15.5: Summary
- Page ID
- 127354
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\(\propto\) \(\_\_\_\_\) is proportional to
\(\sim\) \(\_\_\_\_\) on the order of, is on the order of
Summary
Nature behaves differently on large and small scales. Galileo showed that this results fundamentally from the way area and volume scale. Area scales as the second power of length, \(A \propto L^2\), while volume scales as length to the third power, \(V \propto L^3\).
An order of magnitude estimate is one in which we do not attempt or expect an exact answer. The main reason why the uninitiated have trouble with order-of-magnitude estimates is that the human brain does not intuitively make accurate estimates of area and volume. Estimates of area and volume should be approached by first estimating linear dimensions, which one's brain has a feel for.