Understanding Huge Numbers: If All the Seas Were One Sea…

This post was written by Peter DeCraene, a 2021-22 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

If all the seas were one sea, and all the trees were one tree, just how great of a sea and how great of a tree would that be? If all the cattle shipped to market in a year were one cow, how big would that cow be? And what would 4.5 billion hot dogs look like?

Human beings have long used images to help us wrap our heads around great quantities. By looking at historic newspaper articles and advertisements, students can find examples of the ways these publications used such imagery and analogies to make large numbers more accessible, as well as to emphasize particular ideas.

These kinds of analogies raise questions about the purpose of the article or ad in which they are used. They also provide interesting ways to introduce math concepts like area or proportion. A short blurb in a 1909 issue of the Brookings Register tries to illustrate the number of cows and pigs sent to market, for example, by considering the size of one cow made up of all the other cows. Math questions that might arise include:

• How accurate is the description of the hypothetical giant cow’s size?
• To whom is the “we” in the first sentence referring, the whole country, or just South Dakota? How many cows is the author really talking about here?
• Is the one big cow the same weight or the same volume as all the other cows? And does that distinction matter for the author’s purpose?

Estimation skills and comfort working with large numbers will come in handy here. Students can similarly analyze the claims made about the number of hot dogs consumed in 1935 with a short article from the Evening Star. For example, how would they evaluate the claim that the number consumed, laid end to end, would wrap around the equator 90 times?

Some comparisons are made with graphic images, like this one showing the relative sizes of various European armed forces during World War I. What message does the graphic send to the viewer? Why might this have been an important image to publish in an American newspaper in 1914? How would an icon representing the American armed forces compare to those from Europe? Students might use their math, artistic, and language skills to create other ways to illustrate or describe the numbers; what would be the impact of these different representations?

Advertisers also use analogies to emphasize aspects of their product. How does the addition of the statement “Driven twice around the world!” affect the catchiness of this Conoco motor oil ad? Which has more impact: the number of miles driven or the idea of driving around the world? Is the statement accurate mathematically if not literally?

Vivid descriptions or images help people understand and interpret large numbers. Students can use their math skills to further analyze these descriptions, or develop different images to represent enormous quantities. Perhaps it might even be interesting to more fully describe what the one tree from the nursery rhyme might look like.

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