# Collective human behavior quantified

## Preamble

Here’s a list of interesting quantities around aggregated human behavior.

These are numbers Incidentally, it probably is the case that, deep down, these quantities are very interconnected.

drawn from humans behaving collectively that do not seem to change much over time:

• Traveling time per day
• Social capacity, a.k.a. how many people does the average person really know
• Location capacity, i.e. the number of places usually visited

## Mean traveling time per day across millennia

It turns out that, on average, people spend 1 to 1.5 hour in daily commuting. I first heard about this constant from the Critical Path podcast by Horace Dediu in an episode called Anthropological Constant.

Interestingly, that’s the case no matter the society or the technology employed to transportation – foot, horse, bike, or car.

Indeed, it seems that the mean traveling time per day has been in the 1-1.5h range for at least 10,000 years.

This invariant is known as the Marchetti’s constant. And it was originally stated to be approximately 1 hour.

Marchetti posits that although forms of urban planning and transport may change, and although some live in villages and others in cities, people gradually adjust their lives to their conditions (including the location of their homes relative to their workplace) such that the average travel time stays approximately constant.

Ever since Neolithic times, people have kept the average time spent per day for travel the same, even though the distance may increase due to the advancements in the means of transportation.

Moreover, from Cesare Marchetti’s original paper published in 1994:

This is a mean over the year and over a population, but the tails of the distribution are not spread much around the central value. […]

Even people in prison for a life sentence having nothing to do and nowhere to go, walk around for one hour a day, in the open. Walking about 5 km/h, and coming back to the cave for the night, gives a territory radius of about 2.5 km and an area of about 20 sq km. This is the definition of the territory of a village, and this is precisely the mean area associated with Greek villages today, sedimented through centuries of history.

These observations have been revisited and confirmed by several researchers in multiple contextsRead this 2015 paper for a review of the research and also very detailed data on two Chinese cities: Exploring Invariants & Patterns in Human Commute time by Hongyan Cui, Yuxiao Wu, Stanislav Sobolevskv, Shuai Xu, Carlo Ratti.

. More recently, considering the availability of much more fine-grained data, the observed mean times may be reaching 1.3 hours.

There are, of course, relevant implications of these points to transportation policy:

[…] people are choosing to increase the distance they regularly travel, rather than opting for shorter journey times. While this clearly offers advantages in terms of reaching more desirable locations, the disadvantages are numerous […], such as pollution, congestion, and noise.

In his paper, Marchetti even went on and extrapolated his ideas beyond mean daily traveling time. For instance, he hinted to evidence of the maximum size of historical empires based on the time needed to travel across them:

Speed is a unifying principle, as the case of the evolution of “on foot empires” and “horseback empires” in China shows. They eventually reached the same final dimension measured in time of about one month for a return trip from the periphery to the capital.

If it takes longer, as happened when Rome lost control of the sea, then the periphery splits, building an independent political unit (the Eastern Roman Empire). This one-month maximum time lag in the dominant-to-subject feedback cycle has never been studied to my knowledge but the evidence that comes from the evolution of Roman, Persian, Chinese, and Inca empires […]

Fidelity to the central power has a holding time of one moon.

## Social capacity: the Dunbar’s number (or not)

In the Coevolution of neocortical size, group size and language in humans, Robin Dunbar writes:

My argument has been that there is a cognitive limit to the number of individuals with whom any one person can maintain stable relationships, that this limit is a direct function of relative neocortical size, and that this, in turn, limits group size.

The predicted group size for humans […] is close to the observed sizes of certain rather distinctive groups found in contemporary and historical human societies.

[…] there is no obligation for particular human societies to live in groups of the predicted size: The suggestion here is simply that there is an upper limit on the size of a group that can be maintained by direct personal contact […]

And what is that number? Roughly 150 people.

How did he find it? He built a model on top of the following straightforward regression:

In examining the relationship between neocortical size and group size in nonhuman primates, […] The Neocortex Ratio (neocortical volume divided by the volume of the rest of the brain) gives much the best fit […] accounting for 76% of the variance in mean group size among 36 genera of prosimian and anthropoid primates.

[…] regression equation predicts a group size for modem humans very similar to that for hunter-gatherer and traditional horticultural societies.

Being a model built on few and rough datapoints, Dunbar made sure to add several historical evidence to support that a number between 100 and 250.

Since Dunbar’s paper, there has been a multitude of research on the topic and its adjacencies.

From what I could get online from Wikipedia articles, well-designed studies actually preceded Dunbar’s:

His work on social networks area began in 1972 […] Peter Killworth worked on the small world experiment, examining differences in the answers to questions such as “how many people does the average person think they know?” and “how many people does the average person really know?”

And crucially:

Russell Bernard and Peter Killworth […] came up with an estimated mean number of ties, 290, which is roughly double Dunbar’s estimate. Their median is 231.

The Bernard–Killworth estimate of the maximum likelihood of the size of a person’s social network is based on a number of field studies using different methods in various populations […] the Bernard–Killworth number has not been popularized as widely as Dunbar’s.

For more detailed information, read the presentation slides available at the Honoring Peter Killworth link in Bernard’s website.

## Location capacity: average number of places usually visited

An interesting This is quantity isn’t as classic and strong as the other two described above. Probably because the evidence for it is much harder to collect.

paper called Evidence for a conserved quantity in human mobility states:

We reveal that mobility patterns evolve significantly yet smoothly, and that the number of familiar locations an individual visits at any point is a conserved quantity with a typical size of ~25.

You may ask: what exactly constitutes a familiar location for their purposes?

[…] locations that an individual visited at least twice and where they spent on average more than 10 min per week during a time-window of 20 consecutive weeks […]

Here are some other meaty chunks of the paper highlighting how we as humans behave spatially on average.

First:

A central question concerning the long-term exploration behaviour of the individuals is whether an individual’s set of known locations continuously expands or saturates over time.

They found that the total number of all (unique) locations an individual has discovered up to time $$\footnotesize t$$ grows proportionally to $$\footnotesize t^\alpha$$, where $$\footnotesize \alpha$$ is relatively homogeneous across their datasets with values around 0.7. That is to say, it grows sublinearly and saturates. According to them, this behaviour is a characteristic signature of Heaps’ lawIn linguistics, Heaps’ law is an empirical law which describes the number of distinct words in a document as a function of the document length. More at Wikipedia.

.

Also:

How does the discovery of new places affect an individual’s [set of familiar locations]?

They found that the average probability $$\footnotesize P$$ that a newly discovered location will become part of the set of familiar locations stabilizes, over the long term, at somewhere between 7 and 20%, depending on the dataset.

They also pointed out to the probable connections of their findings about places to social behavior (see Dunbar’s research cited above):

[…] we investigate individuals’ routines across months and years. We reveal how individuals balance the trade-off between the exploitation of familiar places and the exploration of new opportunities.

[…] and we show that individuals’ exploration-exploitation behaviours in the social and spatial domain are correlated.

Reading through the paper, the methodology appears to have been well scrutinized. And they even made available good and extensive supplementary materials to back up their claims!

It’d be great to see a larger set of participants in the future. Their most important data source was an Android app published by Sony called LifeLog. Because of changes in how the app worked, there was a considerable reduction in time coverage for most users during the period of data collection. The researchers then needed to constrain their analysis to only 2.2k users (who knows how biased is this population).