The Goldilocks level of abstraction in science

Science is full of abstractions. A line plot is an abstraction. A false-colour image is an abstraction. Even scientific notation like 6.0 × 1023 is an abstraction. Abstractions like these are central to science, invoked all the time, and easy to understand. Other abstractions are far from simple and may cause more confusion than clarity.

Abstraction is a slippery slope. Things can quickly get out of hand. Let’s start with a simple abstraction like velocity. The units, metres per second or kilometres per hour, tell us what it is: how fast something moves. I imagine most scientists would still be comfortable if I increase the level of abstraction by calculating the acceleration (i.e., moving from m s−1 to m s−2). But what if I had instead starting talking about a quantity in m2 s−1, not m s−2? Diffusivity and viscosity are such quantities; they measure how quickly something spreads. All I did was change m s−1 to m2 s−1 and I’ve taken a concept a kid can understand to something that may trip up an undergraduate physicist.

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