Dynamic Network Analysis 6. What is a network?

Pail Brigade Porcupine Fire - July 9th 1911 [pkdon50 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

John Terrell

AS AN ANTHROPOLOGIST WHO FOR DECADES has been studying how we humans deal with one another and the world around us, I find it fascinating that experts writing about networks and network analysis evidently have difficulty using what I like to call relational thinking.

Here again are the definitions of the two modes of thought I offered in an earlier post in this series:

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.

As evidence of the continuing appeal of categorical thinking even in networks science, here is an answer to the question “What is a social network?” given by David Knoke and Song Yang, two of the leading writers on social network analysis. “A social network is a structure composed of a set of actors, some of whose members are connected by a set of one or more relations” (Knoke and Yang 2008: 8).

Here is another definition, this time by John Scott, also a leading writer in this field, similarly implying that social networks are a particular class of things within the general category called structures. “Social network analysis emerged as a set of methods for the analysis of social structures, methods that specifically allow an investigation of the relational aspects of these structures” (Scott 2000: 38).

In both of these definitions (there are others I could give you), the authors are evidently assuming that there is (1)  a class of things called social structures*  within which (2) people relate to one another in distinct ways making it possible to (3) isolate what they are doing and then label them as “actors” operating within a particular kind or type (i.e., category) of structure.

From the relational perspective I am writing about in this series, however, these supposed structures only exist when—or perhaps I should say throughthe relational acts or events that the identified actors are participating in.

It would be more than simply metaphorical, therefore, to say that networks may have more in common with thunderstorms than with the sorts of things one usually thinks of when somebody uses the word “structure.”

Houses, hotels, banks, and boardwalks are all clearly structures. Why use this word also to talk about social networks?

A little history

Scott has reviewed in some detail the history behind why experts in social network analysis see networks as structures of a certain sort. Put briefly,  contemporary network analysis is rooted in the 20th century development of mathematical graph theory and structuralist approaches to social organization in sociology and social anthropology. As Scott has concluded: “It is undoubtedly the case that social network analysis embodies a particular theoretical orientation towards the structure of the social world and that it is, therefore, linked with structural theories of action” (Scott 2000: 37).

“Johnson’s algorithm is a way to find the shortest paths between all pairs of vertices in a sparse, edge-weighted, directed graph. It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist. It works by using the Bellman–Ford algorithm to compute a transformation of the input graph that removes all negative weights, allowing Dijkstra’s algorithm to be used on the transformed graph. It is named after Donald B. Johnson, who first published the technique in 1977.” By David Eppstein [Public domain], from Wikimedia Commons (https://en.wikipedia.org/wiki/Johnson%27s_algorithm).
He is not alone, however, in saying also that “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 social theory” (page 37).

Perhaps you are like me, and you react to this disclaimer as an example of intellectual artful dodging. Can “methods” really exist apart from ideas and assumptions—also known as “theory”—about the world around us?

Methods and theory

Not everyone writing about network analysis would agree that there is a divide between methods and theory. Stephen Borgatti, Martin Everett, and Jeffrey Johnson, major voices in this academic arena, have taken specific aim at such a claim: “some social scientists, unfamiliar with formal theorizing, have misconceived of the field as a methodology.” They acknowledge that network analysis has cultivated a distinctive mathematical methodology, but we shouldn’t let ourselves be fooled by the formality of these methods: “the theoretical concepts that are so emblematic of the field, such as centrality and structural equivalence, are just that: theoretical concepts that are part of a distinctive approach to explaining the social world” (Borgatti et al. 2013: 10).

In the next post in this series, I will begin exploring the ways in which network analysis can help us both ask and then try to answer well-formulated research questions in the social and historical sciences.

Right now, however, I only want to say that both of the examples these three co-authors offer us in this quotation—centrality and structural equivalence—strike me as far from compelling evidence that there is more to network analysis than just the analytical methods used.

However, there is an obvious question still needing an answer.

What is a network?

Just as the proof of the pudding is in the eating, so too, a definition of what something is supposed to mean is only as good as it proves useful. In a real sense, therefore, this entire series on dynamic network analysis could be seen as an extended dining experience (yes, admittedly a rather unconventional analogy). Even so, we need at least a working definition of what is a network, and I suggest this one might do at least at the start:

A network is an interrelated series of events having consequences affecting the likely repetition of those interactions.

At this stage in this series, I only want to point out a few of the implications of such a definition.

First, just as it takes two to tango, so too, it takes at least two people, things, or places to form a network, i.e., ≥N=2. As discussed previously, the events constituting a dyadic network relationship must be repetitive and not randomly so. Furthermore, what happens as part of such a relationship is dependent at least to a degree on the conditions under which the events occur. Differing situational conditions may give rise to differing interactions. Moreover, when interactions happen may be contingent on what has occurred since the last event in the relationship that has possibly changed the situation and the particulars of the interaction.

Second, while mathematicians may have fun solving abstract mathematical problems using graph theory, it is probably fair to say that many, maybe most, people doing network analysis are not doing so for abstract reasons. I am not alone in thinking that what makes network analysis worth doing is minimally the prospect that such analyses can help us pin down in real-world situations the consequences, positive or negative, of networked interactions.

A basic classification of networks

Therefore, as suggested in Figure 1, it can be argued that networks generally all have the three dimensions I have been labeling as situational, circumstantial, and consequential.

However, when it comes to social network analysis, we need to add the dimension of intentionality, a dimension only briefly mentioned in an earlier posting in this series. Furthermore, the intentionality of social interactions (events) between two or more individuals (network analysts seem to favor calling them agents or actors) is not limited solely to our own species. Ask any dog, cat, or wolf of your acquaintance should you have doubts that this is so.

This having been said, it is also important to recognize a distinction that can be usefully drawn between relationships that are intentional—people and other clever animals can cooperate, for instance, to get things done—and networks that are, in addition, purposeful: they are designed as networks of interactions to get things done even when the intentions of the individuals involved in such networks vary.

Perhaps one of the most exotic examples of such a purposeful network would be the ancient trade routes of the Silk Road connecting East with West.  Or its modern and sinister namesake, the black market for illicit drugs hidden on the Internet. Another shameful example would be the water supply system of the city of Flint, Michigan.

Figure 1
What’s next?

As I will be exploring in later posts, many analysts are chiefly interested in studying networks that have been specifically designed by those involved to accomplish such larger objectives. As the next step in this series, however, I want to ask what studying networks is good for.

* “From the view of social network analysis, the social environment can be expressed as patterns or regularities in relationships among interacting units. We will refer to the presence of regular patterns in relationship as structure” (Wasserman and Faust 1994: 3).

References cited

Borgatti, Stephen P., Martin G. Everett, and Jeffrey C. Johnson (2013). Analyzing Social Networks. Los Angeles: Sage Publications.

Knoke, David and Song Yang (2008). Social Network Analysis, 2nd ed. Los Angeles: Sage.

Scott, John (2000). Social Network Analysis: A Handbook. Los Angeles: Sage.

Wasserman, Stanley and Katherine Faust (1994). Social network analysis: Methods and applications (Vol. 8). Cambridge university press.

This is Part 6 of a continuing series of posts on dynamic network analysis. 7. Why do network analysis?
© 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.

Dynamic Network Analysis 5. What’s a relationship?

NOAA's National Weather Service (NWS) Collection. Location: Orange, Australia. Photographer: Mr. Shane Lear (image wea00628);

John Terrell

DEFINITIONS OF WHAT IS A NETWORK differ in their wording and focus, but a common theme is that different types of relationships give rise to different types of networks.

So if we measure friendship ties, we have a friendship network, and if we also measure kinship ties among the same people, we have both a friendship network and a kinship network . In the analysis we may choose to combine the networks in various ways, but in reality we have two networks. (Borgatti et al. 2013: 3)

In response to such a statement, all I can say is “Oh, really?” The assumptions embedded in these seemingly straightforward words are fairly typical of how network analysis is commonly defined by experts as a way to study the world and our place in it. They are all questionable.

An example of a social network diagram. By Wykis [Public domain], from Wikimedia Commons
What, for example, is “friendship” (Terrell 2014)? Is it even possible to have a single and consistent right answer to such a question so that every friendship included in a network of friendships is predicated on the same or at least comparable human feelings, commitments, and acts? Additionally,  as social anthropologists know well after many decades of study and debate, don’t even try to see “kinship” as a universally consistent type of human social engagement.

What is a relationship?

Let’s reflect a moment on what I just wrote. Except as an academic exercise, does anyone honestly believe the nuanced relationships that humans have with one another can be usefully seen as a layering of separate networks? So much so, that all of the networks included in any given social network analysis are somehow layered together in a fashion that might be described as some sort of “social sandwich”—to offer an admittedly peculiar simile?

You can probably tell without my having to say so that I want to offer you another way to think about networks and doing network analysis.

Networks are a way of thinking about social systems that focus our attention on the relationships among the entities that make up the system, which we call actors and nodes (Borgatti et al. 2013: 1)

Instead of seeing networks the way most analysts do as systems (Kolaczyk 2009: 2) or structures (Scott 2000: 4), I will show you how it is useful as well as more truthful to describe dynamic network analysis athe study of related events in time and space of differing and variable probability. Importantly, whether the events being analyzed are predictable enough to characterize their co-occurrence as a “system” or “structure” is a matter to be investigated as part of any dynamic network analysis, not something to be assumed at the beginning of study.

Before exploring all this with you, however, I first need to tell you what I mean by the word relationship.

Begin at the beginning
By Sidney Paget (1860-1908) (Strand Magazine). Public domain, via Wikimedia Commons

Let’s take things one step at a time. Let’s begin by revisiting what Carlo Rovelli has told us about electrons that got him into trouble with Lisa Randall:

 Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The “quantum leaps” from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another.

Lightning fill in the blank

I don’t think it would be stretching the point too far to say lightning can be said to exist or not exist in a similar way. As helpfully described by the National Severe Storms Laboratory:

Lightning is a giant spark of electricity in the atmosphere between clouds, the air, or the ground. In the early stages of development, air acts as an insulator between the positive and negative charges in the cloud and between the cloud and the ground. When the opposite charges build up enough, this insulating capacity of the air breaks down and there is a rapid discharge of electricity that we know as lightning. The flash of lightning temporarily equalizes the charged regions in the atmosphere until the opposite charges build up again.

To the human observer, the potential for a bolt of lightning to occur is only something suspected, something lurking in the background, so to speak,  before the actual discharge. But the discharge finally neutralizing the imbalance in positive and negative charges that has been developing on the sly doesn’t take place until the relationship between the positive and negative sides of the imbalance finally materializes with what can often be a spectacular display of nature’s given ways.

The famous opening words of a novel by Edward Bulwer-Lytton published in 1830 that are now notorious as an example of purple prose (i.e., overly melodramatic writing). https://www.smith.edu/libraries/libs/rarebook/exhibitions/dickens/16-paul-clifford.htm

Yet the potential for such a dramatic and utterly natural demonstration of light, sound, and at times destructive effect had been there long before this event takes place.

This simple fact raises a basic question. If lightning  is the consequence of a growing imbalance between positive and negative electrical charges, say, on “a  dark and stormy night,” then what makes this kind of dyadic relationship in nature different from the sorts of relationships that can develop between friends, colleagues, and loved-ones? And what does all this have to do with network analysis?


Repeat after me

Despite the old saying, it is a well-known fact that lightning can strike the same place more than once. As one storm enthusiast on the Internet has  commented, given enough time, this outcome is actually inevitable. He adds, however—and more to the point I want to make in case you are wondering why on earth I am still talking about lightning—the electrical activity in the storm that produced it may generate another strike as soon as as the imbalance has again grown strong enough. Once this happens, a previously hit location again becomes fair game as a recipient of the next discharge. If this weren’t so, there would be no practical need for installing lightning rods on tall buildings and such like.

Being fair game in a relationship is hardly grounds for claiming as well that the cloud in question has formed some kind of a relationship with the location previously hit. Nor is there any sure way to predict whether the same cloud will strike the same place.  Maybe another cloud that same day or sometime in the near or distant future may also strike the same place. But there is no guarantee when, and there will be absolutely no  connection—no relationship—between the first responsible storm and the later culprit cloud involved.

So here then is one critical difference between the kind of patterned and (seemingly) repetitive type of dyadic event in nature called a lightning strike and the kind of patterned dyadic relationship that occurs in networks of many types, human and otherwise: a network relationship however materialized is not just dyadic but also repetitive.

Relational data . . . are the contacts, ties and connections, the group attachments and meetings, which relate one agent to another and so cannot be reduced to the properties of the individual agents themselves. Relations are not the properties of agents, but of systems of agents; these relations connect pairs of agents into larger relational systems. (Scott 2000: 3)
What else is involved?

What else does it take to turn a repetitive dyadic relationship between two things, people, or places into a broader network relationship? The easy answer would that there is a lot that can come into play. However, there are at least three critical elements in addition to the requirement that the relationship needs to be repetitive and more than just randomly so. What are they? I like to label them as situational (or circumstantial), contingent, and consequential.  Let’s consider each in turn starting with the first.

SituationalIt is conventionally said in text books about network analysis that there are two basic kinds of data about this world of ours, attribute data and relational data. The former is said to be information about the properties, qualities, or characteristics of the two entities ( for example, the individuals or groups involved) in the dyadic relationship being analyzed—classically, the sorts of information that can be quantified, classified, and analyzed using the many statistical tests of significance that have long been available and are nowadays fairly easy to run on most computers.


Relational data, on the other hand, is information about the linkages, contacts,  and connections (called “edges” or “ties” in network analysis) among the entities (called “nodes” or “vertices”) being studied. All well and good, but as we will be discussing in this blog series, when the entities in particular are individuals and groups of people, for instance, the characteristics of interest in any given study often vary depending on the particulars of the situation—the context—they are dealing with. The relationship between Rapunzel and the prince who courted her in the famous fairy tale, for instance, is situationally quite different from what most lovers must deal with to be with one another.

Contingent—Similarly, when and perhaps even whether a relationship is maintained over the course of time may often be contingent, or dependent, on the situation at any given moment on either, or both, sides of the relationship. For instance, whether you flee from what has been your home and seek refuge elsewhere when faced with an environmental disaster or political turmoil may be contingent on whether you have reason to believe there is someone who will be there at the end of your journey who will take you in and help you survive.

A Yemenite family walking through the desert to a reception camp near Aden, 1 November 1949. [Public domain], via Wikimedia Commons] Part of the Jewish exodus from Arab and Muslim countries. “Between June 1949 and September 1950, the overwhelming majority of Yemen’s Jewish population was transported to Israel in Operation Magic Carpet. After several waves of persecution throughout Yemen, most Yemenite Jews now live in Israel, while small communities are found in the United States and elsewhere. Only a handful remain in Yemen.” https://en.wikipedia.org/wiki/Yemenite_Jews

ConsequentialThirdly, relationships may be as seemingly trivial as saying good morning to your neighbor when you go outside to pick up your  morning newspaper, but network analysis is a way of pinning down and understanding how relationships can have consequences of real significance, even in instances such as remembering to say hello to a neighbor that most times may seem inconsequential, but not always. It not only takes a community to raise a child, but being on good terms with your neighbors can be highly consequential, for example, when you need to raise a new barn, say, to replace one that burned to the ground after it was struck by lightning. 

Barn raising – Leckie’s barn completed in frame. By John Boyd (Public domain) via Wikimedia Commons
What about intentional relationships?
Alice in Wonderland by George Dunlop Leslie (1835-1921).  Public domain, via Wikimedia Commons

When it comes to the analysis of human relationships, there is no doubt whatsoever that more needs to be considered than just the four relational dimensions noted so far: repetitive, situational, contingent, and consequential. 

The relationship between a parent and child, for instance, not only exhibits all four of these characteristics, but is also a motivated or intentional relationship, for better or for worse. Moreover, we humans are not the only creatures on Earth capable of forming and maintaining intentional relationships, as anyone who has ever worked with dogs knows well.

Clearly, therefore, there is more to be said about what is a relationship. However, it is now time to begin asking a similarly basic question. What is a network of relationships?

This is the topic of my next blog in this continuing series on dynamic network analysis.

The Wilderness Hunter: An account of the big game of the United States and its chase with horse, hound and rifle, by Theodore Roosevelt (1903). By Internet Archive Book Images (No restrictions), via Wikimedia Commons

References cited

Borgatti, Stephen P., Martin G. Everett, and Jeffrey C. Johnson (2013). Analyzing Social Networks. Los Angeles: Sage Publications.

Kolaczyk, Eric D. (2009). Statistical Analysis of Network Data: Methods and Models. New York: Springer.

Scott, John (2000). Social Network Analysis: A Handbook. Los Angeles: Sage.

Terrell, John Edward (2014). A Talent for Friendship: Rediscovery of a Remarkable Trait. New York: Oxford.

  • This is Part 5 of a continuing series of posts on dynamic network analysis. 6. What is a network?
    © 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.

Dynamic Network Analysis 4. Exploring the 5th dimension

Highway at night. Source: https://pxhere.com/en/photo/1192661

John Terrell

MY TWIN SISTER AND I were born on 15 August 1942 a month or so premature. However faulty our timing, much later we learned we were part of an alleged birth spike in America back then. We were “Pearl Harbor babies” conceived in the aftermath of the Japanese attack on the United States on December 7th—the day that would live in infamy.

However true or false this categorization, as time goes by the evident reality of time becomes increasingly hard personally for me to ignore. But wait. What exactly is time ? Sure I may be getting older, but does time have anything to do with it?

It is conventional wisdom that whatever it is, time is more than just one thing after another, moment to moment, day to day, year to year, and so on. In fact, we often speak of time as something within which, or over which, we pass the time, as the saying goes.

All this, however, begs the issue. Regardless how we talk about time, what is it we are trying to talk about? More to the point, what does time have to do with exploring something I want to suggest we should call the 5th dimension of reality?

Wayne, Wendy, and Wally

I suspect like most of us, you may agree there are three primary dimensions in the universe, and in English they are called length, width, and depth. If so, I beg to disagree with you at least about one thing. I wish they were instead called Wayne, Wendy, and Wallace (Wally).

Why? Because then it might be more obvious that this famous 3D trio is just something we humans have made up to satisfy our own needs. These dimensions are not really “out there” waiting for us to measure them.


If you don’t care for my choice of names, how about Larry, Curly, and Moe? These names don’t work for me. My twin and I have always hated The Three Stooges. Yet there is no disputing taste. Go for them if they strike your pleasure centers.

What I am trying to get at whatever words are favored is this. When we say things have three dimensions, what we are really saying is that we can pinpoint something  in space by taking three standard (usually orthogonal)  measurements. This doesn’t necessarily mean what we are measuring is unreal. It just means what we are  measuring doesn’t have dimensions. We give it dimensions.

This may sound like gobbledygook, but stay with me. Knowing this means things don’t just have three dimensions. They can have as many as we want to give them. Weight, for instance. Color. Texture. Don’t be shy. Use your imagination.

Where then does time fit in?

No doubt it, taking measurements such as Wayne, Wendy, and Wally—also known as length, width, and depth—can be extremely useful if you are building a house, or trying to get something into the back of your car. But they are still only measurements. They are arbitrary. Made up. We can take them, but we can’t find them. They aren’t a part of nature. They aren’t a part of the universe. They are just one of the ways we try to grapple with the world and the universe we live in.

By many accounts, time is the 4th dimension of reality. This may be so, but isn’t time also something you can run out of? And in contrast, isn’t it true  nobody in their right mind would ever say they are worried or depressed about running out of any of the other three dimensions that time is traditionally associated with—namely length, width, and depth?

So is time a different kind of dimension? Maybe one that is real rather than just convenient or arbitrary?

But isn’t time real?

Commonsense may tell us that time really is something out there to be measured. Yet in truth and also in practice, time isn’t a thing but rather a sequential relationship: a series of events related to one another by the seemingly elementary fact of following after one another.

Hellerick, based on earlier image by CIA with many modifications by other contributors, TimeZonesBoy (Based on File:CIA WorldFactBook Time Zones.svg) [Public domain], via Wikimedia Commons
Time is a centerpiece of Albert Einstein’s theory of relativity. It is reported that he was asked so often to explain his abstruse theory in terms mere mortals could understand that he came up with a jovial illustration: “When you sit with a nice girl for two hours you think it’s only a minute, but when you sit on a hot stove for a minute you think it’s two hours. That’s relativity.”

Ever since Einstein published his special (1905) and general (1915-1916) theories, the conventional idea—popularly credited to Sir Isaac Newton—that time is something that exists both apart from our awareness of it, and also marches to its own drummer has been banished from serious scientific consideration.

But what then is time and what does it have to do with the 5th dimension of reality?

Four dimensional space-time

Once Einstein’s view of time is accepted, time joins length, width, and depth as one of the dimensions of reality that are arbitrary rather than “out there” and absolute. In other words, we can take time but we can’t find time, so to speak. Time is simply one of the ways in which we try to pinpoint something not just in space but in space-time.

In their popular book on the nature of reality The Grand Design, the late Stephen Hawking and his colleague Leonard Mlodinow explore how we as mere human beings are compelled to see things from the limited perspective of our species, however grand we may believe ourselves to be. More specifically, “the measurement of time taken, like the measurement of . . . distance covered, depends on the observer doing the measuring” (page 97).

Said another way, it is not possible to determine for any given event exactly when it happens since different observers will have their own take on time depending on whether they are moving together with one another through space-time, or differently.


If you have read this book by Hawking and Mlodinow, or some other guide to Einstein’s ideas about relativity, you know that his general theory also tells us that space-time is not flat, but is curved and distorted by the mass and energy within it. However, as fascinating as this topic may be, it is time to move on to talk about what I propose should be our shared understanding of what I want to call the 5th dimension of reality.

How many dimension of reality are there?

I have already remarked that since they are arbitrary and not actually a part of nature and the universe, we can have as many dimensions to work with as we have need of. Physicists and mathematicians would apparently phrase this observation in this fashion: if it helps you understand something, then it’s OK to assume that what you are interested in is located within an N-dimensional space. The “N” here meaning the number of dimensions you want to build your ideas around.

There are those today working in theoretical physics who say the number of dimensions needed to understand the fundamental workings of the universe may be as high as 10, possibly even 11. In his well-received popular book Reality Is Not What It Seems (2014, English transl. 2017), the physicist Carlo Rovelli has a lot to tell us about how many dimensions we need to keep in mind while he is surveying what scientists are currently proposing about quantum gravity, that esoteric side of theoretical physics whose practitioners are struggling to combine quantum mechanics with Einstein’s general theory of relativity.

Not all of Rovelli’s peers see eye to eye with him about what he says in this book. In a snarky review in The New York Times in 2017,  Lisa Randall, who is a professor of theoretical particle physics at Harvard University, caustically suggests he is romanticizing physics. (I guess it is possible for some people to be swept off their feet when it comes to quantum gravity.) She also frets that “when deceptively fluid science writing permits misleading interpretations to seep in, I fear that the floodgates open to more dangerous misinformation.”

She may well be on to something when she says what Rovelli tells us isn’t always right, and maybe he does at times misleadingly give us his own ideas as established facts. What strikes me as worth noting, however, is what Randall doesn’t like about what Rovelli says about the lowly electron.

She makes much of the fact that when explaining quantum mechanics, Rovelli says: “Electrons don’t always exist. They exist when they interact.” She says this claim is way off the mark:

Stocks may not achieve a precise value until they are traded, but that doesn’t mean we can’t approximate their worth until they change hands. Similarly electrons might not have definite properties, but they do exist. It’s true that the electron doesn’t exist as a classical object with definite position until the position is measured. But something was there — which physicists use a wave function to describe.

Exploring the 5th dimension of reality

Fools rush in where angels fear to tread. I have absolutely no idea whether Rovelli is or isn’t right about the surprisingly controversial electron. I am not even sure I understand Randall’s objection. On the other hand, I am pretty sure she (and probably he) wouldn’t agree with me about what is the 5th dimension of reality. 

Physicists evidently think they have this one more or less already in the bag.  In my defense, I am going to reiterate that we can have as many dimensions as we need, and I need a fifth dimension to be able to write about dynamic network analysis. Let me now tell you why. 

Randall is right. Rovelli does say in this book  that electrons don’t always exist. But he says a lot more than just that. While telling us about Werner Heisenberg and the mysterious “quantum leaps” that appear to underlie the structure of atomic spectra, he asks rhetorically: “What if the electron could be something that only manifests itself when it interacts, when it collides with something else; and that between one interaction and another, it had no precise position?”

Rovelli then tells us that the hardest key to quantum mechanics is this one: the relational aspect of things (pages 119–120). Because I think his observation is so important, I am going to repeat in full the quotation from his book that Randall (above) has found so objectionable:

Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The “quantum leaps” from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another.

Why do I find this observation so relevant to what I want to talk about in this series of posts on dynamic network analysis and the 5th dimension of reality? For me, the key elements are these:

      • 1.  Dynamic network analysis assumes that things, people, and places can be physically located in space and time.
      • 2.  The focus of analysis is on the characteristics of people (and their behavior), places, and events in space and time.
      • 3.  The premise of dynamic network analysis is that the characteristics of things, people, and places are circumstantial and contingent on the interactions—the relationships—among the elements being studied (I like to call them the ingredients of the investigation).

As I will be exploring in the next post in this series, another and more familiar name for this 5th dimension of reality is what Charles Darwin called “descent with modification.” Also known as evolution, although not necessarily what Darwin himself meant by this familiar and controversial word.

what on earth is this?


NASA’s explanation for the stellar phenomenon shown above: “Blown by the wind from a star, this tantalizing, ghostly apparition is cataloged as NGC 7635, but known simply as The Bubble Nebula. Astronomer Ken Crawford’s striking view combines a long exposure through a hydrogen alpha filter with color images to reveal the intricate details of this cosmic bubble and its environment. Although it looks delicate, the 10 light-year diameter bubble offers evidence of violent processes at work. Seen here above and left of the Bubble’s center is a bright hot star embedded in telltale blue hues characteristic of dust reflected starlight. A fierce stellar wind and intense radiation from the star, which likely has a mass 10 to 20 times that of the Sun, has blasted out the structure of glowing gas against denser material in a surrounding molecular cloud. The intriguing Bubble Nebula lies a mere 11,000 light-years away toward the boastful constellation Cassiopeia.”

This is Part 4 of a continuing series of posts on dynamic network analysis. Next up: 5. What’s a relationship?
© 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.

Dynamic Network Analysis 3. Connecting the dots

1691 Sanson Map of the World on Hemisphere Projection. Source: http://www.geographicus.com/mm5/cartographers/sanson.txt [Public domain], via Wikimedia Commons

John Terrell

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.

Old-fashioned library card catalog https://www.flickr.com/photos/mamsy/ [CC BY 2.0, via Wikimedia Commons
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.

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.

One-sided relationships

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.

Photo via Good Free Photos
Two-sided relationshps

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.

Many-sided relationships

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.

A friend in need, 1903. Public domain, via Wikimedia Commons

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.)

Tim Beckham, catcher John Hicks, umpire Roberto Ortiz in a 2017 game [Keith Allison from Hanover, MD, USA (Tim Beckham) CC BY-SA 2.0, via Wikimedia Commons
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.

Dynamic Network Analysis 2. Relativity

Lined Up Harvest Fruit Source: https://www.maxpixel.net/Lined-Up-Harvest-Fruit-Goldparmaene-Apple-Series-1675775

John Terrell

IN THE INAUGURAL POSTING in this series, I made note of the fact that history  shows us time and again that as a species we have decided strengths and obvious weaknesses.

Why it’s good to be human

On the plus side, our kind of animal is outstanding at reshaping and rebuilding the world around us to make the challenges we face as individuals and as a species as humdrum, predictable, and hence as manageable as possible.

Poets, playwrights, philosophers, and scientists may debate the particulars of human motives and intentions, but there is no denying one of the reasons we spend so much time and effort at redoing the conditions under which we live out our days on earth. The more predictable a situation or event is, the easier it is for our brain to cope with it. And if need be, respond more or less appropriately.

Spice Bazaar, Istanbul. Personal photograph

I also argued in the previous post that to avoid becoming overwhelmed by what our body’s senses—classically said to be five in number—are telling us about the state of things and events both inside and outside our skin, our brain ignores much of what it is being told. Instead it mostly relies on the pragmatic strategy of simplifying what it is hearing, both literally and figuratively, by mentally putting things, people, and experiences into separate and seemingly distinct mind boxes—into different categories.


However, there is a fine line between paying too much attention to what our senses are telling us, and too little. (I like to call this the Goldilocks Line after the 19th century children’s story). Failing to pay sufficient attention to what’s happening inside or outside our body can be disastrous, as anyone who has survived the experience can tell us about why they shouldn’t have been texting while driving.

Why it’s bad to be human

As my mother so often liked to say, things can be both good and bad at the same time. However pragmatic and unintentionally self-centered we are as individuals for understandable evolutionary and psychological reasons, the dark side of our human ways cannot be denied.

I wasn’t being cynical in the previous post, therefore, when I remarked that truth may not be as appealing and important—that is, as useful—to us as human beings as the immediate and pragmatic benefits of things and events (and people, too) that are easy, convenient, and predictable.

However, taking the easy way out, the easy answer, the easy job, and so forth can be costly down the road—sometimes sooner rather than later. Doing so can make it difficult for us to notice and pay enough attention to how things, people, and experiences are linked, intertwined, and interrelated. Said more formally, what I called previously “categorical thinking” can lead to “categorical mistakes.”

The power of words

According to more than just a few of us, life’s big question is Why am I here? Others instead see How come I am here? as the mystery to be solved. Conventionally, people turn to theologians, philosophers, psychologists, and their best friends when they are seeking answers to the first question. The second one falls more in the thoughtful arena of pediatricians, scientists, cosmologists, mystics, and priests.

This division of labor, however, is not absolute, and is certainly not as categorical as such a divide implies.  One common thread crossing between these two realms of expertise is the belief or assumption—sometimes up front, sometimes only lurking in the background—that words are both powerful and are usually grounded in reality except, of course, when someone is “making things up” that they know are untrue.

The belief that words can be both truthful and powerful—that by naming things we are not just “putting into words” something already “out there” in the world, but can create something new as if “out of nothing”—is deeply rooted in the antiquity of our species. A classic example would be invoking the word abracadabra during a magic show to lend apparent substance to some clever illusion. But the roots of seeing words as powerfully creative run deeper than this trivial example.

The Almighty. Genesis cap 1 v 16. De Vos [By Phillip Medhurst [CC BY-SA 3.0, from Wikimedia Commons
For instance, consider the opening words of the Book of Genesis in the Hebrew Bible and Old Testament:

IN THE BEGINNING God created the heaven and the earth.
2  And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
3  And God said, Let there be light: and there was light.
4  And God saw the light, that it was good: and God divided the light from the darkness.
5  And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
Relational thinking

In my first post I said that I am writing this series about dynamic network analysis because I want to explore with you how a different way of thinking about the world and our place in it can make it easier for us to see and make something out of how widely and how often critically things, people, and events are not separate and distinct in neat categorical ways, but instead are interwoven into relationships that make the whole totality of them, as the saying goes, bigger than the sum of the parts. Since what I want to write about, however, is complicated, I need to proceed step by step.

The next step in this second post is a brief quiz I’d like you to take before we move on to take a closer look in Post #3 at what is called network analysis.

Quiz: How good are you at thinking outside the category?

Please take a piece of printer paper and draw a line down the middle from top to bottom. Near the top of the left-hand column, write the word categorical. Do the same for the right column, except make the word relational. Then write in items under these two headings matching those shown here. Note that the last two rows are blank. In a moment I will be asking what you would add in these two bottom rows resonating with the rows above them.

Here’s the question I want to ask: What makes the items in the right-hand column different from those in the left-hand column? Yes, it is OK to use Google if some of the items seem obscure. And yes, this is a categorical question for sure.

The answers I am looking for

There are many ways to talk about the items in the left-hand column.  #1-2 are often viewed nowadays as wasteful single-use items that pollute the environment; #3 is a famous writer who rejected the virtues of altruism, praised individual rights, and is seen by many as a prophet of selfishness; #4 is an organization dedicated to protecting the rights of individual gun owners; #5 is the day each year when a given individual was born; #6 refers to the belief that all things can be boiled down to singular, individual particles called atoms.

In contrast, paper bags and paper straws are being promoted today as more environmentally friendly than their counterparts in the left column. #3 could be described as the high priest of the relativity rather than the individuality of things in the universe. Without trying to pin them down, the remaining three items are similarly all about things, events, and species that are enmeshed with one another.

Now here’s your job. What would you write in the blank rows at the end of this table? For instance, I myself would be tempted to write in one of these rows the card game solitaire vs. the team sport of boat racing.

By National Library of Ireland on The Commons (Waterford Boat Club) [No restrictions], via Wikimedia Commons 
What’s the point I am trying to make?

In the first post in this series, I observed that for entirely understandable reasons each of us is by nature self-centered. Saying this, however, does not have to mean we are also inherently selfish despite the fact that jumping to such a conclusion is unfortunately fairly commonplace even in scholarly circles.  

As we will be exploring in this series, Ayn Rand and others both before and since have been misguided to believe otherwise. The continuing popularity of Rand’s ideas only shows that words can be powerful at least in the limited yet dangerous sense that they can be used to persuade us about what’s real and what’s unreal in the world of yesterday, today, and tomorrow without actual proof.

This is precisely why we need ways of getting outside our heads and dealing directly with the world that force us to “think outside the category.” Why? Because we need ways to confront our hasty impressions, deep-seated desires, wishes, and wants so that we can avoid errors in judgment, however innocent, that tragically can result in the desecration of the world we live in—and if we are not careful, our own extinction as a species.   

This is Part 2 of a continuing series of posts on dynamic network analysis. Next up: 3. Connecting the dots.


© 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.

Dynamic Network Analysis 1. human nature

Highway at night. Source: https://www.maxpixel.net/Long-Exposure-Night-Highway-Motion-Traffic-Light-216090

John Terrell

HUMAN BEINGS ARE BY NATURE highly social animals. Despite claims both popular and scientific, we also are not inherently selfish creatures. Yet we often seem self-centered. Why? Short answer: because we are looking out at the world from inside our skulls.

As my mother used to say, this is both good and bad. Let me explain briefly by offering you a few elementary observations about being human.

Your pragmatic brain

A fully functioning human brain is a remarkable compromise. Your senses are constantly feeding you input—lots of it—about what’s happening in the world around you, and also about what’s going on inside your body. If your brain were to pay close attention to all the details it is receiving about the state of things within and beyond you, it would rapidly become overloaded. That, of course, would make it useless to you as an organ dedicated to helping you in an admittedly self-serving fashion navigate your way more or less successfully from the cradle to the grave.

It is perfectly understandable, therefore, why your brain perpetually walks a fine line between paying too much attention to what it is being told by its senses, and too little.

Figure 1. “I swear they came out the box this way | by frankieleon” https://www.flickr.com/photos/armydre2008/3576170595

One way the brain accomplishes this delicate balancing act is to put things, people, or events striking it as more or less like one another into the same mind box—that is, into the same mental category. By this I mean what a dictionary says this word means:  “a class or division of people or things regarded as having particular shared characteristics.”

well-known rule of thumb illustrates the point I am trying to make: if it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck. A colorful example is shown in Fig. 1.

But here’s the rub. What if your brain draws the line between too much and too little in the wrong place? What if it doesn’t pay enough attention to what it is being told by your senses about the animal your brain has concluded must be a duck? More to the point, what if making such a categorical mistake leads to serious consequences? Say, mistaking a friend coming into a darkened room for an intruder. And impulsively you shoot your friend dead?

Clearly having a pragmatic brain lodged inside that bony vault up there on your shoulders can be both good and bad, just as my mother would observe.

A world of our own making

Here’s another observation about how humans deal with the world. If novelty is the spice of life, then from your brain’s pragmatic point of view, predictability is life’s bread & butter.

Put simply, the more predictable a situation or event is, the easier it is for your brain to categorize it. And then, if need be, respond appropriately (or not).

Figure 2. By Crusier [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0, from Wikimedia Commons
It is again understandable, therefore, why as a species we humans invest so much of our time and effort (and money) into dumbing down the world around us to make the challenges we face as humdrum, predictable, and therefore categorical as possible.

By “dumbing down” I mean our species is remarkably skilled at remaking the world we live in to be less risky and uncertain than it otherwise would be for us. Said another way, we love to make what’s out there in the world fit into simple, convenient, widely applicable mind boxes, i.e., categories.

Humans are not the only creatures on earth who are predisposed to make the things and events they have to deal with as humdrum as they can make them. Many of the earth’s countless species are similarly committed in their own more limited ways—biochemical, physical, or behavioral—to enhancing their surroundings and creating favorable opportunities for themselves (we are not the only self-centered creatures on earth) by making things more suitable, more accommodating, more predictable. And for them, as well, more categorical.

This last remark is important, as I will be explaining in a later posting in this series. The brain's mind boxes called "categories" may or may not have actual words associated with them that we can use to talk about them. This is often why we may find it hard to put our ideas into words. But with this remark I am getting ahead of what I want to say in this first post. 

Figure 3. Termite mound, Litchfield National Park, Northern Territory, Australia [By brewbooks from near Seattle, USA (Cathedral Termite Mound). CC BY-SA 2.0, via Wikimedia Commons
Classic examples of what other species do to dumb down the world for themselves would be beavers constructing dams to create ponds that help protect them against predators; termites building earthen mounds in Africa, South America, and Australia to live in; birds building nests; and earthworms improving the quality of the soil they move through by eating it and passing it through their bodies, over and over again, generation after generation, thereby making life easier and more fulfilling for the earthworms that take their place in the great circle of life.

Clearly, therefore, we are not alone as a species in being both able and crafty enough to improve our lives and living circumstances by making the world a safer and more predictable place to live in.

Even so, we humans are certifiably the Earth’s champions at the fine and skillful art of redoing the world to suit our needs as well as our fancies, however odd the latter may be (let’s all admit, shall we, that the artificial islands of the exotic tourist resort shown in Fig. 4 are an extreme example of our willingness to redesign the world to suit our fancies and our credit cards).

Figure 4. Palm Island Resort, Dubai, United Arab Emirates https://commons.wikimedia.org/wiki/File:Dubai_-_The_Palm_Jumeirah_-_panoramio.jpg
Confronting our pragmatic and often self-centered ways

We have reason, therefore, to be proud of the fact that our species excels all others at creatively dumbing down the world we live in to make the challenges we face humdrum and predictable. But there are genuine risks involved. Why so? Because we are not truly god-like in our powers. We are not all-seeing and wise. We are not always as good as we may think we are at drawing the line between knowing too much about the world and knowing too little.

And furthermore let’s be honest. Despite rhetoric to the contrary, truth (spelled with or without a capital “T”) may not actually be as appealing and important—that is, as useful—to us during our journey from the nursery to the grave as the pragmatic benefits and virtues of things and events (and people, too) that are easy, convenient, and predictable.

Here then is what this series of posts at SCIENCE DIALOGUES will be about:

  • Millions of years of evolution have done a skillful job of making us clever, inventive, and remarkably successful beings.
  • As history shows us again and again, however, our reliance as a species on the pragmatic (and generally self-serving) strategy of mentally putting things, people, and experiences into separate and seemingly distinct mind boxes—into different categories—often makes it hard for us to notice and pay sufficient attention instead to how things, people, and experiences are almost always linked and interrelated rather than separate and distinct. 
  • In this series, I will be calling the first brain strategy categorical thinking, and the second one relational thinking.
  • My goal in writing these posts will be to survey for you how the second way of thinking about the world and our place in it makes it easier for us to see and understand how widely and often critically things, people, and events impact one another—sometimes in unexpected and even disastrous ways (for example, see: Fig. 5).

Moral of the story so far: while understandable from an evolutionary and psychological point of view, being self-centered creatures is a handicap we humans need ways to confront and overcome.

Dynamic network analysis is one such way. I hope to convince you it is a good one, too.

Figure 5. The beach at Kanapou Bay collects debris from throughout the Pacific Ocean. https://www.flickr.com/photos/noaaphotolib/19778606375
This is Part 1 of a continuing series of posts on dynamic network analysis. Next up: 2. Relativity.
© 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.