[Beowulf] IBM's Watson on Jeopardy tonight

Eugen Leitl eugen at leitl.org
Wed Feb 16 04:41:59 EST 2011


On Wed, Feb 16, 2011 at 09:26:53AM +0100, Jonathan Aquilina wrote:
> To be tied with a human though i feel means they are on par with humans.

Here's a slightly different take on the matter

http://www.sciencemag.org/content/early/2011/02/09/science.1200970.abstract


Perspectives 
To put our findings in perspective, the 6.4*10 18  
instructions per second that human kind can carry out on its 
general-purpose computers in 2007 are in the same ballpark 
area as the maximum number of nerve impulses executed by 
one human brain per second (10 17 ) (36). The 2.4*10 21  bits 
stored by humanity in all of its technological devices in 2007 
is approaching order of magnitude of the roughly 10 23  bits 
stored in the DNA of a human adult (37), but it is still 
minuscule compared to the 10 90  bits stored in the observable 
universe (38). However, in contrast to natural information 
processing, the world’s technological information processing 
capacities are quickly growing at clearly exponential rates. 
 
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We estimate the world’s technological capacity to store, 
communicate, and compute information, tracking 60 
analog and digital technologies during the period from 
1986 to 2007. In 2007, humankind was able to store 2.9 x 
10
20
 optimally compressed bytes, communicated almost 2 
x 10
21
 bytes, and carry out 6.4 x 10
18
 instructions per 
second on general-purpose computers. General-purpose 
computing capacity grew at an annual rate of 58%. The 
world’s capacity for bidirectional telecommunication 
grew at 28% per year, closely followed by the increase in 
globally stored information (23%). Humankind’s capacity 
for unidirectional information diffusion through 
broadcasting channels has experienced comparatively 
modest annual growth (6%). Telecommunication has been 
dominated by digital technologies since 1990 (99.9% in 
digital format in 2007) and the majority of our 
technological memory has been in digital format since the 
early 2000s (94% digital in 2007). 
Leading social scientists have recognized that we are living 
through an age in which “the generation of wealth, the 
exercise of power, and the creation of cultural codes came to 
depend on the technological capacity of societies and 
individuals, with information technologies as the core of this 
capacity” (1). Despite this insight, most evaluations of 
society’s technological capacity to handle information are 
based on either qualitative assessments or indirect 
approximations, such as the stock of installed devices or the 
economic value of related products and services (2–9). 
Previous work 
Some pioneering studies have taken a more direct 
approach to quantify the amount of information that society 
processes with its information and communication 
technologies (ICT). Following pioneering work in Japan (10), 
Pool (11) estimated the growth trends of the “amount of 
words” transmitted by 17 major communications media in the 
United States from 1960 to 1977. This study was the first to 
show empirically the declining relevance of print media with 
respect to electronic media. In 1997, Lesk (12) asked “how 
much information is there in the world?” and presented a 
brief outline on how to go about estimating the global 
information storage capacity. A group of researchers at the 
University of California, at Berkeley, took up the 
measurement challenge between 2000 and 2003 (13). Their 
focus on “uniquely created” information resulted in the 
conclusion that “most of the total volume of new information 
flows is derived from the volume of voice telephone traffic, 
most of which is unique content” (97%); as broadcasted 
television and most information storage mainly consists of 
duplicate information, these omnipresent categories 
contributed relatively little. A storage company hired a 
private sector research firm (International Data Corporation, 
IDC) to estimate the global hardware capacity of digital ICT 
for the years 2007-2008 (14). For digital storage, IDC 
estimates that in 2007 “all the empty or usable space on hard 
drives, tapes, CDs, DVDs, and memory (volatile and 
nonvolatile) in the market equaled 264 exabytes” (14). 
During 2008, an industry and university collaboration 
explicitly focused on information consumption (15), 
measured in hardware capacity, words, and hours. The results 
are highly reliant on media time-budget studies, which 
estimate how many hours people interact with a media 
device. Not surprisingly, the result obtained with this 
methodology was that computer games and movies represent 
99.2% of the total amount of data “consumed”. 
Scope of our exercise 
To reconcile these different results, we focus on the 
world’s technological capacity to handle information. We do 
not account for uniqueness of information, since it is very 
difficult to differentiate between truly new and merely 
recombined, duplicate information. Instead we assume that all 
information has some relevance for some individual. Aside 
from the traditional focus on the transmission through space 
(communication) and time (storage), we also consider the 
computation of information. We define storage as the 
The World’s Technological Capacity to Store, Communicate, and Compute 
Information 
Martin Hilbert 1*
 and Priscila López 2
 
1 University of Southern California (USC), Annenberg School of Communication; United Nations ECLAC.  2 Open University of 
Catalonia (UOC). 
*To whom correspondence should be addressed. E-mail: mhilbert at usc.edu 
 
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maintenance of information over a considerable amount of 
time for explicit later retrieval and estimate the installed 
(available) capacity. We do not consider volatile storage in 
the respective inventory (such as RAM), since the ultimate 
end of volatile memory is computation, not storage per se. 
Communication is defined as the amount of information that 
is effectively received or sent by the user, while being 
transmitted over a considerable distance (outside the local 
area). This includes those transmissions whose main purpose 
consists in the overcoming of distances, not the local sharing 
of information (such as the distribution of copies at a 
meeting, or communication through private local area 
networks). We take inventory of the effective communication 
capacity (the actual amount of bits transmitted). We define 
computation as the meaningful transformation of information 
and estimate the installed (available) capacity. 
More precisely, as shown in Fig. 1, we distinguishamong: 
storage of information in bits; unidirectional diffusion 
through broadcasting in bits per second; bidirectional 
telecommunication in bits per second; computation of 
information by general purpose computers in instructions per 
second (or MIPS); and (the estimated computational capacity 
of a selected sample of application-specific devices (MIPS). 
While previous studies tracked some two or three dozen 
categories of ICT over three consecutive years at most, our 
study encompasses worldwide estimates for 60 categories (21 
analog and 39 digital) and spans over two decades (1986-
2007). 
We obtain the technological capacity by basically 
multiplying the number of installed technological devices 
with their respective performances. All estimates are yearly 
averages, but we adjust for the fact that the installed 
technological stock of a given year is the result of an 
accumulation process of previous years, whereas each year’s 
technologies contribute with different performance rates. We 
used 1,120 sources and explain our assumptions in detail in 
Supporting Online Material (16). The statistics we rely on 
include databases from international organizations [such as 
(17–22)], historical inventories from individuals for 
commercial or academic purposes [such as (23–26)], publicly 
available statistics from private research firms [such as (27, 
28)], as well as a myriad of sales and product specifications 
from equipment producers. We filled in occasional blanks 
with either linear or exponential interpolations, depending on 
the nature of the process in question. Frequently we compared 
diverse sources for the same phenomena and strove for 
reasonable middle grounds in case of contradictions. In cases 
where specific country data were not available, we aimed for 
a globally balanced outlook by creating at least two 
international profiles, one for the “developed” member 
countries of the Organisation for Economic Co-operation and 
Development (OECD), and another one for the rest of the 
world. 
Information, not hardware with redundant data 
Although the estimation of the global hardware capacity 
for information storage and communication is of interest for 
the ICT industry (14), we are more interested in the amount 
of information that is handled by this hardware. Therefore, 
we converted the data contained in storage and 
communication hardware capacity into informational bits by 
normalizing on compression rates. This addresses the fact that 
information sources have different degrees of redundancy. 
The redundancy (or predictability) of the source is primarily 
determined by the content in question, such as text, images, 
audio or video (29, 30). Considering the kind of content, we 
measured information as if all redundancy were removed with 
the most efficient compression algorithms available in 2007 
(we call this level of compression “optimally compressed”). 
Shannon (29) showed that the uttermost compression of 
information approximates the entropy of the source, which 
unambiguously quantifies the amount of information 
contained in the message. In an information theoretic sense 
(30), information is defined as the opposite of uncertainty. 
Shannon (29) defined one bit as the amount of information 
that reduces uncertainty by half (regarding a given probability 
space, such as letters from an alphabet or pixels from a color 
scale). This definition is independent of the specific task or 
content. For example, after normalization on optimally 
compressed bits we can say things like “a 6 square-cm 
newspaper image is worth a 1000 words”, because both 
require the same average number of binary yes/no decisions 
to resolve the same amount of uncertainty. 
Normalization on compression rates is essential for 
comparing the informational performance of analog and 
digital technologies. It is also indispensable for obtaining 
meaningful time series of digital technologies, since more 
efficient compression algorithms enable us to handle more 
information with the same amount of hardware. For example, 
we estimate that a hard disk with a hardware performance of 
1 MB for video storage was holding the equivalent of 1 
optimally compressed MB in 2007 (“optimally compressed” 
with MPEG-4), but only 0.45 optimally compressed MB in 
2000 (compressed with MPEG-1), 0.33 in 1993 (compressed 
with cinepack) and merely 0.017 optimally compressed MB 
in 1986 (supposing that no compression algorithms were 
used). Given that statistics on the most commonly used 
compression algorithms are scarce, we limited our 
estimations of information storage and communication to the 
years 1986, 1993, 2000 and 2007 (see Supporting Online 
Material, 16, B Compression). 
Conventionally bits are abbreviated with a small “b” (such 
as in kilobits per second: kbps) and bytes (equal to 8 bits) 
with a capital “B” (such as in Megabyte: MB). Standard 
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decimal prefixes are used: kilo (10 3 ), mega (10 6 ), giga (10 9 ), 
tera (10 12 ), peta (10 15 ), exa (10 18 ), zetta (10 21 ). 
Storage 
We estimated how much information could possibly have 
been stored by the 12 most widely used families of analog 
storage technologies and the 13 most prominent families of 
digital memory, from paper-based advertisement to the 
memory chips installed on a credit card (Fig. 2). The total 
amount of information grew from 2.6 optimally compressed 
exabytes in 1986, to 15.8 in 1993, over 54.5 in 2000, to 295 
optimally compressed exabytes in 2007. This is equivalent to 
less than one 730 MB CD-ROM per person in 1986 (539 MB 
per person), roughly 4 CD-ROM per person of 1993, 12 in 
the year 2000 and almost 61 CD-ROM per person in 2007. 
Piling up the imagined 404 billion CD-ROM from 2007 
would create a stack from the earth to the moon and a quarter 
of this distance beyond (with 1.2 mm thickness per CD). 
Our estimate is significantly larger than the previously 
cited hardware estimate from IDC for the same year (14) 
(IDC estimates 264 exabytes of digital hardware, not 
normalized for compression, while we count 276 optimally 
compressed exabytes on digital devices, which occupy 363 
exabytes of digital hardware). While our study is more 
comprehensive, we are not in a position to fully analyze all 
differences, since IDC’s methodological assumptions and 
statistics are based on inaccessible and proprietary company 
sources. 
Before the digital revolution, the amount of stored 
information was dominated by the bits stored in analog 
videotapes, such as VHS cassettes (Fig. 2). In 1986, vinyl 
Long-Play records still made up a significant part (14%), as 
did analog audio cassettes (12%) and photography (5% and 
8%). It was not until the year 2000 that digital storage made a 
significant contribution to our technological memory, 
contributing 25% of the total in 2000. Hard disks make up the 
lion share of storage in 2007 (52% in total),optical storage 
contributed more than a quarter (28%) and digital tape 
roughly 11%. Paper-based storage solutions captured a 
decreasing share of the total (0.33% in 1986 and 0.007% in 
2007), even though their capacity was steadily increasing in 
absolute terms (from 8.7 to 19.4 optimally compressed 
petabytes). 
Communication 
We divided the world’s technological communication 
capacity into two broad groups: one includes technological 
systems that provide only unidirectional downstream capacity 
to diffuse information (referred to as broadcasting), and one 
provides bidirectional upstream and downstream channels 
(telecommunication). The ongoing technological convergence 
between broadcasting and telecommunication is blurring this 
distinction, as exemplified by the case of digital TV, which 
we counted as broadcasting, even though it incorporates a 
small, but existent upstream channel (e.g. video-on-demand). 
The inventories of Figs. 3 and 4 account for only those bits 
that are actually communicated. In the case of 
telecommunication, the sum of the effective usages of all 
users is quite similar to the total installed capacity (any 
difference represents an over- or future investment). This is 
because most backbone networks are shared and only used 
sporadically by an individual user. If all users demanded their 
promised bandwidth simultaneously, the network would 
collapse. This is not the case for individual broadcast 
subscribers, who could continuously receive incoming 
information. To meaningfully compare the carrying capacities 
of each, we applied effective consumption rates to the 
installed capacity of broadcasting (calling it the effective 
capacity). This reduced the installed capacity by a stable 
factor (by 9 in 1986; 9.1 in 1993; 8.7 in 2000; and 8.4 in 
2007), implying an average individual broadcast consumption 
of roughly 2 hours and 45 minutes per 24 hours. It did not 
significantly change the relative distribution of the diverse 
technologies (Fig. 3). 
Fig. 3 displays the capacity of 6 analog and 5 digital 
broadcast technologies, including newspapers and personal 
navigation devices (GPS). In 1986, the world’s technological 
receivers picked up around 432 exabytes of optimally 
compressed information, 715 in 1993, 1.2 optimally 
compressed zettabytes in 2000 and 1.9 in 2007. Cable and 
satellite TV steadily gained importance but analog, “over-the-
air,” terrestrial television still dominated the evolutionary 
trajectory. Digital satellite television led the pack into the 
digital age, receiving 50% of all digital broadcast signals in 
2007. Only a quarter of all broadcasting information was in 
digital format in 2007. The share of radio declined gradually 
from 7.2% in 1986 to 2.2% in 2007. 
Fig. 4 presents effective capacity of the 3 most common 
bidirectional analog telecommunication technologies and 
their 4 most prominent digital heirs. The 281 petabytes of 
optimally compressed information from 1986 were 
overwhelmingly dominated by fixed line telephony, whereas 
postal letters contributed only 0.34%. The year 1993 was 
characterized by the digitization of the fixed phone network 
(471 optimally compressed petabytes). We estimate the year 
1990 to be the turning point from analog to digital 
supremacy. The Internet revolution began shortly after the 
year 2000. In only 7 years, the introduction of broadband 
Internet effectively multiplied the world’s telecommunication 
capacity by a factor of 29, from 2.2 optimally compressed 
exabytes in 2000, to 65 in 2007. The most widespread 
telecommunication technology was the mobile phone, with 
3.4 billion devices in 2007 (versus 1.2 billion fixed line 
phones and 0.6 billion Internet subscriptions). Nevertheless, 
the fixed-line phone is still the solution of choice for voice 
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communication (1.5% of the total). The mobile phone 
network became increasingly dominated by data traffic in 
2007 (1.1% for mobile data versus 0.8% for mobile voice). 
When compared withbroadcasting, telecommunications 
makes a modest, but rapidly growing part of the global 
communications landscape (3.3% of their sum in 2007, up 
from 0.07% in 1986). Althoughthere are only 8% more 
broadcast devices in the world than telecommunication 
equipment (6.66 billion vs. 6.15 billion in 2007), the average 
broadcasting device communicates 27 times more 
information per day than the average telecommunications 
gadget. This result might be unexpected, especially 
considering the omnipresence of the Internet, but can be 
understood when considering that an average Internet 
subscription effectively uses its full bandwidth for only 
around 9 minutes per day (during an average 1 hour and 36 
minutes daily session). 
Computation 
>From a theoretical standpoint, a “computation” is the 
repeated transmission of information through space 
(communication) and time (storage), guided by an 
algorithmic procedure (31). The problem is that the applied 
algorithmic procedure influences the overall performance of a 
computer, both in terms of hardware design and in terms of 
the contributions of software. As a result, the theoretical, 
methodological, and statistical bases for our estimates for 
computation are less solid than the ones for storage and 
communication. In contrast to Shannon’s bit (29, 30), there is 
no generally accepted theory that provides us with an ultimate 
performance measure for computers. There are several ways 
to measure computational hardware performance. We chose 
MIPS (Million or Mega Instructions Per Second) as our 
hardware performance metric, which was imposed upon us by 
the reality of available statistics. Regarding the contributions 
of software, it would theoretically be possible to normalize 
the resulting hardware capacity for algorithmic efficiency 
(such as measured by O-notation) (32). This would recognize 
the constant progress of algorithms, which continuously make 
more efficient use of existing hardware. However, the 
weighted contribution of each algorithm would require 
statistics on respective execution intensities of diverse 
algorithms on different computational devices. We are not 
aware of such statistics. As a result of these limitations, our 
estimates refer to the installed hardware capacity of 
computers. 
We distinguished between two broad groups of computers. 
The first group includes all computers whose functionality is 
directly guided by their human users. We call this group 
“general-purpose computers” and include 6 technological 
families (Fig. 5). The second group carries out automated 
computations that are incidental to the primary task, such as 
in electronic appliances or visual interfaces. The user may 
have a range of predefined choices regarding their 
functionality, butcannot change the automated logic of these 
embedded systems. We call this group “application-specific 
computers”. 
Although general-purpose computers are also equipped 
with application-specific parts (mobile phones come with 
digital signal processors, and PCs contain microcontroller 
units, etc.), we only include the capacity of humanly guidable 
microprocessors in the respective inventory. The calculator 
laid the cornerstone for modern microprocessors and was still 
the dominant way to compute information in 1986 (41% of 
3.0x 10 8 general-purpose -MIPS). The landscape changed 
quickly during the early 1990s, as personal computers and 
servers and mainframe computers pushed the evolutionary 
trajectory to 4.4 x 10 9 -MIPS. The personal computer 
extended its dominance during the year 2000 (86% of a total 
of 2.9 10 11 -MIPS), to be rivaled in 2007 by videogame 
consoles (1.6 x 10 12  MIPS or 25% of the total of 6.4 x 10 12 
MIPS) and increasingly relevant mobile phones (3.7 x 10 11 
MIPS or 6% of the 2007 total). Nowadays, clusters of 
videogame consoles are occasionally used as supercomputer 
substitutes for scientific purposes and other data intensive 
computational tasks (33). The relatively small role of 
supercomputers (less than 0.5% throughout) and professional 
servers and mainframes might come as a surprise. It can 
partially be explained by the fact that the inventory of Fig. 5 
presents the installed capacity, independent of effective usage 
rates. We also carried out some estimations based on the 
effective gross usage of the computers, which considers the 
time users interact with computers (not the net computational 
time). As a result we get between 5.8% and 9.1% of the 
installed capacity (16, table SA4). The share of servers and 
mainframes grows to 89% in 1986 and 11% in 2007, and 
supercomputers contribute 4% to the effective capacity in 
2007. 
The data also allows us to look at respective growth rates. 
Until the early 1990s, the annual growth rate was quite stable, 
at roughly 40% (Fig. 6). The 1990s show outstanding growth, 
reaching a peak of 88% in 1998. Since then, the technological 
progress has slowed. In recent times, every new year allows 
humankind to carry out roughly 60% of the computations that 
could have possibly been executed by all existing general-
purpose computers before that year. 
Our inventory of application-specific computations is the 
least complete one. The entire group of application-specific 
computers is very large and diverse (for example, dice cups 
and roulette wheels are application-specific, analog, random 
number generators) and it is often not straightforward to 
translate their performance into MIPS. The main goal of our 
inventory of this group was to show that the computational 
hardware capacity of application-specific computers is larger 
than the computational capacity of general-purpose 
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computers (16) (table SA3). To achieve this we focused on a 
sample that includes three prominent groups: digital signal 
processors (DSP), which translate between analog and digital 
signals (including CD, DVD and PVR devices, cameras and 
camcorders, modems and setup boxes, GPS, portable media, 
printer and fax, radio, fixed and mobile phones); 
microcontrollers (MCU) (which regulate electronics and 
appliances); and graphic processing units (GPU) (an 
increasingly powerful microprocessor for visual displays). 
Although microcontrollers dominated our sample of 
application-specific computing support in 1986 (90% of the 
4.3 x 10 8  application-specific MIPS from our sample), graphic 
processing units clearly made up the lion share in 2007 (97% 
of 1.9 x 10 14 MIPS). 
Comparisons and growth rates 
The world’s technological capacity to compute 
information has by far experienced the highest growth (Table 
1). The per capita capacity of our sample of application-
specific machine mediators grew with a compound annual 
growth rate of 83% between 1986 and 2007 and humanly 
guided general-purpose computers grew at58% per year. The 
world’s technological capacity to telecommunicate only grew 
half as fast (CAGR of 28%). This might seem a little 
surprising, as the advancement of telecommunications, and 
especially the Internet, is often celebrated as the epitome of 
the digital revolution. The results from Table 1 challenge this 
idea and move the world’sability to compute information into 
the spotlight. The storage of information in vast technological 
memories has experienced a growth rate almost similar to 
telecommunication (CAGR of 23% per capita over two 
decades). The lower growth rate results from the relatively 
high base level provided by prevalent analog storage devices. 
The main characteristic of the storage trajectory is the 
digitalization of previously analog information (from 0.8% 
digital in 1986 to 94% in 2007). The global capacity to 
broadcast information has experienced the least progress, at 
6% CAGR per capita. Broadcasting is also the only 
information operation that is still dominated by analog ICT. 
As a result, the capacity to store information has grown at a 
much faster rate than the combined growth rate of tele- and 
broadcast communication. In 1986 it would have been 
possible to fill the global storage capacity with the help of all 
effectively used communication technologies in roughly 2.2 
days (539/241.16). In 1993 it would have taken almost 8 
days, in the year 2000 roughly 2.5 weeks, and in 2007 almost 
8 weeks. 
The compound annual growth rates represent the temporal 
average of periods which were experiencing different patterns 
of technological change. General-purpose computation had its 
peak growth around the turn of the millennia (Fig. 6).Storage 
capacity slowed down around the year 2000, but accelerated 
growth has been occurring in recent years (CAGR of 27% for 
1986-1993, 18% for 1993-2000 and 26% for 2000-2007; 
Table 1). The introduction of broadband has led to a 
continuous acceleration of t telecommunication (CAGR of 
6% for 1986-1993, 23% for 1993-2000 and 60% for 2000-
2007; Table 1), whereasbroadcasting had a relatively stable 
rate of change (CAGRs of 5.7%, 5.6% and 6.1% for 1986-
1993, 1993-2000 and 2000-2007, respectively; Table 1). 
The growth rates also allow us to look at the application of 
Moore’s laws (34) for the technological information 
processing capacity of humankind. Machines’ application-
specific capacity to compute information per capita has 
roughly doubled every 14 months over the past decades in our 
sample, while the per capita capacity of the world’s general-
purpose computers has doubled every 18 months. The global 
telecommunication capacity per capita doubled every 34 
months, while the world’s storage capacity per capita 
required roughly 40 months. Per capita broadcast information 
has doubled roughly every 12.3 years. Of course, such 
averages disguise the varying nature of technological 
innovation avenues (35). 
Perspectives 
To put our findings in perspective, the 6.4*10 18  
instructions per second that human kind can carry out on its 
general-purpose computers in 2007 are in the same ballpark 
area as the maximum number of nerve impulses executed by 
one human brain per second (10 17 ) (36). The 2.4*10 21  bits 
stored by humanity in all of its technological devices in 2007 
is approaching order of magnitude of the roughly 10 23  bits 
stored in the DNA of a human adult (37), but it is still 
minuscule compared to the 10 90  bits stored in the observable 
universe (38). However, in contrast to natural information 
processing, the world’s technological information processing 
capacities are quickly growing at clearly exponential rates. 
References and Notes 
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5. C. Perez, Futures 15, 357 (1983). 
6. T. Forester (The MIT Press, 1985). 
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(1981). 
11. I.D.S. Pool, Science 221, 609 (1983). 
12. M. Lesk, lesk.com/mlesk (1997). 
13. P. Lyman, H. Varian (University of California, Berkeley, 
2003). 
14. J. Gantz, et al. (International Data Corporation, 2008). 
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15. R. Bohn, J. Short (University of California, San Diego, 
2009). 
16. Materials and methods are available as supporting 
material on Science Online. 
17. International Telecommunication Union, United Nations 
ICT Indicators Database (2010). 
18. Faostat, United Nations ForesSTAT (2010). 
19. Universal Postal Union, United Nations Postal Statistics 
(2007). 
20. International Federation of the Phonographic Industry 
(1995-2004). 
21. Japanese Recording-Media Industries Association (2007). 
22. TOP500, Supercomputers (2009). 
23. J. Porter, disktrend.com (2005). 
24. R. Longbottom, roylongbottom.org.uk (2006). 
25. J. McCallum, The computer engineering handbook, 136 
(2006). 
26. T. Coughlin (Coughlin Associates, 2007). 
27. Morgan Stanley (2006). 
28. International Data Corporation (IDC) (2008). 
29. C. A. Shannon, Bell. Syst. Tech. J. 27, 379-423, 623 
(1948). 
30. T.M. Cover, J.A. Thomas (Wiley-Interscience, ed. 2, 
2006). 
31. A.M. Turing, Proc. of the London Math. Soc. s2-42, 230 
(1937). 
32. T. Cormen, C. Leiserson, R. Rivest & C. Stein (McGraw-
Hill Science/Engineering/Math, 2003). 
33. B. Gardiner, Wired Magazine Tech Biz IT, 10.17.07 
(2007). 
34. Moore's law measures technological progress of computer 
performance by counting the numbers of transistors on an 
integrated circuit, which has approximately doubled every 
two years since the 1960s. G.E. Moore. Proc. of SPIE, 2-
17 (1995). 
35. D. Sahal, Research Policy 14, 61 (1985). 
36. Assuming 100 billion neurons * 1,000 connections per 
neuron * max 1,000 nerve impulses per second. 
37. Considering a quaternary DNA alphabet, in which each 
base pair can store 4 bits * 3 billion DNA base pairs per 
human cell * 60 trillion cells per adult human . 
38. S. Lloyd. Phys. Rev. Lett. 88, 237901 (2002). 
39. We would like to thank the Information Society Program 
of United Nations ECLAC (in Chile) for its support, Tom 
Coughlin, John McCallum, Don Franz, Miguel Gonzalez, 
Cristian Vasquez, Len Adleman, Manuel Castells and the 
statisticians from UPU (Universal Post Union) and ITU 
(International Telecommunications Union), as well as 
numerous colleagues who motivated us by doubting the 
feasibility of this undertaking. 
 
 
 
 
Supporting Online Material 
www.sciencemag.org/cgi/contebt/full/science.1200970/DC1 
Materials and Methods 
Figs. A1 to E12 
Tables SA1 to SE24 
References and Notes 
29 November 2010; accepted 1 February 2011 
Published online 10 February 2011; 10.1126/science.1200970 
Fig. 1. The three basic information operations and theirmost 
prominent technologies. 
Fig. 2. World’s technological installed capacity to store 
information. Based on Supporting Online Material (16) Table 
SA1. 
Fig. 3. World’s technological effective capacity to broadcast 
information, in optimally compressed Megabytes (MB) per 
year, for 1986, 1993, 2000 and 2007, semi-logarithmic plot. 
Based on Supporting Online Material (16) Table SA2. 
Fig. 4. World’s technological effective capacity to 
telecommunicate information, Based on Supporting Online 
Material (16) Table SA2. 
Fig. 5. World’s technological installed capacity to compute 
information on general-purpose computers, in millions 
instructions per second (MIPS), Based on Supporting Online 
Material (16) Table SA3. 
Fig. 6. Annual growth of installed general-purpose 
computational capacity as percentage of all previous 
computations since 1977 (yeart / Σ[1977, yeart-1]). Based on 
Supporting Online Material (16) Table SA3. 
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