The handshake example was illuminating. Three "equivalent" theories: Theory A: Closed form formula function. Theory B: "Algorithm". Still a function. Theory

The handshake example was illuminating. Three "equivalent" theories: Theory A: Closed form formula function. Theory B: "Algorithm". Still a function. Theory C: Memoized function (constant time!) According to the article "nobody" likes C, especially the article's Chomsky straw man. If one had a procedure to convert C to A, then this whole issue would become hairsplitting. Such a procedure would aim to convert a memoized function back into a form that uses more symbols from a mathematical language. A good criteria of success would be the description length of the resulting procedure in the preferred language. One reason this could be useful to science is that once you identify a value that is useful in many theories it becomes part of the language. Making it available to the next problem may speed up the search for a "good" description of the next phenomenon. Identical procedures that appeared in various algorithms might acquire a special name. One such value might be called "pi", another "foldr" and so on. Of course there may be many good descriptions, just as there are many languages. Also, the example could be extended to statistical modeling situations by adding room for error terms in the suitability criteria. So if, you have a general procedure to convert a table into a definition you can make money and science at the same time!