Valid models require defined levels

ion. So now, let us try to describe abstraction. Here are some dictionary definitions: “abstract adj. 1. Considered apart from concrete existence . . . 4. Thought of or stated without reference to a specific instance.” “abstraction n. The process of extracting the underlying essence, removing dependence on real world objects.” Abstraction allows designers and modelers to describe a problem at a high level by hiding low-level information. In general, the higher the level of abstraction, the more things the system hides from the user. In 1945, Pablo Picasso made a wash drawing of a bull. A month later, he finished his 11th state of abstraction, which was composed of six lines. Célestin said, “When you stand before his eleventh bull, it’s hard to imagine the work that went into it” (Picasso 2006). At another time, he did an abstraction of his wife’s face in six stages. Picasso and Henri Matisse concurrently developed abstractionism in modern art. Digital computer simulations are written in levels Level Name What we know at this level 5 (highest) Coupled component systems Components and how they are coupled together. The components should be systems themselves, thereby producing hierarchical structures 4 State transitions How states are affected by inputs, that is, given an initial state we know the new state after the input is finished; what outputs are generated in each state 3 System experiments Given an initial state, every input trajectory produces a predictable output trajectory 2 Input/output behavior Time-indexed data collected from the source system, which consists of input/output pairs 1 (lowest) Source system Inputs to apply, variables to measure and how to observe them over time Figure 2. A sequence of images going from real to abstract that describe respectively a single person under certain circumstances, dozens of people, hundreds of people, thousands of people, millions of people and (almost) all people. Drawings are by Angelo Hammond. Copyright q, 2005, Bahill, from http://www/ sie.arizona.edu/sysengr/slides/ used with permission. A.T. Bahill et al. 558 D o w n l o a d e d B y : [ B a h i l l , A . T . ] A t : 1 9 : 3 9 2 2 A u g u s t 2 0 0 8