convexity, and the next sentence after the excerpt leads us to…
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.. - Jensen’s inequality!
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.. - “The point is subtle and widely misunderstood. Here’s a simple example. Suppose that the average return is 10%. If $100 is invested for two periods the average payoff is $100(1.1)^2=$121. But on average that is not what happens. More typically, you get say 0% in the first period and 20% in the second period, i.e. $100(1.0)*(1.2)=$120. Notice that the average return is exactly the same, 10%, but the total payoff is smaller in the second and more realistic case”
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And Alex Tabbarok explain why Jensen’s Inequality matters…
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.. - As does Nassim Nicholas Taleb.
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