fp_precision.pdf

I introduce the audience to the intrigues of floating-point arithmetic and provide my own commentary. The lecture begins with an excursion into music theory and its history, by explaining the impressive feat of calculating the square root of 2 to the 25th decimal place for the first time on the abacus, motivated by its use in early modern music. No familiarity with music theory is required; we use Python snippets and modern math notation for everything. We show the computational cost necessary for implement it (on the abacus or computer). Then we visit some modern examples in computing that are directly relevant to the audience's experiences in manipulating geometric entities as floating-point numerical data. Again, using Python for numerical experiments, we demonstrate some precision-enhacing techniques. In the end, I offer some personal takes on the meaning of it all, and treat the audience with some memorable quotes ranging from William Kahan to Dostoevsky. The Appendix contains a summary of "Platonic" vs. "existentialist" styles of error assessment.