advertisement

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 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 1 2 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 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. 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 3 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. (1) 4 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 History 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 5 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) nC 2 3 4 5 0.765 0.777 0.769 0.730 C 0.913 0.844 0.345 0.749 2 (n 1) nC 0.398 0.527 0.656 0.399 C 0.451 0.423 0.382 0.405 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 6 L. Lam 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 O(h2 ) O(h4 ) O(h2 ) O(h2 ) k2r–m2l O(h2 ) O(h2 ) O(h2 ) O(h2 ) k3e–m3c O(h2 ) O(h6 ) O(h2 ) O(h2 ) k3e–m3l O(h ) O(h ) O(h ) O(h2 ) k3r–m3a O(h4 ) O(h6 ) O(h3 ) O(h3 ) 2 4 2 k3e–m3b O(h ) O(h ) O(h ) O(h7 ) k3r–m3d O(h7 ) O(h8 ) O(h6 ) O(h8 ) 5 7 4 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 1g 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 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 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 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 1 unanimously agree2 that (O 2 ) 2 107 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 8 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 Â 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 i 1 (Y ) i (YS X ) (2) 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. Moreover, What History Really Is 9 1 0 1 ( a ) lim R( ) lim (3) Similarly, if 0 a is invertible and | 0 | ( 1a )1 then 0 ( a) (0 ) ((0 a) 1 ) n 1 1 n n0 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 1 Moreover, || a || 1 1||1 a|| and || 1 a 1 || 1|1||1a||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, 10 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 xX 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 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]. More 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 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 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 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 2 The AWA model was introduced by Lam and Pochy [1993]. 12 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. Acknowledgments 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. References 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, Tamsui). What History Really Is 13 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 (www.pantaneto.co.uk). 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. A15. Zipf, G.K. [1949] Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, Massachusetts). 14 L. Lam Start a new page here after the end of your paper. This page is not counted towards the length of your manuscript. Below, write a short biography of yourself less than 120 words— starting with your name in bold, including your brief background, affiliation, and ending with your current interests, and email address (the latter in italic). (One author one paragraph.) This paragraph will be collected into the “Contributors” list at the end of the book, to be arranged alphabetically according to the last name. 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]