FOX News Special Feature - Using Mathematics to Find a Mall Parking Spot
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Video of FOX DC Story
On a chilly night Monday, December 5, 2006 Fox 29 TV came down to the Freehold Raceway Mall in Freehold, New Jersey to interview acclaimed national educator and ebook entrepreneur Joe Pagano to test out his mathematical theory about finding a mall parking spot using mathematics. What came out of this interview are two different, yet equally captivating, stories---one done by anchorwoman Melanie Alnwick for FOX DC, and the other done by reporter Gerald Kolpan of FOX Philly. What is interesting is that the theory of finding a mall parking spot was tested on different occasions, in completely different cities, and during different times of the day---and yet the method worked as predicted. As Gerald Kolpan, the Fox reporter reinforced by his statement: “This method posits an interesting theory. But does it work? Well, we put it to the test, and it does.”
Basically, the method hinges on the two complementary mathematical disciplines of probability and statistics. Much like a mortality table, which is used by insurance companies to predict how many people of a certain age will die in a given year, the parking solution predicts how many cars will “die,” that is vacate their spots, within a given interval of time. Just as an insurance company cannot predict who will die within a given year, only how many; the parking problem cannot predict which car of a group will vacate a spot, only that one of a group will within a given time period.
Because the parking solution is based on what we call a probabilistic model and moreover on certain assumptions (for example the time spent shopping during particular times of the year), there is naturally a certain margin of error built into the method. However, given the limited knowledge about the sample of cars targeted or the shopping habits of the owners of those cars, it is amazing how reliably predictable this method is and how time after time, with of course certain slight variations, the method comes through to yield the desired result.
The above caveat having been mentioned, the purpose of the problem was to show how, using some very basic assumptions and some minimal mathematical theory, a common frustration could be solved. In the problem, the assumption was that the average time spent shopping during the Christmas season was 120 minutes. Using a mathematical curve called the normal distribution and a famous statistical theory, we can predict that more than 99% of the cars in our sample will vacate the designated parking area within 180 minutes. (Remember we used the average mall stay of 120 minutes to get to this 180 minute number.) Of course, as was done in the DC story, by varying the basic assumptions---as for instance time spent shopping or number of targeted cars----different time intervals will be arrived at.
Based on empirical data collected from repeated observations of cars pulling into and leaving parking spots, the normal curve was chosen as the mathematical model to help with this problem. Moreover, the nature of this stochastic process (a stochastic process is a random process involving a sequence of events like cars pulling in and leaving spots) led to the conjecture that over time, the interval between cars leaving would “smoothe” out and that such interval could be calculated by dividing the number of maximum minutes, in this case 180, by the number of designated cars, in this case 20.
With this information in hand, and the basic assumptions granted, we were able to fit a mathematical model to the data so that reliable predictions could be made. Now what could be easier than doing a simple division to show how to find a parking spot? And you thought math was that bad.
