## Introduction

This is the kind of text I write to help myself understand something better. I will also write a little bit about the driving reasons which led me to write about models, which were analysis and design.

It’s generally accepted that a model for something material resembles it. If I tell you I have a model of a plane, you’d usually think of a miniature plane, or some 3D interactive software which simulates the plane performing various movements. Maybe something else. The point is that you usually don’t think about the plane, but about something else which somehow looks like it.

More generally, a model is about something. We should always talk about models mentioning what they’re about. These things are of extreme importance because they form a context for the model.

For something as abstract and general as a model, it’s no surprise that there are many ways for defining one. Back when you were learning, say addition and subtraction, you probably had the “follow the model” kind of exercise. It goes as the following:

Follow the model

1 ? 4 = 5 (+)

7 ? 2 = 5 (-)

1 ? 1 = 2 ( )

9 ? 2 = 7 ( )

5 ? 3 = 8 ( )

2 ? 1 = 1 ( )

To perform the exercise, you’d have to fill in the blanks with the right operator symbols as in the first two cases.

There is a model definition in this exercise. However, as I said before, a model is about something. In this case, what is “the something”? It doesn’t seem obvious, but, in a sense, the model is about how you should solve each item in the exercise. It was defined by two examples of its application. Given the examples, your mind then filled in the blanks and “got it” somehow. It begs the question: which are “the blanks” your mind filled?

A model doesn’t always have to be material (in the sense that it exists outside one’s mind). There are mental models, and those are only thought of. So if you want to communicate them with other people, you must find ways to represent them. That is, you should find a way to communicate something (the representation) that, for your particular purposes, is as good as the actual thing you want to communicate (the model). Representations can be tricky things to understand, but we use them all the time. For example, an angle is different from its measurement, and almost all the time we can talk about one through the other. We can do so because for our purposes, most of the time, an angle is as good as its measurement.

Your professor, then, was expecting you’d interpret the representation of the model (the two examples) and realize the model yourself.

Now I think I can go back to the question I’ve asked before. What are the blanks your mind filled? The answer is the model itself. When you interpreted the representation of the model, you conceived it in your mind.

## Definition

What is a model? A model is a set of properties about something.

A property of something is a statement which is always true for that thing. For example, “in my game, blood is always drawn with red like colors”. The statement “blood is always drawn with red like colors” is true about “my game”, which means this statement is a property of my game.

Some models are mathematical: their statements are always true, regardless of what (they’re exactly true). For example, part of the model for real numbers is that if you have three of them a,b,c and you have that a=b, then it’s also true that a+c=b+c.

## Models Go Mental

You could now be wondering how is a miniature plane a model for a real plane? Is a metal miniature plane a set of properties? It surely doesn’t look like so. One way of looking at this is that models are always mental and “material models” are always representation of (mental) models. Which means that if you think of a model for a plane and construct a miniature plane which looks just like what you’ve thought, then that miniature plane represents the model you have in mind.

The distinction I will make, then, is that a model is restricted to what you think of, but its representation can material (it exists in the real world, outside one’s mind), but not necessarily.

In this sense, it’s more useful to look at a miniature plane as a representation of a model and not as the model itself. In practice, the definition of a model is wide open and includes cases like these too. For now, throughout this article, I am going to use that models are intrinsically mental because I believe that is a more useful way of looking at things (it’s kind of a useful lie for doing thinking on my own).

## Usage, Analysis and Design

Curiously, you can have:

- a geometric model of a plane;
- a mechanical configuration model of a plane;
- models for its electric configuration; and
- many others.

In general, you could conceive several models for the various aspects of a plane. The same goes for laptop computers, software systems, and whatever else you can think of. You can take something S, look at a part P of it, ignore everything else, and build a model for S by only looking at P.

Being able to do such a think helps in analysis. You can, for example, analyze a plane by first looking at its geometry, then at its mechanics, and then at its electronics. Maybe you decide you’ll do this for each individual material part of the plane (whatever you choose those to be). Therefore, from analyzing the parts, you analyze the plane as a whole.

This activity of building a model requires you to think about something so to extract relevant properties out of it.

In general, the process of analyzing something and the process of building a model are connected. In both cases, you accumulate properties about something. For example, when you get the representation of a model, you have to look at it and extract relevant properties so you can build the model you’re expected to. It seems, then, that through analysis, one builds models. This leads us to a better definition of analysis.

Analysis is the process by which given S, you build a model for S. And some times, we talk about the analysis as being the model constructed from the analysis. The distinction should be clear from the context.

Analysis is being thought of extracting properties of something existing. But what about extracting properties of something which doesn’t exist? You can do so by analyzing how this non-existing entity would be. After that, you can derive a model of how to realize that non-existing entity so to make it real. And as it turns out, you can analyze existing things too (how nice!) in order to build models of how they could be realized.

The model of how you could realize/create something is called design. Designing is the process by which you construct a design. So it follows that designing is a creative process.

A good example of analysis and design is in engineering. Engineering is about problem solving as many other activities are. A team of engineers is given a problem. They’ll, then, analyze the problem to build a models (of requirements on the solution, of the environment in which the solution will be inserted in, and so forth). At some point, they have to design the solution or parts of it. Engineering teams are expected to do these analysis and design activities so to solve the problem. For them, analysis and design are major tools which they use to solve problems.

The design is just another model, which means that, by our definition of model, it’s mental. So a design needs representation(s) if you want to communicate it, store it somewhere, etc. In designing, engineers tend to build diagrams, texts, and all sorts of documents representing the design and/or its parts. The same goes for analysis by the way . And there are actually special tools for representing analysis and design models.

Representing models is often useful, but that is another topic. However, it’d be useful if there were documents representing all the produced analysis and designs so that others (and the original engineers themselves) can use those to learn about and/or remember what happened during the project development.

## Final Thoughts

In my experience, and belief, it’s often the case that analysis form a cause for design, which means it’s very common to see analysis and designing as two connected activities. I believe it’s common, in the case there are problems in need of solutions, that there is also a need for good solutions design, which are usually expected to be well founded in good analysis.

To summarize, analysis has the idea of taking things apart because you extract properties of something, while design has the idea of combining things together because you model how to realize something.

Modeling is not just important for analysis and design, you could think, but these two concepts were the reason I decided to write about modeling.

If you can, please share your thoughts. Comment! =)