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Samuel Arbesman
Our lives are governed by centuries of advances that haven t been random, as
mathematician and network scientist Samuel Arbesman argues there s a pattern
that reveals how our knowledge has changed over time.
I had my first experience with the internet in the early 1990s. I activated our
300-baud modem, allowed it to begin its R2-D2-like hissing and whistling, and
began to telnet. A window on our Macintosh s screen began filling with text and
announced our connection to the computers at the local university. After
exploring a series of text menus, I began my first download: a text document
containing Plato s The Republic, via Project Gutenberg. After what felt like a
significant fraction of an hour, I was ecstatic. I can distinctly remember
jumping up and down, celebrating that I had this entire book on our computer
using nothing but phone lines and a lot of atonal beeping.
It took me almost a decade to actually get around to reading The Republic. By
the time I did, the notion that I expressed wonder at such a mundane activity
as downloading a text document seemed quaint. In 2012, people stream movies
onto their computers nightly without praising the modem gods. We have gone from
the days of early web pages, with their garish backgrounds and blinking text,
to slick interactive sites with enough bells and whistles to make the entire
experience smooth and multimedia based. No one thinks any longer about modems
or the details of bandwidth speeds. And certainly no one uses the word baud
anymore.
The changes haven t ended there. To store data, I have used floppy disks,
diskettes, zip discs, rewritable CDs, flash drives, burnable DVDs, even the
Commodore Datasette. Now, I save many of my documents to storage that s
available anytime I have access to the internet: the cloud.
The technological revolution we re currently experiencing is not a one-off,
technology has been changing over the centuries. But what s surprising is that
if you look below the surface you discover that this progress is not random or
erratic, it almost always follows a pattern. And understanding this pattern
helps us to appreciate far more than faster download speeds or improved data
storage. It helps us to understand something fundamental to our success as a
species. It helps us to understand how our knowledge changes and evolves.
Double up
In technology, the best-known example of this pattern is Moore s Law, which
states that the processing power of a single chip or circuit will double every
year. Gordon Moore, a retired chemist and physicist as well as the co-creator
of the Intel Corporation, wasn t famous or fabulously wealthy when he developed
his law. In fact, he hadn t even founded Intel yet.
In 1965, Moore wrote a short paper, entitled Cramming More Components Onto
Integrated Circuits, where he predicted the number of possible components
placed on a single circuit for a fixed cost would double every year. He didn t
arrive at this conclusion through exhaustive amounts of data gathering and
analysis; in fact, he based his law on only four data points.
The incredible thing is that he was right. This law has held roughly true since
1965; it has weathered the personal computer revolution, the march of
processors from 286 to 486 to Pentium, and the many advances since then. While
further data has shown that the period for doubling is closer to eighteen
months than a year, the principle stands. Processing power grows every year at
a constant rate rather than by a constant amount. And according to the original
formulation, the annual rate of growth is about 200%.
But when processing power doubles rapidly it allows much more to be possible,
and therefore many other developments occur as a result. For example, the
number of pixels that digital cameras can process has increased directly due to
the regularity of Moore s Law. This ongoing doubling of technological
capabilities has even reached the world of robots. Rodney Brooks, a professor
at MIT and a pioneer in the field, found that how far and how fast a robot can
move goes through a doubling about every two years: right on schedule and
similar to Moore s Law.
You could argue that this has become a self-fulfilling prophecy. Once Moore s
prediction came to pass, it was simply a matter of working hard to ensure it
continued to do so. The industry has a continued stake in trying to reach the
next milestone predicted by Moore s Law, because if any company ever fell
behind this curve, it would be out of business.
But while Moore provided a name to something, the phenomenon he named didn t
actually create it. If you generalise Moore s Law from chips to simply thinking
about information technology and processing power in general, Moore s Law
becomes the latest in a long line of technical rules of thumb that explain
extremely regular changes in technology over the last few centuries.
Chris Magee, a professor at MIT in the Engineering Systems Division, has
measured these changes. Together with his postdoctoral fellow, Heebyung Koh, he
compiled a vast data set of all the different instances of information
transformation that have occurred throughout history. By lining up one
technology after another from calculations done by hand in 1892 that clocked
in at a little under one calculation a minute to today s machines a pattern
emerged. Despite the differences among all of these technologies, human brains,
punch cards, vacuum tubes, integrated circuits, the overall increase in
humanity s ability to perform calculations has progressed quite smoothly and
extremely quickly. Put together, there has been a roughly exponential increase
in our information transformation abilities over time.
But how does this happen? How can all of these combined technologies yield such
a smooth and regular curve? When someone develops a new innovation, it is often
largely untested. As its developers improve and refine it, they begin to
realise the potential of this new innovation. Its capabilities begin to grow
exponentially, but then a limit is reached. And when that limit is reached
there is the opportunity to bring in a new technology, even if it s still
tentative, untested and buggy. Combine all these successions of technologies
together and what you get is a smooth curve of progresss.
Giant s shoulders
So technological knowledge exhibits rapid growth just like scientific
knowledge. But the relationship between the progression of technological facts
and that of science is tightly intertwined.
Take the periodic table of chemical elements. We know that the number of known
elements has steadily increased over time. However, while the number appears to
have grown relatively smoothly over the centuries, if you look at the data more
closely, a different picture emerges. As science historian Derek de Solla Price
found, the periodic table has grown by a series of logistic curves. He argued
that each of these was due to a successive technological advance or approach.
For example, from the beginnings of the scientific revolution in the late 17th
Century until the late 19th Century, more than sixty elements were discovered,
using various chemical techniques, including electrical shocks, to separate
compounds into their constituent parts.
However, these approaches soon reached their limits, and the discoveries
slowed. But, following a Moore s Law-like trajectory, a new technology arose.
The particle accelerator was created, and its atom-smashing ability enabled
further discoveries. As particle accelerators of increasing energies have been
developed, we have discovered heavier and larger chemical elements. In a very
real way, these advances have allowed for new facts.
Technological growth facilitates changes in facts, sometimes rapidly, in many
areas: sequencing new genomes (nearly two hundred distinct species were
sequenced as of late 2011); finding new asteroids (often done using
sophisticated computer algorithms that can detect objects moving in space);
even proving new mathematical theorems through increasing computer power.
The question is why everything adheres to these exponential curves and grows so
rapidly. A likely answer is related to the idea of cumulative knowledge.
Anything new an idea, discovery, or technological breakthrough must be
built upon what is known already. This is generally how the world works.
Scientific ideas build upon one another to allow for new scientific knowledge
and technologies, and are the basis for new breakthroughs. When it comes to
technological and scientific growth, we can bootstrap what we have learned
towards the creation of new facts. We must gain a certain amount of knowledge
in order to learn something new.
So, while exponential growth is not a self-fulfilling proposition, there is
feedback, which leads to a sort of technological imperative: as there is more
technological or scientific knowledge on which to grow, new technologies
increase the speed at which they grow. But why does this continue to happen?
Technological or scientific change doesn t happen automatically; people are
needed to create new ideas and concepts. The answer is that in addition to
knowledge accumulation, we need to understand another factor that s important
to knowledge progression: population growth.
Rapid spread
In an incredibly sweeping and magnificent article, entitled Population Growth
and Technological Change: One Million BC to 1990, economist Michael Kremer
argues that the growth of human population over the history of the world is
consistent with how technological change happens.
Kremer does this in an elegant way, making only a small set of assumptions.
First, he states that population growth is limited by technological progress.
This is one of those assumptions that has been around since Thomas Malthus, and
it is based on the simple fact that as a population grows we need more
technology to sustain the population, whether through more efficient food
production, more efficient waste management, or other similar considerations.
Conversely, Kremer also states that technological growth should be proportional
to population size. If invention occurs at the same rate for each person, the
more people there are, the more innovation there should be. (More recent
research, however, shows that population density often causes innovation to
grow faster than population size, so this seems like an underestimate.)
Travel and communication must also play a significant role in the spread of
facts and knowledge. For instance, David Bradley, a British epidemiologist,
discovered the extent to which populations have spread in an elegant way.
He plotted the lifetime distances travelled by the men in his family over four
generations. His great grandfather only travelled around the village of
Kettering, north of London which could be encompassed in a square that is
about 25 miles (40 kilometres) on each side. His grandfather, however,
travelled as far as London, defined by a square that is about 250 miles (400
km) on each side. Bradley s father was even more cosmopolitan and travelled
throughout Europe; his lifetime movements could be spread throughout a space
around 2,500 miles (4,000 km) on each side. Bradley himself, a world-famous
scientist, travelled across the globe. While the Earth is not a square grid, he
travelled in a range that is around 25,000 miles (40,000 km) on a side, about
the circumference of the Earth. A Bradley man moved ten times farther
throughout the course of his life with each successive generation, an
exponential increase of an order of magnitude more extensive in each direction
than his father.
Bradley was concerned with the effect that this increase in travel would have
on the spread of disease. But the Bradley family s exponentially increasing
travel distances illustrates not only advances in technology; it is indicative
of how technology s march can itself allow for the greater dispersal of other
knowledge.
The speed at which individuals, information and ideas can spread has greatly
increased in the past several hundred years. And, unsurprisingly, it has done
so according to mathematical rules. The upper limit of travel distances made by
people in France in a single day has exponentially increased over a 200-year
period, for example, mirroring Bradley s anecdotal evidence. Similar trends
hold for air and sea transportation. The curves for sea transport begin a bit
earlier (around 1750), and air transit of course starts later (from the 1920s
onwards), but like movement over land, these other modes of transportation obey
clear mathematical regularities.
These transportation speeds have clear implications for how the world around us
changes. For instance, Cesare Marchetti, an Italian physicist and systems
analyst, examined the city of Berlin in great detail and showed that the city
has grown in tandem with technological developments. From its early dimensions,
when it was hemmed in by the limits of pedestrians and coaches, to later times,
when its size ballooned alongside the electric trams and subways, Berlin s
general shape was dictated by the development of ever more powerful
technologies.
Marchetti showed that Berlin s expanse grew according to a simple rule of
thumb: the distance reachable by current technologies in thirty minutes or
less. As travel speeds increased, so too did the distance traversable and the
size of the city.
So we arrive at the foundations of a variety of ever-changing facts based on
the development of travel technologies: the natural size of a city; how long
information takes to wing its way around the world; and how distant a commute a
reasonable person might be expected to endure. And from communication and urban
growth to information processing and medical developments, the facts of our
everyday lives are governed by technological progress.
While the details of each technological development might be unknown what I
can download, or how many more transistors can be crammed into a square inch,
for instance there are mathematically defined, predictable regularities to
how these changes occur. All of these facts, ever changing, are subject to the
rules of technological change. And more often than not these ultimately follow
a defined pattern: their own mini-Moore s Law.
This is an edited extract from The Half-Life Of Facts: Why Everything We Know
Has An Expiration Date, by Samuel Arbesman. If you would like to comment on
this article or anything else you have seen on Future, head over to our
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