As we’re starting to think about measuring meaning, and qualitative complexity I find Fermi Decomposition to be a tangible example of the value of reducing ambiguity, and thinking beyond (top down) mathematics.
The best-known example of such a “Fermi question” was Fermi asking his students to estimate the number of piano tuners in Chicago. His students—science and engineering majors—would begin by saying that they could not possibly know anything about such a quantity.
Fermi would start by asking them to estimate other things about pianos and piano tuners that, while still uncertain, might seem easier to estimate.
These included the current population of Chicago (a little over 3 million in the 1930s to 1950s), the average number of people per household (two or three), the share of households with regularly tuned pianos (not more than 1 in 10 but not less than 1 in 30), the required frequency of tuning (perhaps once a year, on average), how many pianos a tuner could tune in a day (four or five, including travel time), and how many days a year the tuner works (say, 250 or so).
Tuners in Chicago = population / people per household x percentage of household with tuned pianos x tuning per year per piano/ (tuning per tuner per day x workdays per year)
When this number was compared to the actual number (which Fermi would already have acquired from the phone directory or a guild list), it was always closer to the true value than the students would have guessed. This may seem like a very wide range, but consider the improvement this was from the “How could we possibly even guess?” attitude his students often started with.
This approach to solving a Fermi question is known as a Fermi decomposition or Fermi solution.