The Zero, One, Infinity Disease - Marc's Blog
Rules and heuristics are important. Within our own heads, they are mental shortcuts we use to save ourselves from needing to reason everything out from first principles. Between us, they are devices that we can use to communicate ideas and share complex concepts. Rules of thumb are named patterns of thinking, pointers to complex discussions that can be used in place of talking things through from the beginning every time. They have huge power. Every so often, we should go through our rules and heuristics and throw out the ones that hurt more than they help.
I have a candidate: the zero-one-infinity rule. In spirit, zero-one-infinity is valuable. It counsels against arbitrary limits, and points out that arbitrary limits are a strong hint that system or piece of code was poorly considered.
Numerical instincts are a critical part of the engineer's toolkit. Having the ability to understand the scale and size of a problem, to estimate quickly, and think in terms of upper and lower bounds is exceptionally useful for both science and engineering. This includes the ability to look at a number, or graph, or formula, and quickly decide whether it looks about right or definitely wrong. Many of the best engineers and scientists (most famously Enrico Fermi) have numerical intuition as a strength, or even as a superpower. When it's used well, intuition is irreplaceable. It tells us where to measure, where to calculate, and when to calculate or measure a second time. It's the pure distillation of hard experience into numbers.
