Statistics indicate another 9/11 by 2012
bored physicist | 15.02.2005 00:31 | Analysis
Using Statistical analysis and data of global terrorist attacks between 1968 to 2004 the authors were able to find a predictable relationship between the occurance and serverity of terrorist attack. Statisticaly it is predicted that somewhere in the world another catastrophic attack will happen by 2012 (Please let it be Southampton).
physics/ 0502014 v1 3 Feb 2005
Scale Global Terrorism
Aaron Clauset and Maxwell Young
Department of Computer Science,
University of New Mexico, Albuquerque NM 87131
(aaron,young)@cs.unm.edu
(Dated: February 3, 2005)
Traditional analysis of international terrorism,
now an endemic feature of the modern era, has
not sought to explain the emergence of rare but
extremely severe events. Using the tools of
extremal statistics, we analyze terrorist attacks
worldwide between 1968 and 2004, as compiled
in the National Memorial Institute for the Pre-
vention of Terrorism (MIPT) database [1]. We
find that international terrorism exhibits a “scale-
free” behavior [2] with an exponent close to two.
We conjecture that such power-law behavior is
an extension of the still unexplained scale invari-
ance between the frequency and intensity [3] of
wars [4, 5, 6, 7]. Finally, we brie y consider the
reasons why such scaling may exist and its impli-
cations for counter-terrorism policy.
Although terrorism has a long historical relationship
with politics [8], only in the modern era have small
groups of motivated individuals had access to extremely
destructive weapons [9, 10], particularly chemical or ex-
plosive agents. This dramatic increase in destructive
power has allowed severe terrorist attacks such as the
March 20 1995 release of the Sarin nerve agent in a
Tokyo subway which injured or killed over 5000, the
August 7 1998 car bombing in Nairobi, Kenya which in-
jured or killed over 5200, or the more well known attack
on September 11 2001 in New York City which killed
2823 [1]. Over the course of modern history, such at-
tacks have been treated as outliers. We show here that
discounting these events as special cases ignores signifi-
cant patterns in terrorism over the past 37 years.
To extract and understand these patterns, we use ex-
tremal statistics to characterize the relationship between
the severity and frequency of terrorist events. By sever-
ity, we simply mean the number of individuals injured or
killed by an attack. Although many organizations track
terrorism worldwide, few provide their data publicly or
in anything but an aggregate form. The MIPT database
appears to be unique in its comprehensive detail as it con-
tains, as of January 2005, records of over 19 907 terrorist
events in 187 countries worldwide between 1968 and 2004.
Of these, 7 088 resulted in at least one person being in-
jured or killed. It is itself the compilation of the RAND
Terrorism Chronology 1968-1997, the RAND-MIPT Ter-
rorism Incident database (1998-Present), the Terrorism
Indictment database (University of Arkansas & Univer-
sity of Oklahoma), and DFI International’s research on
terrorist organizations. Each record includes the date,
target, city (if applicable), country, type of weapon used,
terrorist group responsible (if known), number of deaths
(if known), number of injuries (if known), a brief descrip-
tion of the attack and the source of the information.
Tabulating the event data as a histogram of severity
(injuries, deaths and their aggregation greater than zero),
we show the cumulative distribution functions P(x > X)
on log-log axes in Figure 1. That the distributions are
highly right-skewed is immediately obvious, and is exem-
plified by the fact that the means of the distributions are
14.60 ± 114.82, 5.13 ± 43.37 and 12.70 ± 103.38 respec-
tively, while the largest corresponding events are 5000,
2823 and 5291. The regularity of the scaling illustrates
that the extremal events are not outliers, but are instead
in concordance with a global pattern in terrorist attacks.
Surprisingly, this scaling exists in spite of strong hetero-
geneity in the types of weapons, the perpetrating orga-
nizations, locations and political motivations.
FIG. 1: The distributions P ( x > X ) of the severity (injuries, deaths and their aggregation) of terrorist attacks worldwide between 1968 and 2004, from [1]. These distributions are well- modeled by power laws with scaling parameters of alpha = 1 . 867 ±0 . 002, alpha = 1 . 842 ± 0 . 002 and alpha = 1 . 878 ± 0 . 001 respectively.
Hypothesizing that these distributions are power laws
of the form P(x) ~x^-alpha, we bootstrap the numeric max-
imization of the likelihood function 50 times to estimate
the scaling parameter alpha. We find that all three dis-
tributions are well-modeled over several decades in the
tail by a power law with alpha~ 2. Further, the relevant
Kolmogorov-Smirnov goodness-of-fit test [11] indicates
that there is insufficient evidence to reject this hypothesis (pKS > 0.05). On the other hand, we may reject
the hypothesis (pKS 2823) ~ 3 × 10^
−4.
Thus, if this distribution continues to govern the sever-
ity of attacks in the future and the sampling rate remains
constant, we may expect that to see another catastrophic
attack of at least that severity within 7 years, or by 2012.
The authors thank Cosma Shalizi and Cristopher
Moore for helpful conversations. This work was sup-
ported in part by the National Science Foundation under
grants PHY-0200909 and ITR-0324845 (A.C.) and CCR-
0313160 (M.Y.).
[1] National Memorial Institute for the Prevention of Ter-
rorism (MIPT) Terrorism Knowledge Base (Jan. 2005).
www.tkb.org
[2] M.E.J. Newman, Contemporary Physics in press (2004).
cond-mat/0412004
[3] Intensity has several definitions, the simplest being casu-
alties per 10 000 people in the warring nations.
[4] L. F. Richardson, American Statistical Association
43 :523-546 (1948).
[5] L. F. Richardson, Statistics of Deadly Quarrels. Chicago,
Quadrangle Books (1960).
[6] J. S. Levy, War in the Modern Great Power System,
1495-1975. Lexington, Kentucky University Press (1983).
[7] D. C. Roberts and D. L. Turcotte, Fractals 6 :351-357
(1998).
[8] R. D. Congleton, Independent Review 7 :47-67 (2002).
[9] Federal Bureau of Investigation, “Terrorism in the United
States,” (Jan. 1999).
[10] M. Shubik, Comparative Strategy 16 :399-414. (Oct.-Dec.
1997).
[11] M. L. Goldstein, S. A. Morris, G. G. Yen, Eur. Phys. J.
B 41 :255-258 (2004).
[12] R. Ser ing, North American Actuarial Journal 6 :95-109
(2002).
[13] B. Ganor et al., International Policy Institute for
Counter-Terrorism (Jan. 2005). www.ict.org.il
[14] M. Small and J. D. Singer. Resort to Arms: International
and Civil Wars, 1816-1980. Sage Publications, Beverley
Hills (1982).
[15] P. Bak, C. Tang and K. Wiesenfeld, Physical Review Let-
ters 59 :381-384 (1987).
[16] L.-E. Cederman, Proc. of Linkages in World Politics
Workshop, Duke University, (Feb. 2003).
[17] L.-E. Cederman, American Political Science Reviewഊ3
97 :135-150 (2003).
http://arxiv.org/pdf/physics/0502014
Scale Global Terrorism
Aaron Clauset and Maxwell Young
Department of Computer Science,
University of New Mexico, Albuquerque NM 87131
(aaron,young)@cs.unm.edu
(Dated: February 3, 2005)
Traditional analysis of international terrorism,
now an endemic feature of the modern era, has
not sought to explain the emergence of rare but
extremely severe events. Using the tools of
extremal statistics, we analyze terrorist attacks
worldwide between 1968 and 2004, as compiled
in the National Memorial Institute for the Pre-
vention of Terrorism (MIPT) database [1]. We
find that international terrorism exhibits a “scale-
free” behavior [2] with an exponent close to two.
We conjecture that such power-law behavior is
an extension of the still unexplained scale invari-
ance between the frequency and intensity [3] of
wars [4, 5, 6, 7]. Finally, we brie y consider the
reasons why such scaling may exist and its impli-
cations for counter-terrorism policy.
Although terrorism has a long historical relationship
with politics [8], only in the modern era have small
groups of motivated individuals had access to extremely
destructive weapons [9, 10], particularly chemical or ex-
plosive agents. This dramatic increase in destructive
power has allowed severe terrorist attacks such as the
March 20 1995 release of the Sarin nerve agent in a
Tokyo subway which injured or killed over 5000, the
August 7 1998 car bombing in Nairobi, Kenya which in-
jured or killed over 5200, or the more well known attack
on September 11 2001 in New York City which killed
2823 [1]. Over the course of modern history, such at-
tacks have been treated as outliers. We show here that
discounting these events as special cases ignores signifi-
cant patterns in terrorism over the past 37 years.
To extract and understand these patterns, we use ex-
tremal statistics to characterize the relationship between
the severity and frequency of terrorist events. By sever-
ity, we simply mean the number of individuals injured or
killed by an attack. Although many organizations track
terrorism worldwide, few provide their data publicly or
in anything but an aggregate form. The MIPT database
appears to be unique in its comprehensive detail as it con-
tains, as of January 2005, records of over 19 907 terrorist
events in 187 countries worldwide between 1968 and 2004.
Of these, 7 088 resulted in at least one person being in-
jured or killed. It is itself the compilation of the RAND
Terrorism Chronology 1968-1997, the RAND-MIPT Ter-
rorism Incident database (1998-Present), the Terrorism
Indictment database (University of Arkansas & Univer-
sity of Oklahoma), and DFI International’s research on
terrorist organizations. Each record includes the date,
target, city (if applicable), country, type of weapon used,
terrorist group responsible (if known), number of deaths
(if known), number of injuries (if known), a brief descrip-
tion of the attack and the source of the information.
Tabulating the event data as a histogram of severity
(injuries, deaths and their aggregation greater than zero),
we show the cumulative distribution functions P(x > X)
on log-log axes in Figure 1. That the distributions are
highly right-skewed is immediately obvious, and is exem-
plified by the fact that the means of the distributions are
14.60 ± 114.82, 5.13 ± 43.37 and 12.70 ± 103.38 respec-
tively, while the largest corresponding events are 5000,
2823 and 5291. The regularity of the scaling illustrates
that the extremal events are not outliers, but are instead
in concordance with a global pattern in terrorist attacks.
Surprisingly, this scaling exists in spite of strong hetero-
geneity in the types of weapons, the perpetrating orga-
nizations, locations and political motivations.
FIG. 1: The distributions P ( x > X ) of the severity (injuries, deaths and their aggregation) of terrorist attacks worldwide between 1968 and 2004, from [1]. These distributions are well- modeled by power laws with scaling parameters of alpha = 1 . 867 ±0 . 002, alpha = 1 . 842 ± 0 . 002 and alpha = 1 . 878 ± 0 . 001 respectively.
Hypothesizing that these distributions are power laws
of the form P(x) ~x^-alpha, we bootstrap the numeric max-
imization of the likelihood function 50 times to estimate
the scaling parameter alpha. We find that all three dis-
tributions are well-modeled over several decades in the
tail by a power law with alpha~ 2. Further, the relevant
Kolmogorov-Smirnov goodness-of-fit test [11] indicates
that there is insufficient evidence to reject this hypothesis (pKS > 0.05). On the other hand, we may reject
the hypothesis (pKS 2823) ~ 3 × 10^
−4.
Thus, if this distribution continues to govern the sever-
ity of attacks in the future and the sampling rate remains
constant, we may expect that to see another catastrophic
attack of at least that severity within 7 years, or by 2012.
The authors thank Cosma Shalizi and Cristopher
Moore for helpful conversations. This work was sup-
ported in part by the National Science Foundation under
grants PHY-0200909 and ITR-0324845 (A.C.) and CCR-
0313160 (M.Y.).
[1] National Memorial Institute for the Prevention of Ter-
rorism (MIPT) Terrorism Knowledge Base (Jan. 2005).
www.tkb.org
[2] M.E.J. Newman, Contemporary Physics in press (2004).
cond-mat/0412004
[3] Intensity has several definitions, the simplest being casu-
alties per 10 000 people in the warring nations.
[4] L. F. Richardson, American Statistical Association
43 :523-546 (1948).
[5] L. F. Richardson, Statistics of Deadly Quarrels. Chicago,
Quadrangle Books (1960).
[6] J. S. Levy, War in the Modern Great Power System,
1495-1975. Lexington, Kentucky University Press (1983).
[7] D. C. Roberts and D. L. Turcotte, Fractals 6 :351-357
(1998).
[8] R. D. Congleton, Independent Review 7 :47-67 (2002).
[9] Federal Bureau of Investigation, “Terrorism in the United
States,” (Jan. 1999).
[10] M. Shubik, Comparative Strategy 16 :399-414. (Oct.-Dec.
1997).
[11] M. L. Goldstein, S. A. Morris, G. G. Yen, Eur. Phys. J.
B 41 :255-258 (2004).
[12] R. Ser ing, North American Actuarial Journal 6 :95-109
(2002).
[13] B. Ganor et al., International Policy Institute for
Counter-Terrorism (Jan. 2005). www.ict.org.il
[14] M. Small and J. D. Singer. Resort to Arms: International
and Civil Wars, 1816-1980. Sage Publications, Beverley
Hills (1982).
[15] P. Bak, C. Tang and K. Wiesenfeld, Physical Review Let-
ters 59 :381-384 (1987).
[16] L.-E. Cederman, Proc. of Linkages in World Politics
Workshop, Duke University, (Feb. 2003).
[17] L.-E. Cederman, American Political Science Reviewഊ3
97 :135-150 (2003).
http://arxiv.org/pdf/physics/0502014
bored physicist