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One way to explain something is to describe how it is related to other things. The usual way to do this is to imagine that what we want to understand is dependent upon or predicted by a series of other facts about the world that we already know (or can find out) something about.
For example: What determines the form of the human pelvis? The human pelvis must accommodate both upright walking and bearing children. Walking requires a joint at the hip and a way to support and balance the weight of the upper body alternatively on one leg and then the other so as to walk. Giving birth requires a sufficiently large passageway for the enormous human fetus to emerge. So arguably the activities of walking and bearing children determine (explain) the form of the pelvis.
When, for purposes of argument, we describe one feature of the universe (such as pelvis form) as being dependent upon others (such as walking and giving birth), we call it a "dependent" variable. Our goal is to figure out what other variables it depends upon, and if possible how much it depends on each. Seen the other way around, we want to know how well we can predict the dependent variable if we know the values of other variables. (Naturally it is possible in some cases to be mathematically rigorous about this.) In our example the form of the pelvis is the "dependent" variable. What it depends upon (the "determining" or so-called "independent" variables) are the needs of walking and giving birth.
Since we are interested in predicting one variable from the values of other variables, we can start anywhere. For example, we can start with a different problem that involves the same features: What determines how people are able to walk? The ability to walk is dependent upon the form of the pelvis, among other things. Here the ability to walk is what we want to explain, so it is the dependent variable. The form of the pelvis is now taken as a "given," one of the relevant "determining variables" (or "independent variables").
Nothing is inherently a dependent or a determining (independent) variable. It is dependent or determining only in the context of a particular question we are trying to answer.
Another example: In archaeology we may want to explain the location of sites in a particular part of the world. Site location becomes the dependent variable, the thing we are trying to explain. What does site location depend upon? Grossly, resource distribution, but resources may include several different things: available water, access to hunting grounds, shelter from inclement weather, fertile soil for farming, or the location of other human groups (such as predatory raiders or helpful allies). In this particular example, each of these would be interpreted as affecting the dependent variable, i.e., the site location. Each of these, in turn, may involve other things (such as hunting grounds for different kinds of animals).
Ultimately everything in the world seems to be related to everything else, as John Muir famously observed, and our act of isolating dependent and determining variables is destined to be an incomplete abstraction. It is not reality. It is a "model" of reality. "Model" is simply the name we give to a group of related variables and the system of relationships that we believe links them. Another word for a model is "theory," but the word "model" has the advantage of being easy to envision, just as an architect's model of a proposed building is not the building itself, but is like the proposed building in some critical respects. Models are created to contribute to our understanding of whatever it is that they represent.
Explaining human society by developing models of it (or of pieces of it) is the principal project of the social sciences (increasingly in cooperation with historians). Some models are better than others in that they make more accurate predictions or take account of more evidence. For some purposes, such as a class lecture, we may want a very simple model, with only a couple of variables. We may explain the end of the Neolithic occupation at the Jordanian site of 'Ain Ghazal, for example, by environmental destruction caused by burning all available fuel to make plaster and then keeping goats that ate all the seedlings before they grew into more trees.
For other purposes, a far more detailed model may be necessary, one which takes all the determining variables accurately into account. For example, if you are planning the Roosevelt College First Annual Paleolithic Arts Fair and Sun Chicken Look-Alike Costume Contest, you want to be sure you have included all the possible expenses (determining variables) before you set the price (dependent variable). (Don't forget the extra security for the chicken costumes.) Getting the model wrong can be expensive.
An everyday example of model making is financial planning. How much do you need to earn part-time or summers in order to keep paying the regents until you graduate? The target dollar amount is the dependent variable. One of the determining variables it depends upon is how much you have in the bank now. Another is whether you are a resident or not. Another is whether there will be another fee increase. And so on.
An example of a model used in archaeology is the concept of "carrying capacity." Carrying capacity is the maximum number of people that a given piece of land can support. What are some of the determinants of carrying capacity? That is, if carrying capacity is the dependent variable, what are the determining ("independent") variables that we need to know in order to predict it? Some of them are the size of the territory, the climate, the nature of the terrain, the available plant and animal life, and so on. (Obviously each of these is potentially quite complex.) Other determining variables include the knowledge that the humans have of how to use the land and their preferences and beliefs about life. Do they know about farming or do they live by foraging? Farming usually produces a higher carrying capacity than foraging does. Do they think salamanders are edible? If so, the carrying capacity may be slightly higher, if not, then slightly lower. Do they trade with other regions? If so, resources that can be exported (like minerals) may increase the carrying capacity of the land beyond the number of people who eat its plants and animals.
Our model of the carrying capacity of a given region must take account of all of the most important factors that might influence it. Once we have confidence that we have included most of what matters, we can then use the output of the model (the carrying capacity we have found) as an determining ("independent") variable in some other model. We can ask, for example, whether human populations tend to grow till they approximate the carrying capacity of the land, or we can ask whether, as population size approaches the carrying capacity, the rate of innovation increases, thereby further increasing the carrying capacity. Or whether the rate of conflict increases as people compete for resources. Or whether leadership qualities change as leaders have to adjudicate more disputes. And so on.
Historians and social scientists are always concerned with a great many models of human society, although often the models are not formally spelled out in those terms. Here are a few variables that are often of interest:
What does war depend upon?
What determines whether men and women are equal in society?
What determines how hard people have to work?
What does social class depend on?
What makes people violent?
What does the invention of writing depend on?
Is the form of religious belief and practice predictable from anything else in society?
Does social structure depend importantly on religious belief?
Are liberty and equality incompatible?
Why do religious systems so often require sacrifices?
What does the rise of empires depend upon?
What factors are important in the decline of empires?
Is Southern California the pinnacle of human evolution?
If the final exam is the dependent variable, what independent variables predict its form and content?
Obviously, the scheme of dependent and determining variables is a useful way to think about things, and most modern science (including social science) is based more or less obviously upon this intellectual model. Scientists seek to identify determining ("independent") variables and to describe the extent of their effects, individually and collectively, upon dependent variables.
Are there other models? Of course. Probably none is as useful or broadly used as the model of dependent and determining variables. But here is an example of a different kind of model, this time taken from my own research.
I have done extensive studies of arranged marriage. Over most of the world, most marriages involve a "window of opportunity" beginning when a young person is considered marriageable (or engageable) and ending when he or she is regarded as "over the hill" or when the available potential mates are used up. At the beginning of this period, the young person (or the parents or the matchmaker) can afford to be picky, looking over many possible spouses and seeking the most desirable one. Towards the end, as the number of potential spouses drops off, a certain desperation sets in, and the criteria for what constitutes a desirable match become less stringent.
I hypothesize that when a region has more matchmakers, they seek to finalize marriages before their competitors do while there are still potential spousal candidates to be had. Therefore when there are more matchmakers (perhaps because custom awards them a high remuneration), the minimum age at marriage tends to drop, until in some cases children are "spoken for" even before they are born.
It would be possible to recast this model in terms of independent and determining variables, and it would prove in fact to be a series of chained propositions. But doing so is not necessarily the easiest way to envision what is happening. A metaphorical phrase like "window of opportunity" turns out to be a much more efficient way of describing the situation and making sense of the motives of the individuals involved.
By definition, a model is a description of a system of relationships that is abstracted from actual cases to describe a "general" or "typical" situation. The marriage example shows one more important feature of models: a model allows one to hypothesize (predict) yet more relationships. The proposition that more matchmakers produce earlier average age of marriage (or engagement) is not a fact about the world; it is a prediction based on the "window-of-opportunity" model. If that model is "robust," then derived predictions should turn out to be true. When the logically derived predictions turn out to be wrong, it suggests that there is something the matter with the model.
But without the model, we wouldn't have any derivative predictions, and we might very well not collect the data that would allow some of our most interesting discoveries. In this example, nobody has ever collected a data set that can be used to correlate the number of competing matchmakers in a region compared with mean marriage age. Such a finding would perhaps help to explain customs of pre-natal or childhood engagement in many parts of the world. But since nobody has thought of it, the research has not (yet) been done.
Seen slightly differently, until there is a model, there is no logical way to decide what does or does not constitute "data." Devising the model is the creative act that establishes what bits of the world constitute relevant data. Making predictions from the model that turn out to be correct gradually moves the model from hypothesis to theory, and from theory to scientific "fact." Making predictions from the model that are logical but turn out to be wrong shows that the model is deficient and inspires investigators to modify it and try again.
Models, in short, are not reality. But by providing manipulable abstractions from reality they help us to gain insights into reality, and lead us to new avenues of discovery.