Not about Fibonacci

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Arithmetic, geometry, and music in Giovanni Pisano’s pulpit (1301-1310), Duomo di Pisa

Pisa is the international symbol of improbable constructions and therefore a fitting location for this week’s workshop.  Pisa is also a fitting location for meditating on the eternal and impossible question:  do we engage in mathematics because we find it beautiful, or do we find mathematics beautiful because of our programming?  Are Pisa’s medieval arcades beautiful because we are used to them or do we admire Pisa for the beauty of its medieval architecture?

In addition to the Roman sarcophagi that littered Pisa’s underworld and were recycled in medieval times to house the remains of political and military citizens “di primario spicco,” Pisa’s Camposanto contains the gigantic (5.6 x 15 m) 14th century fresco Il trionfo della morte which might have served as a reminder of the urgency of completing the program of this week’s workshop, but which is undergoing restoration and is therefore not visible to the public.  It seems to me the workshop provides a striking illustration of the complex interplay between freedom and inevitability in the design of a mathematical theory, in this case the mod p Langlands program, whose ultimate goals are being defined, democratically as far as I can tell, through workshops and conferences like this one.

Pisa’s medieval walls are also decorated with a variety of political statements.  Someone found it worth his or her while to design a stencil to celebrate an American mathematical personality:

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Seen on a wall in central Pisa. The caption reads “strike where it hurts the most.”

 

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One thought on “Not about Fibonacci

  1. Jon Awbrey

    I have often reflected on the interminglings of the main three normative sciences. In one of my earliest meditations I saw Beauty, Goodness, and Truth as the intersecting circles of a Venn diagram, with the summum bonum the central cell. As far as our ability to approach our object from our origin without, perfect knowledge of the Good would require us to know all the consequences of our contemplated actions while perfect knowledge of the True would require us to know all the axiom sets that never beget a contradiction. As far as I could tell, and as far as I could see deciding with the empirical tests and theorem provers I could morally and mathematically envision devising, these two tasks exceed the talents of mortal humans and all their technological extensions.

    But when it comes to Beauty, our form of being appears to have an inborn sense to guide us on our quest to the highest good. That way through beauty to our ultimate goal I called the human-hearted path.

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