ABSTRACT
There are many situations in which the functions we would like to analyze are mainly known through measurements. Consider, for example, the temperature at time t at some location. Whether this position is in a cup of coffee or a coupling in a rocket engine, it is overly idealistic to assume we can derive, from basic principles alone, a precise formula f (t) describing how this temperature varies with time. Instead, we might measure that temperature at various times — t0, t1, t2, . . . — and then base any further analysis on that sequence of measured values — f (t0), f (t1), f (t2), . . .— along with, of course, our knowledge of thermodynamics.
