A Paradigm of Guessing

boxesThe most interesting thing I’ve read this week comes from Jurgen Schmidhuber’s paper, Algorithmic Theories of Everything, which should be provocative enough to pique the most jaded of interests. And the quote is from way into the paper:

The first number is 2, the second is 4, the third is 6, the fourth is 8. What is the fifth? The correct answer is “250,” because the nth number is n 5 −5n^4 −15n^3 + 125n^2 −224n+ 120. In certain IQ tests, however, the answer “250” will not yield maximal score, because it does not seem to be the “simplest” answer consistent with the data (compare [73]). And physicists and others favor “simple” explanations of observations.

And this is the beginning and the end of logical positivism. How can we assign truth to inductive judgments without crossing from fact to value, and what should that value system be?

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