Lagrange theory is about repeatability in continued fractions. It tells us the window sizes we need if we approximate our irrational number with the set of most irrational numbers.. The most irrational are the Lagrange. The numbers generate the markov window sizes.
So, if the economy is worried about Pi, then it will be stuck around window sizes that reproduce 22/7. It is not using the full Lagrange spectrum. Or, the rank of our generators are generally small number and rarely vary by more than one or two. Our 'log' function is a bit inaccurate by tradebook error, we will be limited in the dimensionality of the spectra we use.
Another way to say this, packing sphere is not the most irrational activity around.
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