Improving Comprehension of Measurements Using Concrete Re-expression Strategies

A collection of tools to take unfamiliar measurements and re-express them in terms of more familiar objects.

People frequently encounter measurements when interacting with digital media. A news article might describe how much a fragment of meteorite discovered on a beach weights (50.3 grams). A data visualization might compare the average amount of daily water use per person in multiple countries (20 to 205 gallons). People often struggle to grasp the quantity that such measurements refer to, limiting their comprehension.

Educators and journalists often re-express unfamiliar measurements in terms of more familiar objects (50.3 grams is about the weight of a golf ball). But this requires time and effort. We present a set of tools for automatially creating concrete measurement re-expressions using familiar objects.

Try it out!

Select a strategy:

Select a measurement type:

Enter a measurement to re-express:

Automated Re-expression Algorithms

We present automated algorithms that enact three strategies used by educators and journalists to make unfamiliar measurements more understandable:

  • Adding Familiar Context

    Presents a measurement (e.g., 28 lbs) alongside objects with similar measurements (e.g., the weight of a tool box, the weight of a microwave).

  • Reunitization

    Re-expresses a measurement (e.g., 3 ft) using a more familiar object as the unit with a multiplicative scale factor for converting from one to the other (e.g., 2 times the height of a single bed).

  • Proportional Analogy:

    Re-expresses a pair of measurements (e.g., the ratio between the volumes of Mercury and Earth) using two familiar objects that have measurements with the same ratio (e.g., the ratio between the volume of a sugar bowl and a watering can).

Our algorithms quantify criteria of effective re-expressions:

  • Measure Variance

    The measured property of the object should not vary greatly between instances of the object so that people can reliably estimate the measurement.

  • Measure Closeness

    The measured property of the object should be close to the unfamiliar input measurement so that people can mentally convert from the measurement of the familiar object to the unfamiliar measurement.

  • Object-Measure Familiarity

    The object and its measured property should be familiar to people based on experience.

Re-Expression API Docs

Building a Database of Familiar Objects

We devise a scalable approach to mining object datasets comprised of three stages:

  • Identify familiar classes of objects

    with WordNet, ImageNet, and crowdsourcing. We first identify criteria for effective re-expression objects like Concreteness, Countability, Rigidness, Low Measure Variance, and Familiarity.

  • Collect instances of the objects

    from online resources like the Amazon product database and Wikipedia

  • Filter false positives and collect familiarity data

    using crowdsourcing

The resulting database contains Weights, Heights, Lengths, and Volumes for 13,465 instances of 1,192 familiar objects.


Improving Comprehension of Measurements Using Concrete Re-Expression Strategies

Jessica Hullman, Yea-Seul Kim, Francis Nguyen, Lauren Speers, and Maneesh Agrawala

Abstract: It can be difficult to understand physical measurements (e.g., 28 lb, 600 gallons) that appear in news stories, data reports, and other documents. We develop tools that automatically re-express unfamiliar measurements using the measurements of familiar objects. Our work makes three contributions: (1) we identify effectiveness criteria for objects used in concrete measurement re-expressions; (2) we operationalize these criteria in a scalable method for mining a large dataset of concrete familiar objects with their physical dimensions from Amazon and Wikipedia; and (3) we develop automated concrete reexpression tools that implement three common re-expression strategies (adding familiar context, reunitization and proportional analogy) as energy minimization algorithms. Crowdsourced evaluations of our tools indicate that people find news articles with re-expressions more helpful and re-expressions help them to better estimate new measurements.

We describe a scalable approach for mining object databases (Amazon, DBpedia) to construct a database of familiar objects and their measurements, using semantic databases (WordNet and ImageNet) and crowdsourcing techniques. We present automated re-expression algorithms that apply the data in this database to re-express unfamiliar measurements in terms of more familiar objects using Reunitization, Adding Familiar Context, and Proportional Analogy strategies. We find that our tools improve measurement estimation and the perceived value of article content involving measurements.


Jessica Hullman Headshot
Jessica Hullman
Concept and Developer

Assistant Professor, Information School, University of Washington

Francis Nguyen Headshot

Informatics Graduate, Information School, University of Washington

Yea-Seul Kim Headshot
Yea-Seul Kim

Ph.D. Student, Information School, University of Washington

Maneesh Agrawala Headshot

Professor of Computer Science, Stanford University