Applied Math and a Liberal Arts Education
Over my lifetime particular conceptual mathematical concepts have stayed with me and been helpful in sorting through a situation. This is all part of what I would call a liberal arts education that aids you in developing critical thinking skills.
I learned the first one in middle school—the concept of sets. Disjointed sets exist where there are two or more sets with no common elements. This is illustrated by two circles that do not overlap. Overlapping sets are defined by a group of items that are in two different sets. This can be illustrated by two circles that overlap—the area found in the overlapping section is part of both circles. And there are equivalent sets—two sets that are exactly equivalent like two circles exactly on top of one another.
I learned the second set of concepts someplace along the way. I remember using these concepts in graduate school to analyze the types of data I was using and how that impacted the graphic symbols used to produce a map. This concept classified data as: 1) Nominal—named. For example, there are apples, oranges, and pears. 2) Ordinal—named and ordered. This is where you would order things in order of the lowest to highest. So we could take the fruit and order it according to which we liked the least to the best. 3) Interval data adds the element of proportional intervals to naming and ordering. The best example is temperature in Fahrenheit temperature data. Temperature is described on a scale with even increments. 4) Ratio data gives us the most precision—named, ordered, intervals, and those intervals can describe ratios. So temperature is not ratio data because you can’t say that 60 degrees is 2X 30 degrees. But you could weigh the fruit and put them in order of weight and be able to put them on a weight scale to be able to describe them in relation to each other to be able to say that the apple weighs 1.2X the pear.
A third concept is more geometric and geographical. Location is a concept that can be divided between relative location—the location of something relative to another place. Grand Rapids, Michigan is 20 miles east of Lake Michigan, for example. And absolute location where a place is identified by asset coordinates such as latitude and longitude. Grand Rapids is 42.9 degrees north latitude and 85.67 degrees west longitude. That is absolutely where it is located.
So why have I been thinking about these concepts. Maybe it was because my grandson was struggling with his math homework. Or maybe it was because my grandson was struggling with his math homework right after I had a frustrating conversation with the local power company.
I called the company to arrange for the electricity at my new-to-be home to be put in my name in the next week. I gave them the full address of the home—4404 Buttercup Run NE, Comstock Park.
The agent’s response was that they did not have a record of that address. She said: “We do have a 4404 on Division but not Buttercup Run.”
I was confused. The correct interval scale—house numbers—was on Buttercup, not Division. So I pointed out that the place where I was moving was not on Division and they in fact were providing service for the present occupant. I looked up the name and gave it to the agent.
The agent didn’t want to look it up because obviously the set of people with this name would be too large to be able to sort through.
I pointed out that, in fact, the overlapping set of people who had both this name and this street address would be just one.
The agent them did find this single overlapping set of one. However, the agent insisted that this address was in Belmont and not Comstock Park. She told me I would have to sort that out first with the person now living there.
I was silent. What would I ask them to do? Change the absolute location of the place? The property is in Comstock Park. I did quickly consider my ordinal scale of living preference. Belmont would be at the bottom, then Comstock Park, and then City of Grand Rapids at the top, but I really didn’t feel I had the power to change the municipal boundaries in order to get them to match the utility company’s flawed data set or my own ordinal preference, given the absoluteness of absolute location. I told the agent that I saw no point in talking to the present occupant.
The agent reiterated that the address was in Belmont.
Puzzled, I asked what the zip code was.
She replied that it was 49321
“Well,” I said. “That is the Comstock Park zip code, not Belmont.” In the back of my mind I was thinking of all the times I have run into systems that now have me put in the zip code and then automatically fill in the city name. And these are the people providing my utilities???
She then admitted that she would have to put in an address correction.
I hated to do it, but I asked that she make sure that she ask them to correct the city to match the zip code and not change the zip code to match the city. I wanted to make sure that my address was assigned to the correct equivalent set of city and zip code.
Afterward I thought about the quality of service and problem-solving capacity of the agent. Would a scale that measured service be an interval scale or a ratio scale? Probably it would have to be an interval scale because on a scale of 1-5 with 1 being low levels of serve and problem-solving and 5 being high, I couldn’t say for sure that a 5 was 5X a 1. But I could say that on a scale of 1-5, the agent got a .5 on the scale. I don’t think she got a liberal arts education.