Why ought there to be a connection between empirical counting and the Principia Mathematica?
There isn't some magical, inherent connection. This isn't a 'mystery of faith' kind of thing. There is a relationship because we designed a relationship, and in the 21st century we know how easy it is to design mathematical constructs that don't map onto any kind of reality. When I studied Number Theory my instructors spent a lot more time than was strictly necessary explaining the Peano Axioms to us so that we would understand that yes, even for something as simple as empirical counting, the relationship to mathematics is there because we designed the axioms, not because of the mystery of faith.
(I've seen the Wigner essay. I think it stretches the point. An essay in the NYTimes magazine that I should try to find again gave me this amazing quote, which is roughly "There are approximately 360 million people in America. That means that a million to one event happens to one of them every day." Surprising relationships do not signify magical relationships.)
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timeasmymeasure
no subject
Date: 2013-01-09 05:38 pm (UTC)There isn't some magical, inherent connection. This isn't a 'mystery of faith' kind of thing. There is a relationship because we designed a relationship, and in the 21st century we know how easy it is to design mathematical constructs that don't map onto any kind of reality. When I studied Number Theory my instructors spent a lot more time than was strictly necessary explaining the Peano Axioms to us so that we would understand that yes, even for something as simple as empirical counting, the relationship to mathematics is there because we designed the axioms, not because of the mystery of faith.
(I've seen the Wigner essay. I think it stretches the point. An essay in the NYTimes magazine that I should try to find again gave me this amazing quote, which is roughly "There are approximately 360 million people in America. That means that a million to one event happens to one of them every day." Surprising relationships do not signify magical relationships.)