Dictionary of Numbers is a tool I developed to help me make sense of numbers. It's a Google Chrome extension that provides three features:
In a blog post, the meteorologist Dr. Jeff Masters talks about the largest US wildfires of 2012. Masters mentions that the largest fire burned about 300,000 acres before it was contained. I have no idea how much 300,000 acres is or what types of things are similar sizes and I suspect few other people do, either.** Apologies to Dr. Masters, who is an excellent science communicator. But we need to understand this number to answer the obvious question: how much of the United States was on fire? This is why I made Dictionary of Numbers.
I noticed that my friends who were good at math generally rely on "landmark quantities", quantities they know by heart because they relate to them in human terms. They know, for example, that there are about 315 million people in the United States and that the most damaging Atlantic hurricanes cost anywhere from $20 billion to $100 billion. When they explain things to me, they use these numbers to give me a better sense of context about the subject, turning abstract numbers into something more concrete.
When I realized they were doing this, I thought this process could be automated, that perhaps through contextual descriptions people could become more familiar with quantities and begin evaluating and reasoning about them. There are many ways of approaching this problem, but given that most of the words we read are probably inside web browsers,It might be interesting to to develop a similar system for use in spoken lectures, especially given the sophistication of current voice recognition technology for numbers. I decided to build a Chrome extension that inserts human explanations of numbers into web pages.
Wolfram|Alpha already has a service similar to this, giving human-understandable explanations of numbers you type in, but there are two basic problems with this approach. The first is that Wolfram|Alpha only has a few human-relatable explanations per order of magnitude of unit, often prompting ridiculous comparisons like 10,000 miles being about as much as 1/43 of the Sun's radius. 1/43? Huh? Explanations in published news articles saying that something is "100 football fields long" are similarly useless.
But more importantly, the second problem with Wolfram|Alpha is that even if it has a decent human-understandable description of a number, you still have to go to the website, copy/paste the number you're curious about, wait for the result, and then find the box that contains the answer. As Bret Victor explains below, inline explanations are an essential part of why Dictionary of Numbers works.
I believe that readers are constantly making tradeoffs between curiosity and laziness, constantly evaluating the effort required to be an active reader. Dramatically lowering the effort barrier can encourage readers to ask every question that comes to mind.- Bret Victor
Making the human explanations available instantly inline with the text answers questions before readers can even ask them.
As I was developing Dictionary of Numbers, I also realized that this tool could be useful for writers as well as readers. Writers could use it to explain quantities to their readers more clearly, and this could all be done immediately as they write without time-consuming research. More, it might serve as a reminder to writers that contextualizing numbers is important in conveying understanding to their audience.
And I do think it's important. One could write Dictionary of Numbers off* * I estimate that the most frequent types of numbers mentioned in news articles are money and number of people. as a tool for mathematically-inclined folk, but the fact is that understanding and reasoning about numbers is an essential part of modern society. After all, it's important to know just how much of the United States was on fire.* * It was an area about the size of Los Angeles.
There are two major features that Dictionary of Numbers is missing that would make a much more effective learning tool. The first is personalization. My previously-mentioned friends would not just give me any old explanation of what a number meant, but made sure to pick an explanation that I specifically would be familiar with. Picking examples with personal knowledge of the audience makes those explanations much more understandable and much more likely to stick. Someone that grew up in Paris might not know the Statue of Liberty's height, but would have a very good idea of how tall the Eiffel Tower is. One relatively simple idea for personalization is the use of location data in contextualizations. For example, "the population of Houston, Texas" is probably a more appropriate comparison for a Texan than "the population of Vancouver, Canada". Internationalization of language and currency, while not a strictly personal feature, would also be very helpful in aiding explanations. I leave it to other researchers to implement these strategies.Gathering and interpreting user-specific data and using that data to suggest better contextual explanations is an open problem.
The second missing feature is better contextualization in a specific domain. When someone encounters a number they don't understand, they might want to know typical values for that number, the minimum and maximum values those numbers can take, and how values they're more familiar with (such as the Eiffel Tower's height) might compare. The best way to make these comparisons is probably visually, in plots or graphs. I don't know if this is possible to automate, but such a feature would make contextualizing numbers much faster and easier to understand.