Brian Castellani and Rajeev
Sociology and Complexity
Science Blog (17 Sept 2019)
NOTE: Please cite
this blog post as follows: Castellani B., and Rajaram R. (2019) 'How large must
a society be to accomplish great things?' Sociology and Complexity Science
Blog, 5 Sept 2019.
THE ROLE OF
POPULATION SIZE IN INTELLECTUAL/ARTISTIC TRIUMPHS
How large must a society be to accomplish great things? Or how about even a region or city or town? Is there a certain population size/density required
for intellectual or artistic genius or brilliance to emerge? In turn, is there a tipping point past which
a population becomes too big, such that only certain types of intellectual or
artistic brilliance are recognised? And
if so, how and why?
These are the kinds of questions that Rajeev
Rajaram and I have been chatting about for the past few years. They come from both a growing list of
empirical examples that have intrigued us, as well as from our involvement in a
series of interrelated fields of study within the complexity sciences, in
particular the study of diversity in complex social systems.
To begin, we will start with our empirical intrigues – each of which sort
of gets at or illustrates what we have been thinking about.
1. The first comes from a biography of the famous British painter, David
Hockney. When asked about the fame he had received for his work, he basically
said that, talent aside, it was somewhat all a matter of luck and being in the
right circumstances. In terms of luck, he explained that, as he rose in
the art scene, he knew lots of hard-working artists who were just as talented
as him (if not more) but who never really obtained the success their work
deserved. It seemed, he said, like there was some sort of restriction on the
number of people who could be artistically famous – most likely, he felt, due
to market pressures and the ridiculous prejudices of art critics and the art
world. And, in terms of being in the right place, he worked in London and then
Los Angeles, which were emerging artistic hubs in the 1960s and 1970s.
2. The second comes
from reading thought the 2019 listing of top UK universities in the 2019 Times Higher Education World University Rankings. It is amazing that, for a country
of only 66.9 million people, the UK has so many universities in the top 100.
Bill Bryson, the famous travel writer, made a similar point in The Road to Little Dribbling. “Britain has 1 per
cent of the world's population, but 11 per cent of its best universities, and
account for nearly 12 per cent of total academic citations and 16 per cent of
the most highly cited studied.... I very much doubt if there is any other realm
of human endeavour in the country that produces more world-class benefit with
less financial input than higher education. It is possibly the single
most outstanding thing in Britain today (p. 357).” In other words, relative to its rather small
population, the UK is an intellectual powerhouse.
3. The third comes
from a documentary on the beginnings of Motown
Records in the States
(1952 to 1972). We cannot remember
exactly who they were interviewing, but we are pretty sure it was Berry Gordy,
the founder. He made an interesting point in response to the massive
talent that came from Motown Records, including Diana Ross and the Supremes,
Marvin Gaye, Gladys Knight and the Pips, Smokey Robinson and Stevie Wonder to
name a few. Gordy explained that, in any given community, as in the case of the
music scene that emerged in Detroit Michigan, there is a tremendous amount of
talent to be found in small places. The challenge, however, is for
someone to recognize this fact and to provide the conduit for it to reach the
heights it was born to achieve. And, in the case of Motown records, this
also meant specifically overcoming racism and discrimination against
African-American musicians in these communities. In other words, a relatively small community
can produce genius, but only if certain key social conditions are present!
4. The fourth concerns
the tremendous challenges one faces in gaining admission to the top
universities in countries like India and China, given the size of their
respective populations. India, for
example, has over 1.34 billion people.
The result is that there are obviously far more talented people than can
enter the university system, making competition massively difficult if not
impossible for some, particularly for those coming from disadvantaged
backgrounds. In other words, it seems that, past a certain tipping point,
populations become too large to make the most of their respective talent.
5. The fifth example
comes from a very interesting study by Michel
Serafinelli (Assistant Professor,
Department of Economics, University of Essex), titled, Creativity and Freedom. Serafinelli explains the thesis of his project on
his blog. He states:
“Creativity is often highly concentrated in time and
space, and across different domains. In the 15th century, Florence was home to
an amazing number of ground-breaking innovators in literature, painting,
sculpture, philosophy, and science. At the turn of the 19th century, Vienna
hosted pioneers in painting, medicine, biology, psychology, philosophy, music,
who all interacted with one another. London in the late 16th century, Paris in
the early 19th century, and San Francisco and New York in the past few decades
are some other examples of clusters of creativity and innovation in a number of
seemingly unrelated domains (Banks 1997, Kandel 2012).
What explains the formation and decay of such clusters
of creativity? Are they driven by wealth, by specific features of local
institutions, or by mere chance? More generally, aside from these exceptional
clusters, how concentrated are creative activities in time and space? Is there
co-agglomeration of creative people from different fields?”
In terms of an initial answer
to these questions, several conclusions were of particular note:
· “First, births of creative people
and famous immigrants are spatially concentrated, generally more so than
population” (See Figure 1).
· Also, the cities
where many of these highly talented people were born or immigrated to were not
necessarily the largest. However, large cities tend
to have a higher level of talent than smaller cities.
· Also, creative cities are often geographically
clustered (See Figure 1).
In turn, many small
cities never establish themselves in terms of significant talent. In other
words, it seems that the majority of small cities never become intellectual or
However, change does
take place across time in terms of the most creative cities. Serafinelli states, “Estimating a
transition matrix, we also find that persistence of creativity is higher at the
bottom of the distribution than at the top. Most small and uncreative cities
remain in that condition. But at the top of the distribution there is more
reshuffling in creative clusters than for population – while most large cities
keep growing and remain large, creative clusters exhibit more change over the
|FIGURE 1: Spatial Distribution of Births of Famous Creatives, 19th Century|
Which takes us to Serafinelli
next point. Relative to the social forces
necessary for such creative accomplishment, he found that:
· “First, the protection of personal and economic freedoms
changed the local culture, making it more receptive to innovations and new
· “Second, the new institutions also changed incentives,
through a more meritocratic and inclusive social environment, but also by
encouraging works of art and innovations that would enhance the prestige of the
· “Third, free cities attracted talented and creative
individuals who escaped censorship and persecution elsewhere, and this created
role models and facilitated social learning, breeding new generations of innovators.”
· “These channels are not mutually exclusive, and it is
likely that they are all relevant, although in our research we cannot
discriminate amongst them. But, whatever the mechanism, the historical evidence
strongly supports the idea that open and democratic institutions breed
innovation and creativity.”
In short, while population size is important and while regional
concentration (particularly in cities) is also crucial, the presence of key
socio-historical and economic and political factors is vital.
INTERRELATED FIELDS OF STUDY
In terms of the fields of complexity science that have motivated our
interest in the relationship between populations and their creativity, the most
important is the study of diversity in systems, which has to do with the role that
differences and variety play in the self-organisation of complex social and
ecological systems. Through the work of Scott Page and others, for example, a major focus is
the role diversity plays in innovation, invention, creativity and advance. And, as developed through our recent work, it has to do with the multiple pathways and
trajectories along which complex systems evolve.
In fact, pace information theory and the work of Claude Shannon, we have developed our own approach, which we call 𝐶𝑐, case-based entropy. (Later in this post we provide a quick
introduction. For an
in-depth review, click here.)
The measurement of diversity in systems is a rich field of study.
For example, do those cities or societies with a greater level of diversity
richness and evenness in terms of artistic and intellectual types, accomplish
greater things than those that do not?
And, if so, could you compute this optimal level or diversity richness
and evenness for any given system, particularly for unknown cases or under
The second field is
the study of tipping points, which has to do with the thresholds at
which complex systems shift from one way of being to another. A related concept, which goes back to the
early work of Per Bak and colleagues, is called self-organised criticality. In the case of the
current study, for example, we want to know if there are population tipping
points that suddenly allow for major artistic and intellectual triumphs?
The third is the study of scale-free networks, which has to do with how the distribution of cases in
many complex networks is skewed-right, such that the majority of cases reside
within the lower bound of probability types.
For us, a similar question emerged: once a certain population threshold
is met, if you used 𝐶𝑐 to plot the
distribution of intellectual and artistic achievements for a city or society,
would it be skewed-right, such that the majority of such cases would be reside
within its lower-bound? In other words,
are most artistic and intellectual accomplishments beholden to some type of
restricted diversity in terms of the notoriety and success that they achieve,
such that the highest frequencies of cases constitute a minor contribution?
The final area, defined as the study
of social systems, has to do with the complex causal factors involved in
how societies are formed, evolve and, in many instances, collapse or fall
apart. Given that such inquiries are of concern across the social sciences,
from sociology and history to anthropology and political science – as well as in
such fields as post-structuralism (i.e., Foucault, Lyotard, etc) and
globalisation studies (i.e., Giddens, Castells, etc) – the available empirical
and theoretical literature upon which one can draw is considerable.
Our focus is fortunately rather specific, as we are interested in the
role that population size/density/clustering play in the accomplishments of a
city or society. As such, we have spent considerable time exploring the work of
Jared Diamond, in particular his two provocative books, Guns, Germs and Steel and Collapse: How Societies Choose to Fail or Succeed. In similar fashion
to Diamond, we are interested in what set of population conditions are
necessary for a city or society to suddenly tip-over into a situation where it
has the capacity to achieve significant intellectual and artistic
accomplishments? Also similar to
Diamond, we want to know if, sociologically speaking, a population can become
too large, such that, relative to artistic and intellectual achievement,
negative relations of power emerge that exclude, marginalise, suppress or
SIX KEY QUESTIONS
So, in summary, we have six
key questions, which others may likewise find interesting or worthwhile
exploring, as we presently have, at best, a tentative or no answer to them:
1. POPULATION MINIMUM: To
begin, is there a necessary minimum population concentration/size needed for a
complex social system (be it a city or society, etc) to achieve a considerable
degree of artistic and intellectual greatness?
2. POPULATION MAXIMUM: Conversely,
can these complex social systems cross a tipping point where the population is
too large for all of its greatest accomplishments to be recognised?
3. MECHANISMS OF POWER:
Also, due to negative relations of power (i.e., social closure, discrimination,
marginalisation, etc) do these complex social systems, once past this tipping
point, limit the richness and evenness of their diversity of recognised talent,
such that a significant amount of artistic or intellectual ability is missed, excluded,
appropriated or oppressed?
4. PROBABILITY ISTRIBUTION OF ACCOMPLISHMENT: Also,
statistically speaking, once the size of a population meets the minimum
threshold for intellectual or artistic greatness, does the distribution of
accomplishments (exclusionary or not) form a skewed-right distribution, such
that the majority of accomplishments are located in the lower-bound? In other words, are the majority of
accomplishments (the highest population frequencies) modestly to minimally recognised
or of importance, similar to how most nodes in a complex network have only a
small number of links?
can this skewed-right distribution be effectively modelled using 𝐶𝑐
– our case-based entropy approach – with or without long‐tail and whether or not
the distribution fits a power‐law?
finally, does this skewed-right distribution fit the 60-40 rule, such that when measured using 𝐶𝑐, 60% (or more) of artistic
and intellectual accomplishments reside within the first 40% (or less) of the
lower bound of equiprobable diversity types— again, with or without long‐tail
and whether or not the distribution fits a power‐law?
To make better sense of our six
research questions, a few quick definitions are in order. First, by 'artistic and intellectual
accomplishments' we mean everything from music and architecture to
the plastic arts and literature to sports and theatre to engineering and
technology to philosophy and the sciences.
we mean accomplishments that inspire people to recognise something as
exceptional and distinct from the everyday; something created that inspires
people or brings them great joy or improved well-being; in short, the things
for which we generally reserve the words 'brilliant,' 'incredibly talented,'
'gifted,' 'genius' or 'remarkable.'
by 'recognised,' we mean
that the relevant people (and potentially even a majority) in a society, city,
town or community are aware of and acknowledge the greatness of the
intellectual or artistic accomplishment and its creator(s).
Fourth, by 'diversity' we mean the richness (number of different types of artistic
and intellectual endeavours) and the evenness (relative abundances of
the different types of endeavours) of a complex system.
By ‘diversity type’ we mean some form of artistic
or intellectual endeavour or area of involvement. For example, Italian cooking, abstract art,
heavy metal, break dancing, science fiction, or studying social complexity. Also, as we have explained
each diversity type in a system constitutes a probability state: one form of
complexity possible for the cases in a complex system. As a category of
similarity, diversity types function as probability states, around which the
cases in a system naturally cluster, given some shared set of characteristics –
descriptive, constructive, organizational, scale, etc. This is not, by the way,
a new idea: in the case of the classic Maxwell-Boltzmann distribution, for
example, mass and temperature determine the probability state (type) for each
particle in an ideal gas, thereby determining the natural distribution of the
diversity of particle speeds at thermodynamic equilibrium. The same capacity to
predict probability seems to be true for the distribution of the diversity of
complexity. Be it the population size of a city, the income of a household or
the market value of a business, the diversity types for a system constitute its
empirically defined range of probability states, along which its cases will
distribute themselves, based on similarities in attributes.
By ‘measuring diversity’ we mean case-based entropy (Cc): 𝐶𝑐 renormalizes the diversity contribution
of any probability distribution 𝑃(𝑥), by computing the true diversity 𝐷 of an equiprobable distribution (called the Shannon-equivalent uniform distribution)
that has the same Shannon entropy 𝐻 as 𝑃(𝑥). In terms of a definition, 𝐶𝑐 is precisely the number of equiprobable
types in a discrete distribution, or the length, support, or extent of the
variable in the case of a continuous distribution, which is required to keep
the value of the Shannon entropy the same across the whole or any part of the
distribution up to a cumulative probability 𝑐.
the Shannon-equivalent uniform distribution for two reasons:
First, it is well
known that, on a finite measure space, the uniform distribution maximizes
entropy: that is, the uniform distribution has the maximal entropy among all
probability distributions on a set of finite Lebesgue measures.
Shannon-equivalent uniform distribution will, by definition, count the number
of values (or range of values) of 𝑥 that are
required to give the same information as the original distribution 𝑃(𝑥) if we assume that all the values (or range of
values) are equally probable.
Hence, the uniform distribution
renormalizes the effect of varying relative frequencies (or probabilities) of
occurrence of the values of 𝑥 without losing information (or entropy).
In other words, if all choices of the random variable are equally likely, the
number of values (or the length, if it is a continuous random variable) needed
for the random variable to keep the same amount of information as the given
distribution is a measure of diversity. In a sense, each new value (or type) is
counted as adding to the diversity, only if the new value has the same
probability of occurrence as the existing values.
Diversity necessarily requires the values
of the random variable to be equiprobable since lower probability, for example,
means that such values occur rarely in the random variable and hence cannot be
treated as equally diverse as other values with higher probabilities. Hence, by
choosing an equiprobable (or uniform) distribution for normalization, we are
counting the true diversity, that is, the number of equiprobable types that are
required to match the same amount of Shannon information 𝐻 as the given distribution.
This calculation (as we have shown elsewhere) can be done for parts of the
distribution up to a cumulative probability of 𝑐. This means that a comparison of 𝐶𝑐 for a variety of distributions is
actually a comparison of the variation of the fraction of diversity 𝐶𝑐 contributed by values of the random
variable up to 𝑐. In terms of measuring the diversity
and complexity of various systems and networks, our approach has two key
𝐶𝑐 provides a scale-free measure to compare distributions without omitting
any of the entropy information, but by renormalizing the variable to one that
has equiprobable values. It can do so
because, regardless of the scale and units of the original distribution, 𝑐 and 𝐶𝑐 both vary from 0 to 1, as such one can plot a curve
for 𝐶𝑐 versus 𝑐 for
multiple distributions on the same axes.
What is more, 𝐶𝑐 allows researchers to compare different parts of the
same distribution, or parts to wholes. That is, one can generate a 𝐶𝑐 versus 𝑐 curve for
any part of a distribution (normalizing the probabilities to add up to 1 in
that part) and compare the 𝐶𝑐 curve of the part to the 𝐶𝑐 curve of the whole or another part to see if the functional dependence
of 𝐶𝑐 on 𝑐 is the
same or different. In essence, 𝐶𝑐 has the ability to compare distributions in a “fractal” or self-similar
For example, in the case of our interest
in the relationship between populations and creativity, 𝐶𝑐 provides a useful way to use ‘diversity
of information’ as a measure for comparing different population-based
distributions of intellectual or artistic talent to one another, as well as to
explore different parts of the same population distribution for any one given
type of artistic or intellectual endeavor.
By 'restricted diversity' we
mean that, when plotted for any given population, as the diversity of
complexity goes toward infinity (primarily in terms of the number of artistic
and intellectual types; but also, secondarily, in terms of the frequency of
cases), a limiting law of restricted diversity emerges, constraining the
majority of cases to simpler types, which do not achieve as high a level of
acclaim or recognition. This restriction
appears to be done by constraining the artistic and intellectual richness of these systems; that is, limiting
the number of highly recognised artistic or intellectual types to a few; and,
in turn, by restricting the evenness of
the intellectual and artistic types in these systems.
|FIGURE 2: Graph of 60/40 Rule for Eight Complex Systems|
In terms of their social mechanics, the restriction of richness
and evenness is probably some combination of true talent and ability (one the
one hand) and also negative relations of power (on the other hand), which seek
marginalise, suppress or close-off competition.
Examples include racism, sexism, elitism, homophobia, classism, social
closure, and the perpetuation of inequality.
By the ‘60/40 rule’ we mean it appears that, for those
complex systems with skewed-right distributions, the clustering of the cases
around the lower bound of the diversity of complexity is not arbitrary.
Instead, similar to the central limit theorem for mild distributions, there is
actually a consistently followed rule hidden in full view within these
To make sense of the 60/40
rule see Figure 2, which comes from a study we completed on a series of
different complex systems (Click here for more). First, there is the
graph. Its purpose is to visualize the diversity contribution 𝐶𝑐 of some set of complex probability types relative to the cumulative
frequency (c) of cases, for each of the eight systems studied. The diversity
contribution for the complex probability types 𝐶𝑐 is shown on the x-axis; while the y-axis shows the cumulative percentage
of cases (c*100) relative to the x- axis. When examining the curves, we noted
that they all passed through the same shaded region on the graph, demonstrating
that, for the systems we studied, 60% (or more) of cases consistently resided
within the first 40% (or less) of a system’s lower bound of complexity.
|FIGURE 3: Table of 60/40 Rule for Eight Complex Systems|
To explore further the
specifics of these curves, see Figure 3, which provides the coordinates for a typical
point in the shaded region, for each of the systems we examined in our study.
The reader can see that, for some systems – as in the case of the
world-wide-web, the velocity spin of galaxies, and the city size by population
– the cumulative percentage of cases was as high as 80/40. Still, while this
insight is useful, the more important point is that all eight systems passed
through the same region on the graph, suggesting that the limiting law of
restricted diversity follows the 60/40 rule.
CAVEAT: 𝐶𝑐 IS NOT THE POWER LAW!
60/40 rule demonstrates that, for a variety of natural and human-made systems,
the majority of cases account for a small percentage of the total diversity of
complexity. Such an insight, however, is not simply the inverse of the Pareto
Principle, otherwise known as the oft misused and misunderstood 80/20 rule.
In other words, the distribution of the diversity
of complexity, as measured by 𝐶𝑐, is not the same as
measuring the decay of a system using the power-law. The Pareto principle only
applies to the tail and not to the total distribution of diversity of
complexity types in a system. The 60/40 rule, by contrast, concerns the
distribution of the lower bound of equiprobable types relative to the
cumulative distribution of complexity in the entire system – which is what
Figure 2 shows. As such, when the 60/40 rule says that ‘‘the majority of cases
account for a small percentage of the total diversity of complexity,’’ it means
that, regardless of the distribution studied, 60% of the cases account for only
40% of the equiprobable types necessary to explain the total information in a
In the case of 2013
household income in the United States, for example, this translates as follows:
60% of all households constitute only 40% of all equiprobable income types; as
such, the majority of households accounted for a small percent of the total
diversity of eco- nomic complexity. In turn, the top 20% of U.S. households in
2013—which is the same group that the Pareto Principle focuses on; and which
amounts to roughly $105,000 dollars or higher—accounted for 34% of the total
diversity of equiprobable types.
CONCLUSIONS AND CONCERNS
As stated at the beginning of this post, we are in the early
stages of investigating our questions.
As such, while we have come to some tentative conclusions, we are not entirely
sure – and probably wrongheaded about some of it. As such, we are sharing
our work for anyone interested in trying to help explore this topic.
QUESTION 1 & 3: POPULATION MINIMUM & MECHANISMS OF POWER
In regard to the first question, it seems that a population does
not need to be very large or concentrated in order for it to draw/achieve a
considerable level of artistic and intellectual accomplishment. However, the
size of such a population clustering probably does need to be city level.
Also, even for a small population cluster, the necessary
socio-economic and cultural and political arrangements need to be in place,
sufficient to attract/produce high levels of artistic and intellectual talent.
In other words, relative to a particularly large population size/concentration,
what seems equally important is the extent/degree of infrastructure support to
accomplish various artistic and intellectual achievements. Such support
includes not only key societal institutions, but also addressing oppression,
marginalisation and discrimination in all of their various forms -- sexism,
racism, homophobia, classism, cultural appropriation, etc -- and making sure
that inequality and disadvantage (economic, political, geographical) are not
negative determinants of success.
A tentative summary: if one has a city-level population clustering and the
necessary support infrastructure, then high levels of artistic and intellectual
accomplishment are likely. We can call such a key combination an artistic/intellectual
The unanswered questions: The question, however, which we have not
answered, and which others might seek to explore, is what this minimum
necessary population size/ concentration is exactly? And has it changed over
QUESTIONS 2 & 3: POPULATION MAXIMUM AND MECHANISMS OF POWER
It seems that, in our densely population globalised society, the
number of cities with the size/concentration and support infrastructure necessary
for considerable artistic and intellectual accomplishment far exceeds that
of the previous centuries. And, relative to this growth, our global population
has likewise grown.
As such, in terms of intellectual and artistic output, these
increases in population size, coupled with (a) significant advances in global
civil society (e.g., women’s rights, educational access, political freedoms,
increased economic wellbeing and health, etc), (b) international relations and
the global economy, and (c) our globalised cyberinfrastructure (digital social
media, the internet, smart devices, global telecommunications, etc) seem to have
allowed for a tremendous (almost exponential) growth in artistic and
intellectual output the world-over. As
such, we have more intellectual and artistic accomplishments to enjoy and
benefit from today than ever before. Therefore, in some
ways, finding some tipping point past which the population is too large or
concentrated to procure the genius within it seems non-existent. In other words, in many ways the world is big
enough for it all.
Then again, perhaps not. If
one is watching global migration trends, it seems that the world is condensing
into major metropolitan regions and mega-cities in response to the growth of
our human population. For example, this New York Times map of the United States reveals how the country is consolidating
into a series of major metropolitan regions.
“Today, 55% of
the world’s population lives in urban areas, a proportion that is expected to
increase to 68% by 2050. Projections show that urbanization, the gradual shift
in residence of the human population from rural to urban areas, combined with
the overall growth of the world’s population could add another 2.5 billion
people to urban areas by 2050, with close to 90% of this increase taking place
in Asia and Africa, according to a new United Nations data set launched today.
The 2018 Revision of World Urbanization
Prospects produced by the
Population Division of the UN DESA notes that future increases in the size of
the world’s urban population are expected to be highly concentrated in just a
few countries. Together, India, China and Nigeria will account for 35% of the
projected growth of the world’s urban population between 2018 and 2050. By
2050, it is projected that India will have added 416 million urban dwellers,
China 255 million and Nigeria 189 million.”
In short, given such a
rise in both the world population and globalised levels of urbanisation, the
existence of artistic/intellectual population hubs may be a way to restrict
complexity into something more manageable. And there appears to be at least three plausible reasons (amongst
others we are sure we are missing):
1. First, as the emergence of
regional metropolitan areas and megacities suggest, the global population has
exceeded (is exceeding) its limits, which is causing the world system to
somehow optimise and rebalance its widening intellectual and creative diversity
– which it does by consolidating itself into more concentrated urban
environments, which have become the new intellectual and artistic hubs of the
world. In other words, the emergence of these urban zones is a way of
decreasing the evenness but also, in
turn, the richness of the global
population by making the population size/concentration necessary for artistic
and intellectual accomplishment larger.
Also, all urbanised
metropolitan regions are, sociologically speaking, not the same. In other
words, due to negative relations of power (i.e., social closure,
discrimination, marginalisation, racism, hetero-patriarchy, xenophobia, etc) many
urban regions throughout the world limit the richness and evenness of the diversity
of recognised talent both within their own populations and the populations of
others. This first instance is particularly prevalent amongst those countries
where civil liberties and human rights are profoundly limited or largely
absent. The second instance is
particularly prevalent today amongst the western societies of the global north where
many (including their leaders) actively seek to retreat from the global
community and from their civil responsibilities to the rest of the world. (For
more on this point, see The Defiance of Global Commitment.)
As the amount of
artistic and intellectual talent grows, so does the challenge of consolidating
all of these accomplishments. An easy example are scientific citation networks,
which are often limited geographically, with scholars in one country ignoring
the work of those in another. (CLICK HERE FOR
The result from such factors
is that a significant amount of artistic or intellectual ability within and
across about globalised society is missed, excluded, appropriated or oppressed.
THE ADJACENT POSSIBLE: However, due to post-industrialization and globalisation, the
above summary might not be exactly the case. The development of the internet
and our global socio-cybernetic infrastructure has redefined notions of space
and time, making the role that a population size/concentration plays more
nuanced and complex. For example, an academic or artist could, to some
degree, live just about anywhere as long as they were able to effectively
interact with the key socio-cybernetic network involved in their work.
Still, as even Manuel Castells and his critics have pointed out, there
are limits to how much one can be 'outside' the physical socio-spatial
concentrations of the key city hubs of the world and still have significant
As a tentative summary: Given what we have so far outlined, it seems that, if
there exists the right combination of population size and support
infrastructure, then high levels of artistic and intellectual accomplishment
are likely. One can call such a key combination an artistic/intellectual hub –
which have historically been cities.
However, past a certain tipping point, a population can become too
large to consolidate and acknowledge the depth and variety of its intellectual
and artistic accomplishments.
In response, the system engages in a form of diversity restriction
– which happens both through an increasing size/concentration requirement for a
population cluster to be a hub, and through increasing social closure and
discrimination, exploitation and so forth. Both of which seek to reduce the
richness and evenness of a population by allowing only a small number of
artistic and intellectual types (and the frequency of people found within them)
to receive the acclaim they deserve. (Remember all three of our plausible
This restriction in diversity, however, is somewhat significantly
challenged through the advances of the world-wide-web, digital social media,
and the expansion of our global cyberinfrastructure, which have redefined
notions of time and place and space.
Still, even with the existence of our global socio-cybernetic
world, as the population and opportunity for engaging in artistic and
intellectual accomplishment increases, so does the competition for recognition
and power and position. Which, to repeat, results in a rather severe
restriction of diversity -- both in terms of richness and evenness -- leaving
an increasing amount of work (and the people who created it) unrecognised and
outside the networks of influence that decide what will be counted as an
The unanswered questions: The question, however, which we have not
answered, and which others might seek to explore, is what this population
tipping point is throughout various regions of the world?
QUESTIONS 4 – 6: PROBABILITY ISTRIBUTION OF ACCOMPLISHMENT
our six questions, the final two require are the most tentative, as such we can
only outline what an answer might look like, which we will state here:
Throughout the complexity
sciences, one regularly finds the distribution of complex systems and networks
taking the shape of a right-skewed distribution – otherwise called, but not
entirely synonymous with heavy-tailed
or long-tailed distributions. Examples
include, as we have mentioned above, studies of intellectual and social
influence (as in the case of citation research) and also popularity. Another
well-known example is the Pareto distribution and the 80-20 rule
(which we also mentioned).
Other examples include
network connectivity, which reveal that only a few nodes in, say, a network of
online retail companies – as in the case of Amazon.com for example – become
widely recognised and therefore the most densely connected nodes in the
network. Furthermore, when these massive networks are plotted as a probability
distribution, one finds that the majority of cases (retail companies for
example) are not as widely popular or recognised.
For us, whether such systems are power-law or
scale-free really doesn’t matter, as all of these studies, supportive or
critical, generally agree that a significant percentage of these complex
systems are taking a similar skewed-right shape (with or without long-tail),
which is of necessary importance, even if the models used to fit them are not
Taking these studies into
account, it seems that complex social systems, in particular, seem to manage or
optimise their diversity by limiting the level of complexity found in the
majority of cases to something relatively simple, while allowing for a small
set of cases and their corresponding types to dominate.
Translated for the purposes
of our discussion here, the consistency of this restricted diversity might
suggest that, when it comes to artistic and intellectual accomplishment, such
forces as social closure, inequality, discrimination and the consolidation of
cities into major metropolitan regions and so forth all amount to producing a
In addition to
trying to answer the unanswered questions posed earlier, our next step is to
examine several empirical cases to see if, using 𝐶𝑐, a limiting law exists for these distributions, which would obey a
· For example, we hypothesize that, if one examined a
distribution of cities similar to that explored by Michel Serafinelli in Creativity and Freedom, we would find that
the majority of cities (vis-à-vis intellectual and artistic creativity) would
not have a high number of highly recognised accomplishments, such that 60% (or
more) of cities would reside within the first 40% (or less) of the lower bound
of equiprobable diversity types, with or without long‐tail and whether
or not the distribution fits a power‐law.
· We also hypothesize that if one explored a
distribution of highly accomplished people (relative to a particular type of
artistic or intellectual endeavour), 60% (or more) of the highly accomplished
artistic and intellectual cases in the distribution would reside within the
first 40% (or less) of the lower bound of equiprobable diversity types, again with
or without long‐tail and again whether or not the distribution fits a
But, again, these are only conjectures which we (or others) need
to explore. For example, we note that, at the end of Serafinelli’s post he has
the following endnote, which we or others might find useful to explore. He states:
A similar historical perspective is taken by a set of studies using microdata
on upper tail human capital. In particular Gergaud et
al. (2016) analyse a database of more than
one million famous individuals and more than seven million places associated
with them throughout human history (3000BCE to 2015AD). Relative to this
work, we focus more specifically on creative individuals, on spatial patterns
(using the city as the unit of analysis), on the flow of ideas, and on the
effects of local self-government institutions on the formation of creative