What's the rumpus (:
I'm Asaf Shapira and this is NETfrix - the Network Science Podcast.
As my friends already know, the engraving on my headstone will say:
I hate to be mistaken, but when this rare event does occur, I like to quote the Israeli proverb:" When you point an accusing finger at someone, at least 3 of your fingers are pointed at your direction."
And now that it happened, I'm here to undo my errors.
It all began when I recently read an interview with Prof. Robin Dunbar in an Israeli newspaper, to promote his new book.
The title of the article went as follows:
" Professor Robin Dunbar has devoted his life to social research and found that humans have 150 friends, no matter in what culture and in which period. " We encountered Dunbar in episode 9 on NETfrix where we referred to the concept of "Dunbar's Number".
So just a quick reminder: "Dunbar's Number" refers to the number of friendships a person can maintain, given a cognitive threshold. According to Dunbar, this threshold is about 150.
In the interview, Dunbar defined a friend as someone who you would feel comfortable to join at a restaurant table if you met by chance, or as someone you'd call at least once a year to ask what's the rumpus. Dunbar came to his conclusions following a study he did on group behavior of apes. He found a correlation between the size of the neocortex, which is
the conscious thinking part in the brain, and the number of relationships the apes had.
Dunbar also noticed that when a shrewdness of apes reached a certain number, a few dozen or so, it tended to split.
Shrewdness, by the way, is the collective noun for a group of apes and that was our Word of the Day.
Back to Dunbar, so, his conclusion was that when a group has reached a certain number of members, it couldn't maintain the intimacy and ties that contributed to its cohesiveness and so it had to split into smaller groups. Dunbar hypothesized that humans also have a limit on the number of friendships they can maintain. Based on the differences between the human brain and that of an ape, he hypothesized that the number would be approximately 150.
When he went on to investigate human networks, Dunbar found that his initial hypothesis was correct and 150 is indeed the threshold to the number of ties a person can maintain. The results of the study were published and the number 150 was nicknamed the "Dunbar Number". Back to the interview, Dunbar told the reporter how the Dunbar Number phenomenon repeated itself in the many experiments he conducted. He also shared an insight that he has developed over the years saying that good health and longevity are closely related to the number of friends a person has. According to Dunbar, lonely people tend to die much earlier than others. The interview wasn't news to me, but I found it amusing to read the talkbacks that were posted by the readers. The interview was published in Haaretz, which is an Israeli newspaper associated with the left-wing and its cross section of readers is usually conceived to be older people of European descent. Here is a translation of some of these talkbacks:
" Most people in the world do not have one hundred and fifty friends that they call once a year to ask how they are doing. This man is delusional."
Or another one:
" Nonsense in tomato sauce. I'm a married woman. What friends should I have?! Whoever wants a friend should adopt a dog!"
(By the way, "Nonsense in tomato sauce", which is an Israeli proverb borrowed from German, is a phrase that came up several times in the comments).
And my favorite:
"If [what Dunbar says is] true [i.e., longevity is conditioned by the amount of friends one have], it seems to me that I do not have much time left."
Weirdly enough, I found similar replies to Alan Alda's tweet after interviewing Dunbar.
For example, one of them replied: "According to [Dunbar's] …math, I died twenty years ago."
I went to the shower while thinking about these talkbacks to the article.
My thoughts were that the readers were being very critical and bitter. No wonder, I told myself, they are also lonely.
And then it hit me.
Since ancient Greece, it is no secret that insights come to a person in the shower.
Pulling an Archimedes, I ran out wet in mid shower to read the article again, and especially the next paragraph in the interview, that I quote almost verbatim:
" Dunbar says that social networks actually helped him gather data on a huge scale - and reaffirm his findings. Quote: "People said to me that this doesn't make sense, because they have more than 500 friends on Facebook. But when we did an accurate analysis of the number of friends of 61 million unique users, we found that on average, the exact number of friends was 149." Dunbar says with satisfaction." End quote.
According to Dunbar, the complaint he usually got from people was the opposite of that of Haaretz readers. He quotes his critics by saying they claim that 150 was actually too small a number. Allegedly, in the age of social networks, we could have thousands of friends. But Dunbar retorts that this perception is purely theoretical.
On a social network we can have thousands of friends only in the technical sense of the word. But in practice, relationships require maintenance, such as personal messaging, response to posts and so on. When looking only on relationships that are well-maintained, Dunbar proclaimed that the number is much smaller than his critics believe it to be and with much satisfaction, he pointed out that the actual number is 149.
So what's the story with Haaretz readers claiming that Dunbar completely exaggerated?
Could it be that they're just a bunch of Eleanor Rigbies with a WiFi connection?
That might be, but it doesn't mean they are wrong. In fact, the Beatles might be onto something.
The thing that should have set off our alarm was Dunbar's quote: " we found that on average, the exact number was 149". and specifically, the word "average". What does "average" mean? In episode 3 on NETfrix we talked about how people like to use averages because it has some magic to it. Though it's just one number, it presumes to portray to us a considerable part of the data. But later in that episode we talked about why this is misleading. This is only true when our data is normally distributed. But when our dataset fits a Long Tail distribution, the concept of average changes its meaning. A Long Tail distribution in networks, for example, means that most of the nodes in the network will have only a few links or none at all. When drawn as a graph, they would look like a long tail across the X axis. But it also means that a few nodes, very few, will have lots of links. Maybe even more than all the other nodes in the network put together. So, when we look at the average number of a Long Tail distribution, the vast majority will be below average and a small, but significant minority will be well above it.
I say significant, because in economics for example, this minority will be the few people or companies that hold the majority of the capital. On social media, these will be the users with orders of magnitude more friends than the rest of us.
Because Dunbar has tested his theory on social networks - and as we all know from episode 3 on NETfrix, social networks fit a Long Tail distribution - something here smells fishy.
Dunbar said he studied a dataset of 61 million users, so I searched for the article and with the help of Prof. Gilad Ravid we believe we found it. Dunbar just did not write it. The paper surveyed 61 million Facebook users who were active on the day of the midterm elections in the United States in 2010. According to the paper, the average number of friends of the 61 million users they surveyed was 149.
Is there a better confirmation than that of Dunbar's claim?
Before we accuse Haaretz readers of misanthropy, let's pay attention to Dunbar's own words.
Dunbar said that Facebook friendships are "technical" in nature and therefore does not necessarily meet the definition he gave to a social tie. This means that it is reasonable to believe that the true number of maintained ties, according to Dunbar's original definition, is lower.
But to be on the safe side, let's use Dunbar's own research to check if our thesis is right.
For example, let's look at a paper by Dunbar et al. in which they studied a social network of 3 million people. While this is only 5% of the 61 million promised it's not something to take lightly. When was the last time you interviewed 3 million people?
And this is where it gets interesting. After collecting the 3 million users, the researchers discovered something surprising:
The social network they were looking at was a Long Tail distribution.
They found relatively few people with many friends and the majority had very few friends or none at all. Everyone who is into network analysis or has listened to episode 3 on NETfrix knows this. So how did they rise to the challenge? I quote the paper: "For the analysis we consider only egos with an average of more than 10 interactions per month, thus selecting "socially active people" since they are particularly relevant for our analysis" Okay. I'll bite. How many "socially active people" did they find in this huge dataset? The answer is about 130,000 in total.
130,000 is about 4% from the original 3 million users. More than 95% of the data, which did not fit the hypothesis, was thrown out because it was labeled as noise. Basically, what we have here is a classic case of what we talked about in Episode 6 on the subject of dynamic networks. In that episode we've shown how the misunderstanding of the chaotic nature of networks, caused many researchers to label most of the data as "noisy" and throw it out, leaving only what suited them.
And in Dunbar's case, we have to ask ourselves: If 95% of the data is "noise", then what is the noise and what is the signal?
As the famous saying goes: When you torture data – it will confess to anything,
Instead of learning from the "noise" we beat it senseless and discard it.
But here comes the best part: even after being stripped and beaten, the average they got on this tortured dataset was still lower than Dunbar's Number.
To be on the safe side, I looked at another paper by Dunbar et al. This time they looked at a mobile network of 6 million users. But it seems to me that it's already pretty clear by now where this is heading.
And indeed, here too the paper complained about the "noise" in the data.
They found that only about half a percent had a Degree of over 100, meaning that only very few made calls to more than 100 devices. Much less than Dunbar's original number.
Since they had to admit that this sample was too small, they revised it to also include users that called to more than 50 devices.
And even after adding these less active users to their sample, it all amounted to about 5% of the data in total.
What this means is that Dunbar "cherry picked" the data he had and discarded 95% of it because it proved his assumptions were wrong.
So, going back to the readers of Haaretz, I think I owe them an apology.
They were right, and Dunbar and I got it wrong. It's rare to have 150 relationships.
And now we can even answer the Beatles' great question: All the lonely people – where do they all come from?
The answer is: from Dunbar's own data.
When we look at it we can see that Eleanor Rigby is not just a face in the crowd.
She is the crowd.
So far, we talked about the fact that network science pulls the carpet out from under Dunbar's thesis. But what about the way he got to his conclusions? After all, Dunbar based his hypothesis on a correlation between the size of a brain and the number of relationships, and from that he concluded that there is a "glass ceiling" to the number of friendships we can maintain. So first of all, it seems clear that Dunbar was right about the fact that there is a "glass ceiling" here, and it's physical. That is, even if we really wanted to, we do not have enough time in the day to pick up the phone to a hundred thousand people and ask them how it's going. But Dunbar adds a cognitive limitation as well. He says our brain is not built to maintain so many relationships and he sets the bar at 150. So is there such a limitation and if there is, is it due to the size of brain parts? My initial instinct is to say: I have no idea. I am not a cognition expert, so I refer to a paper published in 2021 in Sweden that contradicts Dunbar's assumption and you can find the link to it in the episode's transcripts. I can’t be the judge to the arguments they put forward regarding cognition, but the interesting part is their attempt to reconstruct Dunbar’s findings on the relationship between neo-cortex size and the amount of friends or group size of people. Their findings indicated that the average tends to be significantly lower than what Dunbar pointed out. The reason they are unwilling to commit to their own results is because the results spread out on a wide range. Put it in other words, they seem to have discovered a Long Tail distribution that produces on the one side very low results suggesting the Dunbar Number is too high, and on the other end, they found results that were much higher than Dunbar's Number, suggesting that the bar he set was too low. But on a second thought, I think we can use network analysis to test Dunbar's claim on cognition. As a side note I just want to say that one of the cool things about network analysis is its ability to give predictions, or in other words, an analyst can surprisingly come up with good answers, even without being an expert on the specific topic at hand.. I talked about it with network analysts and it often happens that the analyst's conclusions do not surprise the experts, but usually they will lead to one of the following two scenarios: The first, is that the experts might not be surprised, but that does not necessarily mean they could have predicted in advance the data's behavior. Their lack of surprise simply means that the analyst's explanation sounded very logical to them. The second scenario is that sometimes yes, the expert has already reached the same conclusion as the analyst. But the fact is that it required the expert years of expertise on the subject. The analyst came to the same conclusions with the click of a button.
So, what does network's savviness contribute to the question of whether there is a correlation between the size of the neo-cortex and the number of friendships a person can maintain?
OK so, let's assume for a moment that Dunbar is right, and the average number of friendships is 150. Now, since we know social networks fit a Long Tail distribution, we can predict that most of the population will have far fewer friends than the average, but on the other hand, it also means that a small percentage of the population will have an enormous number of friends. Far beyond the average that we imagine to be 150. I'm not an expert on the size of the neo-cortex but I can fairly guess that the size of the adult human brain fits a normal distribution. Because the number of friendships is not normally distributed, but rather a Long Tail , it would mean that comparing the two distributions would produce a non-linear graph. What this means is that if we try to match the normal distribution of brain size to the nonlinear distribution of social ties, it could suggest that the person with the highest number of friends in the world should have a brain the size of a spacious apartment.
I am not claiming that the neo-cortex has nothing to do with the number of friendships a person can maintain. I argue that size is probably the wrong measure.
My guess is, and this is just a guess, that it is the network in the brain, not the size of it, that should be accounted for our ability to maintain friendships.
The answer might lie in the Long Tail of the Degree distribution of the neurons in our neocortex. Maybe.
OK, so we've covered the cognitive limitations of individuals, but what about organizations?
Dunbar said organizational frameworks fall apart or change after reaching their Dunbar Number. According to Dunbar, an organization of up to 150 members, is an intimate group where everyone knows everyone. When it grows beyond this number, the organization needs to rely on more formal procedures to hold everything together, because intimacy is lost. Otherwise, it will break down.
The reason he gives for it is people's limited ability to handle more than 150 social ties.
So, is that no longer true? And what about all the examples we gave of this phenomenon like in episode 9?
Well, the phenomenon might still be true but Dunbar's explanation of it needs to be corrected.
In light of everything we've talked about so far, I'll try the following hypothesis regarding organizations: It's true that when an organization grows - it changes. But not because of a lack of intimacy. There wasn't much intimacy to begin with. What I mean is that not everyone really knew everyone else, certainly on the level Dunbar suggested. How do I know that? Because we've already talked about it in episode 5 on the subject of cliques in the network.
Recall that a clique is a network where everyone is connected to everyone and therefore an organization where everyone knows everyone, is actually a clique.
What we also mentioned in this episode was that small cliques are a fairly common phenomenon in networks. But cliques in the order of magnitude that Dunbar is talking about are quite rare.
So rare in fact, that a clique of 150 users would seem to most analysts as a group of bots rather than that of ordinary users.
So, if Dunbar's presumed intimacy does not keep the organization together, what does?
To understand this, we will need to return to episodes 5 and 6, where we talked about the community structure of networks.
What holds the communities together is not just their strong inner ties but also the hubs in the community. The hubs are the highly connected nodes in the network.
The Long Tail distribution of social networks tells us that there are only a few of them in every network and they will usually be some orders of magnitude more connected than the rest of the nodes in the network.
These hubs are so dominant that the community is often defined by them.
Those key players have a rare ability to maintain many relationships, far above average. And so, the hypothesis I propose here is this:
It is not the cognitive limit of the group's members that causes the organization to change.
What forces the organization to evolve or to split is the cognitive limit of the hubs in the group.
The hub is the glue that keeps it all from falling apart. They do know everyone and are able to bridge between the small cliques that exist in the organization.
But when the hub can't handle it anymore, we add some artificial glue, like formal procedures to keep everyone in line.
And this hypothesis settles beautifully with everything we know about networks.
Now all that's left is to wait for Dunbar to host a podcast and tear me a new one.
Does this mean a mic fight? I say - Bring it on.
In conclusion,
We said that the concept of Dunbar Number, which states that a person has 150 social ties on average is a very dubious one because of the word "average". Averages don’t represent most of our data when we deal with social networks. From our shared understanding of Real-World networks, we know that networks follow a Long Tail distribution. We know that most of us can maintain only a small number of social ties but there are a few that can handle an enormous number of ties - probably much higher than 150 - and these are the network's hubs. This doesn't mean that the concept of "average" is meaningless. If we accept Dunbar's claim that humans have more friends on average than apes, then that gives us something. We can assume from it that we are more socially developed than apes. But claiming, as Dunbar did, that the average number of social ties of humans is 150, is similar to a claim that the world's average wage is X. What does this claim mean? The only thing we can deduce from it is that most of the people earn much less than this average wage and only a few are paid well above it. Is this the first time Dunbar has been exposed to such criticism? No way, but his immediate response was to dismiss it as "nonsense in tomato sauce" as the readers of Haaretz newspaper would put it. So how can Dunbar ignore this? Here I wish to quote one of the smartest people I know who once told me: I spend 1% of my time coming up with theories, and I spend the remaining 99% falling in love with them.
And if this is not a Power Law, what is?
For those who wish to dive deeper into the rabbit hole which is Network Science, the next segment is for you. I recently finished Carlo Rovelli's book "Helgoland" which I first heard about in, oh yes, an interview Rovelli had in Haaretz newspaper.
The book deals with quantum physics and what I found most intriguing is the way Rovelli uses quantum physics to explain how he perceives reality. Rovelli argues that quantum physics teaches us that nothing exists by itself. It's the interactions between things that create reality as we know it. What this means is that it's not that networks model reality. It is the other way around: Networks are reality. Cool, huh? If you want to share this with others and by doing so help Network Science to reach a larger audience, please rate NETfrix on Spotify or on Apple Podcasts. And do not forget to Subscribe on your favorite app.
See you in the next episode of NETfrix.
[1] Prof. Gilad Ravid from BGU was kind enough to send me the paper Dunbar mentioned (though Dunbar wasn't one of its writers). The paper analyzed 61 million Facebook users that were active during the 2010 elections to the USA Congress. According to the paper: "Users in our sample had on average 149 Facebook friends, with whom they share social information, "although many of these relationships constitute ‘weak ties’."
[The post's featured image is by Nithin K Prabu ]
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