God Created the Real Numbers

Summary

God created the real numbers07-14-2025 7:37PM (ET) 08-28-2025 12:03AM (ET) (edited) W. Jherek Swanger writes in his introduction to Camillo Agrippa's "A Treatise on the Science of Arms, with a philosophical Dialogue (1553)" that: "Scienzia [...] was and is often held to relate only to the study of the eternal: that which exists in nature, or was created by God. Thus theology and astronomy/astrology are held to be sciences. Indeed, Ridolfo Capoferro held that strictly speaking fencing is not a science, but rather an art, because it was not divinely created." 16th Century Italy asks then if science is concerned only with divine (natural) knowledge and art is the realm of the secular and human-made, then was Leopold Kronecker right when he said: "God made the integers; all else is the work of man" The integers look little like the natural world and very much like the simple and powerful abstractions that humans find elegant. Much to the frustration of the human mind, that which created fig wasps, Leucochloridium paradoxum, quantum foam, and plasmids, does not create works of abstract simplicity. If such a divinity left fingerprints in mathematics, that inhuman complexity and irrational strangeness can be found in the reals but not the integers. One can imagine the God of the Book of Job creating the square root of two and pi. I have an imperfect rule of thumb for determining if something is of human construction or for the purposes of this exploration, divine. If the something under examination causes a sense of existential nausea, disorientation, and a deep feeling that is can't possibly work like that, it is divine. If on the other hand it feels universal, simple, and ideal, it is the product of human effort. The Hierarchy of Weirdness This distinction science=divine/nature, art=made by human is more complex than just two separate categories. When humans create something, the created thing is contained, and is a function of, what already exists, so while art is the p...