Friday, May 4, 2012

The concrete and the abstract

In 1886, Leopold Kronecker famously said God made integers; all else is the work of man.1 For me, even this claim admits too much abstraction into reality, and a better formulation might be God made quarks, leptons, and photons; all else is the work of man. Abstraction is useful, but I'm thinking that a given set of facts can yield more than 1 abstract model for them.
The lesson for those who develop taxonomies is that there is not a single taxonomy defined by reality. A taxonomy—like any other tool for gaining understanding of a domain, for organizing such tools, or for what have you—is defined by reality and by the intended audience.

1 Well, actually he said Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk, but it comes to much the same thing.

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