Multidimensionality: Finding underlying dimensions

One of the great draws of systems to me has always been identifying very general patterns and principles that you can apply almost anywhere. Our brains are already wired to be excellent pattern matchers, and being a generalist you almost can’t help not discovering these very general patterns. Systems theory and related fields seem to be the ideal formal framework for this generalist mindset, but they also act as a repository of existing models and principles you can use to more simply understand our complex world.

There are five principles of systems that we need to understand as the building blocks for our journey to systems thinking and design. This post is about multidimensionality, which is maybe the most potent of those principles, but also the least obviously “systemic” of them. In other words, I think it’s a great place to start.

I have a story to explain this principle involving two systems scientists, C. West Churchman and Russell Ackoff. It takes place at the University of Pennsylvania in 1946. The two colleagues were heavily interested in the personality trait work of Carl Jung, particularly being introverted or extroverted. To explore the idea, they decided to test some students for the trait.

They first learned that there were several tests to determine whether a person was introverted or extroverted. They got copies of each and gave them to a sample of graduate students. Strangely, the different tests gave inconsistent results. Some would score introverts on one test and extroverts on another test. Were the tests flawed?

The two curious experimenters brought it up to several trusted clinical psychologists. They were not surprised. They explained that paper-and-pencil tests were not a suitable substitute for clinical interviews. Ackoff and Churchman took this advice and arranged for several of them to independently determine the type of each of the previously tested graduate students. Surprisingly, their results were just as inconsistent!

Were the two personality types Jung identified nonsense? This was not a scientific pursuit, it was merely a fun exploration of Jung’s ideas. But with results like this it was not very encouraging. However, Ackoff and Churchman did come up with another possible explanation: maybe introversion-extroversion was more complex than it seemed, in this case involving more than a single dimension. If that were the case, and these tests were naively focusing on different dimensions at the exclusion of the others, they would be giving naive and possibly contradictory results like they were getting. This is where multidimensionality comes in.

Part of multidimensionality is about realizing that things can be more complex than they seem when observed on a single dimension. There was a thought experiment Ackoff and Churchman used that led them to believe introversion-extroversion might be multidimensional. For this experiment, suppose all males could be considered either (American) football players or not football players (similar to supposing everybody is either introverted or extroverted). Then suppose you know the underlying dimensions involved in being a football player: size and weight. In order to be a football player, you must be both big (over a specified height or size) and heavy (over a specified weight). We can make a chart to visualize this:

So being placed on this table based on weight and size will determine whether you’re a football player or not. Okay. Now imagine a person in the big-light category. An observer focusing only on the dimension of size would say they were a football player, and one focusing only on the dimension of weight would say they were not. Their judgments would be reversed for somebody that fell into the small-heavy category. Although it seems obvious in this example that you need to consider both dimensions, you do need to first know what the dimensions are, which isn’t always obvious.

Ackoff and Churchman went back to Jung’s work to try and figure out the underlying dimensions these tests and psychologists were not aware of. They found there was a definite focus on the self vs the environment. Extroverts were considered to be most concerned with and likely to obtain gratification from what is outside the self (their environment), and introverts were considered to be most concerned with and interested in one’s own mental life (their self). This was nothing new.

However, when going through Jung’s writing, they noticed a pattern in the type descriptions that was not made explicit by Jung. The descriptions seemed to fall into two categories: those about the source of stimulus, and those about the target of reaction. Like input and output. You could be stimulated by the self or the environment, and you could then react by affecting the self or the environment.

To make things easy, they came up with some new labels. On the stimulus side, people that were more sensitive to the environment were objectiverts, and those that were more sensitive to the self were subjectiverts. Then for reaction, those more inclined to respond by affecting the environment or the self were considered externalizing and internalizing, respectively. Together, this created 4 types of basic personalities defined as:

• Subjective-Internalizers (SIs): respond to internal stimuli by changing themselves
• Subjective-Externalizers (SEs): respond to internal stimuli by changing their environment
• Objective-Internalizers (OIs): respond to external stimuli by changing themselves
• Objective-Externalizers (OEs): respond to external stimuli by changing their environment

They noted that the SIs and OEs were most aligned with Jung’s introvert and extrovert, so they considered them pure types. They oriented the self or environment in both directions (that is, as input and output). The others were mixed types, where there was orientation to the self in one direction and the environment in the other. We can make a chart to visualize these types:

Ackoff and Churchman took their new findings back to their old data. They found that three-quarters of the tested students fell into the new mixed types. They also found that when examining the tests and clinical interviews, they were each very obviously biased toward one of the new dimensions that were now identified. This meant a student taking a test biased towards one dimension would get labeled an introvert, and then take a test biased towards the other and get labeled an extrovert. Discovering new classifications by finding new underlying dimensions dissolved this inconsistency.

One lesson of multidimensionality is that from multiple interacting dimensions, complex types can emerge. When we discover some of the emergent types first, such as introversion and extroversion, we can be missing part of the picture by not exploring what the underlying dimensions are. That’s what this story shows.

However, there’s another type of situation where multidimensionality is a useful principle to know. Can anybody guess what that is? Hint: false dichotomies.