Get curious about innovative methodologies with Adolfo Espíritu as he applies his curiosities about conceiving the future in the third part of a series on approximating the future for the Corporation of Tomorrow.
A model can be thought as the skeleton of a problem: it has the minimum amount of information that is needed to describe a problem and its dynamics (by dynamics I mean how it evolves and behaves with respect to some other parameters); skeletons--and models--give a representation of some aspect of the real thing. To make this possible, we simplify reality under assumptions, which will determine the quality of our predictions. Three basic steps can be followed to create a model (Blanchard, et. al., 1998):
1. Clearly state the assumptions under which you are going to state the model; they should describe the relationships among quantities that will be studied. This has to do with the observation part, since here we are trying to explain how the problem works; it has to do with understanding the problem and giving the most important aspects of the problem. Physical laws, definitions and empirical observations come into play. For example, if we throw a ball on Earth with certain angle and speed, we know that it is going to go up and then down (that is what we see). However, to make things easier, we are going to ignore friction between the ball and air. We want to predict where the ball land and its maximum height will.
2. Create a full list of the variables and parameters that are going to be used in the model; these are the key players of your predictions.Here, the main idea is to quantify and measure the important aspects of your problem. Here, we distinguish three types of data:
Independent variables: Their value is not influenced by other quantities.
Dependent variables: They depend on other variables; a rule is needed to compute the dependent variable’s value given the independent variable’s value.
Parameters: They are quantities that remain constant in the model.
For example, returning to our example of the ball, the distance travelled (dependent variable) will depend on the elapsed time (independent variable), and we can set as fixed values its initial velocity and position (parameters). This is the least amount of information that we need to derive the model (I claim least because based on observations, we know that the ball is moving, and if we change its velocity and initial position, we are going to get different results. For example, the mass of the object does not affect the result, so it is discarded).
3. Use your assumptions to relate the stated quantities through equations. Finally, we describe the relationship between variables and parameters through equations. Some good advice here is to keep the algebra as simple as possible. In our example, I will omit the model (for further reference, check projectile motion), but what is important in these steps is to get the idea of how to get a representation of our problem.
Finally, once the model is made, it is time for making predictions. The next step is to compare your predictions to your experimental data to determine how good your model is--which can be judged by how accurate your calculations are to the real thing.
We make models because we want to make educated guesses and deliver the solution with fewer iterations; however, it is important to remember that models are not perfect, but approximate. Curiosity is the main fuel of this process, since it is involved in the first step (understanding the problem), stating the input and output data (determine the variables and parameters), and, finally, establishing how the data relates (equations).
What I want you to realize is that this method can help us solve problems at enterprises, since a problem can be modeled (maybe you do not use equations, but this process helps you to understand the essence of the problem and its dynamics), so by identifying these contradictions, it’s easier to focus on the solution because you already know what’s not going to work based on the behavior of the problem. This is one of the essences of the Blue Ocean Strategy, which is an innovation method, so next time you see a model remember that even though it is not perfect, it is a very good starting point for developing your solution.
Want to see a new perspective of innovation through computation lenses? Stay tuned for the next series.
Adolfo Arana Espíritu Santo is a student at the Monterrey Institute of Technology & Higher Learning and loves getting curious about, Math, Physics, and Quantum Computers.
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Projectile Motion. (n.d.) USA: FisicaLab. Recovered from: https://www.fisicalab.com/en/section/parabolic-motion
P. Blanchard, et. al. (1998). Differential Equations. USA: Brooks/Cole Publishing Company.