At a fundamental level, scientific uncertainty begins when we make measurements. What do we use to make a measurement? How well can that tool accomplish a measurement? To what precision can we determine the size or mass or temperature of an object? If we repeat a measurement many times, how closely will the individual measurements agree with each other?

Professor Paulos' comment about measuring bacteria was made in an unusual context that I will tell you more about later. The remark underscores, however, the importance of selecting a measuring device appropriate to the task at hand. One does not need the experience of a laboratory scientist to recognize that the likelihood of obtaining an accurate measurement of the length of a bacterium using a yardstick is intrinsically low. The smallest subdivision of the yardstick, usually 1/16 of an inch, a little less than two millimeters, is so much greater than the dimension of a bacterium (actually about 10,000 times greater) that, on the one hand, one cannot say much more about the length of a bacterium other than it is very much smaller than 1/16 of an inch. On the other hand, a yardstick could, in principle, estimate the length of five million bacteria lined up end to end.

Most textbooks of physics or chemistry introduce uncertainty in the context of measurement.