Dear Soul Surfer

Scientific models are never exact, for three reasons:

System complexity

Most real systems are far to complex for us to have an exact model. If you’re studying a living organism, a weather system, or an economy, the best you can hope for is a macroscopic, qualitative model which accounts for the large-scale features of the data. Thus, medicine, meteorology, and macroeconomics are inherently ‘inexact’ sciences.

Computational Complexity

Even if an exact model exists, rigorous computation within this model is usually impossibly complex. You must always make approximations and idealizations to get any kind of answer. For example, we habitually throw away ‘small terms’ in an equation. Functions are often approximated via Taylor series1 , and the higher-order terms are then discarded.

Measurement error

Physical measurements are always imprecise. The best you can do is quantify the expected error. Science yields not exactitudes, but approximations. In special cases (eg. celestial mechanics), these approximations are in fact incredibly accurate. But it spurious to extrapolate from celestial mechanics to the rest of science.

Conclusion: we need to refine our knowledge continually in the never ending search for exactness and the truth (whatever that is and whether it can ever be realised).