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Lui Lam, Second Author and Third Author
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1. What Is History?
History is the most important discipline of study [Lam, 2002]. Yet, the
link between history and science is underdeveloped.
Science is the study of nature and to understand it in a unified way.
Nature, of course, includes all material systems. The system investigated
in history is a (biological) material system consisting of Homo sapiens.
Consequently, history is a legitimate branch of science, like physics,
biology, paleontology and so on. In other words, history is not a subject
that is beyond the domain of science. History can be studied
scientifically [Lam, 2002].
By definition, history is about past events and is irreproducible. In
this regard, it is like the other “historical” sciences such as cosmology,
astronomy, paleontology and archeology. The way historical sciences
advance is by linking them to systems presently exist, which are
amenable to tests. For example, in astronomy, the color spectra of light
emitted in the past from the stars and received on earth can be compared
with those observed in the laboratory; the identity of the elements
existing in stars is then identified. Similarly, the psychology, thoughts
and behaviors of historical players can be inferred from those of living
L. Lam
human beings, which can be learned by observations, experimentations
and neurophysiological probes [Feder, 2005].
The system under study in history is a many-body system. In this
system, each “body” is a human being, called a “particle” here; these
particles have internal states (due to thinking, memory, etc.) which
sometimes can be ignored. Each constituent particle is a (non-quantum
mechanical) classical object and is distinguishable, i.e., each particle in
the system can be identified individually. This many-body system is a
heterogeneous system, due to the different sizes, ages, races…of the
A historical process, expressed in the physics language, is the time
development of a subset of or the whole system of Homo sapiens that
happened during a time period of interest in the past. History is therefore
the study of the past dynamics of this system. Historical processes are
stochastic, resulting from a combination of contingency and necessity. In
modeling, contingency shows up as probability and necessity is
represented by rules in the model. The situation is like that in a chess or
soccer game. There are a few basic rules that the players have to obey,
but because of contingency, the detail play-by-play of each game is
different. In principle, someone with sufficient skills and patience can
guess the rules governing historical processes, like those in a chess or
soccer game.
In some cases, these two ingredients of contingency and necessity,
through self-organization, may combine to give rise to discernable
historical trends or laws. In other cases, either no laws exist at all or the
laws are not recognized by whoever studying them. Whether there
actually exist historical laws cannot be settled by speculations or debates,
no matter how good these speculations or debates are. A historical law
exists only when it is found and confirmed. Furthermore, any historical
law—like that in physics—has its own range of validity, which may
cover only a limited domain of space and time.
Yet most people, including many historians, do not believe that any
historical law could exist [Gardiner, 1959]. They are wrong. Figure 1a
shows a historical law; it exists. This power law on the statistics of war
deaths is due to Richardson [1960]. Similar power laws are found in the
distribution of earthquake intensities, called Gutenberg-Richter law (Fig.
What History Really Is
Fig. 1. (a) Statistical distribution of war intensities. Eighty-two wars from 1820 to 1929
are included; the dot on the horizontal axis comes from World War I. The graph is a loglog plot; a straight line indicates a power law. (b) Distribution of earthquake sizes in the
New Madrid zone in the United States from 1974 to 1983 [Johnston & Nava, 1985]. The
points show the number of earthquakes with magnitude larger than a given magnitude m.
1b), in the ranking of city populations, and in many other systems [Zipf,
1949]. The fact that human events like wars obey the same statistical law
as inanimate systems indicates that the human system does belong to a
larger class of dynamical systems in nature, beyond the control of human
intentions and actions, individually or collectively. More historical laws
are given below in Sec. 2.
These two paragraphs are to show how equations should be inserted
and numbered. When a molecular ion captures an electron, the molecular
analogues of radiative and dielectronic recombination are in principle
possible, however, they are usually completely overshadowed by a
process which is far more effective than any of the atomic processes
Aq 1  Aq   A  B
where A  B  q  1 and B is in the radiative processes.
L. Lam
The reason for this process being so much more efficient than the
atomic processes is that a molecular ion can stabilize the capture of an
electron by making use of its internal structure, which allows for a
radiationless rearrangement of the nuclei on a time scale (  1 ps) much
shorter than that for radiative transitions (  1 ns). Figure 1 illustrates the
process. The free electron can deposit its excess energy to the molecular
ion either by exciting a bound electron or by exciting a vibrational mode.
The application of ion storage ring technology to the process of
dissociative recombination, and related processes.
2. Two Quantitative Laws and a Quantitative Prediction in Chinese
China has a long, unbroken history, which is probably the best
documented [Huang, 1997]. The dynasties from Qin to Qing ranges from
221 B.C. to 1912, with 31 dynasties and 231 regimes spanning a total of
2,133 years [Morby, 2002]. (A regime is the reign of one emperor; a
dynasty may consist of several regimes.) Some of these dynasties overlap
with each other in time.
Let τR be the regime lifetime, and τD the dynasty lifetime; both are
integers measured in years. The histogram of τR is found to obey a power
law, with an exponent equal to -1.3. This result implies that the dynamics
governing regime changes is not completely up to the emperors,
statistically speaking, but share some common traits with other complex
systems such as those displayed in Fig. 1. This is the first quantitative
law about Chinese history.
3. This Section Contains Examples of Tables and Subsection and
Sub-Subsection Headings
The mechanism for dissociative recombination has been given the
descriptive name the crossing mode. It was for a long time believed that
a favorable crossing was a prerequisite for the occurrence of dissociative
recombination. As we will see in the next section, a second mode of
recombination, the tunneling mode, has recently been recognized as
important. The recognition of this second mode came almost half a
What History Really Is
Table 1. Calculated r-mode frequency
corrections 2 for constant density stars
( n  0 ) and n  1 polytropes. Results are
shown both for the full calculation (nC) and
the Cowling approximation (C). The results
are for barotropic perturbations and the
fundamental l  m modes.
2 (n  0)
2 (n  1)
century after Bates’ seminal paper. Thus, it is natural that the majority of
molecular ions for which theoretical and experimental dissociative
recombination data are available belongs to the crossing mode category.
Table 1 lists all ion storage ring experiments known to the author
concening dissociative recombination that have resulted in a published
paper, a paper that is in press, or a paper that has been submitted for
publication (by August 1998), and the type of results that have been
obtained in these experiments. Examples of the theoretically computed
Doppler spectra. (Thick line: 0 crossing angle, thin line: 90 crossing
angle). The results of the present model depend importantly on our
assumption that the spectra retains a long-term interest.
3.1. Diatomic Hydrogen Ions
Being the simplest diatomic molecule, it is natural that H 2 and its
isotopomers represent benchmark systems for dissociative
recombination, in particular with respect to the comparison of
experiment and theory. The experimental and theoretical studies of DR
of H 2 and its isotopomers in their zeroth vibrational levels are described
in some detail in two recent reviews, and only a brief summary of the
present situation will be given here.
The development of a single-pass merged electron-molecular ion
beams technique played an important role for the understanding of DR of
L. Lam
Table 2. Predicted and observed order of errors for eigenvalues based on various
combinations of stiffness and mass matrices.
Predicted order of error in representing
Observed error for
O(h2 )
O(h4 )
O(h2 )
O(h2 )
O(h2 )
O(h2 )
O(h2 )
O(h2 )
O(h2 )
O(h6 )
O(h2 )
O(h2 )
O(h )
O(h )
O(h )
O(h2 )
O(h4 )
O(h6 )
O(h3 )
O(h3 )
O(h )
O(h )
O(h )
O(h7 )
O(h7 )
O(h8 )
O(h6 )
O(h8 )
Note: The rapid conversion of O(h2 ) to O(h4 ) by ion–molecule reactions.
Source: Takagi (1996).
H 2 . Because of the rapid conversion of H 2 to H 3 by ion–molecule
reactions, H 2 is inaccessible to the afterglow techniques. The merged
beams (see Table 2) technique also allows the measurement of DR crosssections or early experimental and theoretical papers provided the first
qualitatively correct insight into the DR of H 2 , it was not until more
than ten years later that a complete quantitative comparison of
experiment and theory finally was accomplished by the research groups
of Giusti-Suzor and Mitchell. The comparison revealed a good
agreement both in terms of the absolute values of the cross-section and
the positions of several ‘window’ resonances caused by the interference
between the direct and indirect mechanisms.
The comparison concerned only DR at electron energies well below
the ion dissociation energy, where the (2 p u )2 1g resonant state
completely dominates the recombination. It was not possible, however,
to unambiguously assign the experimental results to H 2 populating only
its zeroth vibrational level of the molecule.
3.2. Monohydride Ions
Dissociative recombination of monohydride ions has been reviewed
recently. The process which involves an electronic excitation of the ionic
What History Really Is
core has not been further investigated since the last review.32 An imaging
experiment with OH  in CRYRING led to discovery of a very small
kinetic energy release when the electron energy was sufficient for the
O(3 P)  H(n  2) dissociation limit (see Table 3) to become
energetically allowed.84 Recombination of OH  is known to proceed
through the 2 2  resonant state,85 which dissociates diabatically to
O(1 D)  H(n  1) . The imaging result (see Table 4) shows that part of
the dissociating flux is redirected, probably at avoided crossings between
the 2 2  state and the 3 2  , 4 2  and 5 2  states, which all correlate
diabatically to the O(3 P)  H(n  2) limit. It is thus reasonable to
approximate the actual pressure with its time average over one period
(that is, set p  0 ) provided the radius R.
It shows changes in proportions of the central government’s projects
and local projects in the total capital construction investment of stateowned sector. Investment decisions of central projects are generally
made by the line ministries and the State Planning Commision, and that
of local projects, (see Table 5) are made by local governments and
3.2.1. Transition in the Theoretical Work
The thermal rate coefficient for O 2 occupies an unusual role in the
respect that different experiments over a time span of thirty years almost
unanimously agree2 that  (O 2 )  2  107 cm 3 s , the very recent
measurement based on cross-section data from CRYRING being no
exception.86 With few exceptions,87 most theoretical work has been
devoted to the understanding of the formation of O( 1 S ) in dissociative
recombination of O 2 . It is the O( 1 S )  O( 1 D ) transition in neutral
atomic oxygen which gives rise to the green airglow at 5577 Å in the
terrestrial atmosphere. It is worth noting that the earliest mention of
dissociative recombination was made in an attempt to identify a source
of the green oxygen line.88 Guberman showed89,90 that DR of O 2 (  10)
leading to the production of O(1 S ) must occur through the 1  u state of
O2 that dissociates to O(1 S )  O(1 D) , and proceeded to calculate, using
the MQDT approach, the partial rate coefficient for DR of O 2 through
the 1  u state.91
L. Lam
Test for Lists and Theorem Environments
item one,
item two,
item three.
Items may also be numbered in lowercase roman numerals:
(i) item one
(ii) item two
(iii) item three
(a) lowercase roman letters for lists within lists,
(b) second item
(iv) item four
Theorem 1: In any unital Banach algebra A, the spectrum of each a  A
is a non-empty compact subset, and the resolvent function is analytic on
C ‚ sp(a)
We see that the crucial assumption of the mechanism is that despite
the vanishing of the bare fermion mass, the physical mass m of the
fermion is nonzero. Since the bare fermion mass m0  0 , we have A  C ,
see Theorem 1 and so we obtain the self-consistency equation for the
physical mass of fermion.
Proof: On Y ‚ ( A P1 ) , p is just h and its singularities are isolated. The
notation A stays for   Y .
The first statement immediately follows from the definition of the
spaces Y and X. As for the second statement, we have the homotopy
 i 1 (Y )  i (YS  X  ) 
We need a condition which implies a certain level of connectivity of each
pair ( Bi  YD  Bi  X c ) . A condition that fits well is the rectified
homotopical depth of the total space X. This condition does not depend
on the stratification of the space.
What History Really Is
  1
 0
  1  ( a )
lim R( )  lim
 
Similarly, if 0  a is invertible and |   0 | ( 1a )1 then
(  a)   (0   ) ((0  a) 1 ) n 1 
This also shows that the resolvent is open. Since sp( a ) has been shown
to be bounded, sp(a) is compact. We have also shown that the resolvent
function is analytic on the complement of the spectrum.
Definition 2: A Banach algebra A is said to be unital if it admits a unit 1
and ||1||  1 Banach algebras in 3.
Lemma 3: Let A be a unital Banach algebra and a be an element of A
such that ||1  a || 1 Then a  GL( A) and
a 1   (1  a ) n 
n 0
Moreover, || a ||
1||1 a||
and || 1  a 1 || 1|1||1a||a|| .
Remark 4: The Gelfand representation theorem for commutative C  algebras is fundamentally important. Even in a non-commutative A we
often obtain useful information of A via the study of certain commutative
C  -subalgebras of A . So Theorem 1 certainly plays an important role in
studying non-commutative C  -algebras as well. Theorem 2 shows that
to study commutative C  -algebras, it is equivalent to study their
maximal ideal spaces. So the commutative C  -algebra, theory is the
theory of topology. Much of general C  -algebra, theory can be described
as non-commutative topology.
Corollary 5: The only simple commutative unital Banach algebra is C
Proof: Suppose that A is a unital commutative Banach algebra and a  A
is not a scalar. Let   sp(a) Set I  (a   ) A Then I is clearly a closed
ideal of A No element of the form (a   )b is invertible in the
commutative Banach algebra A By 3,
L. Lam
(a   )b  1 1.
So 1
 I and I is proper. Therefore, if A is simple, a must be a scalar,
whence A  C
Example 6: Let X be a compact Hausdorff space and C ( X ) the set of
continuous functions on X C ( X ) is a complex algebra with pointwise
operations. With f  sup xX  f ( x)  C ( X ) is a Banach algebra.
4. Modeling History by Active Walks
An important step towards the scientific study of any subject is to pick
the right tool to tackle it. Historical processes are stochastic (i.e., with
probability involved somewhere), resulting from necessity and
contingency. The kind of physics suitable for handling many-body
systems ingrained with contingency is statistical physics. Furthermore,
the historical system is an open system with constant exchange of energy
and materials with the environment and is never in equilibrium. Thus, for
history, the appropriate tool is the stochastic methods developed in the
statistical physics of nonequilibrium systems [Lam, 1998; Paul &
Baschnagel, 1999; Sornette, 2000]. In particular, active walk1 can be used
to model history. In fact, a common metaphor for history is that it is like a
river flowing; people talk about the “river of history.” This metaphor is not
so off mark if the water flowing in the river is able to reshape the landscape
as it flows and the river is allowed to branch from time to time under
certain conditions. Active walk is a natural in matching such a metaphor. It
is then no surprise that a whole class of probabilistic AW models are found
to be relevant in studying history [Lam, 2002].
For example, (1) the two-site AW model (see Sec. 4 in [Lam, 2005a]) is
able to explain the real case in economic history that an inferior product
Active walk is a paradigm for self-organization and pattern formation in simple and
complex systems, originated by Lam in 1992 [Lam, 2005a]. In an AW, the walker
changes the deformable landscape as it walks and is influenced by the changed landscape
in choosing its next step. Active walk models have been applied successfully to various
biological, physical, geological and economic systems from both the natural and social
sciences [Lam, 2006b]. More recently, it has been used to model human history [Lam,
What History Really Is
such as the QWERTY keyboard [David, 1986] can actually win out in the
market [Lam, 2002]. Other examples are the competition between Apple
computers and PC’s, as well as VHS and Beta videotapes.
(2) The active-walk aggregation (AWA) model22 is able to shed light
on the debate in evolutionary history, initiated by Stephen Gould. The
question raised by Gould [1989] is that if life’s “tape” is replayed, will
history repeats itself and humans still be found on earth? Gould’s answer
is “no”; the AWA model says “maybe” [Lam, 1998]. It is “maybe”
because if the world lies in the sensitive zone (see Fig. 6 in [Lam,
2006b]), then the growth outcome may not be repeatable; otherwise, it is
5. Conclusions and Outlook
This article has focussed almost exclusively on the use of ion storage
rings for the study of dissociative recombination of positively charged
molecular ions with electrons. It is pertinent at this point to recall that ion
storage rings by no means are confined to the study of this particular
molecular process. Dissociative excitation has already been mentioned in
passing, with a reference given to a recent review of the topic. But there
are also other aspects of molecular physics that can be addressed by
means of the storage ring technology, as discussed in a recent article by
Zajfman, and as witnessed by publications on electron impact
detachment of negative molecular ions, laser photodetachment
spectroscopy of fullerenes, and laser photofragment spectroscopy.
Dissociative recombination of the simplest ion, H 2 and its
isotopomers, is beginning to be well understood. Yet, discrepancies
between experiment and theory still remain. They will most probably be
cleared up within the next couple of years. A good understanding of DR
of HeH  is also emerging, although there are still large discrepancies
between experiment and theory for some of the isotopomers.
The importance of HeH+ lies in fact that it is the simplest is to
recombine the (tunneling mode). The primary actors of the modern
corporation are shareholders, the board of directors, and managers. These
The AWA model was introduced by Lam and Pochy [1993].
L. Lam
three entities can be found in companies in developed countries, although
variant forms of organization exist in some countries. Shareholders have
all the rights related to property rights.
This work was supported by the Swedish Natural Science Research
Council, the Göran Gustafsson Foundation, and by the Human Capital
and Mobility programme of EU. I would like to thank those who
provided preprints or unpublished material that was used in this article,
and A. Suzor-Weiner, G. H. Dunn, and W. Shi for valuable comments on
the early drafts.
Axelrod, R. & Bennett, D.S.[1993] “ A landscape theory of aggregation,” British J.
Political Sci. 23, 211-233.
David, P.A. [1986] “Understanding the economics of QWERTY: The necessity of
history,” in Economic History and the Modern Economist, ed. Parker, W.N.
(Blackwell, New York) pp. 30-49.
Feder, T. [2005] “Lab webs brain research and physics,” Phys. Today April, pp. 26-27.
Fukuyama, F. [1989] “The end of history?” The National Interest 16 (summer), 3-18.
Galam, S. [1998] “Comment on ‘A landscape theory of aggregation’,” British J. Political
Sci. 28, 411-412.
Gardiner, P. (ed.) [1959] Theories of History (The Free Press, Glencoe, Illinois).
Gould, S.J. [1989] Wonderful Life: The Burgess Shale and the Nature of History (Norton,
New York).
Huang, R. [1997] China: A Macro History (M.E. Sharpe, Armonk, NY).
Johnston, A.C. & Nava, S. [1985] “Recurrence rates and probability estimates for the
New Madrid seismic zone,” J. Geophys. Res. 90, 6737-6753.
Laherrère, J. & Sornette, D. [1998] “Stretched exponential distributions in nature and
economy: ‘fat tails’ with characteristic scales,” Eur. Phys. J. B. 2, 525-539.
Lam, L. & Pochy, R.D. [1993] “Active walker models: Growth and form in nonequilibrium
systems,” Comput. Phys. 7, 534-541.
Lam, L. [1998] Nonlinear Physics for Beginners: Fractals, Chaos, Solitons, Pattern
Formation, Cellular Automata and Complex Systems (World Scientific, Singapore).
Lam, L. [2001] “Raising the scientific literacy of the population: A simple tactic and a
global strategy,” in Public Understanding of Science, ed. Editorial Committee
(Science and Technology University of China Press, Hefei, China).
Lam, L. [2002] “Histophysics: A new discipline,” Mod. Phys. Lett. B 16, 1163-1176.
Lam, L. [2004] This Pale Blue Dot: Science, History, God (Tamkang University Press,
What History Really Is
Lam, L. [2005a] “Active walks: The first twelve years (Part I),” Int. J. Bifurcation and
Chaos 15, 2317-2348.
Lam, L. [2005b] “Integrating popular science books into college science teaching,” The
Pantaneto Forum, Issue 19 (
Lam, L. [2005c] “Science communication: What every scientist can do and a physicist’s
experience,” Science Popularization No. 2, 36-41 (2006). See also Lam, L., in
Proceedings of Beijing PCST Working Symposium, June 22-23, 2005, Beijing, China.
Lam, L. [2006a] “How long can a Chinese dynasty last?” (preprint).
Lam, L. [2006b] “Active walks: The first twelve years (Part II),” Int. J. Bifurcation and
Chaos 16, 239-268.
Marvick, A. [2001] The New Nature of History (Lyceum, Chicago) p. 248.
Morby, J.E. [2002] Dynasties of the World (Oxford University Press, Oxford).
Paul, W. & Baschnagel, J. [1999] Stochastic Processes: From Physics to Finance
(Springer, New York).
Richardson, L.F. [1960] Statistics of Deadly Quarrels (Boxwood, Pittsburgh, PA).
Sornette, D. [2000] Critical Phenomena in Natural Sciences (Springer, New York).
Stanford, M. [1998] An Introduction to the Philosophy of History (Blackwell, Malden,
MA) p. 228.
The Seventies Monthly (ed.) [1971] Truth Behind the Diaoyutai Incident (The Seventies
Monthly, Hong Kong).
Xie, Xi [2005] “Historical feel regained,” World Journal (Millbrae, CA) April 16, p.
Zipf, G.K. [1949] Human Behavior and the Principle of Least Effort (Addison-Wesley,
Cambridge, Massachusetts).
L. Lam
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An example is given below.
Lui Lam obtained his B.Sc. from the University of Hong Kong, M.Sc.
from the University of British Columbia, and Ph.D. from Columbia
University. Prof. Lam invented bowlics (1982), one of three existing
types of liquid crystals in the world; active walks (1992), a new
paradigm in complex systems; and a new discipline called histophysics
(2002). Lam published 11 books and over 160 scientific papers. He is the
founder of the International Liquid Crystal Society (1990); cofounder of
the Chinese Liquid Crystal Society (1980); founder and editor-in-chief of
the World Scientific book series Science Matters, and the same for the
Springer book series Partially Ordered Systems. His current research is
in histophysics, complex systems and science matters. Email:
[email protected]
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