The professor waved his arms enthusiastically and told us to stop thinking. “Orders of magnitude only!” he explained. “Let’s call it 1 cm/year. What about rates of mountain uplift in active regions, like the Himalayas and New Zealand?” The answer, to an order of magnitude, was 0.1 cm/year.
Now his point was obvious: plates drift faster than mountains rise, but both move at similar speeds. This relationship – normally hidden behind numbers like 7.3 and 0.4 – was suddenly clear in the comparison of 1 and 0.1. We had lost some precision, but had gained clarity, which we would easily remember.
Randall Munroe charted money and prices across 15 orders of magnitude.
Dictionary of Numbers is a Chrome extension by Glen Chiacchieri that uses orders of magnitude to insert useful comparisons into the text of webpages. For example, if I’m reading an article about a flood that affected 300,000 people, the extension will note that this is approximate to the total population of Iceland.
Ultimately, thinking by orders of magnitude can put the world in new perspectives. NASA’s budget for a small interplanetary probe and the average total campaign contributions to a presidential candidate are equal to an order of magnitude. However, the cost of a new aircraft carrier and the total damages inflicted by a major hurricane are two orders of magnitude greater.