Most have heard of the 80/20 power law or Pareto principle that governs the distribution of wealth in the world: one-fifth of the population has four-fifths of the assets, but in turn one-fifth of that one-fifth owns 4/5 of the 4/5 (4% has 64%), and so on.

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The religion of prediction and the knowledge of the slave

In calculus, infinitesimal quantities are an idealization, and the concept of limit, provided to support the results obtained, is a rationalization. This dynamics going from idealization to rationalization is inherent to the liberal-materialism or material liberalism of modern science. Idealization is necessary for conquest and expansion; rationalization, to colonize and consolidate all that conquered. The first reduces in the name of the subject, which is always more than any object x, and the second reduces in the name of the object, which becomes nothing more than x.

But going to the extremes does not grant at all that we have captured what is in between, which in the case of calculus is the constant differential 1. To perceive what does not change in the midst of change, that is the great merit of Mathis’ argument; that argument recognizes at the core of the concept of function that which is beyond functionalism, since physics has assumed to such an extent that it is based on the analysis of change, that it does not even seem to consider what this refers to.

Think about the problem of knowing where to run to catch fly balls—evaluating a three-dimensional parabola in real time. It is an ordinary skill that even recreational baseball players perform without knowing how they do it, but its imitation by machines triggers the whole usual arsenal of calculus, representations, and algorithms. However, McBeath et al. more than convincingly demonstrated in 1995 that what outfielders do is to move in such a way that the ball remains in a constant visual relation —at a constant relative angle of motion- instead of making complicated time estimates of acceleration as the heuristic model based on calculus intended [65]. Can there be any doubt about this? If the runner makes the correct move, it is precisely because he does not even consider anything like the graph of a parabola. Mathis’ method is equivalent to put this in numbers.

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Questions of program —and of principle, again: calculus, dimensional analysis and chronometrology

In physics and mathematics, as in all areas of life, we have principles, means and ends. The principles are the starting points, the means, from a practical-theoretical point of view, are the different branches of calculus, and the interpretations the ends. These last ones, far from being a philosophical luxury, are the ones that determine the whole contour of representations and applications of a theory.

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