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Numeracy and Crowd Science

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This post was written by 2021 Junior Fellow Amal Charara.

It is likely that at some point in our lives we have found ourselves in a crowd of people.  Perhaps it was at a graduation ceremony, a concert, on a train platform or at an airport. We may have referred to it as small, large, or even dense.  For smaller events, like a birthday party, we may be able to estimate the number, because it takes place in a small space, but larger spaces with people standing next to each other presents a challenge – particularly when tasked with trying to determine an exact number. How do we estimate the sizes of such massive crowds?

Five children sitting around the table looking at a woman with a birthday cake and candles on the table hanging from the chandelier
A birthday party.May 1943.

Numeracy plays a big role in the lives of data journalists, geographers, and demographers who research and measure large crowds. There are several approaches or strategies used to determine these numbers or estimates. In the Oxford English Dictionary, numeracy is defined as  “the quality or state of being numerate; ability with or knowledge of numbers.”  With numeracy skills we can more easily add, subtract, multiply, and divide.  Advanced skills, to include mental arithmetic, can facilitate a conversation in a business transaction.

Early texts from the 19th century reveal numeracy as a pathway to logical thinking as evidenced in word problems. Instruction was given to young children in solving problems unique to the family farm, small businesses, and the measurement of cloth and other wares. A simple word problem, such as: a gardener set out 30 peach trees, in rows, putting 5 trees in a row. How many rows were there? North American Arithmetic by Frederick Emerson, was used to train children in mental math, which would allow them to use their imagination and which gave them the ability to perform simple calculations using arithmetic. This methodology created a way for them to come up with answers.

Educational poster featuring numbers. Box one has one squirrel, two has two owls, three has three girls, four has four birds, Five has five strawberries, six has six plums, seven has seven blackberries, eight has eight butterflies, nine has corn ears, and ten has ten apples and also have the equivalent of roman numerals
Counting and Writing Numbers, or Numeration and Notation , 1890.

It was estimated that at George Washington’s 1789 inauguration at Federal Hall in New York City, there were 10,000 people in attendance. We do have images drawn by artists depicting smaller groups of more well-known individuals.  But, according to The Fred W. Smith Library for the Study of George Washington, no one really knows. Tim Wallace, in his article, “From Lincoln to Obama, How Crowds at the Capitol Have Been Counted,” in the January 18, 2017, issue of the New York Times, notes that some people think the National Park Service is tasked with estimating the number of people who attended the inauguration of a President, or even how many people attended the Million Man March in 1995. However, in 1997, Congress included language in an appropriations bill for the Department of the Interior prohibiting the National Park Service from conducting such crowd estimates.

View of the million man march taken from the capital with the Ulysses S. Grant Memorial and the Washington Monument in the distance
Aerial view of marchers on the National Mall during the Million Man March, looking towards the Washington Monument. Washington D.C, 1995, M. Keating, photographer.

At the inauguration of President Lincoln on March 4, 1861, the crowds were immense. As we see in the image below, grids would be used to calculate the number of people that occupied the space and a specific number in each area is estimated. Calculations are done by determining how many people occupy a specific square footage in a given area, which also includes its density.

crowd in front of the East side of the capital watching the inauguration with cranes working on building the Capitol dome in the background
Inauguration of Abraham Lincoln – March 4, 1861.
Photograph of crowds in front of the east side of the Capitol with the Senate side in the distance and one photographer on a ladder looking away and another photographer in the foreground looking at the camera
Inauguration, Crowds. , 1921.

Numeracy skills are acquired over time with a key element, such as memorization of multiplication tables, being critical to the communication process. Crowd science depends on strong numeracy skills as well.  Today, data scientists work with sophisticated technology, satellite imagery, and drones, yet even with advanced modeling techniques, they still rely on the same numeracy skills from the past. Specific to crowd science, numeracy skills have been analyzed and practiced and are used to ensure safety as logical approaches to move large groups of people. This is particularly important in disaster management situations when aid needs to be delivered to large populations spread across several areas. Further, in more sophisticated models, crowd science provides for the ability to estimate how quickly spaces can fill and how crowd density can affect the safety of all individuals present. Often, calculations based on visuals have to be done while asking for immediate assistance, particularly in instances of fire and rescue.

Examining the resources available in the Science, Technology & Business Division has been an incredible journey which has enabled me to learn a tremendous amount. The research we have conducted addressing arithmetic, numeracy, literacy, and imagination enhanced my appreciation of the Library of Congress and the wonderful team that I have had the pleasure of working with. The books and items we have researched from the 1800s and 1900s were fascinating and invaluable in supporting my topic of numeracy, as well as the study of crowds.


  1. Very informative and I appreciated the read, as it’s something that we take for granted and do not truly think about.

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