trends and cycles of the internet evolution and worldwide impacts

Trends and cycles of the internet evolution and worldwide impacts

Luiz C.M. Miranda a,⁎, Carlos A.S. Lima b

a Instituto Nacional de Pesquisas Espaciais, São José dos Campos, SP, Brazilb Universidade Estadual de Campinas, Campinas, SP, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 March 2011Accepted 7 September 2011Available online xxxx

In this paper we present a quantitative analysis of the evolution of some Internet and ICT evo-lution indicators. It focuses on the number of Internet hosts, the Internet penetration index, theICT development index and the software/protocols development. In addition, we analyzed theseries of most impacting events building up the Internet along the last fifty years. These ana-lyses were carried out using the multi-logistic procedure recently proposed by the authors.Our results for hosts counting, penetration index and software/protocols development arecompatible with the onset of some radical changes in the Internet technology to be currentlyunderway and we forecast new growth rate peaks to occur by 2015. The software/protocolswere found to having been powered by bursts of creativity with periods of the order of theKuznets and Kondratiev economic cycles. Similar conclusions were drawn from the series ofmain events building up the Internet. Despite the clear signs of worldwide improvement inthe ICT infrastructure and usage between 2002 and 2007 obtained from the ICT developmentindex, its cross-correlation with the human development index (HDI) revealed the presence ofa group of countries whose improvements in the operational ICT index are disconnected fromtheir corresponding HDI improvements.

© 2011 Elsevier Inc. All rights reserved.

Keywords:Information and communication technologiesWorld GDPInformation development indexFunctional and operational informationdevelopment indicesInternet evolutionInternet socio-economic impactsMulti-logistic modelingGlobal digital inequality

1. Introduction

Throughout History, the means for both people locomotion and transmission of information, from barefoot walking and ani-mal riding to automobiles and spaceships, on one side, and from wooden drums and smoke signs to today's ICT and Internet, onthe other, has played a decisive role in shaping the evolution of mankind. Currently, the modern information and communicationstechnologies (ICT), together with the conventional physical means of transportation (by land, sea, air and space), may be viewedlatu sensu as composing what we can denote as the “generic transportation vector”.

From a system's standpoint, we may view human society dynamics as a self-feedback system primarily consisting of a triad ofmutually interacting sub-systems, namely, the population size N, the resources feeding supply sub-system, F, encompassing boththe natural resources and food supply, and K the accumulated technological and scientific knowledge sub-system. We accordinglypropose a “N–F–K triangle” to represent these three mutually interacting fundamental sub-systems in their cooperative driving ofhuman social dynamics, with the “generic transportation vector”, T, being the interaction carrier among them. This N–F–K interact-ing system engenders all possible human outputs of which the Gross Domestic Product (GDP) is of utmost social dynamic impor-tance and most evident economic significance. In this context, such engendering would be schematically represented by apyramid with the N–F–K triangle at its base triangle and the GDP at its apex, all of them mutually interacting through the carrierT. Entering here into a detailed account of our “N–K–F interaction triangle” and its associated “social output pyramid”, as a “worlddynamics” modeling, would be unnecessary and, actually, it would distract us from sticking to the specific mainstream goals of

Technological Forecasting & Social Change xxx (2011) xxx–xxx

⁎ Corresponding author at: Rua Serimbura 60 403-A, 12243-360, S. J. Campos, SP, Brazil. Tel.: +55 12 33222333.E-mail address: [email protected] (L.C.M. Miranda).

TFS-17483; No of Pages 22

0040-1625/$ – see front matter © 2011 Elsevier Inc. All rights reserved.doi:10.1016/j.techfore.2011.09.001

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Technological Forecasting & Social Change

Please cite this article as: L.C.M. Miranda, C.A.S. Lima, Trends and cycles of the internet evolution and worldwide impacts,Technol. Forecast. Soc. Change (2011), doi:10.1016/j.techfore.2011.09.001

http://dx.doi.org/10.1016/j.techfore.2011.09.001

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this paper, namely, the analysis of the trends and cycles of the Internet evolution and its socio-economic impacts. The brief outlinegiven above suffices for the current purposes. The details of the above system modeling will be presented in a separate paper.

The plane projection of such system is schematically shown in Fig. 1.The returns from the GDP feedback are instrumental for improving all three sub-system performances and that of the carrier T

as well with important impacts upon life expectancy, living standards, and so on, of the human population.The early ICTs were based on the use of wooden drums, smoke and fire signals, human messengers, flags, heliographs (use of

mirrors reflecting sunlight), and so on. They were essentially either slow or short distance limited means of information transport.The so-called modern ICTs, some of them already approaching the 150 years old mark, comprise quite a few that operate at thespeed of light, thus providing the fastest possible means of information transportation on Earth. Its roots are traced back to themiddle of the nineteenth century when the electric telegraphy emerged as the first fully-fledged system of telecommunication.The global flow of information from then on radically changed the space and time relationships and freed human interactionsfrom restricting to proximity or neighborhood. By directly interfering in the global exchanges and flows of goods, information,people and knowledge among geographically and socio-culturally diverse places, the ICT helped building up the global sphereand co-shaped the globalization process introducing new actors, new places and new practices to this realm, as well as new asym-metries and divides due to the uneven structuring of its network and other access barriers, as one contemplates its diffusionthroughout the world.

Different aspects regarding the evolution of the Internet and telecommunications have been extensively reported in recent lit-erature. Some [2] focused on the impacts of structural components like entrepreneurial disruptions, firm innovations, worldwidemarket expansion and government regulations that markedly affected the explosive expansion of telecommunications over the20th and 21st centuries. Others, like Vinton Cerf [3] and Modis [4] aimed at a near future forecast of the evolution of numberof Internet hosts and users. In a different, yet complementary approach, Devezas et al. [5] presented a detailed discussion of In-ternet growth dynamics in relation to the long wave theory as well as a quantitative analysis of the evolution of Internet hosts,software and protocols.

Cerf explored the available data for the number of Internet hosts between 1988 and 2001 and came to forecasting that by 2006this number would be nearing the figure of one billion hosts worldwide. Modis, instead, explored the number of worldwide In-ternet user data, covering from 1994 to 2005, coming from five different databases, using a logistic model to describe it. Hismodeling, carried out considering a set of nine pertinent points, led him to conclude that the Internet world penetration index(i.e. the number of users as percentage of the world population) should approach a saturation level corresponding to about14% of the world population. A similar conclusion regarding this worldwide slow down in the growth rate of the Internetusage, and pointing towards the reaching of a ceiling level by 2010, was independently reached by Devezas et al. [5] in their anal-ysis of two different Internet indicators, namely, one describing the evolution of the number of computer communication soft-ware and protocols, and the other one referring to the evolution of the number of Internet hosts.

In this paper, our recently proposed methodology for the logistic analysis of evolutionary growth processes time series [6,7] isapplied to the analysis and forecasting of the evolution of the main Internet and ICT indicators. The indicators we have chosen are:i— the number of Internet hosts as a measure of the available ICT infrastructure size; ii — the Internet penetration index (numberof Internet users as percentage of the world population) as a measure of the global Internet access and use; and iii — the overallICT Development Index (IDI) developed by the International Telecommunications Union (ITU) [8] to track, in a single index thatcombines several indicators, the progress in the development of ICT in the different nations, and to monitor the global digital di-vider. In addition, we have also analyzed the time series of the main events characterizing the evolution of programming

Fig. 1. Plane projection of the pyramidal representation of the human society dynamics viewed as a closed feedback system. This pyramid has the “primary driversinteraction triangle” at its base and the world GDP, as a social output, at the apex. The triangular basis consists of three mutually interacting sub-systems, namely,the population size sub-system, N, the feeding sub-system, F, encompassing both the natural resources and food supply, and the accumulated technological andscientific knowledge sub-system, K, to be referred to as the N–F–K triangle base. The carrier T of the mutual interactions among these three sub-systems is whatwe have called the “generic transportation vector” that also connects them to a final human output product, generically represented by the world GDP at the apexof the pyramid.

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image of Fig.�1


languages and communication protocols as well as that of the main events building up the Internet. The paper is organized as fol-lows. In the next section we present a brief historical outline leading to the birth of modern ICT. The following five sections arededicated to the presentation of the results of the application of our methodology to the aforementioned Internet and ICT indica-tors and the two time series regarding the evolution of programming languages and communication protocols and the chronologyof the Internet building. We conclude with a comparative analysis of these results and a discussion on their implications for thefuture of ICT.

The historical data on the internet host count, covering the time lapse between August 1981 and July 2010, was taken fromInternet Systems Consortium (ISC) [9]. The ISC carries on routine domain surveys in an attempt to account for every host onthe Internet and publishes its results on a quarterly basis. The data on the world total number of users as well as on the internetpenetration index, as percentage of the world population, was taken from the Internet World Stats [10] covering the period be-tween 1995 and September 2010. Finally, the chronological sequence of the main events leading to the build up of today's Inter-net was taken from the detailed listings available in [11].

2. 1950 — the great divider

No matter which measuring standard (economic, sociologic or any other) one uses to evaluate the time evolution of humansociety, at least, two important aspects inevitably show up and draw our attention. The first one refers to the concept of evolu-tionary cycles. These cycles are typically characterized as a three-phased bell-shaped process: a growing phase, a maturityphase somewhere along half the way through the cycle endurance, and an ultimate dying phase. This seems to be the overall pat-tern with which Nature seems to have endowed the evolution of life itself, as well as any other natural or manmade processes.These cycles are essentially responding to whatever motors are there driving the given evolutionary process and are accordinglyaccountable for clocking the time rate of the overall trend curve representing it. The second striking aspect is that the post WorldWar II period seems to be a landmark in the history of human society evolution. Designated by the late economist Angus Maddi-son [12] in his analysis of the capitalism development as the “golden phase”, this period is characterized by an unprecedentedboom in practically all dimensions of our society. In the economic domain this was a period of unparallel worldwide economicgrowth. In social and political terms, its second decade has been marked by the decolonization phase and the subsequent civilwars rise following the independence of many states, the capitalism–socialism world hegemony disputes that lead into theCold War, as well as by the dawn of a great number of social movements (civil rights, environmentalism, feminism, anti-warand antinuclear, among others) that would irreversibly change our society in the years to follow.

This critical divider character of the second half of the 20th century is clearly evident in Figs. 2 and 3. There we display theevolution of some relevant global economic, social and political indicators. The parameters chosen to represent these dimensionsof human society activity were the world's gross domestic product (GDP) and population, as representative of the economic andsocial dimensions, respectively, and the number of civil war conflicts as a measure of the political unrest ever present along theevolutionary trajectory of human society. Fig. 2 displays the evolution of the world's GDP and population from 1700 through 2008using Maddison [13] historical statistics for the world economy. Maddison's world GDP data is expressed in constant 1990 US dol-lars converted at international Geary–Khamis purchasing power parities (PPP). A sharp inflection by the year 1950 is clearly seenin the plots of both indicators. As a matter of fact, the vertiginous growth of both indicators is intimately linked to the advance-ment of knowledge that took place in the Modern Era as has been recently pointed out by Miranda and Lima [14]. Using two timeseries spanning the last five centuries (1500 to 1999), consisting of 1499 and 401 entries for the most impacting scientific discov-eries and technological inventions, respectively, these authors have shown that world GDP is exponentially correlated with boththe scientific discoveries and the technological inventions. We refer to Ref. [14] for further discussion and details on this subject.

In Fig. 3 we show the time evolution of the number of civil wars from 1816 to 2005 using version 1.52 of Gleditsch [15] ex-panded war data consisting of a listing of 373 civil wars in the aforementioned time period. Similarly to the previous plots,Fig. 3 shows a marked change in the rate of the accumulated number of conflicts by 1960, sharply separating two regimes: afirst regime between 1816 and the end of the 1950 decade, with an average number of 4.79 conflicts per year, and a second re-gime from 1960 to 2005, with a much higher average number of 16.42 conflicts per year. We note that the inflection point in thisfigure seems to correspond to the period of decolonization, and the emergence of new independent states that for various reasonsmay be more prone to conflicts as remarked by Sambanis [16].

This singular role played in human history by the events that took place along the second half of the 20th century is essentiallyconnected to the explosive advancement of the scientific and technological knowledge that mankind has experienced in the Mod-ern Era, particularly during the 19th century and the first half of the 20th century. The technological inventions and innovationsthat took place during this period were decisive in changing the pace of the mankind evolution, as they started responding to thelargely consensual basic human needs for energy, transportation, education, food and water supply, and sanitation. Energy andtransportation can be thought as infrastructural, i.e. supporting, demands. Their adequate supply is fundamental to enable thesocio-economic welfare of any society. The other three demands are related to the basic human needs and convey indeclinableexpectations for individual wellbeing. As a matter of fact, the needs for food, education and health are strongly interwovenamong themselves and, at the same time, intrinsically tied to energy and transportation. Yet, though the solutions are essentiallyat hand one cannot escape acknowledging, to everyone's regret, that their effective appropriation by more than one third of theworld population, is still a long way to go.

Another important aspect to be noticed regards the evolution of the speed of the means of transportation. By 1500, during thegreat navigations period, the speed range was typically of the order of 20 km/h, while by 1825 it had doubled with the setting in

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operation of the first public steam railway service in the world, namely, the Stockton and Darlington railway in Northeast En-gland. Roughly one hundred years later, by 1930, the typical speed of commercial aviation was of the order of 400 km/h. By1952 the first commercial jet airliners (de Havilland Comet) flew at a cruise speed of about 700 km/h and only ten years later as-tronaut capsules were orbiting the Earth at speeds exceeding 20,000 km/h. These observations are graphically displayed in Fig. 4where a marked change in trend by 1950 is also evident. The double arrow in this figure emphasizes the sharp transition in theaverage speed of the characteristics means of transportation.

The overall social outcome of the changes promoted in these areas and so many others by the explosive advancement ofknowledge was that, at the dawn of the 20th century, people lived longer than ever before, education was becoming compulsory

Fig. 3. Evolution of the accumulated number of civil wars between 1816 and 2005. The dotted lines in this plot represent two linear regression corresponding tothe periods 1816 to 1960 and 1960 to 2005 aiming at emphasizing the sharp transition between the two distinct regimes of the data trend.

Fig. 2. Evolution of the world's gross domestic product (GDP), in trillion 1990 international Geary–Khamis PPP dollars, and population (in billion inhabitants)from 1700 through 2008 using Maddison [13] historical statistics for the world economy.



image of Fig.�3

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in some advanced countries, which meant ending children's labour, and both new occupations and services in new emerging in-dustrial sectors started to appear, providing for new employment opportunities. Tourism was among these, as a result of theboom that the shipbuilding industry experienced over those years as well as of the increase in people and enterprises wealth, es-pecially in Europe. Amongst the new industrial sectors, probably the energy generation, telecommunications (radio communica-tions, in those days) and transportation (led by the automobile and aircraft industries) were among those that most rapidly andeffectively helped shaping society in the early decades of the 20th century. Roughly fifty to sixty years later, we would beexperiencing a similar but whole new radical change in these sectors with the advent of the aerospace industry, nuclear powerindustry, the modern semiconductor electronics and photonics sector, and so on.

It was in this revolutionary new context that the modern ICT was nested. During the first two decades after the greater tech-nological divider landmark year (1950), the improvements in transistor technology, the developments of magnetic tape drive,moving head disk drive, integrated circuits and the early bases of the electronic data computing, among so many other fundamen-tal devices, as well as of influential computer languages, such as Fortran and Algol, set the stage for the explosive development ofthe information and communication sector. In 1971 the number of transistors in a microprocessor was of the order of a few thou-sands (more specifically, 2300 transistors in Intel's 4004 processors with a footprint size of 10 μm). By 2010 the transistor count-ing in Quad-Core Itanium processor had reached the spectacular mark of 2 billions with a manufacturing technology of 65 nm.Taking the risk of overestimating their undeniable tremendous impacts, we could close these remarks by saying that the WorldWide Web surge, one hundred years after the first radio transmission, together with nanotechnology and biotechnology, eitherby themselves or in an unavoidable symbiotic association, are the new technologies that will be mostly accountable for shapingthe 21st century.

In fact, some radical changes driven by these new technologies are already beginning to become apparent in some importantareas such as Medicine. During the first decade of the 21st century we have witnessed a clear tendency in gradually moving fromessentially curative anatomy based Medicine into an essentially preventive genetics and epigenetic based Medicine, as the indepth knowledge of the human genome is unveiled. In semiconductor industry, too, the so far prevailing silicon based technology,approaching its physically feasible limits, is bound to be challenged and eventually replaced by the newly emerging nanotechnol-ogies. For instance, in a recent paper by Moktadir et al. [17] the authors claim to have achieved a breakthrough in a non-siliconbased transistor technology, by succeeding in constructing a viable graphene field effect transistor (GFET) with a uniquelydesigned nano-scale channel structure. Their new transistor achieved a record high-switching performance (1000 times higheron/off switching ratio) which will make future electronic devices even more functional and higher-performing. These andother equally recent developments [18] in the graphene technology lead us to foresee that graphene integration might potentiallyreplace, or at least be used side by side with, silicon integration. In other words, we are just apparently witnessing, these verydays, the birth of a new radical change in ICTs.

As Victor Hugo once stated, “it is possible to resist to any army invasion, but it is not possible to resist the invasion of ideas”.This statement reflects quite aptly the current and future situation of mankind development at the dawn of the 21st century.

3. Time evolution of the Internet infrastructure

As mentioned in the Introduction, we have assumed the number of hosts as an adequate indicator to measure the evolution ofthe Internet infrastructure. In our analysis, we used the corresponding historical data collected by the Internet Systems Consor-tium (ISC), from August 1981 to July 2010. It is a remarkable fact that while the ISC registered, in August 1981, just 213 hosts,this number soared to the absolutely impressive figure of 769 million hosts by July 2010, with its first million having beenattained in July 1992. We have restricted our analysis of the time evolution of the number of Internet hosts, as well as of their

Fig. 4. Evolution of the estimated average speed of some typical means of transportation from 1500 to present. We refer to the text for details.



image of Fig.�4


growth rates, from July 1989 on, when the number of ISC counted hosts had just crossed the one hundred thousand barrier. Thisdata was modeled using our multi-logistic methodology [6,7,14] by writing the corresponding model function as

f tð Þ ¼ ∑N

i¼1Ai

e t−t cið Þ=τi

1þ e t−t cið Þ=τi ; ð1Þ

where Ai denotes the excursion towards saturation during the ith growth sequence, tci is the inflection point corresponding to themaximum rate of change of f in the sequence i and τi−1 its growth rate.

After successive trials it was found that the data was best fitted using a five-logistic growth model. The results of our multi-logistic modeling are shown in Figs. 5 and 6. Fig. 5 displays the results for the evolution of the number of Internet hosts whileFig. 6 refers to the evolution of its yearly growth rate along the considered time period.

The values of the data fitting parameters as obtained from the above modeling are listed in Table 1. Apart from the carryingcapacity, A, the inflection point, tc and the characteristic time, τ, of each logistic phase we have also included in Table 1 the dura-tion time, Δt, for the excursion of each component of the logistic process to go from 10% to 90% of its corresponding carrying ca-pacity. The overall error of the data fitting procedure and the coefficient of determination were 8.8% and 0.9991, respectively. Thesolid lines in Figs. 5 and 6 represent the results obtained from the five-logistic modeling and its time derivative, respectively. Bothfigures show a relatively good agreement between the empirical data and the model.

Overall, these results indicate that the evolution of the number of Internet hosts did not follow a single monotonically growingtrajectory. On the contrary, it progressed through a sequence of relatively sharp phases. In fact, along the period of the collectedempirical data here considered (1989 to 2010), it comprised four distinct phases centered roughly at 1996, 2000, 2004 and 2009.The model further forecasts that, should the currently prevailing technology maintain itself, the Internet hosts number will con-tinue to evolve during the 2010 decade into a broader phase, with its growth rate going through another peak at about 2015 whenit should reach the impressive figure of just about one billion. From this point on the hosts number should start to asymptoticallyapproach saturation estimated to be of about 1.4 billion by the year 2030. This forecasted saturation of the number of hosts isclearly depicted in the inset in Fig. 5 displaying the extrapolation of our modeling up to 2030, whereas the distinct logisticphase plots are shown in Fig. 6.

These conclusions contrast with those in Refs. [4,5] where a worldwide slowing down of the growth rate of the Internet to-wards a ceiling by 2010 was forecasted. Another interesting aspect regarding these results refers to the average time lag alongthe five logistic phases disclosed by our modeling. Using the data listed in Table 1 regarding the logistic phases center positions(i.e., the tc's) we find that the various logistic phases are, on the average, 4.7 years apart, an interval that matches the typical orderof magnitude of the Kitchin inventorial cycles [1].

The logistic phases of the host counting evolution disclosed by our modeling can be related to the successive changes in useand infrastructure of the Internet along the corresponding period. For instance, the creation of the NSFNET backbone in 1986prompted the stage for an explosion in Internet connections and consequently in the number hosting devices. To wit, while by1988 only six countries had joined the NSFNET, by 1996 this number had soared to one hundred and thirty eight countries, repre-senting approximately 90% of the world population. Also, it was still during the period corresponding to the first logistic phase,that a number of international organizations, like the World Bank (1992) and the United Nations (1993), came on-line, as didmany government's administrations, too.

The second logistic phase centered at the year 2000 coincides with the deployment of Internet 2 backbone network whichmade possible, among other things, uncompressed real-time gigabit HDTV transmission to take place on the Internet. This periodconsiderably benefited from emerging technologies such as wireless devices and grid computing, too. It was also strongly influ-enced by the launching of better CPU's, like the Pentium 4 on November 20, 2000, which ultimately resulted in more efficient use

Fig. 5. Five-logistic function modeling of the time evolution of the cumulative number of Internet hosts. The solid line in the plot represents the results of the datafitting for the period from July 1989 to July 2010. The inset includes the extrapolation of the data fitted result up to 2030.



image of Fig.�5


of the Web. The third phase, centered at 2004, was largely dominated by the growth of social networking that, though being al-ready in operation for some years, profited from the advancement of newer, ever friendlier, interfacing technologies.

One could expect that, to cope with the fast increasing amount of information being pumped through the Internet, it would besoon realized that some service should be provided to search for URLs and DNSs, indexing them and helping to people in acces-sing them when a query sent to one such provider matched somehow its index. Huge hosting services were so organized as toprovide these indexes, which made them, in short time, first rate indicators of the web contents growth and thereby, of the cor-responding spectacular growth of the number of Internet hosts and users. The explosive growth observed in fourth phase, cen-tered at 2009, cannot be best illustrated than by observing what happened with Google's index page records. The originalGoogle's index that comprised 26 million pages in 1998 soared to 1 billion in 2000. By 2008 Google reached the incrediblemark of 1 trillion pages, that is, approximately 160 pages per world inhabitant. As to the technological advances underlyingthe increase in the hosting capability to cope with the corresponding Internet traffic we may quote the a more efficient use ofthe Internet became possible with the advent of multi-core technology, launched on July 2006, with Intel's Core 2 processorsthat would, by 2008, practically supersede Intel's “NetBurst technology” of the Pentium 4 CPU's. Both were highly instrumentalin that regard, as was also the case of with AMD's Athlon microprocessors family. As to the predicted fifth logistic phase we be-lieve it will be credited, apart from further advances in microprocessors technology, to the ongoing trend in the development ofprogramming languages, including communication protocols, as we shall discuss in details later on in Section 6. It wiil be seenthere that a peak in the development of programming languages is equally predicted to take place between 2015 and 2016.

4. Internet penetration index

The data on the time evolution of the internet penetration index (the number of Internet users as a percentage of the worldpopulation) used in this study was taken from Ref. [10], covering the period between 1995 and Sep 2010. Our first attemptwas to carry on a single logistic function modeling of the data. The results are displayed in Fig. 7 and summarized in Table 2.

According to these results the internet penetration should reach a peak in its growth rate by the middle of the year 2013 whichwould then slow down towards saturation at about 79% of the world population, by the year 2040. In other words, it is predictedthat it will take approximately 45 years for the Internet penetration process to be globally accomplished. Though these resultsseem qualitatively plausible, we notice that a single logistic model does not seem to adequately account for the different “phases”of the time evolution of the Internet penetration index hinted by the data, especially in regards to its earliest phase of the process.

Next, aiming to improving our model, we carried out a multi-logistic fitting to the Internet penetration index data, just as wedid before, in the case of the evolution of the number of Internet hosts. Similarly to that case, the best fit here was also achievedwith a five-logistic function model. The results are shown in Fig. 8 and summarized in Table 3.

Fig. 6. Time evolution of the growth rate of the number of Internet host. The solid line represents the time derivative of the five logistic model for the host countingshown in Fig. 5. We refer to the text for details.

Table 1Values of the characteristic parameters obtained from the five-logistic data fitting to the number of Internet hosts.

Parameters Phase 1 Phase 2 Phase 3 Phase 4 Phase 5

Ai 25.61 87.23 184.94 493.43 618.46tci 1996.22 2000.07 2004.08 2009.00 2015.09τi (yr) 0.77 0.59 0.77 1.63 3.28Δti (yr) 3.37 2.61 3.38 7.14 14.40R2 0.9991 Average error 8.8%



image of Fig.�6


The model indicates that the time evolution of the Internet penetration index consists of a sequence of five logistic phases withgrowth rates peaks around 1998, 2001, 2004, 2008 and 2015. The average time lag between these phases is thus of approximately4.25 years. It is also predicted that by 2015 the penetration index should reach 50% of the world population and from then on itshould asymptotically approach saturation at about 89% of the world population by 2035, as indicated in the inset in Fig. 8.

On comparing both the plots in Figs. 7 and 8 and the fitting parameters in Tables 2 and 3 it is apparent that the five-logisticmodel does work better in describing the time evolution of the Internet penetration index than the single logistic one. Yet, theindividual multi-logistic fits for Internet's host counting and penetration index data display both striking similarities and wide dif-ferences in their time evolutions. Similarities are seen, for instance, in observing that the center positions (i.e., the tc values) of thelogistic phases are quite close (see Tables 1 and 3). In fact, the average time lag among the five logistic phases is around 4.7 yearsin the host counting case (see Fig. 6) and 4.25 years for the Internet penetration index. A marked difference, however, is seen inregards to the values of characteristic times, which leads to sharper logistic phases in the case of the Internet penetration indexthan for the host counting, except in regards to the predicted fifth phases where the opposite occurs. These subtle differences inthe multi-logistic modeling for host counting and the penetration index can be better visualized in Fig. 9 where one can get a clos-er look at the evolution of both growth rates. There, the solid and dotted lines refer to the time evolution of the growth rates of theInternet hosts counting and penetration index, respectively.

The five-phase pattern of the growth rates in both cases is clearly seen there. However, while in host counting the growth ratepeaks increase monotonically over the four phases peaks up to 2010 (this can also seen in the inset in Fig. 6, too) in the penetra-tion index this increasing pattern is broken in the third and fourth peaks. This is indicating that some sort of decelerating pertur-bation affecting its growth rate may have occurred around 2004. Yet, from 2010 onwards the penetration index growth rateexhibits a fifth more intense and broader phase centered at 2015, contrasting with the profile of the equivalent host countingthere.

To understand these differences we need more details on the main factors affecting the worldwide Internet penetration. TheInternet penetration in (and within) a given country society depends of a complex blend of factors. Physical infrastructure, sizeand skills (reflecting the capacity necessary to use ICT effectively) of the population, plus geographic extension and topographyof a country rank among the chief components determining the pace at which Internet penetrate there. On the top of that, thelocal level of economic development probably acts as the most prominent factor. No wonder developed countries have alwaysbeen in the top list of countries with the best Internet penetration indicators. In fact, efforts for laying infrastructure and improv-ing the Internet accessibility may be considerably modified as a result of changes in the market environment, enhanced invest-ments, costs cuts, or the introduction of new technologies in the market. In other words, in the globalized economy of ourdays, this is utterly dependent on the global economy stability. The relative decrease of the Internet penetration index growthrates intensities around 2004 and 2008, as compared to those of the first two phases, displayed in Fig. 9, may be an example ofthe influence of the impact of both global and local economic environment stability upon the Internet penetration rate. During

Fig. 7. Single logistic function modeling of the Internet penetration index time evolution. The solid line in the plot represents the results of the corresponding datafitting for the considered time period. The inset in this figure includes the extrapolation of the data fitted result up to 2045.

Table 2Values of the characteristic parameters obtained from the single logistic data fitting to the Internet penetration index, including the duration time for the logisticprocess, Δt.

Parameters Statistics

A 79.46 Number of points 45tc 2013.47 Residual sum of squares 27.23τ (yr) 5.17 R2 0.9886Δt (yr) 22.7 Average error (%) 24.7



image of Fig.�7


the 2002 and 2004 period several developed and developing economies went through different economical and financial crises,while by 2008 the recent US financial crises triggered a worldwide recession. A detailed discussion on the chronology of the eco-nomic and financial crises can be found in [19].

As to the widest and the relatively most intense phase of the Internet penetration growth rate, predicted to peak by 2015, wefind worthwhile considering initially some data regarding the world distribution of the Internet usage by the several geographicregions. The data was gathered from references [8,10], including the latest 2010 ITU report. In Table 4 we present a summary ofthe relevant data.

It follows from Table 4 that, as percentage of their regional populations, the Internet penetration index for Europe, NorthAmerica and Oceania have reached in 2010 an average penetration index of approximately 65.7% of their combined population,even though they account for just approximately 16.2% of the world population according to the latest UN world population pros-pects [20]. In contrast, Asia, Middle East and Latin America show an average penetration index of just 28.6% of their combinedregional population, even though these regions account for some 68.8% of the world population. The inevitable conclusion thatcan be drawn is that the predicted fifth phase in the evolution of the Internet penetration index is bound to be attributable tothe advance of Internet access over Asia, Latin America and Africa in coming years.

This conclusion is further supported by comparing the Internet usage data of some prominent developed and developingcountries as listed in Table 5.

This table indicates between 2007 and 2008 the Internet usage of the selected developed countries experienced an averagegrowth of about 5%, whereas the corresponding growth rate for the so-called BRIC countries was of the order of 25.5%, that is,roughly five times larger. This suggests that beyond 2010, the Internet penetration growth should take place predominantly inAsia and Latin America and, eventually, in Africa too.

Finally, we have next analyzed the residuals of the five logistic data fitting using the procedure outlined in [6,7,14]. As in thethese references, the residuals reconstruction was carried out by fitting the data-to-model residuals to a truncated sine series ofthe following type,

R ¼ ∑N

n¼1an sin 2πnf0 t þ ϕnð Þ: ð2Þ

Here, an and ϕn represent the amplitude and the phase of the nth harmonic and f0 stands for the frequency of the fundamentalmode, and N is the number of harmonic modes in the sine series. We started with a truncated sine series reconstruction of thetype given in Eq. (2) by firstly restricting the series up to the 8th harmonic. After successive trials, a sufficiently good

Fig. 8. Five-logistic function modeling of the Internet penetration index time evolution. The solid line in the plot represents the results of the corresponding datafitting for the considered time period. The inset in this figure includes the extrapolation of the data fitted result towards 2030.

Table 3Values of the characteristic parameters obtained from the five-logistic data fitting to the Internet penetration index. In the last line of this table we list the valuesof some relevant statistical parameters characterizing the present data fitting procedure.

Parameters Phase 1 Phase 2 Phase 3 Phase 4 Phase 5

Ai 2.73 3.17 1.87 1.47 79.59tci 1998.0 2001.0 2003.99 2008.02 2014.97τi (yr) 0.40 0.29 0.37 0.18 3.94Δti (yr) 1.75 1.30 1.63 0.80 17.31Residual sum of squares 4.97 R2 0.9974 Avg. error: 4.8%



image of Fig.�8


reconstruction of the residuals came out by taking just the first four harmonics. The results are shown in Fig. 10 and the fittingparameters are summarized in Table 6.

We note that the four harmonic modes listed in Table 6 have all comparable strengths an. Accordingly, the average period, bpN,of the residual fluctuations may then be defined as the amplitude weighted mean of these four periods, as follows,

bpN ¼∑n

an pn

∑n

an; ð3Þ

where for the nth harmonic mode pn is equal to p0/n. Substituting into Eq. (3) the values listed in Table 6 one gets, bpN=4.3 yrs,which is quite close to the 4.25 yrs found for the average phase peaks separation in the five logistic modeling of the penetrationindex.

5. Programming languages evolution

In a strict sense programming languages and communication protocols are integral part of the Internet infrastructure. It dealswith the man–machine interface and a great deal of the appeal of the Internet to the users is the availability of ever more friendlysoftware. However, since this is a field with a considerable range of interests beyond the user–computer interfacing, having itsown development characteristic and life cycle, we decided to dedicate a separate Section to it. The data source for the presentanalysis was taken from web source [21]. It is a compilation from several others, including those available in the history of com-puting project [22] and that in [23]. Overall, it gives a good general and pertinent accounting.

We have discarded the data prior the 1940s and considered the programming language evolution from 1950 onward. The1940 decade data is rather scarce consisting of no more than just 10 records, all of them basically involved with the developmentof the ENIAC coding system. The resulting number of programming languages evolution data used comprised 274 records span-ning from 1950 through 2009. In Fig. 11 we plot the cumulative number of programming languages as a function of time. The solidline in this figure represents the output of the data linear regression that produced a slope of 4.77 languages per year and a co-efficient of determination of 0.996.

As discussed in [6,14], our modeling of a characteristic variable describing a given evolutionary process yields two importantresults, namely, the trend function describing the events, provided a suitable model function has been picked, and a sequence of

Fig. 9. Comparison of growth rates patterns between the Internet host counting and penetration index (see text for details).

Table 4World Internet usage statistics distribution among several geographic regions taken from references [8] and [10].

Region Internet users(Jun 2010)

Penetration as % region population(2010 est.)

Penetration as % world population(2010 est.)

User growth2000–2010

Africa 110,931,700 10.9 5.6 2357%Asia 825,094,396 21.5 42.0 622%Europe 475,069,448 58.4 24.2 352%Middle East 63,240,946 29.8 3.2 1825%North America 266,224,500 77.4 13.5 146%Latin America 204,689,836 34.5 10.4 1033%Oceania/Australia 21,263,990 61.3 1.1 179%World 1,966,514,816 28.7 445%



image of Fig.�9


data-to-model residuals. The trend function is as coarse-grained description indicating the trajectory the process has followed sofar, and allowing for projections of its evolution into the future. The residuals, on the other hand, usually exhibiting a wavelikebehavior, allow us to look for eventually hidden important information regarding the clocking of the driving motors of thegiven process. In other words, our modeling of an evolutionary process is not exhausted by simply providing a good model func-tion for the trend of the control variable, as extensively discussed in [6,7,14]. It takes also into account the residuals analysis touncover the underlying clocks driving the process.

The data-to-model residuals resulting from the linear regression were then analyzed using the same procedure adopted in theprevious Sections, that is, by fitting in a truncated sine series of the type given by Eq. (2). It was found that keeping the first sixharmonics was sufficient to reproduce the residuals data satisfactorily. The results are displayed in Fig. 12, where we have includ-ed its extrapolation towards 2035. The values of the corresponding data fitting parameters are listed in Table 7.

In Fig. 12 the solid lines, besides exhibiting a good data-model fitting, when extrapolated into the near future predict anotherpeak in the number of programming languages development by 2015–2016. This predicted burst in programming languages co-incides with the forecasted peaks in both the Internet hosts counting and penetration index growth rates, as discussed in the pre-vious two Sections.

Furthermore, it follows from Table 7 that the dominant modes of this residuals reconstruction are the first three harmonicscorresponding to periods of 62.3, 20.9 and 31.2 years, respectively. That is, the wavelike behavior of the residuals is essentiallydescribed by combinations of three modes oscillating with periods of the order of the Kondratiev and Kusnetz cycles [1]. Overall,the picture that comes out of this analysis is that programming languages have been growing since 1950 essentially in a linearfashion at a rate of about 4.77 language programs per year. This evolution is powered by creativeness bursts with periods ofthe order of the Kuznets (15–25 years) and Kondratiev (40–60 years) economic cycles accompanying the economical changesin infrastructure, and long radical technology transformations periods, respectively.

Table 5Internet usage statistics, as given by the numbers of users per 100 inhabitants, for some selected countries during the first decade of the 21st century. The datalisted here were taken from reference [8] including the latest 2010 ITU report.

Country 2002 2007 2008 2008/2007

Developed countriesCanada 61.6 72.8 75.4 3.6%France 30.2 63.6 68.2 7.2%Germany 49.0 72.4 75.3 4.0%Italy 28.0 38.3 41.9 9.4%Japan 46.4 74.3 75.4 1.5%South Korea 59.4 75.5 76.5 1.3%United Kingdom 56.0 71.9 76.2 6.0%United States 59.6 71.8 74.0 3.1%

BRIC'sBrazil 9.2 30.9 37.5 21.4%Russia 4.1 24.7 32.0 29.6%India 1.1 3.9 4.4 12.8%China 4.6 16.0 22.3 38.3%

Fig. 10. Data-to-model residuals from the Internet penetration index time evolution modeling as described in Fig. 8. The solid line represents the result of a truncatedsine series reconstruction.



image of Fig.�10


6. ICT development index

So far we have focused our discussion on some of the relevant indicators describing the quantitative evolution of Internet. Theexplosive developments of modern ICTs raised, and still do, important questions regarding not only the way it will grow in thenear future, as those we addressed in the previous Sections, but regarding as well its social impacts, in particular, the so-calleddigital divide.

Since the early stages of the rapid growth of modern ICTs, ITU and Orbicom (a joint initiative between Unesco and the Univer-sity of Quebec at Montreal, aiming the promotion of communications' development), initially working independently and later ina joint operation, have engaged in developing an index that could provide a clear view of the magnitude of the digital divide. Itwould also provide a methodological framework to monitor progress in the use of ICT aiming at achieving internationally agreeddevelopment goals, including those of the United Nations' Millennium Development Goals. The work between the two institu-tions towards a single index continued until they finally agreed upon a final single index, the so-called ICT Development Index— IDI. The name chosen (ICT Development Index — IDI) reflected the main objectives of the index, namely, to track progress inthe development of ICTs in countries, and to monitor the global digital divide. This index was presented in ITU report entitled“Measuring the Information Society: The ICT Development Index 2009” [8], in which a detailed historical account of the work towardsproducing such index is also presented.

The ICT Development Index (IDI) combines three components, namely, infrastructure and access; usage, and skills. This lastcomponent is central in determining the effective use of the technologies and critical towards maximizing the potential impactof ICTs on socio-economic development. As has always been the case with the introduction of any new radical technology, eco-nomic growth and social development will remain below their true potentialities in economies that are not capable of exploitingthese technologies and fully realize their benefits.

For each of these components there is an associated sub-index. The access sub-index, denoted henceforth as IDIA includes fiveinfrastructure and access indicators (fixed telephony, mobile telephony, international Internet bandwidth, households with com-puters, and households with Internet). The use sub-index, denoted as IDIU consists of three usage indicators (Internet users, fixedbroadband, andmobile broadband), and the skills sub-index, denoted as IDIS, comprises three indicators (adult literacy, gross sec-ondary and tertiary enrolment) for accessing the ability of individuals to effectively use the ICTs. The final computation of the IDI,as proposed by ITU, is done using a weighted arithmetic mean of these three sub-indices. The access and use sub-indices are givenequal weight (40% each), whereas the skills sub-index is given less weight (20%) since it is based on proxy indicators. We refer tothe 2009 ITU Report [8] for a detailed discussion on the IDI construction and thorough analysis of the evolution of the digital di-vide and the socio-economic impacts of ICT. This Report presents the IDI results for 154 countries for the years 2002 and 2007,whereas its latest 2010 edition presents the data for 158 countries in 2008.

Table 6Values of the truncated sine series parameters obtained from the Internet penetration index time evolution data-to-model residuals reconstruction. The funda-mental period, p0, was found to be equal to 8.97 years.

Parameters 1st harmonic 2nd harmonic 3rd harmonic 4th harmonic

an 0.113 −0.124 0.130 0.185ϕn 1.671 −4.022 1.340 −2.679

Fig. 11. Time evolution of the cumulative number of softwares between 1950 and 2009. The solid line represents the data linear regression. Please refer to the text formore details.



image of Fig.�11


This weighted average procedure adopted by ITU to produce its final IDI deserves further consideration in face of those con-sidered by other UN Programs in composing indicators to obtain a complex social index. As an example, we recall that when com-bining three independent sub-indices (income, life expectancy and education) to produce the Human Development Index (HDI),the UN Development Program opted for taking the geometric mean of the three indices instead of an arithmetic mean. In the caseof the three ICT development sub-indices we note that two of them, namely, IDIA and IDIU, are somewhat entangled to each other.In other words, they are essentially dependent variables, and, as such, they were assigned equal weights in ITU's calculations. TheIDIS sub-index, in contrast, is quite independent from the other two. This suggests that we could take as an alternative index thegeometrical mean of the IDIS with a second independent sub-index, which we shall designate by IDIOP, the operational sub-index,given by the arithmetic mean of IDIA and IDIU. We accordingly propose the adoption of this functional IDI, denoting it by IDIF, as analternative to the ITU's index IDI in measuring the global ICT development (infrastructure, access and effective use) or, for thatmatter, the digital divide. The IDIF is then mathematically defined given by the relations:

IDIF ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIDIOP×IDIS

p; IDIOP ¼ IDIA þ IDIUð Þ=2 : ð4Þ

Using the above definitions and setting z=IDIOP/IDIS, measuring the relative size of the compounded operational sub-index tothe skills sub-index, we get IDI = IDIS (0.8 z+0.2) and IDIF = IDIS √z, so that IDI/IDIF=(0.8 z+0.2)/√z. It can be shown that for0.0625bzb1 the ratio IDI/IDIF is smaller than unity. Now, from the data in [8] we actually find that, for both 2002 and 2007, theratio parameter z fulfills this condition so that IDIFN IDI for the vast majority of the countries in the ITU's database. This is showngraphically in Fig. 13 in which we plot the ratio z for the 2007 data as a function of the ranking of the countries according to ITU's2009 Report. The dashed lines in this figure represent the limits (z=0.0625 and 1) within which the IDI/IDIF is smaller than unity.

It is a known fact that in some developing and underdeveloped countries there remains a high degree of illiteracy and a lowrate of enrollment in secondary and tertiary schools. This would tend to lower IDIS and increase the ratio z. Yet, in a number ofsuch countries, for one reason or another, one occasionally finds a relatively low level of penetration and use of the ICT. Itseems therefore that both circumstances combine to make z comparatively small, as Fig. 13 indicates. The overall outcome ofthese results is that wemay say that the ITU index IDI somehow underestimates a country's digital situation, probably due to min-imizing the importance of IDIS on their weighted averaging. In that regard, our proposed index IDIF may give a more realistic ac-counting of the digital improvement among developed, developing and underdeveloped countries by better accounting for theIDIS.

In what follows we present a quantitative analysis of the ICT development indicators. The approach is centered on the con-struction and analysis of the indicator-wise distribution of the various countries included in [8], using the data collected thereinfor the years 2002, 2007 and 2008. Overall, our procedure may be summarized as follows. From the data in [8] we have produced

Fig. 12. Data-to-model residuals from the linear regression of the programming languages time evolution. The solid line represents the result of a truncated sineseries reconstruction.

Table 7Values of the truncated sine series parameters obtained from the programming languages time evolution data-to-model residuals reconstruction. The fundamen-tal period, p0, was found to be equal to 62.3 years.

Parameters 1st harmonic 2nd harmonic 3rd harmonic 4th harmonic 5th harmonic 6th harmonic

an 4.418 −2.641 −3.508 1.856 1.027 1.025ϕn 0.294 4.525 −2.155 −0.943 −2.743 −1.409Fundamental frequency, f0 0.016 Period, p0 62.3 R2 0.84



image of Fig.�12


tables consisting of lists of countries in an increasing order of the corresponding indicator values. Next, we counted the cumula-tive number of countries up to a given value x of the indicator under consideration. By normalizing the data so obtained with re-spect to the total number of countries, we could then calculate the probabilities of finding a country with the indicator X being lessthan or greater than or equal to a given value x. Here, X denotes one of the three indicators, namely, the ITU's IDI, the IDIOP andIDIF. These probabilities were denoted as P(Xbx), for the probability that a country has an X less than x, and P(X≥x) for the prob-ability that a country has X greater or equal to x. In statistics these quantities are usually referred to as the cumulative distributionfunction, in the case of P(Xbx), and the complementary cumulative distribution function P(X≥x)=1−P(Xbx). The cumulativedistribution function is related to the probability density function f(x) by,

P Xbxð Þ ¼ ∫x−∞dx f xð Þ; f xð Þ ¼ dP Xbxð Þ

dx; ð5Þ

where X denotes the indicator under consideration.We begin by considering the two indices IDI and IDIF. While the skills sub-index contributes with only 20% in the computation

of the IDI it is fully taken into account in the IDIF calculation. In Figs. 14 and 15 we show the cumulative distribution functions andthe probability densities of both indicators for 2002.

The peaks in Fig. 15 reflect the categories at which the countries are stratified as a function of their ICT development indices.The marked quantitative and qualitative differences among the plots shown in Figs. 13 and 14 indicate that the ICT developmentindex is highly dependent on the way we take into account the skills sub-index into its final computation. In the case of our pro-posed geometric mean approach (the IDIF index) the probability density tends to become segmented into a larger number of cat-egories and flatter in a wider range of values of the indicator as compared to the ITU index (IDI).

Fig. 13. The ratio z = IDIOP/IDIS, for the 2007 data, as a function of the ranking of the countries (taken from the ITU's 2009 Report).The constant z dashed hori-zontal lines at z=0.0625 and z=1, in the plot, set the limits within which the IDIFN IDI. Notice that essentially all countries represented fall in between theselimiting lines.

Fig. 14. Cumulative distribution functions for both IDI and IDIF for 2002.



image of Fig.�13

image of Fig.�14


In view of this we decided to focus our attention on the analysis of the evolution of the IDIOP index, measuring in less arguableterms the worldwide advancements of the ICT infrastructure and use, and opted, instead, to evaluate the socio-economic impactsthrough the IDIOP correlation with the human development index. In Fig. 16 we show the results of a multi-logistic modeling ofthe IDIOP distribution functions for the years 2002 and 2007. The down (up) triangles in Fig. 16 denote the 2002 and 2007 data,respectively. The inset in this figure displays the pattern of the distribution function that would be expected in the hypotheticalsituation (which probably will never be realized) in which all countries have their indices between 4 and 5. The pattern in thiscase of practically full equality would then be that close to a step function. The cumulative distribution function for 2002 wasbest fitted by a six logistic functions model, whereas for 2007 the best data modeling was achieved with the use of five logisticfunctions. The results obtained by the corresponding modeling are displayed in Fig. 16 by the solid gray lines and the valuesfound for the fitting parameters are listed in Table 8.

Some important aspects that come out of the results displayed in Fig. 16 deserve additional comments. The first one is that therange of values of the IDIOP in 2007 (i.e., from 0.405 to 7.08) is about 30% wider than the corresponding range for 2002, namely,from 0.16 to 5.285. The second one regards the fact that the cumulative distribution functions were all best fitted by a multi-logistic model. This means that the IDIOP distribution functions are somehow stratified into a sequence of categories probablyreflecting the inequalities (IDIOP dispersion) as well as similitudes (IDIOP clustering) among the set of 154 countries, as alreadyaforementioned. The third aspect to be noted is that there is a tendency to some sort of flattening of the distribution functionsfrom 2002, the steepest one, to 2007 indicating a possible trend towards the pattern of the ideal case (see the inset in Fig. 16).

The corresponding probability density functions are readily obtained from the modeled P(IDIOPbx) by taking its derivativewith respect to x, as indicated in Eq. (5). The results are shown in Fig. 17, presenting a comparison between the 2002 and2007 data. The solid lines in Fig. 17 represent the results as obtained from the multi-logistic modeling. Fig. 17 clearly showsthe above mentioned tendency towards a flattening of the probability densities, too, as well as the widening of the spectrum ofIDIOP values.

Fig. 15. Probability densities for both IDI and IDIF for 2002.

Fig. 16. Multi-logistic modeling of the IDIOP distribution functions for the years 2002 and 2007. The solid lines are the results of least square best fits to 5 and 6logistic functions, for 2002 and 2007, respectively. The inset displays a hypothetical pattern for the distribution function that would be expected in the hypothet-ical situation in which for all countries having their indices between 4 and 5.



image of Fig.�15

image of Fig.�16


The widening of the range of values of the IDIOP clearly reflects the remarkable worldwide spread of ICTs during this period oftime.

As additional statistical information to characterize the changing shapes of the probability density functions shown in Fig. 17,we have also calculated their corresponding first three moments. The first moment is its mean given by

x ¼ ∫∞

0

dx xf xð Þ; ð6aÞ

the second is the variance, σ2, measuring, so to speak, the width of the distribution,

σ2 ¼ ∫∞

0

dx x−Px Þ2 f xð Þ;

�ð6bÞ

and the third moment, the skewness, s,

s ¼ 1σ3 ∫

∞

0

dx x−Px Þ3 f xð Þ

�ð6cÞ

indicating how the distribution is skewed from its mean. The corresponding results are summarized in Table 9 in which it is alsoincluded the gap, Δ, between the highest and lowest values of IDIOP for each year.

Of particular interest is the behavior of the skewness. The skewness value can be positive or negative, or even undefined. Qual-itatively, a negative skew indicates that the tail on the left side of the probability density function is longer than the right side andthe bulk of the values (including the median) lies to the right of the mean. A positive skew indicates that the tail on the right sideis longer than the left side and the bulk of the values lies to the left of the mean. The value of the skewness of the 2007 probabilitydensity function is approximately 66% that of 2002. This, as well as all the values of the other two parameters, confirms the ten-dency towards the flattening and the widening of the distribution function. As already mentioned, this reflects the widespread

Fig. 17. Probability density functions. The solid lines represent the derivatives with respect to x of the multi-logistic function best fitted to P(IDIOPbx) (seeEq. (5)). The plots allow for comparison between the 2002 and 2007 results. The tendency of the probability densities to get flatter, as well as the widening ofthe spectrum of IDIOP values is distinctively clear.

Table 8Values of the characteristic parameters obtained from the multi-logistic data fitting to the IDIOP cumulative distribution functions for the group of countries asreported by ITU for the years 2002 and 2007. It is also included in this table the values found from the data fitting for the residual sum of squares (RSSQ) andthe coefficient of determination, R2, characterizing the present data fitting procedure. The numbers in parentheses refer to the distinct IDIOP categories associatedto each single logistic component of the overall multi-logistic modeling.

Parameters 2002 2007

(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5)

Ai 0.277 0.274 0.224 0.036 0.030 0.167 0.309 0.191 0.203 0.044 0.311xi 0.494 0.874 1.595 2.740 3.319 4.358 0.828 1.675 2.537 4.048 6.030δi 0.036 0.116 0.310 0.033 0.010 0.398 0.131 0.188 0.276 0.059 0.766RSSQ 4.83×10−4 R2 0.9998 RSSQ 0.0019 R2 0.9994



image of Fig.�17


advances in ICT infrastructure and use in the majority of countries, even though the gap between the highest and lowest IDIOPvalues kept increasing.

We next consider the correlations between the human development index (HDI) and IDIOP for the 2002 and 2007 data basis.The HDI data corresponding to the countries in the IDI 2002 and 2007 listing were taken from the 2004 and 2009 UN's humandevelopment reports [24], respectively. The 2002 HDI database did not include two economies (Macao and Taiwan) in their list-ing so that the correlation in this case was carried out for 152 countries instead of the original 154 countries in the IDIOP listing.For 2007, Zimbawe, too, was also not included in the HDI database which resulted in a further reduction to 151 of the total num-ber of countries involved in our correlation analysis. The HDI in classified according to selected range values into three main cat-egories: the high development level, corresponding to HDI greater than 0.8; medium development level, for 0.5bHDIb0.799, andlow development level, for HDI below 0.5.

In Fig. 18 we show the correlation plots of IDI versus HDI 2002 and 2007.As a function of the HDI values, the correlation plots in Fig. 18 may be split into two main ranges designated as range 1, for

HDI≤0.6, and range 2 for HDI≥0.75, and a third range in between. The main parameters characterizing these ranges are summa-rized in Table 10. Range 1 comprises 43 countries out of the 152 (28.3%) for the 2002 data, and 37 countries out of the 151 (24.5%)in 2007. The plots in Fig. 18 indicate that in this range the IDIOP is practically independent of the HDI values, with average IDIOPvalues equal to 0.495±0.120, for the 2002 data, and 0.791±0.191 for 2007. In other words, for the countries in range 1, the im-provements in ICT infrastructure and usage, of the order of 60% in their average IDIOP, apparently bear no relationship to the over-all improvement of the human development index. It corresponds to countries that, somehow, have been left behind by thedigital divide so that their developments are, so far, disconnected from an effective access to the new information and communi-cation technologies.

Range 2, in contrast, exhibits a clear linear correlation comprising a total of 81 countries within it for the 2002 data, and 88 for2007. For 2007, the data linear regression in range 2, with a coefficient of determination of 0.83, yielded a slope that is

Fig. 18. Linear correlation plots for IDIOP versus HDI for both 2002 and 2007 data. Quite distinct behaviors are seen in the ranges HDI≤0.6 and HDI≥0.75 (see textfor details).

Table 9Mean, variance, skewness and Δ=[max (IDIOP)−min (IDIOP)] for the probabilitydensity functions for the years 2002 and 2007, depicted in Fig. 16.

Parameters 2002 2007

Mean 0.406 1.270Variance 1.051 3.685Skewness 3.598 2.363Δ 5.13 6.68



image of Fig.�18


approximately 24% greater than that obtained from the linear regression for the 2002 data, with a coefficient of determinationequal to 0.86.

Some of the main conclusions regarding the results presented in this Section may be summarized as follows:

• There has been a clear worldwide improvement in the ICT infrastructure and use from 2002 to 2007. This is reflected in theshifts of the lowest values of IDIOP from 0.160 in 2002 to 0.405 in 2007. This shift, however, was also accompanied by a similarshift of the highest values of IDIOP, from 5.285 in 2002 to 7.080 in 2007, which resulted in the overall increase of the gap Δ be-tween the highest and lowest IDIOP, as shown in Table 9.

• This increasing trend of the IDIOP gap from 2002 to 2007 contrast with the overall, though modest, decrease of the HDI, from0.683 in 2002 to 0.631 in 2007.

• Despite of these facts, it was found from the IDIOP versus HDI correlation analysis that the number of countries in the low rangeof HDI values decreased from 2002 to 2007, at the same time that the number of countries entering range 2 increased.

• We have also found that there is a group of countries (those in range 1) whose improvements in their operational ICT index aredisconnected from their corresponding improvements in the human development, whereas for countries with top medium andhigh human development levels (namely, countries with HDI≥0.75) there is a close correlation between the two indices.

The last two conclusions indicate that although there persist a number of countries whose improvements in ICT are not effec-tively impacting their human development indices, there also is a growing group, in fact the majority of the surveyed countriesthat are, indeed, taking advantage of these new technologies for their social and economic developments. This is a nice exampleof technological innovation diffusion. In general, innovations, and knowledge development at large, start in the leading techno-logically empowered countries and slowly spread out to other countries in a diffusive manner quite frequently described bysome kind of learning curve such as the logistic function.

7. Internet building up chronology

We nowmove on to presenting a quantitative analysis of the time series of the main events characterizing the development ofthe Internet during the last fifty years using our multi-logistic approach to study evolutionary series. To start with we needed acomprehensive listing of the most impacting events that paved the way through our days to build the Internet. Browsing throughthe pertinent works, it seemed to us that the Hobbe's Internet timeline [11], compiled from a wide number of sources, fulfillsquite well that purpose. The resulting listing consisted of some 487 entries spanning from 1958 through 2009.

We started by modeling the cumulative number of events using our multi-logistic approach. The time derivative of this modelwas then compared to the yearly rate of events. Next, we analyzed the data-to-model residuals resulting from the model fitting.Fig. 19 shows the result of the multi-logistic modeling of the cumulative number of events. The best data fitting was accomplishedwith a three-logistic model. The corresponding data fitting parameters are listed in Table 11. Apart from the carrying capacity, theinflection point, tc and the characteristic time, τ, for each logistic phase, we have also included there the duration time, Δti, for theexcursion of the logistic process to go from 10% to 90% of the carrying capacity value for each logistic phase.

Table 10Main parameters for IDIOP×HDI linear correlation for both 2002 and 2007 data.

Total number of countries Countries in range 1 Countries in range 2 Average IDIOP in range 1 Slope in range 2

2002 152 43 81 0.495±0.120 18.492007 151 37 88 0.791±0.191 22.89

Fig. 19. The multi-logistic modeling of the cumulative number of the events building the Internet. The best fitting came with a three-logistic function model.



image of Fig.�19


The inset in Fig. 19 shows the extrapolation of the three-logistic model towards 2030.These results indicate that the evolution of the events leading to the building up of the Internet came in as a sequence of three

logistic phases with growth rate peaks located at about 1971.8, 1985.38, and 1997.96. The phase peaks stood approximately13 years apart, on the average. These phases are best displayed in Fig. 20 in which we compare the yearly distribution of eventswith the curve obtained by computing the time derivative of the fitted three-logistic model function given in Fig. 19.

The present modeling of the cumulative number of events predicts that, the current technology keeping unchanged, the total num-ber of leading events contributing to the evolutionary pace of the Internet should asymptotically saturate by 2015–2020, when thisnumber should reach 502 events. This forecasting comes from extrapolating the three logistic modeling beyond the time bracket ofthe data, as shown in the inset in Fig. 19. That is, by the middle of the current decade we can expect an exhaustion of the current in-ternet technology. Concurrently a radically new generation of Internet technology should be on the rise. Furthermore, we cannot fail tonotice that, counted from the inception of the Internet in 1958, the interval from 1958 to 2015–2020 corresponds to a time span of 57–62 years coinciding accordingly with the period of a K-wave.

Finally, in Fig. 21we present the reconstruction of themodel-to-data residuals, using our truncated Fourier series approach that inthe present case required keeping the first eight harmonics. This yielded a fundamental period of about 30.28 years (a typical gener-ational time scale), and two dominantmodeswith periods of 15.14 and 4.33 years. The last two reinforce the influence of the Kuznetsstructural cycles (15 to 25 years long) and brings in also the influence of the Kitchin inventory cycles of the order of 3 to 5 years long.

The solid line is a truncated Fourier sine series reconstruction of the model-to-data residuals for the cumulative number of themain events building the Internet, after modeling it with a three-logistic function. The vertical arrows shown in Fig. 21 points atsites along the extrapolation of the residual reconstruction beyond 2009 where peak fluctuations in the residuals are predict tooccur, that is, in 2014 and 2030. Now, the year 2014 is quite close to the onset of saturation of the current internet technology,as predicted by our model, and indicated in Fig. 19. In other words, both the multi-logistic modeling of the cumulative numberof the most impacting events in the development of the Internet and the analysis of the data fitting residuals are consistent intheir predictions that by 2015 one should expect some radical changes in the Internet technology to take place.

8. Discussion and conclusions

In this paper we have used our recently advanced multi-logistic analytical procedure for evolutionary time series [6,7,14] to per-form a quantitative analysis of some of the main Internet and ICT indicators time evolutions. For that purpose, four indicators have

Fig. 20. Plot of the data for the yearly number of events building the Internet. The solid line is the time derivative of the fitted three-logistic model function. Thethree phases are clearly displayed.

Table 11Values of the characteristic parameters obtained from the three-logistic data fitting to the cumulative number of the most impact-ing events building up the Internet. In the last line we list some relevant fit statistics.

Parameters Phase 1 Phase 2 Phase 3

Ai 68.02 61.49 372.04tci 1971.80 1985.38 1997.96τi (yr) 2.70 2.58 3.84Δti (yr) 11.85 1.33 16.86RSSQ 276.85 R2 0.9997



image of Fig.�20


been chosen, namely, the number of Internet hosts as a measure of the Internet infrastructure size, the Internet penetration index,defined as the number of Internet users as a percentage of the world population, to describe its global access and use, the softwareand protocols time evolution as a complementary indicator of the Internet infrastructure associated with the man–machine inter-face, and the ICT development index to track the global development of the new ICT, measuring the access and effective use ofICT in different countries and the resultant digital divider. In addition to these indicators we have also analyzed the most impactingevents building up the Internet along the last fifty years aiming at exposing eventual subjacent cyclical structures engendered bytheir driving motors.

Our main conclusions may be summarized as follows. The Internet hosts counting and the penetration index were both bestmodeled by a sequence of five logistic phases whose average center positions stood roughly 4.7 and 4.3 years apart, respectively.In both cases, the fifth phases were predicted to occur by the year 2015. The analysis of the time series of the most impactingevents building up the Internet also shows that its development underwent a sequence of logistic phases; in this case, threephases with a time lag of roughly 13 years between their center positions. In other words, bell-shaped phase structures were un-covered for the growth rate of the Internet evolution indicators here considered. The locations of their central peaks and theirhaving relatively sharper or large breath could be ascribed to pertinent effects of their driving motors (of either social, economicor political nature). In all these cases, too, it is forecasted that, under the current technological knowledge, all these should reachsaturation between 2030 and 2035, with 2015 being the year of occurrence of their peak growth rate before reaching their futuresaturation values. At saturation the Internet host counting is forecasted to be close to 1.4 billion with the Internet penetrationindex nearing 89% of the world population. In line with these predictions, the analysis of the software development time evolu-tion also points to a coming peak by 2016, just about the same year (2015) as that predicted for the peaking rate in the otherindicators.

We must emphasize, even at the risk of redundancy, that the analysis of the data-to-model residuals of the several indicatorsconsidered in this paper has demonstrated that the exhibited sequence of phases are consistent with a constructive interferenceof a series of fundamental drivers describing cyclical behaviors in the economy, namely, the economic cycles. In fact, the residualsreconstruction for the Internet penetration index had a fundamental period of about 9 years with the amplitude weighted averageperiod of the four dominant harmonics modes equal to 4.3 years. This fundamental period of 9 years is of the order of the Juglareconomic cycles related to fixed investments in machines and equipments. The reconstruction of the residuals of the software andprotocols development time series, in contrast, showed that it is dominated by a fundamental period of the order of 62 years andits second and third harmonics corresponding to periods of about 31 and 21 years, respectively. That is, the evolution of the timeseries for the programming languages was powered by bursts of creativity with periods of the order of the Kuznets and Kondra-tiev economic cycles accompanying the economic changes in infrastructure and long radical transformation periods of approxi-mately 62 years time span. Similar conclusions were also found from the residuals analysis of the time series of the mainevents building up the Internet.

The analysis of the ICT development index was carried out following a different approach. In this case we have used the stan-dard statistical distribution functions to study the distribution of countries as a function of their corresponding indicators. FromITU's data base we constructed two indicators, namely, the operational indicator, IDIOP, defined as the mean between ITU's accessand use indicators, and the functional indicator, IDIF, defined as the geometric mean between IDIOP and the skills sub-index, IDIS.The comparison between the IDI and IDIF indicated that the ITU's indicator tends to minimize the impacts of the skills sub-indexon its compound indicator. We have then focused on the analysis of the evolution of IDIOP between 2002 and 2007 as well as on

Fig. 21. Truncated Fourier sine series reconstruction of the three-logistic model-to-data residuals for the cumulative number of the main events building theInternet.



image of Fig.�21


their correlations with the human development index for the corresponding years. The results found may be summarized asfollows:

• There has been a clear worldwide improvement in the ICT infrastructure and use from 2002 to 2007, notwithstanding the ob-served increase of the gap between the highest and lowest IDIOP during the same time period.

• This increasing trend of the IDIOP gap from 2002 to 2007 contrasts with the overall, though modest, decrease of the HDI gap,from 0.683 in 2002 to 0.631 in 2007.

• Despite of these facts, it was found from the IDIOP versus HDI correlation analysis that the number of countries in the low rangeof HDI values decreased from 2002 to 2007, at the same time that the number of countries entering high range increased.

• We have also found that there is a group of countries whose improvements in their operational ICT index are disconnected fromtheir corresponding improvements in the human development, whereas for countries with top medium and high human devel-opment levels (namely, countries with HDI≥0.75) there is a close correlation between the two indices.

The importance of the Internet for human society is constantly increasing. In four decades the Internet has moved from being arestricted network of computer science researchers into being the global backbone of the information society, currently amassingthe impressive total of over one billion people that use it to communicate, search and share information, conduct business andenjoy entertainment. So far engineering efforts have been to cope with the scaled up bottlenecks caused by the explosive growthof the user base and by novel application requirements. Nevertheless, it must be brought into mind that the Internet and its ar-chitectural principles were designed in the 1970s, mostly for purposes that resemble very little to the current and foreseen usagescenarios. These new usages are questioning the ability of the Internet to cope with the current and forthcoming challenges. Theneed to meet the increased awareness of such problems, as well as to the new possibilities that the Internet is continuously of-fering, has stimulated the establishment of various initiatives to study its future. These comprise, the Future Internet Assembly[25], in Europe and the US based Future Internet Design [26] among others. In this regard, it must be pointed out that, althoughthe technical shortcomings may eventually be recognized and equated, this might not be enough since the Internet evolution isalso affected by economic, political and social forces whose influences need to be understood and taken into consideration so thattechnical solutions are adopted, accepted and used successfully everywhere. In fact, the inertia of the Internet caused, if not forany other reason, by its sheer size needs to be taken into account when planning the deployment of new technical solutions.

Scenario planning [27] is an established tool for exploring complex situations with high uncertainty. Thus, creating scenarios iscertainly one way to deal with the complex uncertainties related to the Internet ecosystem evolution, since this is, in general, builtupon identifying driving forces consisting of both predetermined trends and uncertain elements. Different scenarios have beenused in dealing with high uncertainty of emerging technologies in the realm of ICT, such as those proposed by Karlson et al.[28], creating four possible scenarios for the evolution of wireless industry from 2003 to 2015, and that of Smura and Sorri[29], studying the wireless local area access market concentrating on indoor access and especially on rivalry between WLANs(wireless local area networks) and femtocells [30], the small base stations that may turn out to be a new revolution in the ICTdomain. In addition to that we should also add the challenges introduced by the new network paradigm, referred to by Ian Akyil-diz as the Internet of nano-things [31] that will result from the interconnection of nano-scale devices with existing communica-tion networks and the Internet, in terms of channel modeling, information encoding and protocols for the interconnection ofnano-networks.

Key trends give important clues as to what is certain or very likely to get realized. They become then basic elements of anyscenario planning with significant impact on the final resulting scenarios. In this regard we hope that the results presented inthis paper may be useful for the Internet scenario planning practitioners in their endeavors.

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summary of his invited talk is available at www.ict2011.org.

Luiz C. M. Miranda Dr. Miranda got his D.Phil. in Physics from Oxford University, UK, in 1972. Along his scientific career he has published over three hundredpapers in international scientific journals. He was a John Simon.Guggenheim Fellow at the University of Arizona during 1975–76 and has exerted several admin-istrative positions in different Brazilian academic and scientific institutions, such as Dean of Undergraduates at the University of Brasilia, Vice-Director of the In-stitute of Advanced Studies of the Aerospace Technical Center, Scientific Director of the Rio de Janeiro Polytechnic Institute, and director of the National SpaceResearch Institute. He is currently a retired senior researcher of the National Space Research Institute acting as an independent consultant.

Carlos A. S. Lima Dr. Lima earned his Ph. D. in Physics from University of California at Berkeley, USA, in 1973 (Fulbright Commission fellowship). His academiccareer accomplishments took him into USA, France, Mexico, Hungary, Chile and Brazil and he has published several tens of papers. Posts held: Full Professor andHead of Physics Dept at University of Brasilia, Director of the Brazilian Physical Society, Director Extension School and Deputy Dean of Research and of Grad.School (Univ. of Campinas, São Paulo). He implanted the Experimental Physics Section for the Grad. School at Univ. Concepcion, in Chile. The Minister of Scienceand Technology of Brazil appointed him (2003–2004) Secretary for the Coordination of the Research Institutes. He is currently a retired Full Professor at Univer-sity of Campinas.



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trends and cycles of the internet evolution and worldwide impacts

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