related: there is a short series of exercises in SICP that explore the idea of building an interval arithmetic library. i.e. numerical values are represented by

related: there is a short series of exercises in SICP that explore the idea of building an interval arithmetic library. i.e. numerical values are represented by intervals [a, b] which encode their uncertainty/error: http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html#%_sec_2.1.4 http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html... Exercise 2.14 and onwards point out that two expressions that are algebraically equivalent for perfectly accurate values stop being equivalent once we introduce uncertainty. This is only for a toy example expression with 2 variables. Suppose we want to solve a linear system of equations in 100s of thousands of variables. Is it tractable to track the uncertainty for all of those variables at once? Will their uncertainties be dependent? ...