1691 Sanson Map of the World on Hemisphere Projection. Source: http://www.geographicus.com/mm5/cartographers/sanson.txt [Public domain], via Wikimedia Commons
CATEGORICAL THINKING, WHICH I WROTE ABOUT in the first two posts in this series, may at times be too pat for our own good, but this pragmatic (although potentially knee-jerk) way of dealing with things, people, and events is rarely based solely on nonsense.
Why not? Because the world is not an entirely unpredictable place. What happens to us, good or bad, is seldom purely random or plain crazy. Life actually does have patterns that can be real enough, although they can also be far from clear-cut and hard to see. Even so, patterns can be categorized. Not always successfully (just ask any weather forecaster), but that doesn’t mean we shouldn’t try to do so.
But this is enough about categorical thinking for now. I want to move on and write instead about what I have previously referred to as relational thinking.
The National Council of Teachers of Mathematics defines this way of thinking as the “mindful application of place value and the properties of number, operations, and equality in solving mathematics problems.” If this confuses you as much as it does me, note this organization adds: “A student with a disposition toward relational thinking has a habit of thinking before acting.”
This seems like an uncommonly low bar. Certainly not the definition I have in mind. Nature‘s online magazine Science of Learning offers an alternative: “At the core of all human learning and performance . . . is the foundational ability to perceive patterns that thread through all of nature, including human nature.”
This isn’t quite it, either. In fact, to me this sounds more like a definition of categorical thinking. So let me give you my own take on what pairing these two words together means:
Categorical thinking assumes things exist apart from one another, and may then become connected with one another. Relational thinking assumes instead things exist because they are connected.
If my definition sounds too mystical to you, let me offer you several examples of what I mean.
It seems likely that no relationship is solely one-sided if looked at closely enough. While granting this likelihood, there is no doubt that relationships can be so out of balance that it is not just a technicality that one side is more influential than the other. Critically, the character and perhaps the very existence of one side in such an imbalanced relationship may depend, maybe entirely, on the relationship it has with the other side.
A classic example of such a one-sided connection is the relationship between the Sun in our solar system and all the other planets (and then some) revolving around it, including Planet Earth.
Even without venturing into the exotic realm of modern cosmological theories about quantum gravity, it is obvious enough nowadays except perhaps to those who believe the Earth truly is flat that if it were not for the gravitational relationship between the planets and our Sun, the Earth would not exist at all and neither would we. Our reliance on the Sun is that one-sided and decisive. There would also be no life at all on our planet without the Sun serving as life’s ultimate source of energy, however otherworldly such a statement may sound.
Technical note: In formal network analysis, a relationship between two things (the two nodes or vertices in the relationship) is said to be dyadic (two-sided). When both are taken together, they are called a dyad. Furthermore, such two-party connections can be either undirected (more or less balanced or symmetrical from the point of view of each), or they can be directed (each party has a different take on the relationship). From this perspective, the relationship between the Earth and the Sun is a directed dyadic relationship, and it is a relationship that is decidedly one-sided.
It has been said that human beings have an innate sense of fairness and an ingrained willingness to do something for others when they are reasonably confident that a favor, whatever it is, will be returned, if not in kind, at least in some other way having equal value.
This judgment of our willingness to engage with others in two-sided relationships is far too cynical. Available evidence suggests instead that most of us are basically predisposed to be kind, collaborative, and helpful to others. That’s how we have evolved as a social species.
Moreover, humans as a rule are not only ready, willing, and able to forge and maintain relationships with others. We are also remarkably skilled at coming up with playful excuses to do so.
Although jogging, bicycling, and other forms of exercise, for instance, can be done easily enough as solitary tasks, people often find ways of turning even such seemingly self-centered healthy activities into broadly social occasions.
Although a more sedentary activity than a physically healthful one, this observation holds true also for online computer gaming, which is now a major leisure-time social activity for millions around the globe.
Technical note: A racket sport such as tennis is an example of an undirected dyadic relationship (accepting, of course, that only one of the players can win). Yet tennis is also a spectator sport, and as such, creates a directed dyadic relationship between sports fans and players.
It is obvious enough that spectator sports such as tennis or baseball involve more than just simple dyadic relationships between players and spectators. The social complexity of team sports is even more apparent for sports such as soccer and football that call for the coordination of players both within and between the two opposing teams on the field.
Side note: There seem to be few team sports that call for more than two teams on the playing field at the same time—maybe they should be called “dyadic sports”—although a few examples do come to mind if you are willing to bend the definition of what is a sport: many kinds of card games, many types of board games, some varieties of billiards, some forms of bicycle racing, etc.
But the many-sided complexity of most human relationships isn’t just obvious while watching players interact with one another on a playing field. The general complexity of human relationships is more than apparent also among the fans watching the game being played right there before their eyes. Indeed, in the case of some sports, it could be argued that “most of the action” is actually in the bleachers, not down on field. (You may be able to tell I don’t like baseball, and I am not too fond of football, either.)
How can we tackle the complexity of human relationships?
Classic definitions of social network analysis as a way of coming to grips with the complexity of human social relationships commonly read like this one from John Scott’s highly successful book Social Network Analysis: A Handbook: “social network analysis is an orientation towards the social world that inheres in a particular set of methods. It is not a specific body of formal or substantive theory” (page 37, 2nd ed., Sage Publications, 2000).
I find such a view naive, however well-intentioned. It is quite impossible to isolate methods from theories and then claim to be doing good science. This is an observation I will explore further in the next posting in this series.
This is Part 3 of a continuing series of posts on dynamic network analysis. Next up: 4. Exploring the 5th dimension.
© 2018 John Edward Terrell. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. The statements and opinions expressed are those of the author(s) and do not constitute official statements or positions of the Editors and others associated with SCIENCE DIALOGUES.