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Discussion questions
A. Single-celled animals must passively absorb nutrients and oxygen from their
surroundings, unlike humans who have lungs to pump air in and out and a
heart to distribute the oxygenated blood throughout their bodies. Even the cells
composing the bodies of multicellular animals must absorb oxygen from a
nearby capillary through their surfaces. Based on these facts, explain why cells
are always microscopic in size.
B. The reasoning of the previous question would seem to be contradicted by
the fact that human nerve cells in the spinal cord can be as much as a meter
long, although their widths are still very small. Why is this possible.
1.4Order-of-Magnitude Estimates
It is the mark of an instructed mind to rest satisfied with the degree of preci-
sion that the nature of the subject permits and not to seek an exactness
where only an approximation of the truth is possible.
Aristotle
It is a common misconception that science must be exact. For instance,
in the Star Trek TV series, it would often happen that Captain Kirk would
ask Mr. Spock, “Spock, we’re in a pretty bad situation. What do you think
are our chances of getting out of here.” The scientific Mr. Spock would
answer with something like, “Captain, I estimate the odds as 237.345 to
one.” In reality, he could not have estimated the odds with six significant
figures of accuracy, but nevertheless one of the hallmarks of a person with a
good education in science is the ability to make estimates that are likely to
be at least somewhere in the right ballpark. In many such situations, it is
often only necessary to get an answer that is off by no more than a factor of
ten in either direction. Since things that differ by a factor of ten are said to
differ by one order of magnitude, such an estimate is called an order-of-
magnitude estimate. The tilde, ~, is used to indicate that things are only of
the same order of magnitude, but not exactly equal, as in
odds of survival ~ 100 to one .
The tilde can also be used in front of an individual number to emphasize
that the number is only of the right order of magnitude.
Although making order-of-magnitude estimates seems simple and
natural to experienced scientists, it’s a mode of reasoning that is completely
unfamiliar to most college students. Some of the typical mental steps can be
illustrated in the following example.
Section 1.4Order-of-Magnitude Estimates