I am starting to compile my pile of notes to write a paper investigating the notion of "orthogonality."
Currently, we have a decent understanding of "concatenation" that is, when building a theory it is better to have more independent variables than dependent variables. When creating a diagram of a theory, for example, we want to have more than one causal arrow pointing toward each box.concept/variable. However, it is rather difficult to decide which variables are "best". For a negative example, it is reasonable to say that more pay from teaching work and more pay from royalties are two causal variables that lead to more money in the bank. However, those two are "additive."
While true and reasonable, they are not very interesting - they provide a broader understanding, but don't provide a deeper understanding. They are so similar that they cannot be considered "orthogonal" to one another.
Instead, if one were to say "more labor and more parts both combine to create more finished widgets" we could more easily see labor and parts as orthogonal to one another. They are multiplicative instead of additive. There will be no resulting finished widgets if either causal variable drops to zero.
Another way to look at it is as a process of abstraction/categorization. That is, for example, when we do qualitative research, we take the responses from interviews and clump them into categories or themes. Big problem here... are those the best categories - or are they representative of shallow understanding? When we are interviewing people about heir eating habits, we might find ourselves talking about apples and oranges, do we create two categories (apples and oranges) and "oh look, these are different categories of peoples' preferences" *or* do we create more subtle categories such as color, flavor, acidity, sweetness, etc. which would provide a deeper understanding? With that deeper understanding, we might (for example) suggest alternative fruits (or, who knows, at a deeper level, understand the genetic structure of the fruits - OK - that's not really qualitative... but you get the idea... different categories might give us deeper understanding).
If we are able to understand how to create themes/categories that are orthogonal to one another, we can generate more effective research results to create better theory to better understand our world and enact effective change.
So... I hope to write an article that will help theory-builders understand that relationship and provide some tools for building better theories.
And, I would appreciate your thoughts, insights, etc!
I would concentrate on expressing myself in the English language. Terms such as orthogonality and concatenation are designed to confuse rather than enlighten and create an image of intellectuality . Just ignore them and decide exactly what you would like to study in plain English.
Frank, I partly agree. Certainly plain language is preferable where possible. However, we have specialized words to represent certain things. I certainly appreicate your interest - what word would you recommend I use in place of "concatenated"?
Use several words. If it means it is better to have more independent than dependent variables say that. Personally, I do not believe that that proposition is true.
I suggest editing title from "Orthogonality in Building Theory", to Orthogonality in Building a Theory", to avoid a certain misleading meaning on your general concern.
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