Crystallized Imagination
What Information Theory, Genetics, Thermodynamics, and
Networks, can teach us about what the economy is and how it
evolves.
By Cesar A. Hidalgo
To Iris, Anna and Mridu
PART I: The Complexity of
Dreams
“We talk much of imagination. We talk of the imagination of poets, the imagination of
artists, and I am inclined to think that in general we don’t know very much exactly what
we are talking about.
It is [that] which penetrates into the unseen worlds around us, the worlds of science. It is
that which feels and discovers what is, the real which we see not which exists not for our
senses.”
Ada Lovelace
“Imagination: Faculty of the mind which forms and manipulates images. mid 14.c”
Online etymology dictionary
“Imagination will often carry us to worlds that never were. But without it we go
nowhere.”
Carl Sagan
“This world is but a canvas to our imagination.”
Henry David Thoreau
Chapter I: The Secret to Time Travel
The chair where I waited for my daughter’s delivery was not that comfortable. My
wife Anna and I had arrived at MGH1 at 6:30pm that Saturday. We had stayed at
home waiting for her contractions to evolve and decided to hit the hospital when
these were only a few minutes apart. Her contractions intensified when she was
in triage, but the epidural she received a couple of hours later brought her the
numbness she needed to rest. It was now 2am. The night was peaceful. All that
we could hear was the infrequent noise of the pump that inflated her blood
pressure monitor. The room was lit by the lights of a few monitors and by the
streetlights bouncing off the Charles River. In that dim light all that I could see
was Anna resting peacefully in her bed. I held her hand as I waited for the
delivery of my daughter in a plasticky armchair, that as I told you, was not that
comfortable.
At 3am the nurse and doctors told us that it was time for Anna to start pushing.
Anna was fully dilated and Iris—my daughter—was making one of the most
important trips of her life. It took only 26 minutes for Anna to push Iris into the
hands of the focused but nervous medical student that received her. Twenty-six
minutes sounds like a short time for delivery, and it is. Yet, I will argue that the
trip that Iris made that night was not a 26-minute trip down a few inches of birth
canal, but an eighty thousand year trip from a distant past to an alien future. In
twenty-six minutes Iris travelled from the ancientness of her mother’s womb to
the modernity of the 21st century society. Birth is in essence, time travel.
Up until that night, with the exception of a few sounds, Iris had experienced a
world that was no different from the one experienced by babies eighty thousand
years ago. She had been carried inside her mother’s womb hearing mostly the
voice of her parents. During a period of 40 weeks Iris developed oblivious to the
complexity of the world that buzzed around her. That obliviousness changed that
night.
1
Massachusetts General Hospital
Iris was born at 3:26am in a room that was not illuminated by sunbeams, but by
fluorescent and incandescent light bulbs. Her paternal grandparents, who were
anxiously waiting to hear about her delivery, saw her face for the first time
through an email attachment. The music that filled the delivery room minutes
after Iris was born 2 did not come from the birds or the trees, but from the
speakers of a tablet computer that obeyed the orders of an algorithm that chose
a song for us. Iris’ trip that night was only a few inches long and lasted a few
minutes, but in a deep sense, it was an eighty thousand yearlong journey. That
night, she traveled from a distant past and into a present that was literally
fantastic.
Iris’ trip is special to me, although this form of time travel is not uncommon. Being
born in the 21st century is an alien experience for most babies. The 21 st century
is a world that is quite different from the one where our species evolved. It is a
surreal world populated by objects that were dreamed before they were
constructed.
The delivery room where Iris performed her journey was full of tangible objects.
Yet, the tangibility of the beds, pillows, scales and monitors that populated Iris’
delivery room was not what made the destination of her trip modern. The tactile
nature of the reality embodied in mundane objects, such as blankets and night
tables, can mislead people to believe that our world is made mostly of atoms,
when instead, it is made of a much more mysterious intangible. That intangible is
information.
During the last million years the atoms that populate the earth have not changed,
but the world has changed. The difference between the world where Iris was
born and the world of early hominids, does not reside in the physicality of matter
but in the way in which matter is arranged. That physical order is information. Iris’
night delivery was not facilitated by objects, but by the information embodied in
2
Raindrops, by Cillo. It played in Pandora and I thumbed up the song that night.
these objects. Her night delivery was not illuminated merely by light bulbs, but by
the understanding of electricity, energy, and materials that is embodied in light
bulbs. Iris was not kept warm that night by a random collection of threads, but by
blankets that weaved together matter, knowledge and imagination. Paradoxically,
Iris was born in a non-fictional world that although tangible, is made of fiction.
This is a world that was not different from the one where she evolved, except by
the way in which matter was arranged.
The fact that the objects that populate our world are made of information, and
imagination, may seem obvious. Information is as old as life itself. After all, the
replication of information rich molecules, such as DNA and RNA, is not the
replication of matter, but the replication of the information that is embodied in
matter. Yet, what is different between us and other species is that we have
developed the ability to encode large volumes of information outside our bodies.
Unlike ants, who can excrete a few predefined messages as pheromones,
humans can encode information in the form of objects, whether these are the
books we read or the physical and digital artifacts that populate our world. The
information that we encode in objects, however, is not haphazard. It is primarily
information that was begot in our minds. So our ability to build the houses that we
imagine, and the software that we dream about, is a simple answer to the eternal
question: what is the difference between us—humans—and all other species?
The answer is that we—humans—are able to create physical instantiations of the
objects we imagine, while other species are stuck with nature’s inventory.
In the next pages I will argue that the process of economic development is
nothing more than the process by which our civilization develops its capacity to
accumulate physically embodied information and the capacity to process
information—which I define as knowledge. This is the information that is
embodied in the physical and digital objects that we make, and in the human
networks that allow us to create these objects. In fact, I will argue that our ability
to create objects that are made primarily of information is what endows our
species with fantastic capacities. Our ability to arrange atoms according to our
imagination is what allowed a few of us to walk on the moon, and it is what allows
many of us to enjoy long distance communication, food refrigeration, and long
distance travel.
The ability of ancient civilizations to construct objects plays a central role in the
way in which we understand history and the development of human civilization.
Our understanding of the civilizations that predate writing is derived largely from
the artifacts they left behind, since these long predate written records 3. In fact,
our ability to encode information in objects predates the invention of writing by at
least sixty thousand years4, and that of cave paintings by at least thirty thousand
3
Dating the origins of human language is difficult, since oral expressions largely predate writing.
The earliest records of written language date back about 8,000 years, so archeologists wanting to
estimate the origins of spoken language need to consult other forms of evidence, such as the
complexity of the products found in the archeological record. The idea that complex products can
be used to date the origins of human language is based on two lines of argument. First, an
individual able to produce a complex tool, such as a spear or a carburetor, is an individual that
understands how different parts fit together, much in the same way that human languages allow
us to combine different words into sentences, and sentences into narratives. In other words,
individuals that can build complex tools are likely to be individuals that have an internal way of
representing each of the parts involved in the construction of the tool, and can think about the
sequences of actions required to put these pieces together. The mental process required to
ideate and assemble a complex product can be thought of as a primitive grammar, and it has
been found to define similar patterns of brain activity. Making complex products is enabled by a
similar combinatorial capacity than the one present in human languages. So, even though the
combinatorial capacity of product creation does not necessarily imply the use of a human
language, it is reasonable to assume that these two combinatorial cognitive capacities emerged
together.
The second line of argument supporting the use of complex objects to date the origins of
language relates to the diffusion of the knowledge required to make complex objects, such as
arrows and spears. The proliferation of arrows and spears can be seen as an indication of the
existence of early forms of human language, since learning how to build an arrow is different than
learning how to use a rock to crack open a walnut. Simple tasks can be learned easily through
observation and imitation, while the production of complex objects involve nuances that are
communicated much more effectively among individuals that share a language. For instance,
individuals sharing a language can more effectively learn how to safely handle the poison used to
make arrowheads, or how to fasten a stone ax to a wooden handle.
Current archeological records show that Homo sapiens were fashioning tools that were as
complex as that of some modern hunter-gatherers as far back as 100,000 to 70,000 years ago.
This shows that our ability to crystallize imagination largely predates our ability to write about it,
and date the origins of language, and complex products, to the time before we left Africa. This
suggests that it is not the use of simple tools what separated our great ancestors from other
species, but their ability to create complex objects, objects that were superior to those found
naturally in the environment. (Reference EO Wilson, The Social Conquest of Earth, and Yuval
Harari, From Animals to Gods)
4 EO Wilson The Social Conquest of Earth, Yuval Harari, From Animals to Gods.
years. The development of human civilization is the development of our ability to
embody information in objects, and it is hence, a process that begun with the
creation of simple concoctions of bits and atoms, as simple as arrows and
spears.
Although the ability of people to make products is central to our understanding of
human civilization, the ability of countries to make products of increasing
complexity is not a central theme in our understanding of economic development.
When we look back in history we talk about civilizations that learned to dominate
Stone, Bronze5 and Iron. These are civilizations that used their dominion over
these materials to fabricate weaponry, jewelry and household items. Twenty first
century nations are not separated by their dominion over simple metals, but still
differ largely in their ability to build physical and digital products. These are no
longer bows and arrows, but engines, generators, synthetic materials, video
games, and mobile phones, among a myriad of other products.
Our world is marked by differences in the ability of countries to make products,
and hence, it is marked by difference in the ability of countries to embody
information into matter. This puts the few countries that are more successful at
embodying information at the cutting edge of modern civilization. These are the
countries that are able to design and create almost every product that we have
imagined, and by doing so, get to enjoy most of the wonders of modernity 6.
5
Bronze Age civilizations, separated by long stretches of space and time, had remarkable
similarities. Both, ancient Egyptians and Aztecs dedicated much of their efforts to the creation of
pyramids that were mostly solid. Both ancient Egyptians and Aztecs had a two-calendar system
involving a religious calendar and an operational calendar that regulated activities such as
harvesting and tax collection. Both Aztecs and Egyptians had pictographic writing systems that
where augmented with phonograms—pictures that represented sounds. And certainly, both
ancient Egyptians and Aztecs knew how to smelt copper and tin to make bronze, but were unable
to crystallize their ideas in Iron.
6 Certainly, one could argue that not all products increase welfare. Think of an atomic bomb, for
example. This line of criticism, however, can be misleading because it fails to separate the use of
a technology with the technology itself. In fact, most technologies are double edge swords.
Knives can be used to make a tomato salad, or to kill a fellow human being. A wrench can be
used to repair a car, or to knock someone unconscious. A pillow can be used to rest at night, or to
smother someone to death. The distinction between the uses of technologies, which can be
Yet, most countries are not at the cutting edge and witness the benefits of our
species’ ability to embody information mostly from the sidelines. These countries
get to enjoy the benefits of the information that is embodied in these products
mostly when they are lucky enough to have valuable rocks or mineral fuels that
they can trade for them. When that is not the case, their inclusion into the global
economy is marginal.
Our evolving ability to make products is at the core of the process of economic
development. Yet, as I mentioned, neither our ability to make products nor the
difficulties involved in developing this ability are at the core of the practice of
economic development. During the twentieth century the practice of economic
development went through two big panaceas. Both panaceas boomed and failed.
The first panacea was inspired by the Marshall plan, which was the plan through
which the United States supported the reconstruction of Germany after WWII.
The Marshall Plan was wrongly interpreted as evidence that financial aid was all
that was needed to make a prosperous country out of a pile of rubble 7 . The
overestimation of the Marshall Plan’s effects gave rise to a first panacea
involving the creation of institutions that lent money to developing countries with
the hope that the removal of financial constraints would help developing
countries advance their economies. The proposal was even rosier, since the
hope was not only to jump start development through finance, but also to do so
at a profit for those willing to risk the funds. Cleary, money wasn’t enough and
development through loans failed to reproduce what pundits thought the Marshall
Plan had accomplished.
positive or negative, and their ability to open new possibilities, which is a positivistic statement
about the space of what is possible, is well exemplified in a quote that Richard Feynman liked to
repeat when talking about nuclear energy. This is: “To every man is given the key to the gates of
heaven. The same key opens the gates of hell.”
7
Collier the Bottom Billion (CITE, page)
Later in the twentieth century the practice of development went through a
different panacea. This second panacea involved formal institutions. These are
the institutions created with the intention of governing human behavior, such as
political systems, and the laws that governments impose on their citizens.
The institutional debate of the second half of the twentieth century was colored
largely by the tension between the different institutional models that were in
conflict during the cold war. Countries wanting to prosper needed to adopt the
institutions of the already prosperous western nations: open up to trade, privatize
inefficient public sector industries, provide autonomy to their central banks, allow
their currencies to float, and elect their governments democratically.
The big experiment of this second panacea was the dissolution of the Soviet
Union. As the Soviet Union collapsed, western powers pushed for what they
called a “shock therapy” 8 . A shock therapy implied a quick reformation of a
country’s formal institutions that mimicked the institutions that had evolved over
centuries in the west. This shock therapy neglected the strength of informal
social institutions, which are the inherited social behaviors that are not enforced
by law. The naïve assumption was that social institutions changed as the
incentives provided by formal institutions changed. Yet, through repeated failures
we have learned that history is more stubborn than we originally thought. Markets
and democracies are not strong enough to produce virtuous social institutions,
but virtuous social institutions are strong to produce virtuous markets and
democracies.
As a case in point consider the collapse of the Soviet Union. This was seen by
some as the perfect opportunity to show the world that a drastic change in a
country’s formal institutions could put a developing nation in the right track. As
the iron curtain melted, prefabricated laws and institutions where imported. The
imported institutions, however, failed to produce the changes that pundits
8
Jeffrey Sacks, The End of Poverty
expected. Almost a quarter century has now passed and it is hard to argue that
the post-soviet Russia that has been ransacked by private oligarchs, and its
democratically elected officials, is in a better shape than the soviet republic of
Russia. If we consider communist Russia as the proof that communism and
central planning did not work, then, we should consider post-communist Russia
as the proof that neither “democracy”9 nor capitalism work either.
If there is any consensus left in the field of economic development, it is that
economic development is a complex process that we don’t fully understand. Yet
the lack of consensus in the field does not imply a lack of new theories and
explanations. During the last decade a new stream of thought, focused on the
ability of countries to make complex products has begun to timidly tickle into the
economic development mainstream10. Much like archeologists, who focus on the
ability of a civilization to make artifacts, this stream of thought focused on the
ability of a country to make products. These are the products that embody the
modernity of the destination of Iris’s time travel, the products that pack increasing
amounts of information. An umbrella term for this emerging body of literature is
9
One might argue that what Russia has at this time is not necessarily democracy, so it is
important to take this comment with a pinch of salt.
10 The development of this literature started with work that questioned some assumptions that
although naïve, had been engrained in economics. In Economic Development as Self-Discovery
(2003), Hausmann and Rodrik call attention to the fact that for entrepreneurs to be able to
produce a product or provide a service, they need to first discover the cost of producing at a given
location. These discovery costs, where costs that were absent from mainstream economic
models. In “What You Export Matters” (2007), Hausmann, Hwang and Rodrik classified products
into “rich” or “poor” country goods based on the level of income of the countries that produced
them. They used this continuous metric to show that poor countries producing “rich” country
goods exhibit higher levels of aggregate economic growth (GDP per capita growth). In “The
Product Space Conditions the Development of Nations” (2007), Hidalgo et al. showed that a
country’s future exports were more likely to be products that were similar to the ones a country
already exported. This showed that the ability of countries to upgrade their productive structure
was highly constrained by the mix of products that a country was currently making. Finally, in The
Building Blocks of Economic Complexity (2009), Hidalgo and Hausmann showed that information
about income was not needed to explain future growth, since most of the relevant information
was contained in the structure of the network connecting countries to the products they export
(see also Hidalgo (2009)). The elimination of measures of income provided a change of language
that eschew away from terms such as rich country goods and poor country goods by focusing on
the complexity of products instead. Much of this book will be dedicated to explore what the
complexity of products means.
economic complexity11, since this is the stream of thought that focuses on the
evolution of a country’s ability to make complex products.
But why would anyone want to create a theory of economic development by
looking at the products that people make, instead of the people that make them?
Isn’t that backwards?
There are pragmatic and philosophical reasons that support the creation of a
theory of economic development that hinges primarily on the ability of countries
to make products—or create physical packets of embodied information. First, we
will explore the pragmatic reasons, which hinge on practical considerations such
as the availability and quality of data. Unlike measures of development based on
surveys, or formal institutions, the production and commercialization of complex
products represents data on economic development that is harder to cheat or
forge. Countries can change their rules on paper with relative ease, and improve
their scores in indicators based on surveys and formal institutions, such as those
produced by the World Bank’s Doing Business Report 12 . Yet, it is hard for
countries to cheat on indicators based on the products that other countries report
as imports. Becoming a competitive exporter of sophisticated products, such as
medical imaging devices or helicopters, is not easy, and represents hard data on
the ability of a country to pack knowledge and information into the products they
make. Much like the transformation of ancient civilizations from Stone to Bronze,
and from Bronze to Iron, the transformation of an economy from the export of
basic commodities to high tech software and hardware tells us something deep
about its people. This brings us to the second pragmatic reason why creating a
view of economic development based on products is informative: which is the
indirect information about an economy that data on products can provide.
11
This new stream of literature has also been called New Structural Economics, although I prefer
to avoid the “new” in the branding since at some point, it won’t be new. The use of the word “new”
to name economic sub-disciplines is often conventional, and devoid of poetry and explanatory
power. In some cases, it is used to the extreme. Economics has trade theory, a new trade they,
and recently, a new new trade theory.
12 http://www.doingbusiness.org/methodology (accessed October 7, 2013)
The ability of countries to make complex products has been marginal, yet present
in past theories of economic growth and development. As we review in detail in
part III, past theories of economic development were constructed on the
accumulation of coarse factors, such as physical capital, human capital and
social capital. Certainly, the assumption was that these factors help countries
produce economic activities that are more sophisticated, or that add more value.
Yet, even though these theories have been useful to explain a number of
phenomena, their focus on factors that are considered inputs, rather than the
products that emerge as an economy’s output, constraints their empirical
validation. Data on inputs factors is often much noisier and incomplete than the
data on outputs that comes from industrial production. As a result, the validation
of these theories has hinged on imperfect proxies of the real world, such as
surveys to measure social capital and metrics on the years of schooling of a
population to measure human capital. Certainly, what people answer on a
survey, or the amount of time a child spent in a building labeled “school”, are
poor reflections of the complexity of our reality. There should be better ways to
capture these important aspects of the world and looking at the industrial output
of a country is a good alternative.
In general, the ability of countries to make complex products gives us indirect
information on processes that are otherwise hard to measure, including the
formal and informal institutions of a population and the specific human capital
they posses. As we will see, making complex products is difficult, since it
requires the accumulation of vast amounts of productive knowledge, which is
highly specific13 and that lives embodied in people and networks of people. The
accumulation of productive knowledge is limited by the ability of people to form
the networks where this knowledge is accumulated—such as firms and markets.
If the ability of people to form these networks, and pack knowledge into them, is
13
As we mentioned in the introduction, the idea that factors are more specific than what is usually
assumed is an idea that is already present repeatedly in the writings of Wassily Leontief and
Michael Porter.
constrained by factors such as formal and informal institutions14, education, civil
liberties, or infrastructure, then the ability of a country to make complex products
will inform us about the quality and availability of these factors.15. Hence, if we
are uncomfortable with measures of development that hinge in the complexity of
products, we can still consider them to be indicative of other social and economic
processes that we might consider relevant but are hard to measure directly.
A third pragmatic reason to create a description of economic development
centered on the complexity of the products that countries are able to make
comes from the experience of East Asian economies. The rapid development of
Japan, Singapore, Taiwan, South Korea and China, highlights the link between a
country’s ability to make and export complex products and its ability to bootstrap
itself out of poverty. Later, we will argue that the ability of countries to make
complex products is in essence economic development since—among other
things—it precedes economic growth. For the time being, however, it suffices to
call attention simply to the obvious miracle represented by the rapid development
of East Asian countries, and in particular, to the rapid development of China16.
The case of China is particularly vexing for the western pundits that grew
convinced of the need of a modern democracy as a pre-requisite for economic
development17. While I agree that civil and political liberties are important aspects
of human development 18 , it is clear that the development of China, although
lacking important civil liberties, has removed other important deprivations from
the homes of millions of Chinese people. The industrial development of China,
which hinges largely on a superb capacity to manufacture products, now at all
14
And it is. We will review this literature in part II
In his book Trust, Francis Fukuyama uses this connection by linking social capital to the size of
firms present in a country. For those interested in his views I suggest reading Chapter 3 of Trust:
Scale and Trust.
16 Rodrik, What’s so special about chinese exports? (2005)
17 It is also a problematic case for Francis Fukuyama, since in the mid 90’s he discounted China’s
ability to sustain high levels of growth based on what he perceived as weak social institutions: a
familial society with low levels of trust.
18 As defined by Amartya Sen
15
levels of complexity, is a good example of the importance of developing the
ability to make complex products.
Yet, these pragmatic reasons do not represent the main motivation to create a
description of the process of economic development centered on the ability of
countries to make products. The main reason to focus on the creation of
products, if we take the meaning of products in its broadest sense, is that by
focusing on products we can create a theory of economic development centered
on knowledge and information. Creating a description of economic development
based on products is creating a description of the process of economic
development based on the ability of our society to pack and unpack information
into the physical bundles we call products. It is the creation of a view of the
process of economic development that is based on the accumulation of
information in its many forms, the crystallized forms that are represented by
products, and the dynamic forms that are represented by the networks of
humans that hold the knowledge required to make these products 19 . So by
focusing on products we are focusing on the accumulation of physically
embodied knowledge and information, instead of more traditional forms of
economic value. This is the accumulation of the knowledge embodied in the
bodies of surgeons and of the machines that help them, the knowledge
embodied on the minds of teachers and on the textbooks and software they use
for their lessons. This is the knowledge embodied in the minds of film directors,
fireman, and bakers, and the information embodied in the movie cameras, fire
engines, and ovens they use. The evolution and development of economies is
19
As a historical footnote it is worth noting that Marx also used the word crystallization to describe
products in some of his writings: “A commodity has a value because it is a crystallization of social
labor. The greatness of its value, or its relative value, depends upon the greater or less amount of
that social substance contained in it; that is to say, on the relative mass of labor necessary for its
production” (MARX in Value, Price, and Profit). For the reader that might be to quick to use this
coincidence to make inferences of my political affiliation, or motives, I must say that my use of the
word crystallization is not an endorsement of Marx, or a signal of my political affiliation. In fact, I
learned about this quote at a time in which this book was almost completed, and I added it to
make the historical linkages presented more comprehensive. For the reader that would like to
learn about the difference between Marx’s use of the word crystallization to describe products,
and mine, is that I see products as the crystallization of information, rather than social labor. This
distinction should become clear after reading part I.
nothing other than the evolution and development of our species ability to
accumulate and use information. This is the evolution of our ability to pack
information into products, and to unpack information into the knowledge that
resides in the networks of people that make these products. It is nothing more
than the continuation of the most fundamental of all dualities: the duality between
matter and information.
In the following pages I will construct a description of the process of economic
development based on the ability of countries to make products that embody the
practical uses of knowledge and information. My exposition of this topic will be
divided in three parts. The first part is an attempt to create a description of
products based on their ability to carry information and the practical uses of
human knowledge. The second part of the book returns its gaze to humans, and
mainly, to the constraints that limit the ability of humans to accumulate the
knowledge they need to make complex products. The third part of the book will
use the description of products, and of the networks of people that create them,
to expand current theories of economic growth and development.
Finally, for those readers that are interested in things other than economies, I will
show that a theory of economic development based on the ability of countries to
pack information into products will help unify the process of economic
development with other natural processes, such as the development and
evolution of biological organisms and statistical physics. Personally, I find this to
be the most exciting stop in our journey, since I find there is grandeur in a view of
the world that unifies different branches of science. As you will see in the next
pages, the connections between biology, statistical physics, information theory
and economies are not simply metaphorical. The connections are deep, and are
related mainly to the discreteness of the networks that are needed to accumulate
knowledge, and the constraints that this discreteness imposes in the ability of
countries and organisms to accumulate knowledge and information.
Chapter II: The Physicality of Information
“To invent, you need a good imagination and a pile of junk.”
Thomas A. Edison
A few months ago an article on the front page of a Chilean newspaper
business’ section caught my eye. The article talked about a Chilean having
bought the world’s most expensive car. The car, a Bugatti Veyron, had a sticker
price of more than 2.5 million dollars, and represented one of the most
flamboyant acts of conspicuous consumption I have ever seen.
After a quick web search I estimated the per-kilo price of the car, which
turned out to be roughly $1,300 U.S. dollars, or $600 dollars a pound20. To put
this into context, we can look at the per-kilo price of gold and silver. Depending
on the day, the price of a kilo of pure silver is about $1,000, while that of a kilo of
gold is around $50,00021. For comparison, consider that the per kilo price of a
regular car ranges from $10 for a Hyundai Accent, to $60 for a top of the line
20
My friend—and undergraduate advisor—Francisco Claro suggested this calculation to me a
few years ago. His example at that time was a fighter jet.
21 Based on data on January 14, 2013 16:45 NY Time, on goldprice.org, the exact number was
$53,586.
BMW—like the M6. So, although the Bugatti is not worth its weight in gold, its
worth more than its weight in silver and a Hyundai is worth at least its weight in
Bronze.
Now, you may argue that comparing a kilo of Bugatti and a kilo of silver is
pure nonsense, since there is not much you can do with an actual kilo of Bugatti.
Yet, this nonsensical has much to teach us about the connection between
physical order and the information that is packed in a product.
Imagine for a second that you just won a Bugatti Veyron in the lottery.
Pumped up, you decide to take your new car for a test drive. In your excitement,
you crash the Bugatti into a wall, escaping unharmed but a little sad, since you
did not have any car insurance. The car is a total wreck; you have blown it to
smithereens. Now, how much is that kilo of Bugatti worth?
The answer to this question is perfectly obvious. The sticker price of the
car evaporated in the seconds it took you to crash it against that wall, but not its
weight. So where did the value go? The pre-crash Bugatti had a great resale
value, as least as measured by its price, whereas the resale value of the postcrash Bugatti is not that hot. The resale value of the Bugatti evaporated in the
crash, not because the crash destroyed the atoms that make the Bugatti, but
because the crash changed the way in which these were connected. As the parts
that made the Bugatti were pulled apart and twisted, the information that was
embodied in the Bugatti was largely destroyed. This is another way of saying that
those two million dollars were not stored in the car’s atoms, but in the way in
which these atoms were arranged22, and that is information23.
22
There are many good references discussing the connection between thermodynamics and
economics that we discuss here. A good discussion of this can be found in Eric Beinhocker’s The
Origin of Wealth (2005) Harvard Business School Press.
23 You might argue that there is much more to the value of a Bugatti than its physical order or
information. I agree with you, and suggest you to keep on reading. I will be adding these
additional considerations gradually.
So it looks like the value of the Bugatti is connected to physical order 24,
which is the same as information. But what is information? Defining information is
not easy, but I will give it a shot. According to Claude Shannon 25, the father of
information theory, information is a measure of the minimum volume of
communication required to uniquely specify a message. Now, I know this sound
like a mouthful, and it does not appear to connect directly to the Bugatti example,
but in the next lines I will unpack Shannon’s idea and connect it with the
information that is embodied in the Bugatti26.
Since most of us will never own a Bugatti Veyron, I will use a more
accessible product instead: a tweet. For those that are not familiar with twitter 27,
I’ll just say that twitter is a micro-broadcasting platform where users post
messages of up to 140 characters. A tweet is just one of these messages, or a
little packet of information. So now that we know what a tweet is, we are ready to
ask Shannon: how much information is contained in each tweet?
An important disclaimer we need to make before introducing Shannon’s
definition of information is that Shannon separated information from meaning 28.
Information is the minimum volume of data we need to specify a message, any
message, and whether this message is a tweet that is all A’s, or the funniest
tweet you ever saw, is irrelevant from a pure information theory perspective—but
it will become relevant later.
24
Since order is a word that has many different meanings, I would like to clarify the meaning of
the word order that I will be using. Going forward I use order to mean physical order, meaning the
way in which the parts of a system are arranged. By definition, this is the same as information. It
is the order you wish to have in your closet, but not the order that involves a command; such as
the order you place in a restaurant. Physical order is what differentiates the Bugatti before the
crash from the wreck that was left after the crash. Physical order cannot transform lead into gold,
but in the case of the Bugatti can transform steel into silver, and in the case of the Hyundai
Accent, it can transform steel into Bronze.
25 Norbert Wiener arrived at the same formula in his formulation of information theory, which he
coined cybernetics.
26 Please note that the information packed in the Bugatti is information in its physical meaning of
order, which is different from the computational meaning of communication. Yet both of these
definitions have a deep mathematical equivalence that allows us to move from one to the other.
27 Either because you don’t have access to the technology, you don’t use it, or because you are
reading this in a future in which twitter is no longer popular.
28 James Gleick, The Information
To understand the information content that is contained in a tweet,
consider two hypothetical twitter users: Abby and Brian. Both Abby and Brian
have a book that contains every possible tweet and are using this book to play
the “guess game”. In this game, Abby randomly chooses a tweet from her book
and asks Brian to guess it using only yes or no questions. According to Shannon,
the amount of information that is embodied in a tweet is equal to the number of
yes or no questions that Brian needs to ask to guess Abby’s tweet with 100%
accuracy29. But how many questions is that?
For simplicity, we will assume that Abby and Brian are using a set of 32
characters and that both know this. You can think that they are using the English
alphabet in lowercase plus a few extra characters, such as the space ( ), the
colon (:), the slash (/), the comma (,), the period (.), the at (@) and the hash (#).
Also, this time without any loss of generality, we will assume that Brian and Abby
both have a table that maps each character to a number (a=1, b=2, etc…).
A sure way for Brian to guess Abby’s tweet is to guess each character,
and the best way to search for each character is to use each question to cut the
number of possible characters in half. If Brian decides to guess the tweet by
guessing each character, then his first yes or no question should be: “Is the first
character larger than 16?” If Abby answer’s no, then Brian will know that the first
character on Abby’s tweet is in the first fifteen rows of his character table. By
asking that question Brian reduced the number of possible first characters in
Abby’s tweet by half. His second question does the same for the possible
characters that remain, and it is: “Is the first character larger than 8?” If Abby
This is the simplest possible case we can use to illustrate Shannon’s theory, since it assumes
all tweets and characters are equally likely. In reality, all characters and strings of characters are
not equally likely. It is much more likely for a tweet to contain the sequence of characters “http://”
than the sequence of characters “qwzykq”. If Brian knows about these differences he could
exploit them to reduce the number of questions he needs to ask in order to guess the tweet. If
you are uncomfortable with these simplifying assumptions, assume that Abby and Brian come
from different planets, and that the only thing that Brian knows about Abby’s alphabet is that it is
based on 32 different characters.
29
says yes, Brian will now that the first character on Abby’s tweet is between
character 9 and 16 of his character table. Now, you should be able to guess what
Brian’s next question will be? This is “Is the first character larger than 12?”
As you can see, with each question Brian is cutting the number of possible
characters in half. After five question Brian should always be able to guess a
character, since there are 32 possible characters and we need to divide 32 by 2
five times in order to cut down the set of options to just one. Finally, since there
are 140 characters in a tweet, Brian will need 140x5 guesses, which is a total of
700 yes or no questions, or bits, to uniquely identify Abby’s tweet 30.
Shannon’s information theory is the basis of modern communication
systems. By quantifying the information content of messages Shannon helped
develop the technologies needed to encode and decode messages, and hence,
create digital communication technologies. So in a profound way we can say that
the ghost of Shannon lives in every tweet, email and computer file, since all of
these make use of a theory that evolved in his brain 31 . But as we will see,
Shannon’s theory can also help us understand the amount of information that is
embodied in a product.
Shannon’s theory tells us that information is related to search, since the
amount of information that is embodied in Abby’s tweet is equal to the number of
yes or no questions that Brian needs to ask in order to search for it in a list
containing all possible tweets32. But how many yes or no questions do we need
to identify a Bugatti?
30
Notice that this 700 number was the one that was sitting on top of the 2 700, which is the total
number of possible tweets. The general formula in this case is N log2(S), where N is the number
of characters and S is the size of the alphabet. This is equivalent to log2(SN) where SN is the total
number of possible tweets. In general, notice that the information content of a message goes as
the base two logarithm of the number of possible messages. This is because the most efficient
way to search for a message, or uniquely identify it, is to iteratively cut the search space in half.
31 Not denying the contributions of his contemporaries such as Warren Weaver, Alan Turing and
Norbert Wiener.
32 Note that the number is arrived by assuming an optimal search strategy that assumes no
information about the possible tweet or the regularities of the languages used to write it. Brian
The case of the Bugatti is not as simple as that of a tweet. After all, it
involves positioning gazillions of atoms and not just 140 characters. Also, in the
case of the Bugatti, we are not searching for any possible configuration of atoms,
but for those that produce something that is like a Bugatti, or at least similar
enough for us to be unable to tell the difference. Unlike the case of twitter, where
we consider all tweets to be equivalent, the case of the Bugatti is one in which
we consider groups of configurations that are similar. For example, one group is
the one containing all configurations that are equivalent to a Bugatti’s wreck, no
matter whether the wreck resulted from crashing the Bugatti into a wall or driving
it down a cliff. Another group contains all configurations that are equivalent to
what we would call a Bugatti in perfect condition. This group includes
configurations in which the tires have been rotated or where the windshield
wipers have been exchanged.
By creating groups we are rephrasing our problem, from the information
required to identify a unique element of a set to the information required to
identify subsets of configurations that are equivalent according to a criterion. As
Shannon famously said “The fundamental problem of communication is that of
reproducing at one point either exactly or approximately a message selected at
another point”. Making a distinction between unique elements and sets of
elements is important because it helps us differentiate between the information
needed to transmit a message with content or to transmit gibberish. Technically
speaking, an image in which the color of each pixel is chosen at random is
uncompressible, and hence, requires more information to be transmitted than the
image of a face or a landscape. Yet, if we consider all such random images to be
could have tried to guess the tweet by asking less informative yes or no questions, such as: “is
the tweet: Why Washington politics are as successful as Washington sports teams?” Yet a search
strategy based on guessing fully formed tweets is extremely inefficient, since instead of cutting
the search space in half with every question, it will only by eliminating one of the 2700 possible
tweets. On the other hand, if Brian knows that the tweet is not gibberish, and it is written in
English, he could design strategies to guess the tweet in less than 700 questions, since the
language contains correlation that make the next letter non-uniformly distributed once the
previous letters are revealed.
equivalent, the information needed to transmit them becomes tiny. In fact, we can
transmit a random image from an arbitrary size easily using less information than
that needed to write one tweet 33 . Ultimately, these equivalences tell us two
things. The first one is that when we talk about information we are not looking to
exactly specify a message or object, but to specify it with enough detail to identify
a message or object that is equivalent to the one we had in mind. The second
one is that much of what we interpret as information is not the raw counts of bits
needed to transmit a message, but the correlations that exist within a message or
an object, which technically can reduce the amount of bits needed to transmit it.
These are the correlations that make music predictable enough to dance to it, or
that make the picture of a landscape seem smooth and harmonious, and quite
different from a collection of random pixels. Hopefully, the discovery of these
correlations within this text motivates you to keep on reading this book.
So let’s use these last insights to get back to the Bugatti example. To
quantify the amount of information that is embodied in the Bugatti assume you
are now in a game show where the Bugatti is hiding behind a mystery door, but
where you don’t know if it is in perfect condition or not. The game lets you ask
yes or no questions about the position of each molecule in the Bugatti’s body, but
not questions such as “Is the Bugatti a wreck?” These are cumbersome
questions such as: “Is the molecule in position (1.3545422334, 3.756545121) a
rubber molecule?” but for our though experiment they will have to do. In this
game the amount of information that is physically embodied in the Bugatti is the
number of yes or no questions that you need to identify whether the Bugatti is in
perfect condition or not. Now, it should be perfectly clear that the number of yes
or no questions needed to make sure that the Bugatti is not in perfect condition
is much smaller than the number of yes or no questions needed to make sure the
car is in perfect condition. This should be clear because there are many ways for
the Bugatti to be a wreck. After all, you don’t know if the Bugatti was wrecked
33
In pseudo-code, we can write an expression encoding an image of one million times a million
pixels as: for x=1:1,000,000; for y=1:1,000,000, Image(x,y)=random_number; end; end.
from the front, or the back; or whether it has a small boo-boo caused by the
opening of a door in a parking garage34. So to make sure the car is in pristine
condition you will need to ask enough questions to map out the Bugatti in full
detail. Since we need to answer many more yes or no questions to identify a
Bugatti in pristine condition, than a wreck, the moral of the story is that a Bugatti
in perfect condition carries more information than a Bugatti wreck, and that
information is destroyed in a car crash. This tells us that although the Bugatti is
made of many atoms, what distinguishes it from a wreck is information. And
hence, we can say the Bugatti is made of embodied information, much like
everything else.
Shannon’s theory helps us quantify the amount of information that is
embodied in a tweet or in a Buggati. Taking Shannon to the extreme we can say
something like: “a Bugatti is made of ~1027 atoms and one terabyte of
information, while a Bugatti wreckage is made of the same number of atoms but
only a few hundred megabytes of information.”35 Yet, there are some important
questions that Shannon’s theory leaves unanswered, at least when it comes to
Bugattis. One of these questions is: what are the relevant groups that we need to
consider when searching for the arrangement of atoms that we call products?
After all, grouping Bugatti’s with rotated tires in one group and grouping
wreckages in another group makes perfect sense to us, not because I have
explained it, but because we—humans—have a great sense of intuition. So to
develop a deeper understanding of the information that is contained in a product
we need to ask the question: how do we define the groups of arrangements of
atoms that are relevant as products? As you will see, by defining these groups
we will begin to bring back the idea of meaning into our definition of information.
34
A scratched door is not equivalent to a wreck, but is also not equivalent to a car in absolutely
perfect condition. So the number of yes or no questions you would need to ask to check whether
the car is in perfect condition would need to include making sure that the car does not have any
scratches.
35 Don’t quote me on these numbers.
Grouping Bugattis with rotated tires on one group, and wreckages on
another, made perfect sense to us because we intuitively know that the members
of each of these groups can perform different functions. A wrecked Bugatti and a
pristine Bugatti mean something different to us because these are groups of
atoms that we associate with different functions. So we will hijack the word
meaning to indicate configurations that convey the same context specific
information to the recipient. In the case of twitter, this will group in the same
category the tweets “Baby I love you?” and “I love you baby”, since a recipient of
either of these tweets would identify them as the same. Hence, both of these
tweets would be performing the same function36, telling your baby that you love
her.
The association between the information embodied in a digital or tangible
object, and the functions associated with it can take some time to comprehend,
so I will a second example. Consider a library. In a library we can order books by
title, topic, publication year, size or language. Each of these orders contains
information, but the information embodied in each order facilitates different
functions. In the case of the library these are search functions. For instance,
ordering books by topic and publication year can help us quickly identify the
earliest books on quantum mechanics, while ordering the books by the last name
of their authors can help us quickly find all of the works of Mark Twain. The latter
is true whether we order books in alphabetical order or in reverse alphabetical
order. This tells us that there is a correspondence between alphabetical order
and reverse alphabetical order that makes both of these orders equivalent, at
least with respect to the search function they help perform. So going forward, we
define the information content of a product, not merely as the information that is
embodied in the way in which its atoms are arranged, but as the information
embodied in any of the configurations of atoms that are able to perform a given
function. This is true whether this is the search function that helps us find a book
36 What it means for something to be useful is a philosophically difficult question that I am
avoiding to discuss here. I will touch upon this topic in the next chapter.
in a library, or the transportation function that allows us to ride a group of atoms
down the road.
The case of the Bugatti is a bit more nuanced that the one of the library
because the set of functions that people expect from a vehicle are larger and
more complex than the ones that people expect from a library catalog. They are
also, much more social. In the case of the Bugatti, you can think that its Chilean
owner did not have only transportation in mind, but also was hoping to look like a
douche while cruising down the streets of Santiago37.
So the Bugatti example teaches us that physical order, or information, is
partly what makes the Bugatti comparable to silver and gold. It also tells us that
each good does not only have information, but a “meaning”, which is represented
by the practical and social functions that the good helps us perform. Yet,
functions are not the only way to differentiate between alternative configurations
of atoms. We can also differentiate between different configurations of atoms by
looking at the amount of effort, or energy that is required to construct each of
them38.
To get a hold on the differences in the amount of information that is
embodied in a product, and it’s relation to the energy needed to create a product,
consider a do-it-yourself bookcase and a do-it-yourself car. Certainly, most
people are fine assembling their own IKEA furniture, at least after pulling out a
handful of hair or two. Most people, however, would stay away from buying a car
from the Internet if this was shipped dissembled in a box with a set of
instructions. This is because finishing cars requires embodying more information
37
Although not quite a Bugatti, a BMW can perform a similar function at a more modest price.
Some orders are not only harder to create, but also more delicate. Consider the order required
to make the Bugatti run. This is an order that can be disrupted by a broken transmission. A
broken transmission, however, will not disrupt the recycling process, so we can say that the order
required to make a car go is more delicate than the order required to prepare the parts of the
same car for recycling. The orders that are more delicate are, in general, orders that require more
information, since the fact that they can be disturbed by small changes means that the number of
equivalent configurations that pertain to the same group as them is small.
38
than bookcases, and this tells us that the information that is embodied in a car
requires a greater effort to be embodied than the information that is embodied in
a bookcase. It is important to note, however, that information and effort are not
perfectly equivalent. We need more effort to assemble one thousand bookcases
than a single bookcase, but a thousand bookcases do not carry more information
than a single bookcase, since the last 999 bookcases are redundant with the first
one.
We began this chapter by wrecking an imaginary Bugatti to illustrate that
products are not made of atoms, but information. This is the information that is
contained in the way in which the atoms that make a product are arranged. The
Bugatti example is tangible, and it gives us a tactile experience. Yet, what is true
for the Bugatti is also true for digital products, whether these are as simple as a
tweet or as sophisticated as a Shakespeare play. In the case of a tweet, or a
Shakespeare play, we might fail to see the physicality of the information, but
information is always physically embodied. If that tweet is stored in your harddrive, its physicality is embodied in the spins of the electrons that represent each
of its 700 bits. If the tweet is being transmitted through Wi-Fi, its physicality is
embodied in the electromagnetic waves that have been modulated to transmit
the message. Information, whether tangible or digital, is always physically
embodied. In fact, talking about physically embodied information is redundant,
since there is no such thing as information that is not physically embodied. Yet,
information is weightless and immaterial. It exists in a magical duality with matter
that leads people to sometimes believe information is not physical. My favorite
example to explain this duality is to consider a deck of cards. Every time we
shuffle a deck of cards we are changing the information that is contained in it, but
not its weight. Information is not a substance, yet it cannot exist divorced from
matter. The subtlety of this duality is often elusive, so I will use the redundant
phrasing “physically embodied information” often throughout the text, even
though saying: “physically embodied” is technically redundant when talking about
information.
Going back to products we find no difference in physicality between
tangible products, like a Bugatti, and intangible products, like a Shakespeare
play. Both types of products exit as physically embodied information. Yet, digital
products differ from tangible products in the ease with which we can reproduce,
amplify and create them. There is a great difference between our nascent digital
world, which is being built on methods that help us quickly embody information in
electrons and photons, and the world where we could only embody information in
tangible macroscopic products, by bluing molecules and atoms. Whispering
dance moves to photons or rearranging electrons in a circuit is a more flexible,
energy efficient and quicker way of embodying information than rearranging
atoms, even though it has its own limitations39. This difference might grow to be
as large as that between the world of modern humans and that of our distant
evolutionary cousins. Yet, before we get ahead of ourselves and get sucked into
the rabbit hole of the futures opened by modern information technologies, we will
continue to explore some general aspects of the information that is physically
embodied into tangible and digital products. The goal we are trying to achieve is
to develop a description of the process of economic development that is based
on our species ability to accumulate physically embodied information. Shannon’s
theory brings us a long way, but there is certainly more to a product than the
information that is embodied in the way in which its atoms are arranged or the
functions that it can perform. Think of the information that is embodied in
medicine. It is hard to argue that the information that is embodied in a pill can be
reduced to that which is contained in its tiny active chemical component. This
invites us to explore other aspects of the information that is embodied in a
product. The first one of these aspects is the origins of the information embodied
in them. The second one is the ability of the information that is embodied in
products to amplify the availability of the practical uses of the knowledge that was
required to make them. So here is where we will go next. The next stop in our
journey is an exploration of the origins of the information that is embodied in a
39
Virtual houses do not protect us from the rain.
product. This will help us understand what’s so special about the apples that do
not grow on trees.
Chapter III: The difference between apples and apples
“That’s all the motorcycle is, a system of concepts worked out in steel. There’s no part in it, no
shape in it, that is not out of someone’s mind”
Robert M. Pirsig (1974)40
“I paint objects as I think them, not as I see them.”
Pablo Picasso
Consider two types of apples. Those that you buy at the supermarket, and grow
on trees, and those that you buy at the Apple store, and are designed in Silicon
Valley. Both are traded in the economy, and both crystalize order, whether in
silicon chips or biological cells. The main difference between them is not their
number of parts, or their ability to perform functions—edible apples are the result
of tens of thousands of genes that perform sophisticated biochemical functions.
The main difference between apples and apples, is that the apples we eat
existed first in the world, and then in our heads, while the apples we use to check
our email existed first in someone’s head and then in the world. Both of these
apples are products, but only one of them—the silicon apple—is a crystal of
imagination41.
Thinking about products as crystals of imagination is important because it
highlights that products do not differ only on the information that they embody,
40
Zen and the art of motorcycle maintenance (page 174)
Why do I choose a crystal as a metaphor? In my opinion a crystal is the right metaphor
because it is an ordered arrangement of atoms that is static. When we create products, we create
tangible and digital objects that contain a frozen instantiation of a process that is much more fluid
and dynamic: imagination. Once a car is built, it becomes the 2013 model, and it is basically
frozen until the next model comes out. The same will be true for this book. Revisions to later
editions—if any—will be unable to change the information that was physically embodied in the
first edition. In that sense, the products that we create are crystals of imagination; they are static
instantiations of our ideas.
41
but on the source of that information. Edible apples existed before we had a
name for them, a price for them, or a market for them. They were present in the
world, and as a concept, we simply imported them into our minds. On the other
hand, iPhones and iPads are mental “exports” rather than “imports”, since they
are products that were begot in the mind before they were distributed throughout
the world. So the main difference between apples and apples does not reside on
the existence of physical order, but on the source of their physical order.
Thinking about the world in terms of crystallized imagination is poetic, but also
useful, since it provides a different way of parsing out the diversity of products
that make the economy and provide us with an alternative perspective from
which to understand important economic processes. Consider international trade.
When we think of products as crystals of imagination global trade becomes
nothing more than a global exchange of physically embodied ideas. The idea of
crystallized imagination tells us that a country’s export structure carries
information about more than just their abundance of capital and labor. Countries’
export structures tell us about the ability of people in that country to create
tangible instantiations of imaginary objects, such as cars, espresso machines
and motorcycles. In fact, the composition of a country’s exports informs us about
the productive knowledge available in that country. A country that exports
motorcycles is country shouting: If you imagine a motorcycle, we can figure out a
way to build it 42 . Countries that are able to create what people imagine are
countries that can mine the depths of human ingenuity in search for new
products, and as we will see, this is a capacity that is highly industry specific,
hard to create, and that evolves and diffuses slowly.
Thinking of product exports in terms of crystallized imagination tells us that we
live in a world in which some countries are net importers of imagination, while
others are net exporters of it, and that these countries are not the same than
42
Certainly, firms rather than countries are the ones that export. But since the export basket of a
country is the combination of that of many firms, here I will discuss exports using countries for
simplicity.
those with a positive or negative trade balance. For example, consider the export
of a BMW. This Bavarian vehicle is clearly an export of imagination, since BMWs
crystallize ideas of German design and engineering that are hardly embodied in
Ecuadorian bananas. The balance of trade between two countries—monetary
value of exports minus imports—is not always the same as their imagination
balance. Saudi Arabia and Russia both have a positive balance of trade, due
mostly to large reserves of mineral resources, but negative imagination balance,
since their export economies are based mostly on exchanging oil and natural gas
for luxury SUVs and sports cars.
Indeed, there are many pairs of countries with balances of trade that run opposite
to their balances of imagination. Consider Chile and Korea. The exports of Chile
to Korea in 2010 amounted to roughly 4.3 billion dollars, with refined and
unrefined copper representing 52% of this amount43. The exports from Korea to
Chile during that year were only about 3.3 billion dollars, but these included
almost a billion and a half dollars in vehicles and vehicle parts 44. Chile’s trade
balance with Korea is clearly positive, by as much as one billion dollars, but
Chile’s imagination balance with Korea is clearly negative, when we consider the
nature of the goods exchanged.
43
44
http://atlas.media.mit.edu/explore/tree_map/export/chl/kor/show/2010/
http://atlas.media.mit.edu/explore/tree_map/export/kor/chl/show/2010/
Exports from Chile to Korea in 2010 (from atlas.media.mit.edu)
Exports from Korea to Chile in 2010 (from atlas.media.mit.edu)
Another example is Brazil and China. In 2010 Brazil exported nearly USD 31
billion to China, and imported only USD 26.5 billion. Brazil is one of the few
countries that enjoy a positive balance of trade with China (Chile is another). Yet,
Brazil has a negative imagination balance with the largest Asian economy, since
its trade involves mostly the exchange of iron ore and soybeans for electronics,
chemicals and even processed metals.
Exports from Brazil to China in 2010 (from atlas.media.mit.edu)
Exports from China to Brazil in 2010 (from atlas.media.mit.edu)
So classic economic concepts, such as the balance of trade between two
countries, seem incomplete once we reinterpret products as crystals of
imagination. Yet, there are other examples of economic ideas that need to be
revisited after realizing that the source of a product’s information might be of
economic relevance. One of these is the way in which we classify industries and
products
45
, which are essential groupings we use to create mental
representations of the economy 46 , and hence, represent an essential building
block of the language we use to describe economic processes.
45
To be clear, the difference between an industry, and a product, is the difference between the
makers of a product and the product. For instance, a shoe is a product that is made by the
footwear industry.
46 These groupings are not equivalent to those discussed in chapter 2—the ones we used to
explain the configurations that are equivalent in the case of the Bugatti.
Classifying products and industries is essential to connect theoretical and
empirical representations of the economy. Yet, finding classifications that work in
both theory and practice is not easy because the empirical world is characterized
by a diversity of products that is hard to categorize and classify. Products are
quirky. They include pineapples, trashcans, flowerpots, bicycle racks, chimneys
and ATM machines, among many others. Yet theories are constructed on
numbers and concept that have trouble with this quirkiness, and hence, are not
good at generating representations of products such as pineapples or
rollercoasters. The problem is that to connect our theories with our data we need
to represent both data and theories in the same language, and usually this
requires us translating the language of one into that of the other. During the last
centuries the usual compromise has been not to create a theory that includes
pineapples, but to bundle pineapples with other goods in a coarse classification,
such as agriculture. This coarsening pushes as to talk about industries and
products in terms of raw materials, agriculture, services and manufactures, or in
terms of capital-intensive industries or labor-intensive industries. Yet, this
coarsening might not be the best way to parse the complexity of our world.
Consider industries traditionally classified as services, such as movies, music or
video games. These are industries that crystallize the imagination of their
creators, just like cars, guitars and video cameras, which would be considered
manufactures, not services. From the perspective of crystallized imagination,
however, a video game studio is conceptually closer to a guitar manufacturer
than to a retailer, since the main difference between a video game and a guitar is
that video game designers crystallize their imagination in bits, while guitar
manufacturers do so in atoms. A video game studio is not an industry that
provides a service, like serving coffee or providing lodging, but an industry that
takes ideas and embodies them in a sharable physical form.
The distinction between services that serve, and services that manufacture using
bits, is important in a world where people often associate “service” industries with
higher levels of development, when in reality, services are a mixed bag. Think of
the 21st century United States. The big gaps in income in the US are mostly gaps
between the services that serve, or administrate, and those that crystallize
imagination 47 . Software manufacturers who concoct computer code to create
new digital products are paid excellent salaries and are driving the technology
boom of San Francisco, Boston and New York. At the same time, fast food
workers, who also participate in the “service” sector, are struggling to make ends
meet. Our traditional definition of services is a mixed bag—a bag that instead of
mixing apples and oranges is mixing Silicon Valley engineers working on
complex algorithms, with fast food employees, working on the concoction of a
priori specified sandwiches. Talking about “services” is not longer an appropriate
use of language in a world in which the occupations that fall into the service
worker category have little to no relation48. Certainly, talking about products and
services is not the best way to parse out economic activities. It is just a
convenient language we have grown used to.
A better way of parsing the economy is to think of economic activities in terms of
the information that they embody. When we consider the origins of that
information, we will be talking about the imagination that an industry crystallizes
or its relation to other industries that crystalize of imagination. Certainly, not all
economic activities are involved in crystallizing imagination directly, since crystals
of imagination need to be transported, financed and marketed, and these are
processes that do not crystallize a much imagination. In fact, a large number of
economic activities do not focus on embodying information in tangible or digital
products, but focus on chaperoning the flow of embodied information. The
47
San Francisco split by Silicon Valley's wealth http://www.latimes.com/business/la-fi-siliconvalley-backlash-20130814,0,7114762.story
48 Certainly, there are more nuances in the academic literature than in the colloquial use of the
word services that I describe here. For instance, it is common in some circles to talk about
knowledge intensive business services (KIBS). I note, however, that my distinction does not focus
on the knowledge that is required as an input to a service activity, but on whether these activities
result in the embodiment of that knowledge into a crystal of imagination.
existence of these chaperoning activities, however, does not contradict the fact
that the economy is made of information, since all of these activities orbit around
our ability to crystallize imagination and would not exist in its absence. There
would be no economy in a world in which crystals of imagination do not exist,
since there would be nothing worth transporting, trading or financing. Sure, we
can think of an economy in which hominids just trade fruits, but this would be
only hypothetical, since our civilization has been built for more than eightythousand years in the gradual exchange of objects that were begot by our
minds49.
We can illustrate the centrality of the process of crystallizing imagination in the
economy by looking at the paths connecting each economic activity to a crystal
of imagination. Consider the retail industry. According to the National Retail
Federation (NRF), retail represents roughly 8% of the GDP of the United
States 50 . Yet, retail depends critically on crystallized imagination since there
would be no retail in the world if it weren’t for the clothes, cars, and furniture that
are transacted in shops. So retail is an activity that is derivative of our species
ability to crystallize imagination.
Another example of an activity that is derivative of our species ability to
crystallize imagination is mineral extraction. Mining is not a service, yet it has a
purpose only in a world where people use the atoms we harvest from the ground
to crystallize imagination, no matter whether these are the lithium atoms needed
to make rechargeable batteries or the oil used to transport these atoms to the
centers of “crystallization”. The financial sector, on the other hand, is a sector
allegedly involved in allocating the financial resources needed to help prioritize
productive processes. While we may doubt this claim, we do not need to enter
that discussion to realize that the financial sector helps lubricate the transactions
of some crystals of imagination. For instance, the financial sector provides the
49
50
Although subsets of the economy can make a living that way
http://www.nrf.com/modules.php?name=Pages&sp_id=1214
mortgages required for homes—which are crystals of the imagination of
architects and constructors—to change hands. Finally, consider the transport,
logistics and communication sectors. These are sectors involved actively in the
movement of crystals of imagination, or the atoms and bits required to make
them. In fact, once we interpret the economy in terms of crystallized imagination
the analogy between the Internet and the US highway system becomes even
more obvious. Both, the Internet and the highway system help the crystals of
imagination created by some to reach others51, and hence, are related to crystals
of imagination in an analogous manner: helping the crystals of imagination made
by some reach others.
In sum, crystallized imagination is a simple way to conceptualize the
informational soul of the world economy. The economy gravitates around our
species ability to transform imaginary objects into a tangible or digital reality.
Even though the embodying of information is not necessarily the activity that
collects the major financial rewards52, all economic activities are connected either
directly or indirectly to this unique human capacity.
Finally, thinking about products in terms of crystals of imagination helps us
understand the importance of the source of the information that is embodied in a
product. Now we know that the information that is contained in products was born
in the minds of the hairless apes that can create what they imagine. Complex
products are not just arrangements of atoms that perform functions, but ordered
arrangements of atoms that were originated as virtual ideas. It is therefore the
origin of the information embodied in products what helps us resolve the paradox
51
As an example, we note that during 2012 Netflix and YouTube accounted for nearly 50% 51 of
all Internet traffic in the US. We note that there is an imperfect match between the bits involved in
digital content and their online traffic due to services that help buffer content, such as the services
provided by Akamai. These services can reduce Internet traffic without reducing the amount of
content being distributed.
52 The reader should not that it is wrong to equate the activities that generate individual financial
rewards, with those that generate economic value. Often, the greatest financial rewards are not
for those who create new crystals of imagination, but for those who control their trade or bet on
others through financing.
of the pill that I posed at the end of last chapter. The mental origins of the
information embodied in products tell us that there might be important additions
to the information that is embodied in physical order that rides implicitly in
products. Hence, there is more information in a pill than the one crystallized in
the structure of its tiny active chemical component. This additional information is
more “meaningful” and less mechanical, in the sense that it is context dependent.
It is information about the effects that the chemical compound will have in the
human body, and on the mechanisms used to validate that information. This is
information that we do care about when we buy a pill, but that it is not encoded in
its active compound.
For the time being, however, we will conclude by asking: Why do hairless apes
bother to make tangible instantiations of their imagination? Why do we put so
much effort to create complex products? As we will see, it cannot be just
because we are able to do so, but also it cannot be because of either greed or
self-interest 53 , as Gordon Gecko moronically suggested. After all, crocodiles,
zebras and all the wild animals are not limited by a lack of greed or self-interest,
but are nevertheless unable to crystallize imagination as we do. So now that we
53
The view of the world in which humans act to maximize utility is logically unsound when
combined with its own empirical validation—the idea of revealed preferences. In simple terms, it
is easy to understand the circularity of the argument by considering separately the theory—utility
maximization—and its empirical validation—individual choices reflect individual preferences. If we
consider the idea that individuals maximize utility to be a hypothesis, then to test it, we need a
test in which one of the possible outcomes is to observe that individuals do not maximize utility.
Revealed preferences is not that test, since it assumes that the actions taken by an individual are
always aligned with the choice that maximizes her preference, and hence, is a test that by
construction cannot result on an individual making a choice that does not maximize their utility.
So together, the ideas of utility maximization and revealed preferences cannot be considered a
proof of individuals acting on self-interest, or of anything else for that matters. Francis Fukuyama
points this out as well in his book Trust (chapter 1, page 19). When referring to utility
maximization, and the attitude of economists to this idea he writes: “Some economists try to get
around this problem by broadening the definition of utility beyond pleasure of money to take
account of other motivations such as the “psychic pleasure” one receives for “doing the right
thing,” or the pleasure people can take in other people’s consumption. Economists assert that
one can know what is useful by their choices—hence their concept “revealed preference.” The
abolitionist dying to end slavery and the investment banker speculating on interest rates are both
said to be pursuing “utility,” the only difference being that the abolitionist’s utility is of a psychic
sort. At its most extreme, “utility” becomes a purely formal concept used to describe whatever
ends or preferences people pursue. But this type of formal definition of utility reduces the
fundamental premise of economics to an assertion that people maximize whatever it is they
choose to maximize, a tautology that robs the model of any interest or explanatory power.”
have a better definition of what is the information that is embodied in products,
we will continue our journey by exploring the reasons why we make products.
The next section will continue to explore what hairless apes have to gain through
their tireless commitment to transform dreams into reality.
Chapter IV: Knowledge Amplifiers
“Any sufficiently advanced technology is indistinguishable from magic.”
Arthur C. Clarke (1962)54
“We don’t make most of the food we eat, we don’t grow it, anyway. We wear clothes other people
make, we speak a language other people developed, we use a mathematics other people
evolved and spent their lives building. I mean we’re constantly taking things. It’s a wonderful
ecstatic feeling to create something and put it into the pool of human experience and knowledge.”
Steve Jobs, 198355
In my talks, I often ask the attendees to raise their hands if they have used
toothpaste that morning. I find this to be a good way to get audience participation
since the embarrassment of not having used toothpaste encourages even the
shyest attendee to raise her hand. After almost everyone has raised their hands,
and some people have giggled, I ask audience members to keep their hands up
only if they know how to synthesize sodium fluoride. As you can anticipate, all
hands go down. This shows that products do not only give us access to
embodied information, but also, to the practical uses of the knowledge that is
required to make them. That is, they give us access to the practical uses of
knowledge residing in the nervous systems of other people, and that is amplified
by our ability to crystallize imagination.
In this chapter I will discuss the practical applications of our ability to crystallize
imagination. I will focus on four aspects of products. First, I will discuss the ability
54 Profiles of the Future: An Inquiry Into The Limits of the Possible (1962; revised 1973)
55
http://bits.blogs.nytimes.com/2014/01/24/the-30-year-old-macintosh-and-a-lost-conversationwith-steve-jobs/?_php=true&_type=blogs&_r=0
of products to distribute the practical uses of the knowledge used in their
production. Second, I will explore the role of products as a mean of creative
expression. Third, I will describe products as a source of human augmentation.
And finally, I will describe the importance of products to enable combinatorial
creativity. Together these four abilities will help us understand the benefits of
crystallizing imagination, and therefore, will help explain our want for crystals of
imagination. By exploring the practical uses of products we will also learn that
products are not just deposits of information, but also, that they represent a
unique form of human communication56. Products are unique in their ability to
communicate, because unlike messages, they are not shared to be understood,
but to be utilized. This utilization does not require much understanding. We do
not need to know how a car or a computer works to reap their practical benefits.
The same is true for soap. Finally, we will build on these ideas to refine our
definition of the economy. In this last section, we will move our gaze away from
definitions of the economy that focus on the allocation and distribution of
resources, and instead, will focus on the ability of the economy to amplify the
practical uses of knowledge and information.
Going back to our toothpaste example we can note that when we are buying
toothpaste we are not simply buying paste in a tube. Instead, we are buying
access to the practical uses of three things: the creativity of the person who
invented toothpaste, the scientific knowledge informing the chemical synthesis
that is required to make toothpaste, and the productive knowledge required to
synthesize sodium fluoride, put it inside a tube, and make it available across the
planet. Something as simple as toothpaste gives us indirect access to the
practical uses of the imagination and knowledge that exist, or existed, in the
nervous system of people we probably never met.
Which echoes Marshall McLuhan definition of medium as used in his famous quote: “The
Medium is the message” (McLuhan, Understanding Media, The extension of man). McLuhan
defined medium as “any technology that ... creates extensions of the human body and senses”
56
The ability of toothpaste to provide us with access to the practical uses of
knowledge residing in a stranger’s nervous system is quite magical. Yet the
magic of toothpaste, much like that of any product, does not reside solely on its
ability to gives us access to the practical uses of knowledge residing in the
nervous system of others. Products are magical also because they endow us
with capacities that escape our individuals’ abilities. Products augment us, and
this is a great reason to want them.
Think of a guitar. Guitars allow us to sing with our hands by combining
knowledge on Pythagoras’ twelve-tone scale with expertise on what is the right
wood to build a guitar and how to shape it. If the guitar is electric, it will also
embody knowledge of how musical waves can be captured using capsules, and
how these sounds can be amplified into the sounds that many of us enjoy. All of
these are capacities that are needed to make music, at least the kind of music
that requires an electric guitar, but that do not need to be capacities of the
musician. The musician access the practical uses of this knowledge through the
guitar, and by doing so, he is augmented in his capacities as a musician.
Products are magical largely because they augment our capacities. Planes
endow us with the ability to fly, ovens with the ability to cook, and toothpaste with
the ability to keep our teeth until an older age.
So a good reason of why humans desire products is because products augment
our capacities by providing us with access to knowledge that resides in the
nervous system of other people. Yet, our need to create complex products does
not emerge only from their ability to embody knowledge or augment us. There is
an expressive component in the creation of products that we also need to
consider. We crystallize imagination because this allows us to transform our
ideas into a sharable reality. By default, thoughts are trapped in the prison of our
minds and crystallizing our thoughts into products is what allows us to share
them with others. A musician records her music, as a way to perfect her art, but
also, as a way of creating copies that can be shared with others. Without these
copies her talents would be trapped in her body, much like those of the chef that
does not cook, the painter that does not paint, or the writer that does not write 57.
Crystallizing imagination is what allows us to make copies of our thoughts and
share them with others, and that makes crystallizing imagination the essence of
creative expressions.
But does this mean that products are simply a form of communication? Not quite.
Our ability to crystallize imagination into products, although communicative, is
different from other forms of communication. In particular, it is essentially
different from our ability to verbally articulate ideas since products can augment
our capacities in ways that narratives can’t. Talking about toothpaste does not
help you clean your teeth, just like talking about the chemistry of gasoline will not
fill up your car with gas. It is the physical embodiment of the knowledge of how to
synthesize sodium fluoride, or refine gasoline out of oil that exists in the product
what is needed to share the practical uses of the knowledge that was used in
their creation. Without this physical embodiment the practical uses cannot be
transmitted. Crystallizing imagination is therefore, essential for sharing the
practical uses of the knowledge that we accumulate in our minds. Without our
ability to crystallize imagination, the practical uses of knowledge would not exist,
because that practicality does not reside solely on the idea, but hinges on the
tangibility of the implementation. Once again, the physicality of products—
whether tangible or digital—augments us. And it is in this augmentation that
products help us “communicate” something that words cannot: the practical uses
of knowledge.
Emphasizing the ability of products to augment human capacities can help us
refine what we understand as the economy. The ability of products to augment
our capacities helps us see the economy not as the careful management of
resources, the wealth of a nation, or the network of financial transactions that
57
Certainly, the talents will also be underdeveloped.
lead us to booms and turmoil; but as a system that amplifies the practical uses of
knowledge by the physical embodiment of information. This is an interpretation of
the economy as a knowledge amplifier, or knowledge amplification engine: a
complex socio-technical system able to produce physical packages containing
the information needed to augment the humans that participate in it58.
Emphasizing the ability of products to augment human capacities can also help
us refine our understanding of wealth. The augmentation that is provided by our
ability to pack the practical uses of knowledge as information is what allows
people to live at comfort levels that are much larger than what they would be able
to sustain in isolation. This provides an important connection between the
comforts that we associate with wealth and our species ability to augment its
capacities. Without the ability of the economy to amplify knowledge and
imagination, our lives would be no different from those of other animals, or that of
a castaway on a deserted island. Our ability to crystallize imagination teaches us
an important lesson about the complexity of economies: markets do not make us
richer, but wiser, since they produce wealth as long as they give us indirect
access to the practical uses of the knowledge and imagination that our species
has been able to accumulate.
To illustrate the knowledge amplification powers of the economy consider
Michael Faraday. Faraday was a 19th century physicist that among other things,
develop the laws of induction that are central to the generation of electricity. Yet
Faraday also got his hands dirty and crystallized his ideas by embodying them in
practical objects. Faraday is credited with the invention of the electric motor that
was later perfected by Tesla59. So when we blow our hair, vacuum our floors, or
make a daiquiri in a blender, we are receiving a favor by non-other than Michael
58
This echoes ideas from Jane Jacobs. When Jane Jacobs was asked about the importance of
greed and self-interest in the economy she remarked: “You are leaving out the most important
things about economies. You can’t have greed unless there is something to be greedy about.“
59 Which Nikola Tesla perfected later.
Faraday, someone who we, our parents, or even our grandparents are unlikely to
have met.
The economy is the system that amplified the practical uses of the knowledge
developed and accumulated in Faraday’s brain—and inspired in part by Ada
Lovelace60. Faraday’s ghost, therefore, lives in all electrical products, together
with that of Tesla, Edison, Maxwell and many other great scientists that we know
only through their work. Ultimately, the world of products is more social than what
we would naively imagine, and in a deep metaphorical sense, it is a world that is
populated densely by ghosts.
So our ability to crystallize imagination benefits us for three main reasons. First, it
helps us create a society of “phony geniuses”, a society in which the capacities of
individuals greatly surpass their individual knowledge. This is the direct result of
the augmentation that is enabled by our ability to embody knowledge into
tangible and digital gadgets. Second, crystallizing imagination is essential for us
to share the practical uses of our knowledge with others. Without our ability to
crystallize imagination there would be almost no creative outlets, since the
practical uses of our knowledge would be trapped in the prison of our minds, and
would die as words disappear in the air. Finally, the augmentation provided by
products helps liberate people’s search for new form of expressions and gives
rise to new capacities. This is the combinatorial creativity that emerges from our
species’ ability to crystallize imagination. If Jimmy Page had to mine metals and
chop wood to build his own guitars, we would probably have not been able to
enjoy ‘Stairway to Heaven’. If Hemingway had to build his own pens,
manufacture paper, and invent the printing press, he probably would not have
been able to write ‘The Old Man and The Sea’. By the same token, if I had to
build my own laptop, you would not be reading this book. So the knowledge
amplification powers of the economy are essential to liberate the creative
60
Cite The Ten Most Beautiful Experiments.
capacities that allow our species to create new products—which continue to
augment us—and new forms of artistic expression.
Yet, our ability to create products that were begot first as imaginary objects does
not only augment us, but also, gives rise to more complex forms of social
organization. To illustrate this, I will consider the example of ant colonies
advanced cleverly by Norbert Wiener in his 1950 book: The Human Book of
Human Beings
61
. There, Wiener reminds us that our ability to embody
information outside our bodies is not unique to our species. In fact, our ability to
print information in our environment makes us similar to other eusocial species,
such as Ants. Single ants, as he notes, are not very clever, but their ability to
deposit information as pheromone traces makes ant colonies extremely savvy.
Ant colonies solve difficult problems of transportation, construction, ventilation
and routing, not because ants are smart, but because they can leave behind
traces of information that can be “read” by other ants. As humans, we have a
similar capacity. Yet, instead of leaving behind chemicals we leave behind
physical instantiations of imaginary objects, such as wrenches, screwdrivers,
dishwashers, and beer bottles. By doing so, we leave behind traces of
information that endow us with capacities that are even more impressive than
those of Ants, since we can pick up information that is not merely
communication, but packaged in forms that augment our capacities.
So like ant colonies, our species social and economic organization depends
critically on our ability to deposit information in our environment. Unlike ants, we
have the ability to leave behind traces of information that are not chemical, but of
imaginary origins. As a result, the traces we leave behind form an everexpanding set. This is the set of products that made the birth of my daughter,
much like that of any other baby, an act of time travel
Although I have taken the liberty to expand this example substantially, since in Wiener’s book,
is not mentioned in a very straightforward way and is weaved into a weird cold war political
argument. The Human Use of Human Beings. Norbert Wiener (1951?)
61
As my daughter continues to develop she will grow up in a world filled with
strange objects that will be mundane to her, such as laundry machines, Internet
memes and infographics. She will grow up believing that water comes from
faucets and switches command light, only later learning why. Iris’s was born in a
futuristic world where she has not only access to the knowledge of those that live
beside her, but also, to the practical uses of the knowledge that our species
accumulated for centuries and that resides in the objects populating the city she
is learning to call home62.
This alternative interpretation of the economy, as a knowledge amplification
engine, help us reinterpret the process of economic development as the process
by which groups of people develop the capacity to crystallize imagination and
amplify the practical uses of their knowledge. It helps us understand trade as the
transaction of physically embodied ideas, rather than just physical objects and
invites us to see international differences in prosperity not in terms of the ability
of countries to buy, but in terms of their ability to make. Certainly, the ability to
buy and make should be aligned in a world where you need to pay for what you
buy. But since this alignment is hard from perfect63, it is important for nations to
focus on their ability to make, since living from the land is not a sustainable in the
long run.
So now that we have understand that products are physical embodiments of
information carrying the practical uses of knowledge, we will move on to explore
the constraints that limit the ability of people to develop networks required to
store the knowledge needed to make these products. But before doing so, we will
make one final stop, and explore one aspect of the information that is embodied
in products that we have so far neglected. This is the physical origin of
information.
62
The cumulative nature of knowledge is known by cultural anthropologists as cumulative culture
(cite Boyd and Richerson, not by genes alone)
63 Since you can cheat for short periods of time by borrowing or for longer periods of time if you
have a mineral treasure buried underground.
Chapter V. The Four Billion Year Anomaly: frozen whirlpools and the nonhuman origins of information
Add Prigogine quote
In the last chapters we dissected the origins and implications of the information
that is embodied and transmitted in tangible and digital products. We showed
that products are made of information, which they store as physical order. Yet,
we showed also that the economic and social relevance of products does not
hinge simply on the fact that they are made of information, but on the sources of
this information and the practical uses of knowledge that this information helps
carry. The ability of products to implicitly carry the practical uses of knowledge is
what allows a product as simple as a pill, whose physical order is contained
primarily in its active compound, to carry the practical uses of chemistry and
medicine that were used in its creation. Information is therefore, the essence of
the economy. It is what we create and transact. It is the connection between our
minds and the products we make, and therefore, it is the connection between our
minds and that of others.
Yet, humans did not invent information. Information was present before we
evolved, and as I will show in this chapter, information and computation were
present in the universe even prior to the development of life. So an
understanding of the economy based on the information rich nature of products
needs to be anchored in a fundamental understanding of the non-human origins
of information. Otherwise, we leave a loose end. The purpose of this chapter is to
describe the non-human origins of information to make sure that loose end does
not linger.
Our universe is pregnant with information 64 . That’s a fact. Giraffes, cranes,
flowers and chandeliers are all part of this planet’s reality. The information rich
nature of the universe is obvious for any lay observer, but was in conflict with the
understanding of the universe that was available to 19th century physicist.
Nineteenth century physical theories suggested a universe where information
would tend to vanish rather than proliferate, a universe where information tended
to be destroyed rather than created. Nineteenth century physical theories
suggested a world where the information rich nature of our planet and our
universe was anomalous, and even though that anomaly was acknowledged, it
was hard to solve. The physics known until early in the twentieth century
described a world where life, humans and machines, were all part of an anomaly
that had been going on for the last four billion years. Scientists knew that this
could not be the case, and that this contradiction pointed to a deeper truth about
the universe that we did not yet understand.
Nineteenth century physicists did not deny the information rich nature of the
universe. They had trouble explaining it. The information rich nature of the
universe was as obvious to them as it is to you, and was the main puzzle that
Ludwig Boltzmann attempted to solve. Boltzmann was inspired by Darwin 65, who
he saw as the discoverer of the origins of biological order and information.
Inspired by Darwin, Boltzmann wanted to explain information at a more
fundamental level than biology. His goal was to explain why the arrow of time
moves from simplicity to complexity, but his work ended up showing the opposite.
The problem of the arrow of time has been a fundamental problem that physicists
had to wrestle with for centuries. According to Newton’s laws of motion—and
64
Recent findings have estimated the number of earthlike extra solar planets in our milky way in
the tens of thousands. This does not mean we must have been able to communicate or received
visitors from any of them. http://www.reuters.com/article/2013/11/04/us-space-exoplanetidUSBRE9A311820131104
65 Cite ref for this from Prigogines’s book
Einstein for that matter—time is reversible66, and hence the direction of time is
arbitrary. Newtonian dynamics explain a movie going forward as well as going
backwards67. In fact, according to Newton and Einstein the direction of time is
arbitrary, and this is true for simple physical systems, such as a frictionless
pendulum. You can see this by imagining a movie of a frictionless pendulum
running backwards, and noting that it is equivalent to the movie of the same
pendulum going forward. Yet, for more complex systems the reversibility of times
makes no sense. Newton’s laws of motion have no problem with Bugattis being
crashed into wrecks, or wrecks self-assembling into Bugattis. This ridiculous
contradiction led Boltzmann and others to lead an effort that could help explain
the arrow of time in terms of the dynamics of microscopic particles. These
attempts failed, in the sense that were unable to explain the irreversibility of time
as a result of particle dynamics, but they succeeded by suggesting that the
irreversibility of time probably indicated the existence of a physical principle that
escaped those proposed by Newton and that was not based on the dynamics of
particles, but on the statistical properties of the collections of particles that Gibbs
and Einstein later called ensembles.
Boltzmann success came in an 1878 paper showing that systems composed of
many particles tended towards states that had as little information as possible.
This is what is known as the second law of thermodynamics, which had been
anticipated decades earlier by Clausius. The second law of thermodynamics
states that the entropy of closed physical systems always tends to increase, but
this is hardly a good explanation. To grab Bolztmann’s idea with a mental picture,
In physics, such equivalence is called ”symmetry”. Symmetries can be thought of as change of
variables that do not affect the outcome of a physical model. The time reversal symmetry is as
simple as noticing that equations of motion are still valid after we change time t by –t. This means
that a world in which the time runs backwards does not contradict the physical principles used to
derive these equations of motion, and therefore, is valid with respect to them.
67 Thinking about past, present and future is problematic—although common in time travelling
movies. Our current understanding of physics tells us that the future does not exist. It is being
constructed at every instant. In fact, there is only a present that is being computed constantly
from the immediate past, in a non-fully predictable manner—there is chaos after all. Please note
that by saying that the present is constructed from the immediate past we are not denying the
influence of information from the distant past. We are only requiring that information to be
physically embodied somewhere in the most immediate past to affect the present.
66
consider dropping a drop of ink into a glass of water. The initial state, the one in
which the drop of ink is localized, is information rich, since from all of the possible
configurations in which ink can be distributed in water, there are only a few where
the ink is localized. The final state, the one you obtain after waiting for the ink to
diffuse, is information poor, since there are many ways for the ink to be
distributed more or less uniformly in the glass68. So in the case of a drop of ink in
a glass of water, the arrow of time is clear, the universe moves from an
information rich state to an information poor state 69 and Boltzmann’s theory
explained that perfectly.
Yet, the universe is filled with examples that are not like the drop of ink,
examples where information and complexity are seen to increase, such as the
development of human babies or the natural reforestation of a burned down
forest. So where does that information come from? The universes predicted by
Boltzmann and Maxwell, and later refined by Helmholtz, Gibbs and Einstein,
were universes that evolved into homogenous soups. Soups where there was no
information and energy was no longer free 70 . If there was any arrow of time
implied by the thermodynamics of the universe this was an arrow of time that
pushed systems away from complexity. It was an arrow of time contradicting the
nature of the universe described by Darwin and the industrial revolution that
accelerated in the faces of Boltzmann, Maxwell, Gibbs and Einstein. Yet the
question of the arrow of time was not settled even by Einstein, whose dynamics
involved a “spatialized” interpretation of time, in which time is an axis that can be
travelled left and right. Certainly, this is ideal for Sci-Fi movies 71 but fails to
capture the conspicuous irreversibility of our reality.
68
We are assuming that the ink and the water have the same density. They are not like oil and
vinegar.
69 This is known as the second law of thermodynamics, which states that the entropy of a system
never decreases.
70 This is a bit of a game of words, since Free Energy is a technical concept defined as the
energy of a system that can be used to produce work. This is the energy that is not thermal.
Imagine having a bowling ball on a top shelf. The total energy of the system is the thermal energy
of the bowling ball, since this is not absolute zero, plus the potential energy of the bowling ball in
the shelf. The free energy is just the energy of the bowling ball in the shelf.
71 Einstein quotes form Prigogine’s book
During the twentieth century our understanding of the arrow of time and the
physical origins of information got reconciled with the physical nature of reality.
New theories were able to show that information was something to be expected.
These theories did not contradict the dynamics of Einstein and Newton, or the
statistical mechanics of Boltzmann, since they showed that the origins of
information and the arrow of time hinged on additional physical principles and
considerations. The key thinker in this area was the Russian born and Belgian
raised statistical physicist Ilya Prigogine, who was awarded the 1977 Nobel Prize
in
Chemistry “for his contributions to non-equilibrium thermodynamics,
particularly the theory of dissipative structures". Prigogine had many important
insights, but the one that is of our concern here is the idea that information
emerges naturally in the steady states of physical systems that are far from
equilibrium. Now, that sounds complicated, but if we go carefully through a
sequence of examples we will realize it is not. So in the next paragraphs, I will
unpack the meaning of that sentence to a point in which it’s meaning will become
obvious, and the poetry of its message will be exposed.
To understand the physical origins of information we need to understand a few
things first. The first one is the idea of a steady state. The second one is the
difference between a dynamic steady state and a static steady state. The
simplest case of a static steady state is a marble dropped into a bowl. We all
know what happens here. After a short period of time the marble will just sit at
the bottom of the bowl. The marble sitting quietly at the bottom of the bowl
represents a static steady state. A more interesting case is that of a box filled
with gas. If we put gas inside a box, and wait for a bit, the amount of gas in the
right side of the box will be equal to that in the left side of the box. The steady
state of a box filled with gas, however, is not analogous to that of a marble sitting
in the bottom of a bowl. In a box filled with gas, each molecule is not resting in a
fixed position. They are moving constantly and the steady state is reached when
the number of gas molecules travelling from left to right is equal to the number of
molecules travelling from right to left. This is different from the marble in the
bottom of the bowl because it is a dynamic steady state.
Now, we will consider the steady state of a non-equilibrium system. The battle
horse example in this case is that of the whirlpool that forms when you empty the
bathtub. As soon as you remove the plunge of the bathtub, and water starts
racing down the pipe, water begins to organize into a whirlpool. The whirlpool is a
steady state, since it is stable as long as there is water flowing in the system. It is
also an information rich state, since whirlpools are rare configurations of water
molecules that do not appear spontaneously in still water72. The information rich
state of the whirlpool, however, emerges naturally. It is an information rich state
that we get for free in an out-of-equilibrium system. Going back to our original
sentence, we can say that the whirlpool is an example of information that
emerges naturally in the steady states of physical systems that are far from
equilibrium 73.
Yet the whirlpool is not our only example. There are many other examples of
order that emerges spontaneously in far from equilibrium systems, such as the
swirls of cigarette smoke, the hypnotic movement of campfire, and the glow of
your computer screen, since your computer screen is definitely far from
equilibrium when it is turned on. You and your mobile phone are also examples
of physical systems that are far from equilibrium. In your case, you eat to stay far
from equilibrium, while in the case of your cellphone, you recharge it every night.
Prigogine realized that, although Bolztmann’s theory was correct, it did not apply
to what we observe on earth, or the universe, because these are systems that
are being constantly driven away from equilibrium. In fact, our planet has never
72
A whirlpool is an information rich steady state, since the distribution of the velocities of water
molecules in a whirlpool is far from random. Yet, as Prigogine notes “for a long time turbulence
was identified with disorder or noise. Today we know that this is not the case. Indeed, while
turbulent motion appears as irregular or chaotic on the macroscopic scale, it is, on the contrary
highly organized in the microscopic scale.”
73 Notice that this is almost exactly the same sentence we wanted to unpack. Hopefully, this
second time around its meaning is much more obvious.
been on equilibrium, since the energy of the sun and the nuclear decay taking
place in the earth’s core ensure that there is plenty of energy flowing through our
planet’s surface. So to understand the information rich nature of the universe we
needed to understand the statistical properties of the systems that were far from
equilibrium. These are different from the systems studied by Boltzmann and
include the cases where order came for free.
Prigogine’s breakthrough certainly was more than conceptual, since it included
the derivation of some of the mathematical laws and principles that govern the
behavior of far from equilibrium systems. Prigogine’s work showed that the
universe is organized in a beautifully peculiar manner with information being
hidden on the other side of chaos. To understand what this sentence means
consider boiling water in a frying pan. First, consider turning the heat on for just a
little bit. If you do that, a small quantity of water at the bottom of the pan will
warm up. These molecules will start moving around a bit faster—that’s what
temperature is. Yet, since you turned off the heat quickly, the water in the pan will
quickly lose the information it was storing in the its non-random distribution of
molecular velocities. Now consider turning the heat long enough for the water to
start moving. As the water starts moving the fluid becomes turbulent. It is chaotic.
This is a state that already contains information, much like that of the swirls of the
cigarette smoke. Now keep the heat up long enough for the pot to enter a steady
state of convection. If your pot is wide enough, like that used to make a paella,
you will see hexagons of convection emerge. After chaos, the system organizes
into a state that is highly organized, full of information. Prigogine showed that the
steady states that matter reaches far from equilibrium tend to be this way. Behind
chaos there is information.
The good news about out-of-equilibrium systems is that they are characterized
by information rich steady states, helping us understand where information
comes from. In a far from equilibrium system, such as earth, the emergence of
Information is expected. It is no longer an anomaly. The bad news of far-from-
equilibrium steady states is that whirlpools vanish as soon as we put back the
plunge or run out of water. This might lead us to think that the universe is quick at
taking away the information rich steady states that out-of-equilibrium systems
gives us for free. Yet fortunately, this is not how the universe works. In fact, the
physical laws of the universe imply that information is quite sticky, and there are
two good reasons why this is the case.
The first reason is quite technical, and involves the idea of thermodynamic
potentials. Yet, once again, there is no need to worry, since the basic intuition
that we want to draw from this technical field is one that is quite easy to
understand. What we need to assume here is that the steady states of physical
systems can be described as minimums of mathematical functions, which are
known as thermodynamic potentials. We are all familiar with the basic idea of
potentials from high-school physics, since we know that marbles end up at the
bottom of bowls because this is a minimum of potential energy. Now, the thing is
that not all of the steady states of physical systems minimize energy. Many
steady states minimize or maximize other quantities74. Yet, here we do not need
to go into the details of all of these quantities75, since we are interested primarily
in far-from-equilibrium systems, and we can therefore, “cut to the chase” and go
directly to the potentials that are involved in that case. So what is the potential
that non-equilibrium systems, such as our bathtub whirlpool, minimize? Ilya
Prigogine showed that the steady state of non-equilibrium systems minimize
entropy production, or in our language, minimize the destruction of information.
While later it was found that Prigogine’s result was not absolutely general—and
had to be expanded to a more general potential 76 —Prigogine’s take-home
message seems to still prevail. The take home message is that the information
rich steady states that the universe gives us for free are not wasteful, that is, they
74
Some of these quantities are related to energy, but others are not. For instance, in the case of
Boltzmann’s gas in a box, the system maximizes entropy, which is the opposite of information.
75 The gas in the box, for instance, minimizes Helmholtz Free-Energy. Other examples includes
76 Prigogine’s contribution showed that the steady state of a far from equilibrium dissipative
system is a local minimum of the rate of entropy production (J. England Notes on Stat Mech. MIT
2013).
destroy as little information as they can. In the words of Prigogine: “When the
boundary conditions prevent the system from going to equilibrium it does the next
best thing; it goes to a state of minimum entropy production”77.
Prigogine showed us that far-from equilibrium systems beget information, and
minimize information destruction. Yet, even though physical systems try to hold
on to the information that emerges when they are far-from-equilibrium as much
as they can, it is hard to see how these systems can hold on to that information
for long periods of time. Whirlpools disappear and the smoke of cigarettes looses
its beauty as smoky swirls diffuse into hazy clouds. Non-equilibrium statistical
physics can help us understand the non-human origins of information, but not its
permanence. Yet, it is the permanence of information what allows information to
be recombined. The permanence of information, is therefore, as important as its
origin. The permanence of information is what allows information to beget more
information, but the permanence of information is not guaranteed in the laws that
explain its origin. Once again, there must be something else going on.
As Schrodinger noted in his 1944 book “What’s Life”, we cannot understand the
permanence of physically embodied information if we limit our thinking to the fluid
systems that we have been using for all of our examples. Cigarette smoke,
whirlpools, drops of ink, and gas in a box, are all fluids, and much of their
evanescence comes from this fluidity. So the second reason why physically
embodied information is sticky is because much of the information that we have
in the universe is stored in solids, and not in the dynamical steady states of nonequilibrium fluids. Once again, consider the bathtub whirlpool, but now assume
you have a magic wand that allows you to freeze, or “crystallize”, the bathtub and
the whirlpool with a single twist of your wrist78. Now take an imaginary icepick
and chisel the whirlpool out of its icy confines. What you now hold in your hand is
77
Order out of chaos, page 139
This thought experiment is not physically accurate—the whirlpool will stop as you freeze it—but
you can run it in your head thanks to the powers of imagination. The purpose of the mental image
is primarily illustrative.
78
a little “quantum” of information. As long as you don’t unfreeze the whirlpool,
much of the information that was present in that information rich steady state will
remain there79. The whirlpool will be a crystal of order that would last longer than
what it takes to empty a bathtub. By solidifying the whirlpool we trapped
information that was generated in a fluid world, and gained a crystal of
information that we can use to help construct the complexity of our world.
Freezing whirlpools is not physically possible 80, but it gives us a good mental
picture that we can use to understand the important of solids in the permanence
and evolution of information. According to Schrodinger, the solid or crystalline
nature of information is essential to explain the information rich nature of our
universe. In “What’s Life?” Schrodinger strongly emphasized the essentiality of
solids to explain the information rich nature of life. In the early 1940’s,
Schrodinger—as well as every biologist in the world—understood that the
information required to build a biological organism was hidden somewhere inside
the cell, in either proteins or DNA81. From a physical perspective, both proteins
and DNA are technically crystals, and more precisely, are aperiodic crystals.
Schrodinger understood that aperiodicity was needed to store information; since
a regular crystal would be unable to carry much information: “the gene is most
certainly not just a homogeneous drop of liquid. It is probably a large protein
molecule, in which every atom, every radical, every heterocyclic ring plays an
individual role, more or less different from that played by any of the other similar
atoms, radicals, or rings”. According to Schrodinger, the phenomena of life
hinged on both, the aperiodicity of biological molecules and their solid, crystalline
nature. The aperiodicity was essential to carry information82. The solid nature of
the molecule was essential for this information to last.
79
Certainly, the information encoded in the positions of the water molecules will be there, but the
one that was contained in their velocities—or momentum—disappeared.
80 At least to the best of my knowledge.
81 We note that the Avery-MacLeod-MaCarty experiment from 1944 showing that DNA carries
genetic information coincide with the publication of Schrodinger’s book, so Schrodinger was not
aware that DNA, rather than proteins, carried genetic information.
82 A regular structure cannot carry information. Think of a sheet of music where the same four
notes repeat over and over. The information carried by that sheet would be minimal compared to
So by combining the ideas of Prigogine and Schrodinger we can understand
where information comes from—steady state of non-equilibrium systems—and
why it sticks around—because it is stored in solids. The poetic oddity of this
combination is that it tells us that our universe is both frozen and dynamic. From
a physical perspective a solid is “frozen” because its structure is stable to the
thermal fluctuations of the environment—it is not melting in a fluid state83. Our
cities are made of solids, such as cars, buildings, bus stops, subways and
sidewalks. Our homes are made of solids, such as kitchen sinks, refrigerators
and washing machines. Our cells are also made of solids, which are the tens of
thousands of proteins that help run the cellular show. Yet, cars and proteins are
solids that move around. Cities are dynamical systems where many solids are
not static. The solid nature of these objects allows us to accumulate physically
embodied knowledge and information at a low cost, since the energy needed to
move a subway from one stop to the next is relatively small compared to the
energy required to build a subway.
The frozen and dynamic nature of our cities and biology contributes to more than
our ability to accumulate information. The key implication of our counterintuitive
universe is not that matter can self-generate some of the information that it
physically embodies, but that matter is able to process information. Far from
equilibrium matter can compute. The key insight of the far-from-equilibrium
statistical physics literature that we have reviewed is that matter can process the
information that is embodied in it. For a poetic example consider a tree. A tree, in
its semi-frozen state driven by sunlight, is a computer. A tree in New England
reacts to the length of the day, running a different program in the summer than in
the winter. It figures out when to shed its leaves, and when to sprout. A tree
one in which variations and departures are prevalent. Information in this case, is therefore carried
in the aperiodicity of music.
83 Certainly, this depends on the scale. We can consider a solid to be frozen when thermal
fluctuations are too weak to alter its structure. This is true of a building and a car at room
temperature. A protein, on the other hand, lives much more at the edge of order and disorder,
since thermal fluctuations are important for a protein to fold but a protein structure is still stable to
the thermal fluctuations that take place at room temperature.
processes the information that is available in its environment. Its proteins,
organized in signaling pathways, help the tree figure out how to grow its root
towards the water it needs and how to grow its leaves toward the sun it craves. A
tree does not have the consciousness or language that we have, but it shares
with us a general ability to process information, even though it processes
different information than the one we do. A tree is a particular type of computer
that is not plugged into an outlet, but to the sun. It is a computer that, just like us,
cannot run Matlab, but unlike laptop computers and us, knows how to run
photosynthesis. Trees process information, and they are able to do so because
they are steady states of systems that are out-of-equilibrium.
Yet since a tree is alive it cannot help us illustrate the pre-biotic nature of the
ability of matter to process information. To show this we need to describe more
fundamental systems. Here is where the chemical systems that fascinated
Progogine come in handy. Consider a set of chemical reactions that takes a set
of compounds {I} and transforms them into a set of outputs {O} via a set of
intermediate compounds {M}. Now consider that we feed this system with a
steady flow of the compounds {I}. If the flow of inputs {I} is small, then the system
will settle in a steady state where the intermediate inputs {M} will be produced
and consumed in such a way that their numbers do not fluctuate much. The
system will reach a state of equilibrium. In most chemical systems 84, however,
once we crank up the flow of {I} this equilibrium will become unstable, meaning
that the steady state of the system will be replaced by two or more stable steady
states that are different from the original state of equilibrium85. When these new
steady states emerge, the system will need to “choose” among them, meaning
that it will have to move to one or the other, breaking the symmetry of the system
and developing a history that is marked by those choices. If we crank up the
inflow of the compounds {I} even further, however, these new steady states will
84
Assuming that these systems have non-linearities that come from the fact that the production of
some intermediate compounds {M} or outputs {O} require, respectively, combinations of inputs {I}
or intermediate states {M}.
85 Technically this is known as a bifurcation.
become unstable and new steady states will emerge. This multiplication of
steady states can lead these chemical reactions to highly organized states, such
as those exhibited by “molecular clocks” which are chemical oscillators where
compounds change periodically from one type to another. But is such a simple
chemical system a system with the ability to process information? Now consider
that we can push the system to one of these steady states by changing the
concentration of inputs {I}. Such a system will be “computing”, since it will be
generating outputs as a reaction to inputs much like transistors do. In a crude
way, this example represents a simple metabolism. In a more general way, it
represents a cell differentiating from one cell type to another. Here, cell types are
abstracted as the steady states of these systems, as Kauffman suggested a few
decades ago86.
Far-from-equilibrium statistical systems, whether they are trees reacting to the
weather, or chemical systems processing information about the inputs they
receive, teach us that matter can compute. These systems tell us that
computation precedes the origin of life, as much as information does. The
chemical changes encoded by these systems are modifying the information
encoded in these chemical compounds, and therefore, represent a fundamental
form of computation. The irreversibility of time that motivated our discussion on
the non-human origins of information is explained in this footnote87.
86
This is one of the central ideas described by Kauffman in The Origins of Order and it is
implication of his model on random Boolean networks.
87 This footnote contains my own version of the description of time irreversibility explained in both,
Prigogine and Stengers, Order out of Chaos, and Prigogine’s The End of Certainity. For a more
detailed explanation please refer to these and other sources on the topic.
According to our modern understanding of statistical physics the irreversibility of time is a
property that emerges as a consequence of the recurrent chaotic interactions that characterize
large physical systems. To understand this process, I suggest the following mental picture.
Consider a ginormous box filled with trillions of Ping-Pong balls. Now imagine that balls collide
with one another without losing energy, such that the interactions take place in a recurrent
manner—they never cease. Now, assume that you started observing the system at a moment in
time in which all of the Ping-Pong balls were located neatly in one quadrant of the box, but were
also endowed with initial velocities, or energies, that were large enough to scatter the balls across
the entire box.
Now, imagine what happens when you “run this movie” forward: Ping-Pong balls fill up the box
with their incessant motion. In this thought experiment we can rephrase the question of time
The lessons of out-of-equilibrium statistical physics put our understanding of the
social and economic origins of the information that we transact in our economy in
a grander context. This is a context that helps connect physics, biology and the
social sciences, by showing that the evolution of complexity that was
conspicuous but elusive to Boltzmann, is the result of two fundamental properties
of physical matter: its ability to self-generate information, and its ability to
reversibility to the question of whether it is possible to choose velocities for each of the Ping-Pong
balls such that it looks like the same “movie” was playing backwards. That is, we are not
reversing an exogenous time, such as the “linearized” times of Newton and Einstein, but making
a statistical system evolve in a way that we would identify as the dynamics of time going
backwards. Finally, we ask the time reversal operation to require finite information.
After the balls have been bouncing around for a few days you are now ready to give time reversal
a shot. To make things easier, we will assume that we have two machines, one which is able to
take any number of balls and modify their positions and velocities instantly, if and only if, we
provide the machine with a file containing the desired positions and velocities. We also assume
that the machine has infinite precision, but executes instructions with the precision of the
information that it is fed. That is, if positions and velocities are provided with a precision, of let’s
say ten-digits, then the machine will assign the non-specified decimals of these positions and
velocities at random. The second machine can measure the position and velocity of each ball with
a precision that is determined by its memory, which we abstract as a long tape of paper. So the
question is, can we use these imaginary machines to make the time flow backwards?
Assume that we measure the position and velocity of each of the trillion balls with a precision of
two digits, meaning that a velocity in the x direction of vx=0.2342562356237128… will get
recorded in the tape as vx=0.2. If for each digit we need 4 bits, then this encoding will require a
tape of 2x6x4x1012=4.8x1013 bits (the six comes from three coordinates in space and three
coordinates of velocity).
Now, that is a long tape, but is this tape long enough to encode the precision needed to reverse
time? The answer is certainly not. A system of trillions of non-dissipative ping-pongs like the one I
am describing here is by definition chaotic, meaning that small differences in initial conditions
grow exponentially over time. The chaotic nature of the system implies that a precision of two
digits will not be enough to put the system back into a “trajectory” that will bring it to its original
configuration—while also going through every intermediate step. So how about a precision of 10
digits, 20 digits, or 100 digits? The answer is that no matter how precisely we measure the
position and time of each particle, the imprecisions of our measurements will grow to dominate
the system. We can make the tape as long as we want, but this will still not allow us to make the
movie play backwards because the last digits, those representing the smaller numbers, over the
long run will be the ones dominating the dynamics. Because of this chaos, the movie will always
looks as it is playing forward, except for a short period of time soon after we reversed the
velocities. This means that time is irreversible, and that this irreversibility if not the result of
dynamic properties, but of statistical properties (a single particle moving in the box looks the
same going forward or backwards in time). That is, time does not flow backwards because setting
up a system that would make the forward dynamics equivalent to the backwards dynamics would
require an infinite amount of information. This is infiniteness is what Prigogine calls the entropy
barrier, and it is what provides a perspective of time that is not spatialized like those of Newton
and Einstein—for both Newton and Einstein it is ok to present times as an axis that is exogenous
to the system. In this interpretation of time only the present exists. The past is unreachable
because the infinite entropy barrier forbids us from putting the universe in a “trajectory” that would
make it go backward. The future does not exist. There is only a present that is being calculated at
every instant.
compute. These two properties are essential for the emergence of biology, as
much as the emergence of biology is essential for the emergence of the
economy. These two properties of matter, however, also push our discussion into
a new light, since so far we have mostly discussed the ability of matter to
embody information and carry the practical uses of knowledge. The
computational capacities of matter, however, tell us that in the best case we have
only discussed half of the story. This is the half dealing with the ability of matter
to embody information, and to generate the tangible and digital objects that
augment our capacities. The half of the picture that we are missing is the one
concerning the ability of the universe to process information. So this is where we
will go next. The next part of our journey will move its gaze away from crystals of
imagination, and the information that they carry, and into the dynamic networks
that accumulate the knowledge required to physically embody this information
into tangible and digital products. We will move from information to computation,
but in a peculiar way. As we will see, the constraints that limit the capacity of
system to process information—which I have defined as knowledge—is what will
help us explain much of the difference between rich and poor countries and
understand the evolution of economic complexity, and that’s what I promised at
the outset.
Intermezzo: Why the brain is not a tape
If I had to think of two branches of science that have a similar goal 88, but differ
largely in their approaches, I could not think of a better example than the contrast
between economics and biology.
Both economics and biology study organized complexity, and the question of the
emergence of diversity is central to both economics and biology. Darwin
constructed his theory of evolution as an explicit attempt to explain the biological
diversity that he observed in his travels and that was conspicuous to his
contemporaries89. Darwin understood that the essential contrast that separated
the discipline he was giving birth to—from the until-that-time most successful
science of physics—was the diversity of the phenomena he was looking to
88
In full disclosure there are historically a good number of examples of information transfer
between biology and economics. A historical one is Alfred Marshall, who emphasized the
importance of drawing analogies from biology to understand economic systems as early as 1890.
In Book IV, Chapter VII of his Principles of Economics, he writes: “Malthus' historical account of
man's struggle for existence started Darwin on that inquiry as to the effects of the struggle for
existence in the animal and vegetable world, which issued in his discovery of the selective
influence constantly played by it. Since that time biology has more than repaid her debt; and
economists have in their turn owed much to the many profound analogies that have been
discovered between social and especially industrial organization on the one side and the physical
organization of the higher animals on the other. In a few cases indeed the apparent analogies
disappeared on closer inquiry: but many of those which seemed at first sight most fanciful, have
gradually been supplemented by others, and have at last established their claim to illustrate a
fundamental unity of action between the laws of nature in the physical and in the moral world.
This central unity is set forth in the general rule, to which there are not very many exceptions, that
the development of the organism, whether social or physical, involves an increasing subdivision
of functions between its separate parts on the one hand, and on the other a more intimate
connection between them. Each part gets to be less and less self-sufficient, to depend for its
wellbeing more and more on other parts, so that any disorder in any part of a highly-developed
organism will affect other parts also.”
A more recent example is Nelson and Winter’s 1982 book: An Evolutionary Theory of Economic
Change. In there Nelson and Winter criticize orthodox economics, among other things, on the
grounds that this is a theory based on systems solving themselves forward based on the
expectations of agents. Instead, they argue that much like in evolutionary biology, the biggest
constraints, and determinants of economies, come from their past and not from agent’s
expectations of the future.
89 As Darwin highlighted in the introduction to On The Origins of Species: “When on board H.M.S.
‘Beagle’, as naturalist, I was much struck with certain facts in the distribution of the inhabitants of
South America, and in the geological relations to of the present to the past inhabitants of that
continent. These facts seemed to me to throw some light on the origin of species—that mystery of
mysteries, as it has been called by one of our greatest philosophers. ”
explain. In the Origin of Species he said: “There is grandeur in this view of life,
with its several powers, having been originally breathed into a few forms or into
one; and that, whilst this planet has gone cycling on according to the fixed law of
gravity, from so simple a beginning endless forms most beautiful and most
wonderful have been, and are being, evolved.”
The built world, populated by skyscrapers, hairdryers, and tennis racquets, is as
colorful and diverse as the world populated by lions, zebras and capybaras. Yet,
the study of economies—in its macro incarnation—has shunned away from the
study of diversity in lieu of what in biological terms would be known simply as
biomass. For Darwin, an elephant was not the same as ten tigers, one zebra, two
chimps and a million ants. Diversity was the true puzzle that Darwin wanted to
solve. Yet, the difference between biology and economics that is evident from
their emphasis on diversity is only one of the many aspects that separate these
disciplines90. Since Darwin’s origin of species these fields have continued to grow
apart, being differentiated among other things, by the importance they give to the
processes of physically embodying information.
With the discovery of the gene, biology discovered quickly that the central
questions it needed to tackle were questions about information, and about the
way in which information was packed and unpacked, not question about volumes
or quantities. Biology evolved from being a science of mass and energy into a
science of information. From the hands of Rosalind Franklin, James Watson,
Francis Crick, Francois Jacob and George Gamow, among many others, biology
90
In the opening of chapter of On The Origin, Darwin notes that human interventions in plants
and animals give rise to increases in variation among the individuals of the species being
intervened. Hence, he correctly identifies that the economic actions of humans do give rise to
increases in variation, and hence implicitly, to increases in information : “When we look to the
individuals of the same variety or sub-variety of our older cultivated plants and animals, one of the
first points which strikes us, is, that they generally differ much more from each other, that do the
individuals of any one species or variety in a state of nature. When we reflect on the vast diversity
of the plants and animals which have been cultivated, and which have varied during all ages
under the most different climates and treatment, I think we are driven to conclude that this greater
variation is simply due to our domestic productions having been raised under conditions of life not
so uniform, and somewhat different from, those to which the parent-species have been exposed
under nature. ”
underwent a revolution that refocused its efforts on questions of information
storage, transmission and duplication. Biology became binary—or more precisely
quaternary—as it begun to explore the development of organisms and Darwin’s
endless forms. As biology went digital, it began to explore the code that
translated nucleic acids into RNA and RNA into proteins. It began to explore the
mechanisms by which biological organisms copy information and correct errors.
During the middle of the twentieth century economics also underwent a
revolution, but this revolution was different from the one of biology. During the
20th century economics mathematized growth through the use of continuous
quantities that echoed classical physics more closely than genetics. As biology
discovered the bits and bytes of life, economics continued to be concerned with
labor and capital, the quintessential substances that Smith had suggested nearly
two hundred years ago and that Marx reiterated in the same city of London
where Huxley and Wallace popularized and defended Darwin’s theory.
But what if Smith and Marx where trapped by a limited language? After all, the
word information was unknown to them. What if Smith and Marx, and those who
came after, confused labor, or effort, with information? Effort is needed to write a
book, but a book is not a result of sheer effort. Effort is needed to smitten words
into a page, but it is the ability of the writer to put words in order what
differentiates a book from the pages typed by Borges’ proverbial monkeys. Yet,
the luxury of working with information is not an exclusive privilege of the writer,
but the essence of all productive activities. What are garbage men but writers,
that instead of moving words to the right place of a sentence, rearrange urban
waste by moving trash out of homes and into dumpsters? What are waiters, but
mobile communication agents that carry information between a restaurant’s
customers and the kitchen? What is doing laundry, but a sequence of motions
that help edit undesirable particles out of a garment? What is folding laundry, but
an act of information processing involving the pairing, sorting and storing of
physical objects? Information is the essence of both biological and economic
reality, no matter whether information is stored in bits, genes, electrons, magnetic
domains or pairs of socks. The common need of biology and economics to
explain diversity is, therefore, satisfied only by looking at the world under the
microscope of information.
Understanding products as crystals of imagination, and the economy as a system
that has evolved to amplify the practical uses of knowledge and imagination, puts
information and diversity at the center of the economic puzzle. The discrete
nature of information pushes us to think about the diversity of types rather than
the accumulation of aggregate quantities, and also pushes us to think about
economies in terms of the ability to accumulate, and transmit, knowledge and
information. It brings gravity to simple questions, such as what is the knowledge
storing capacity of a network of neurons, or people? And, how do people
organize to store knowledge and embody the practical uses of the knowledge
they have into the discrete packets we call products. A car leaving an assembly
plant is like an RNA molecule leaving the cell nucleus, or maybe like a protein
leaving the ribosome. Either way, the analogy is not superficial, since it shows
that problems of information storage and transmission lie at the core of any
system that exhibits organized complexity. By putting information at the center of
economic systems we find that long accepted facts, such as economic growth
being non-existent before the 19th century, are nothing but an expression of the
stupidity of our accounting, since these “facts” fail to account for the contributions
of Newton and Leibniz, the works of Leonardo, Michelangelo and Brunelleschi,
the plays of Shakespeare and the philosophy of Socrates, Plato and Aristotle.
They fail to account for the invention of the telescope, Guttenberg’s press and
the mechanical clock. They fail to account the growth that is worth counting: the
growth in knowledge and information that begets the commercial growth in
consumption. Certainly, counting knowledge is not easy, but that does not mean
that the renaissance or enlightenment were periods of per capita stagnation, it
means that we have been abstracting the world from a perspective that leaves
essential aspects of development out of view.
The contributions of Newton, Shakespeare and Brunelleschi are an essential
form of growth in our ability to crystallize imagination, and therefore, represent an
essential form of economic growth. Hollywood is still inspired by Shakespeare as
much as Newton’s lessons are embodied in the minds of most modern
engineers. Brunelleschi’s perspective is still used in architectural drawings and
stands as strong as the Duomo of Santa Maria del Fiore that crystallized his
genius using more than four million bricks.
So where we are headed next is into an exploration of the economy based on the
ideas that captured biology more than half a century ago. These are ideas on
how knowledge and imagination are stored and transmitted, and how the storage
and transmission of knowledge and information are constrained by fundamental
quanta. Our goal can be phrased popularly as an attempt to explain variations in
wealth, but in full disclosure, it is closer in spirit to that of Darwin since it is not
aggregate wealth what I look to explain, but diversity. Diversity is what I see in
the photographs of cities, the aisles of supermarkets and under the Christmas
trees of fortunate children91. Differences in the diversity of products and activities
that take place in different locations—whether these are countries or cities—are
what seems to me to be the most profound economic puzzle, and the one where
a perspective centered on information, rather than more traditional notions of
economic value, is key. But before we move on to explore the informational
nature of the economy, we will borrow one more page from the book of biology,
and another one from the book of physics. These pages will help us make an
important distinction between the physical embodiment of knowledge and
information.
The page we will borrow from the book of physics is the idea that information is
always physically embodied. We have seen this before, but for completeness, we
will reiterate it briefly. The physical embodiment of information is obvious in some
cases, such as in the case of DNA, or in the oil and canvas that painters—such
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I am an atheist that thinks that the invention of Santa Claus is a great idea.
as Van Gogh—used to crystallize their ideas. Yet, there are other cases in which
the physical embodiment of information is not that obvious because the physical
embodiment of information is invisible, intangible, or massless, and therefore
seems imperceptible. Yet, this is never unphysical. Imagine that you are in
Amsterdam’s Van Gogh museum standing ten feet away from one of Van Gogh’s
fabulous paintings. The information that is contained in the painting is clearly
embodied in the position of pigments, but where is the information embodied as it
travels between the wall and your eyes? The short trip that transports the
information from the canvas, to your retina, is a trip where the physical vehicle of
the information is the swarm of massless photons that rushed to your eye after
bouncing of the painting. The same is true for music, which is embodied in
invisible pressure waves that harmonically compress the air between a
loudspeaker and your eardrums. Information is always physically embodied. Bits
cannot exist without atoms, electrons, photons or physical fields, since bits are
not objects, but information that is encoded in the way in which these physical
objects are arranged. Information is not physical, per se, but is always physically
embodied thanks to the unbreakable marriage that exists between the order of
physical particles and information.
Information always needs to be physically embodied, but how about knowledge?
Both knowledge and information need to be physically embodied, but the
physical embodiments of knowledge and information are not the same. To
understand this difference, let’s borrow a page from the book of biology and
consider photosynthesis. Photosynthesis is the biological process by which
plants obtain much of the carbon they use (C), which they collect from the carbon
dioxide (CO2) that is in the air. Photosynthesis is not a simple process. It is a
complex computation involving a large number of enzymes that work together to
create complex structures inside a plant’s chloroplasts—the cellular organelle
that is responsible for photosynthesis. Chloroplasts “know” how to make
photosynthesis, and they have their own DNA. But does the DNA of
chloroplasts92 “know” how to make photosynthesis? Or is this a property of the
chloroplast, but not its DNA?
To make sure we are on the same page I note that by knowing, I am not implying
any consciousness or purpose, but simply the ability of a system to perform a
function, which in the case of photosynthesis, means collecting carbon from air.
In the case of photosynthesis, we can distinguish between the information that is
physically embodied in DNA, and the knowledge that is embodied in the network
of enzymes and compounds that are able to perform photosynthesis. By this, I
am separating the word knowledge from wisdom, by defining knowledge more
abstractly as the ability of a dynamic network to process information, to compute
by rearranging physical particles. Going forward, I will use this definition to make
a general distinction between the physical embodiment of knowledge and
information by claiming that the physical embodiment of knowledge always
requires the presence of dynamic networks, such as the networks of enzymes
that perform photosynthesis, or the networks of people that run a business.
Moreover, I will claim that what these dynamic networks do is to process
information. So while information is stored in molecules, paintings, hard-drives,
punch cards, and printed books, information is processed in networks, such as
the networks of molecules we know as chloroplasts, or the networks of cells that
you call your brain. The brain is not a tape because it holds knowledge, not just
information. Networks process information. Networks are needed to copy, mutate
and amplify information. To make decisions. Networks know how to change the
information that is physically embodied in molecules and objects. They know how
to read DNA or the pages in this book. A tube that is filled with nothing but a copy
of chloroplast DNA cannot perform photosynthesis. It does not know how to, and
it cannot know, since it has no network where to contain that knowledge. A
solitary piece of DNA is like a hard-drive without a computer, or a music sheet
without an orchestra. It is a static piece of physically embodied information, which
lives in stark contrast to the dynamic nature of knowledge.
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Chloroplasts have their own DNA, which is separate from the one in the cell plant’s nucleus.
As an example consider a dancer. The nervous system of a dancer processes
information by transforming music into motion, although her DNA does not know
how to dance. Consider a restaurant. What is a restaurant but a network of
individuals that processes information by transforming recipes into dishes? And
what about a musician? What is a musician but a network of neurons that has
learned to play by encoding, decoding and creating information in the form of
sounds? By the same token, what is a chloroplast but a network of molecules
that knows how to perform the thermodynamically upstream battle needed to
collect carbon out of CO2? What is knowledge but the ability of a dynamic
network to process information? What is knowledge but the dynamic ability to
modify physical embodiments of information by combining operations of editing,
duplication, sorting, searching and selection?
Differentiating between the physical embodiments of information and knowledge
is essential to understand the informational nature of economies, since it is the
crucial difference that we need to make to separate the crystals of imagination
that people make, and the people that makes them. With the exception of
computers, which live somewhere between the physical embodiment of
information and knowledge 93 , products are deposits of the practical uses of
knowledge
and
imagination—which
we
can
call
information—but
not
knowledge94.
By separating between the physical embodiment of information, and that of
knowledge, we separate between the information content of products, and the
knowledge that resides in the networks of people that begets them. This
separation helps us understand the process of economic development as the
evolution of the networks that embody the knowledge required to process
physically embodied information; from the creation of a sandwich, to open heart
93
Since I am not ready to discount future advances in A.I.
In some popular strands of literature this is known as codified knowledge. For those who have
followed that literature I note that I am calling Polanyi’s codified knowledge information.
94
surgery, and from the removal of trash, to the construction of a particle
accelerator.
In the next section we move our focus away from products and concentrate on
the evolution of the networks of people where the knowledge needed to make
products is embodied. This will help us understand the constraints that drive the
emergence of differences in economic diversity and that are expressed in
differences in the ability of countries and cities to crystallize imagination.