Hierarchies

Outlines and Hierarchies

by Roger Ehrich
and Amy Ramsey

In the beginning there was only endless time. For early man, time started at birth and ended at death. It is interesting to imagine whether the very earliest of humans might even have been aware of anything but the present. They had to feed, and they had to rest, but for these earliest of ancestors, was there any sense that these events were ordered in time? Did they really understand that there was both a past and a future, and that past, present, and future had an unchangeable order? Did they have any sense of how large the past and the future might be? It is hard to imagine what that must have been like, before man had learned language and before man had learned to write or to keep records. Life must have been a continous flow of consciousness between birth and death.

Because of the motions of the solar system and the rotation of the earth, man began to divide time into smaller chunks because these chunks were natural divisions of time that affected their lives. These chunks were days due to the earth's rotation, months due to the movement of the moon around the earth, and years due to the earth's movement around the sun. For example, years were important to them because as temperature, rainfall, and daylight varied, the food supply varied as well. As man's memory developed, they began to realize that since times of plenty had occurred often in the past, they would be likely to occur again in the future. They began to divide the year into the various times of hardship and times of plenty and to celebrate the coming and going of each.

To these early people, day and night and the phases of the moon began to be used to pace their lives, though they had no understanding of either. But they began to subdivide time into these chunks for several reasons...

Keeping Track of the Pieces

Because the earliest of humans could not make measurements very well, they were probably not bothered by little problems with their ordering of time. For example, 12 lunar months fall 11.6 days short of a year. A solar year consists not of 365 days but actually of 365 days, 5 hours, 48 minutes, and 45.5 seconds. Thus the solar year is not evenly divisible into days. But it is so useful to divide years into days that we have worked out ways to do that.

The Gregorian calendar that we use today has a leap year every 4 years when February has a 29th day. Since that would mean that there are too many days in a year, Pope Gregory XIII decreed that only century years divisible by 400 could be leap years. Thus the year 2000 will be a leap year, but not the year 2100. Still, it is so useful to use to subdivide time into centuries, years, seasons, months, weeks, days, hours, minutes, and seconds that we continue to do this, despite disagreement about how to do it. We have created weeks for religious purposes, so that we may rest from labor every 7th day, and we have ended up with months of unequal length.

Modern man has become so dependent upon timekeeping that many schemes have been found to keep track of time and its various subdivisions. Three of them are shown in the following figure:

Display (a) is a familiar digital clock, and it shows only the present. Clock (b) is much more remarkable since it shows that half days are subdivided into 12 hours, that each hour is divided into 60 minutes, and that each minute is divided into 60 1-second chunks of time, all on the same display. To eliminate any confusion, the seconds are shown to be less important than the minutes by using smaller dots, and so forth. This simple display shows 43200 distinct subdivisions of the half day, and being circular, it repeats forever. By simply cutting the round clock and pulling it straight we get a linear clock (c) which, lacking hands and circularity, can show us only as many major divisions and subdivisions as space permits.

What we have learned is that in order to understand big things we have to break them down into smaller parts. If these smaller parts are still too hard to understand, we have to break them apart even further until we can understand the little pieces. But that isn't all...how we draw the whole and its various subdivisions makes a big difference in how well we can see all the smaller pieces and their relationships to the larger ones.

Getting Organized

Time isn't the only thing that is subdivided into smaller and smaller pieces. The world's land is subdivided into countries because the people who live in each country are in some way more similar to others in the country than to those in other countries. Larger countries like the US may be subdivided into states, and the states into counties. For still another example, think about your school. Your school district is divided into 20 schools, each school is divided into grade levels, each grade is divided into classrooms, and finally each classroom has a group of students.

Let's think about ways we can explain how your school is organized. We could just write an alphabetical list of teachers' names followed by the grade level. Then, to find all the 3rd-grade teachers you would have to scan the list from top to bottom and mark all the 3rd-grade teachers. Another way to show the organization would be to use an outline, which would look like this:

The nice thing about the outline form is that it is easy to find the names of all the teachers for a particular grade level.

Sample Classroom Assignments

There is another way to see how the Riner classrooms are organized, however. The drawing below is called a tree. The yellow dots are called nodes, the dot on the left labeled Riner is called the root, and the lines between the dots are called its branches. The root node refers to all the students at Riner Elementary School, the node labeled 4 refers to all the 4th-grade students, and the node labeled Daniels refers to all Ms. Daniels' students.

All of the nodes in the tree stand for groups of students, but the farther from the root of the tree we look, the the smaller and more specific the set of students gets. We can call each set of students by the name written next to its dot.

Sample Classroom Assignments

Organizing Computer Storage

In many ways the disk in your computer is like a big grocery store, and to find anything we need to make up the right kind of tree. As you know, information in a computer is made up of files. We keep all these files in folders...each folder is the node of a tree.

The trouble with computers is that there are many different kinds of files, just like the items sold in a grocery store. There are pictures, word processor files, programs, World Wide Web files, sound files, mail files, drawings, to name but a few. If we just put them all into one big folder we would never be able to tell what was what because there are several thousand files on your hard drive. But it's worse than that. Some of these files belong to Windows '95 (they make the computer work), some belong to you, some belong to your partner. Even those that belong to you might have different purposes...you may have Word files for social studies and other Word files for science. Will you be able to tell them apart if you put them all into the same folder? Should you put your files into the same folder as your partners'?

Classroom Discussion Questions and Exercises

On a computer we have one really important rule...we never put program files for the computer into the same folder as your own data files. That is so that if someone wants to change a computer program, they will know that all the files in a folder belong to the program. So let's take a look at the way things are organized now on your computer...here's part of the tree (a lot of the nodes aren't drawn because the drawing would be too complicated). Each node is called a folder or a directory.

Program Files and Windows are programs that make your computer run. You should never store any of your files here. MS Office is where your word processor programs are stored, psp4 is where your graphics programs are located, and nm is where your networking programs (and your Email files) are located. work was put there so that you could store your own files there.

Classroom Discussion Questions and Exercises

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