Philip Engel

Articles by Philip Engel:


BWV 849

in Issue 21 | Raw Materials (Oct 2012)

Bach’s Prelude and Fugue in C-sharp Minor - along with harmony, was considered impious - isolating the theme - the tolling of church bells - by truncation, then inversion, then diminution - the chiasmus hypothesis - sobriety (slow), pain (chromatic), and sadness (minor-key)

The Dangers of Self-Reference

in Issue 15 | The Elements (Apr 2012)

the standard liar’s paradox - illegitimate totalities - psychohistory is not a fatalistic science - incompleteness and inconsistency - arithmoquining - true but unprovable

The Makings of a Mathematical Abstraction

in Issue 9 | Reconstruction (Oct 2011)

accusatory, questioning, rhetorical, and exasperated! - the most certain kind of proof - more and more properties - the coincidences and the certainties - live in a delineated space - enough words to talk about Z