Quantitative Reasoning 46:
The Visual Display of Quantitative Information
Alyssa A. Goodman

1. Start with a map of Cambridge, which can be obtained from a number of online sites, including http://maps.yahoo.com and http://mapquest.com. Pretend that you are from central Iowa, where all roads are two-way, and rush-hour does not exist. Under these assumptions, which are known as symmetry (direction doesn't matter) and time-independence (no rush hour), calculate how long it takes to get from the (Church Street entrance of) the T-station in Harvard Square to the T-station in Kendall square by car and on foot. (If you need help locating the T-stations on a street map, try http://www.mbta.com.) Explain your assumptions clearly (e.g. how fast can one drive/walk on various streets/sidewalks, roughly how many traffic lights might there be, and how long does it take to wait at them?) Illustrate on a map the naïve way one would drive/walk from Harvard to Kendall (forgetting about one-way streets, etc.)
   
   
2. Now get real. Find a map that shows the one-way streets in Cambridge (you might need to consult an "analog" map). Re-do the calculations of part a.) without the symmetry assumption. How long does it take to get from Harvard to Kendall Square, by car, in that case? And how long from Kendall to Harvard? On a custom map that you draw (either manually or with a computer), show each driving step, and how long you expect it will take, at a non-rush-hour time of day. Show some of the assumptions you have made directly on the map, being careful not to overcrowd it with information (e.g. you might show average speed and total step time, but you won't have room, or need, to show speed, time, and distance). Take a look at the famous map of Napoleon's march on p. 176 of The Visual Display of Quantitative Information, by E. Tufte, for some ideas.
   
   
3. Try getting driving directions for Harvard/Kendall and Kendall/Harvard from an on-line site (e.g. http://mapquest.com). Print out what you get as part of this project. On the print out, (neatly) scribble comments, based on the principles discussed in class, about good and bad features of the on-line service. (Can you read the little maps? Are the directions accurate? Do they agree with yours?)
   
   
4. You will hopefully conclude that your custom driving map is superior to the on-line map service's one. Suggest ways in which the on-line service might be improved in order to offer a product more like yours. (Extra credit: Discuss the computer programming issues involved with actually making these improvements).
   
   
5. Now, account for rush hour in your driving time estimates. Construct a graph of an overall "traffic slowdown rate" as a function of time-of-day. For those of you without cars in Cambridge, you might want to either blindly guess, or spend a day watching how much traffic goes by from a good site (maybe your own window) at various times of day in Cambridge. Explain how your answer to part b.) needs to be modified in order to take the "time dependence" imposed by rush hour into account.
   
   Part II (2nd Week):
   
   
6. How about taking the subway? See what you can find out (from official or unofficial sources) about how frequently T-trains serve this route at various times of day. Construct a graph of train frequency as a function of time at each station. (Hint: The train frequency might not be the same at each stationŠif it's not familiar, ask someone what the phrase "express to Park" means at Harvard Square.) Calculate how long the train takes to travel between various stops. Construct a graph of the approximate travel time between Kendall and Harvard, and vice-versa, as a function of time-of-day. (On our next project set, we'll do better than just the "approximate" time and show a real statistical distribution for travel time, as a function of time of day... see h.), below.)
   
   
7. Assuming walking takes the same amount of time at any time of day, and in either direction (Harvard/Kendall vs. Kendall/Harvard), construct a graph showing how long it takes to walk, drive, or take the T between Harvard and Kendall Square as a function of time-of-day. Then, construct the same graph for the Kendall to Harvard direction. Display these graphs in such a way that any "asymmetries" in the Harvard/Kendall and Kendall/Harvard paths will be apparent.
   
   
8. To collect information for our next Project Set, please go take the T (if you prefer walking, see i., below. At some random time of day, go for a little trip to Kendall Square, by T, and record the following information, on a good chart you will submit as part of the current project:
   
   • Time of arrival on the platform in Harvard Square Station.
   • Time of train arrival (and thus the time you waited for the train).
   • Time to travel to Central Square.
   • Time spent stopped at Central Square.
   • Time of arrival at Kendall Square (and thus Central-Kendall travel time).
     (Then, go do whatever you like in Kendall Square... I highly recommend the Blue Room for dinner!)
   • Time of arrival on the platform in Kendall Square Station.
   • Time of train arrival (and thus the time you waited for the train).
   • Time to travel to Central Square.
   • Time spent stopped at Central Square.
   • Time to travel to Harvard Square (and thus the Central-Harvard travel time).
   
   
   
9. As an alternative to h., if you prefer walking, go for a walk from Harvard to Kendall and back. If you do this, please: walk through Harvard Yard to Broadway; take Broadway all the way to Kendall Square, taking care to record your exact route, and the following data, on a chart that you will submit with the current Project Set :
   
   • Time of departure from Harvard Square T-station's Church Street entrance.
   • The weather on the day you went for this walk.
   • Your age, height, weight, and gender on the day you went for his walk (optional... but we'll see that a lack of answers will introduce a statistical bias).
   • Time of arrival at Kendall Square T-station entrance.
   • Time of departure from Kendall Square T-station entrance.
   • Time of arrival at Harvard Square T-station entrance.
     
     On our next Project Set, we will use all of the information from parts h. and i. to focus on statistics and probability, and we will construct more sophisticated answers to parts f. and g., above.