1
WHAT HISTORY REALLY
IS
Lui Lam, Second Author and Third Author
The abstract should summarize the context, content and conclusions of the paper
in less than 200 words. It should not contain any references or displayed
equations. Typeset the abstract in
10 pt Times Roman with baselineskip of 12 pt.
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 st
ars and received on earth can be compared
with those observed in the laborator
y
; the identity of the elements
exist
ing
in stars is then identified. Similarly, the psychology, thoughts
and behaviors of historical players can be inferred from those of living
L. Lam
2
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
partic
les 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
particles.
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.
H
istorical 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,
s
omeone
with sufficient skills and patience
can
guess the rules governing historical processes, like those in a chess or
soccer game.
In some cases, t
he
se
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 studyi
ng
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, includin
g 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
3
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 indicat
es 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 eq
uations 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 m
ore effective than any of the atomic processes
1
q q
A A A B
(1)
where
1
A B q
and
B
is in the radiative processes.
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 log

log plot; a straight line i
ndicates 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
.
L. Lam
4
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 ma
king 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
Q
uantitative
L
aws and a
Q
uantitative
P
rediction in Chinese
H
istory
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 regim
es spanning a total of
2,133 years [Morby, 2002]. (A regime is the reign of one emperor; a
dynasty may consist of several regimes.)
S
ome of these dynasties overlap
with each other in time.
Let
τ
R
be the regime lifetime, and
τ
D
the dynasty lifetime; both ar
e
integers measured in years. The histogram of τ
R
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 comm
on 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 recombin
ation 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
5
century after Bates’ seminal paper. Thus, it is natural that the majority of
molecular ions for which theoretical and experimental dissoci
ative
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 pa
per 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
be
ams technique played an important role for the understanding of DR of
Table
1. Calculated
r

mode frequency
corrections
2
for constant density stars
(
0
n
) and
1
n
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
( 0)
n
2
( 1)
n
nC
C
nC
C
2
0.765
0.913
0.398
0.451
3
0.777
0.844
0.527
0.423
4
0.769
0.345
0.656
0.382
5
0.730
0.749
0.399
0.405
L. Lam
6
H
2
.
Because of the rapid conversion of H
2
to H
3
by ion
–
molecule
reactions, H
2
is inaccessible t
o the afterglow techniques. The merged
beams (see Table
2) technique also allows the measurement of DR cross

sections 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 va
lues 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 1
(2 )
u g
p
resonant state
completely dominates the recombina
tion. 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 r
eviewed
recently. The process which involves an electronic excitation of the ionic
Table
2. Predicted and observed order of errors for eigenvalues based on various
combinations of stiffness and
mass matrices.
Type
Predicted order of error in representing
Observed error for
K
M
k2r
–
m2c
2
( )
O h
4
( )
O h
2
( )
O h
2
( )
O h
k2r
–
m2l
2
( )
O h
2
( )
O h
2
( )
O h
2
( )
O h
k3e
–
m3c
2
( )
O h
6
( )
O h
2
( )
O h
2
( )
O h
k3e
–
m3l
2
( )
O h
4
( )
O h
2
( )
O h
2
( )
O h
k3r
–
m3a
4
( )
O h
6
( )
O h
3
( )
O h
3
( )
O h
k3e
–
m3b
5
( )
O h
7
( )
O h
4
( )
O h
7
( )
O h
k3r
–
m3d
7
( )
O h
8
( )
O h
6
( )
O h
8
( )
O h
Note
: The rapid conversion of
2
( )
O h
t
o
4
( )
O h
by ion
–
molecule reactions.
Source
: Takagi (1996).
What History Really Is
7
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 ene
rgy release when the electron energy was sufficient for the
3
O( ) H( 2)
P n
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
1
O( ) H( 1)
D n
. 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
3
O( ) H( 2)
P n
limit. It is thus reasonable to
approximate the actual pressure with its time average over one period
(
that is, set
0
p
) 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 state

owned sector. Investment decisions of central projec
ts 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
enterprises.
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 agree
2
that
(O
2
)
7
2 10
cm
3
s
1
, 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 showed
89,90
that DR of O
2
( 10)
leading to the production of
1
O( )
S
mus
t occur through the
1
u
state of
O
2
that dissociates to
1 1
O( ) O( )
S 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
8
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
sp( )
a
C
‚
We see that the crucial assumption of the mechanism is that despite
the vanishing o
f the bare fermion mass, the physical mass
m
of the
fermion is nonzero. Since the bare fermion mass
0
0
m
, we have
A
C
,
see Theorem
1 and so we obtain the self

consistency equation for the
physical mass of fermion.
Proof:
On
1
( )
A
Y P
‚
,
p
is just
h
and its singularities are isolated. The
notation
A
stays for
ˆ
A Y
.
□
The first statement immediately follows from the definition of the
spaces
Y
and
X
. As for the second statement, we have
the homotopy
equivalences
1
( ) ( )
i i S
Y Y X
(2)
We need a condition which implies a certain level of connectivity of each
pair
( )
i D i c
B Y B X
. A condition that fits well is the rectified
homotopical depth of the total space
X
. This condi
tion does not depend
on the stratification of the space.
Moreover,
What History Really Is
9
1
lim ( ) lim 0
1 ( )
a
R
(3)
Similarly, if
0
a
is invertible and
1
0
1
0
( )
 
a
then
1 1 1
0 0
0
( ) ( ) (( ) )
n n
n
a a
This also shows that the resolvent is open. Si
nce
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 admit
s 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  1
a
Then
( )
a GL A
and
1
0
(1 )
n
n
a a
Moreover,
1
1
1 1 
 
a
a
and
1 
1
1 1 
 1 
a
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 commu
tative
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
( )
a A
I
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
10
( ) 1 1.
a b
So
1
I
and
I
is proper. Therefore, if
A
is simple,
a
must be a sc
alar,
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
sup ( )
x X
f 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 contingenc
y
is statistical physics. Furthermore,
the historical system is an
open
system with constant exchange of energy
and materials with the environment and is nev
er 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 walk
1
can be used
to model histo
ry.
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 allowe
d 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) t
he two

site AW model (see Sec. 4
in [Lam, 2005a]
) is
able to explain the real case in economic history that an inferior product
1
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]
.
Mor
e recently, it has been used to model human history
[Lam,
2002].
What History Really Is
11
such as the QWERTY keyboard [David, 1986] can actually win out in the
market [Lam, 2002]. Other examples are the competition bet
ween A
pple
computers and PC’s, as well as VHS and Beta videotapes.
(2) The active

walk aggregation (AWA) model
2
2
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
repeatable.
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 elect
rons. 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 i
ons, 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 exper
iment 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
2
The AWA model was introduced by Lam and Pochy [1993].
L. Lam
12
three entities can be fou
nd in companies in developed countries, although
variant forms of organization exist in some countries. Shareholders have
all the rights related to property rights.
Acknowledgments
This work was supported by the Swedish Natural Science Research
Council, th
e 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 comment
s on
the early drafts.
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Xie,
Xi [2005] “Historical feel regained,”
World Journal
(Millbrae, CA)
April 16
, p.
A15.
Zipf, G.K. [1949]
Human Behavior and the Principle of Least Effort
(Addison

Wesley,
Cambridge, Massac
husetts).
L. Lam
14
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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 li
quid 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:
lui2002lam@yahoo.com
.
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