Can mathematics explain natural intelligence? (Q1087846)

I discuss four algorithms that have one thing in common with the brain: they learn to predict future events based on past experience. The first is the classical predictor \(\hat x_{t+h}=3x_ t-3x_{t-h}+x_{t-2h}\) for the values of a quadratic progression. The second predicts the values of linear functionals. The third predicts the vector outputs of an orthogonal operator. The fourth predicts the letters or morphemes of a text. The first, second, and fourth are simple enough so that mechanisms appropriate for the computations that they require could exist in our brains. I prove estimates of the sum of the absolute squares of errors for the second and third algorithm.