Symbolic Manipulation Research Articles

A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches.

We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying common intermediates is performed via comparison of these contraction topologies. The definition of the contraction topology is completely general for non-antisymmetric Goldstone diagrams, which enables our algorithm to deal with noncommuting excitations in the cluster operator that arises in the unitary group based CC formulation for open-shell systems. The resulting equations are implemented in a new code, in which tensor contractions are performed by successive application of matrix-matrix multiplications. Implementation of the unitary group adapted CC equations for closed-shell systems and for the simplest open-shell case, i.e., doublets, is discussed, and representative calculations are presented in order to assess the efficiency of the generated codes.

Quantum algebras as quantizations of dual Poisson–Lie groups

A systematic computational approach for the explicit construction of any quantum Hopf algebra (Uz(g), Δz) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δz is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λg) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for Uz(g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for Uz(g) are given by the unique Poisson–Lie structure Λg on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full Uz(g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as , the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions.

Fast modal simulation of paraxial optical systems: the MIST open source toolbox

This paper presents a new approach to the simulation of optical laser systems in the paraxial approximation, with particular applications to interferometric gravitational wave detectors. The method presented here is based on a standard decomposition of the laser field in terms of Hermite–Gauss transverse modes. The innovative feature consists of a symbolic manipulation of the equations describing the field propagation. This approach allows a huge reduction in the computational time, especially when a large number of higher order modes is needed to properly simulate the system. The new algorithm has been implemented in an open source toolbox, called the MIST, based on the MATLAB® environment. The MIST has been developed and is being used in the framework of the design of advanced gravitational wave detectors. Examples from this field of application will be discussed to illustrate the capabilities and performance of the simulation tool.

Intencionalidade e pano de fundo: Searle e Dreyfus contra a teoria clássica da inteligência artificial

According to the theory of artificial intelligence (AI), the human mind is a formal system made of symbols that operate following a set of instructions, which allow the manipulation of symbols according to their physical form. Against the conception that mental states and processes can be defined only from a syntactic perspective, John Searle used the Chinese Room thought experiment by which he intended to demonstrate that the human mind is more than a formal structure, having a semantic content as well. The semantic content of the human mind is given by intentionality, a feature that belongs exclusively to biological organisms. Starting from here, Searle shows that the logical structure of intentionality and the conditions for functioning of the intentional states cannot be explained by the computational approach of the human mind. Another perspective, which invalidated the AI theory, belongs to Hubert Dreyfus who considers that an adequate understanding of the human mind needs to start from the understanding of the phenomenological structures by means of which we relate to the world. Therefore, cognition and intentionality are explained from the perspective of an embodied being that, due to his body skills, is ontologically and dynamically coupled to the world. In this case, it is not the biological dimension of the human body that matters, but the phenomenological one that does not treat intentionality as knowingthat, whose role is to grasp the world’s objective features, but as a way of constituting the world of the subject according to his concerns and interests. Key words: AI theory, intentionality, logical analysis, phenomenology, background, context.

Beyond the chalice: monuments manifesting utraquist religious identity in the Bohemian urban context in the fifteenth and early sixteenth centuries

The article argues for the internal development of Utraquism towards ideological denominational stabilisation as revealed in urban monuments made for the Bohemian Utraquists in the late fifteenth and early sixteenth centuries. The first hundred years of Utraquism was marked by the development of independent elements of its denominational imagery, mostly in an urban context. Even before the spreading of Luther's teaching in Bohemia, the Utraquists were able to operate various modes of denominationally-charged communication in urban public space. I look at the vestiges of Utraquist cultural production to demonstrate the subtle manipulation of religious and political symbols, and iconography in public monuments to illuminate their contribution to the construction of the town's imagined political and denominational identity. Using the example of two public monuments from Eastern Bohemian town of Hradec Králové, I demonstrate ways of communicating messages through monuments. The decoration of the Hradec Králové fountain and the anti-Brethren inscription on its city's gate represent two alternative approaches to public denominational expressions around 1500, mediated through cultural objects. Whilst produced by the same religious community and proclaiming Utraquist faith of Hradec Králové's citizens, they demonstrate different intensities of instruction on religious identity, the complexities of mediated messages, as well as the practice of using public media to communicate religious attachments. The two monuments illustrate the gradual internal confessionalising process of Utraquism: whereas the decoration of the first preferred “appeasing” public symbolic language and avoiding indignation, the second communicated Utraquist intolerance towards religious secessionist groups. Both monuments, however, using different means, delineate the meaning of Utraquism as the “right” faith and should be read as attempts to a denominational appropriation of urban public space.

FORM version 4.0

We present version 4.0 of the symbolic manipulation system Form. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Gröbner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Finally, Form 4.0 has become available as open source under the GNU General Public License version 3. Program summaryProgram title: FORM.Catalogue identifier: AEOT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 151599No. of bytes in distributed program, including test data, etc.: 1078748Distribution format: tar.gzProgramming language: The FORM language. FORM itself is programmed in a mixture of C and C++.Computer: All.Operating system: UNIX, LINUX, Mac OS, Windows.Classification: 5.Nature of problem:FORM defines a symbolic manipulation language in which the emphasis lies on fast processing of very large formulas. It has been used successfully for many calculations in Quantum Field Theory and mathematics. In speed and size of formulas that can be handled it outperforms other systems typically by an order of magnitude.Special in this version:The version 4.0 contains many new features. Most important are factorization and rational arithmetic. The program has also become open source under the GPL. The code in CPC is for reference. You are encouraged to upload the most recent sources from www.nikhef.nl/form/formcvs.php because of frequent bug fixes.Solution method:See “Nature of Problem”, above.Additional comments:NOTE: The code in CPC is for reference. You are encouraged to upload the most recent sources from www.nikhef.nl/form/formcvs.php because of frequent bug fixes.

Generating and using examples in the proving process

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: experience of utility of examples in proving, personal example spaces and technical tools, formulation of the problem, and relational necessity. Our analysis led to integrating two theoretical ideas: the alignment of conceptual insight and technical handle when trying to prove; and manipulating, getting-a-sense-of, and articulating as phases of work associated with example construction.

Enumeration of substitutional isomers with restrictive mutual positions of ligands. II. Counts with restrictions on (sub)symmetry

The present paper extends our previous discussion of paper I on “Overall Counts”, still focusing on enumerations of substitutional isomers with restrictive positioning of ligands. But now, we address the counts of such isomers with a specified subsymmetry of the symmetry of the parent skeleton. Constrained analogs of Polya’s cycle index still appear, but now we introduce more powerful technical tools to include subsymmetry-specified generalizations of the cycle index. This involves differential-operator approach for analytically treating newly derived hybrids of the the generalized cycle index and suitable F-polynomials. As a simple illustration of the general mathematical exposition, a specific problems are solved and some tasks for possible further consideration are also stated, where again the Maple symbolic manipulation package proves useful.

Teaching with new technology: four ‘early majority’ teachers

This paper explores how four good teachers, who do not have a special interest in technology, meet the challenge of introducing the rapidly developing mathematics analysis software (e.g. spreadsheets, function graphers, symbolic algebra manipulation and dynamic geometry) into their classrooms. These teachers’ practice is viewed through the lens of Roger’s framework for the diffusion of innovation and Pierce and Stacey’s pedagogical opportunities map. Data on teachers, views and practices were collected over 2 years. ‘Pedagogical Maps’ give a picture of the teachers’ perception and uptake of pedagogical opportunities. New practices have been added slowly to each teacher’s repertoire and their increasing fluency in practical ability to teach with the technology resulted in some changes to the classroom didactic contract. Overall, new technology seemed to have been absorbed into current practice, more than changing practice. At this stage of their development, these teachers do not identify the distinctive new mathematical capabilities as contributing to the major relative advantage of the innovation. Instead, they see the relative advantage mostly in the incremental improvements to capabilities of earlier calculators, and meeting the need for students to be up to date. One of the current challenges is that significant changes in both software and hardware design have been happening so rapidly that these early majority teachers felt almost constantly hampered by the need to learn and teach new technical skills and so continue to make limited progress in taking advantage of opportunities to approach mathematics concepts in new ways.

Turing is among us

Turing's present-day and all-time relevance arises from the timelessness of the issues he tackled, and the innovative light he shed upon them. Turing first defined the algorithmic limits of computability, when determined via effective mechanism, and showed the generality of his definition by proving its equivalence to other general, but less algorithmic, non-mechanical, more abstract formulations of computability. In truth, his originality much impressed Gödel, for the simplicity of the mechanism invoked—what we nowadays call a Turing Machine (or program)—and for the proof of existence of a Universal Turing Machine (what we call digital computer)—which can demonstrably mimic any other Turing Machine, i.e. execute any program. Indeed, Turing Machines simply rely on having a finite-state automaton (like a vending machine), and an unbound paper tape made of discrete squares (like a paper roll), with at most one rewritable symbol on each square. Turing also first implicitly introduced the perspective of ‘functionalism'—though he did not use the word, it was introduced later by Putnam, inspired by Turing's work—by showing that what counts is the realizability of functions, independently of the hardware that embodies them. And that realizability is afforded by the very simplicity of his devised mechanism, what he then called A-machines (but now bear his name), which rely solely on the manipulation of symbols—as discrete as the fingers of one hand—wherein both data and instructions are represented with symbols, both being subject to manipulation. The twain, data as well as instructions, are stored in memory, where instructions double as data and as rules for acting—the stored program idea. No one to this day has invented a computational mechanical process with such general properties, which cannot be theoretically approximated with arbitrary precision by some Turing Machine, wherein interactions are to be captured by Turing's innovative concept of oracle. In these days of discrete-time quantization, computational biological processes, and proof of ever expanding universe—the automata and the tape—the Turing Machine reigns supreme. Moreover, universal functionalism—another Turing essence—is what enables the inevitable bringing together of the ghosts in the several embodied machines (silicon-based, biological, extra-terrestrial or otherwise) to promote their symbiotic epistemic co-evolution, since they partake of the same theoretic functionalism. Turing is truly and forever among us.

A Stupidity‐Based Theory of Organizations

abstractIn this paper we question the one‐sided thesis that contemporary organizations rely on the mobilization of cognitive capacities. We suggest that severe restrictions on these capacities in the form of what we call functional stupidity are an equally important if under‐recognized part of organizational life. Functional stupidity refers to an absence of reflexivity, a refusal to use intellectual capacities in other than myopic ways, and avoidance of justifications.We argue that functional stupidity is prevalent in contexts dominated by economy in persuasion which emphasizes image and symbolic manipulation. This gives rise to forms of stupidity management that repress or marginalize doubt and block communicative action. In turn, this structures individuals' internal conversations in ways that emphasize positive and coherent narratives and marginalize more negative or ambiguous ones. This can have productive outcomes such as providing a degree of certainty for individuals and organizations. But it can have corrosive consequences such as creating a sense of dissonance among individuals and the organization as a whole. The positive consequences can give rise to self‐reinforcing stupidity. The negative consequences can spark dialogue, which may undermine functional stupidity.

Explaining Embodied Cognition Results

From the late 1950s until 1975, cognition was understood mainly as disembodied symbol manipulation in cognitive psychology, linguistics, artificial intelligence, and the nascent field of Cognitive Science. The idea of embodied cognition entered the field of Cognitive Linguistics at its beginning in 1975. Since then, cognitive linguists, working with neuroscientists, computer scientists, and experimental psychologists, have been developing a neural theory of thought and language (NTTL). Central to NTTL are the following ideas: (a) we think with our brains, that is, thought is physical and is carried out by functional neural circuitry; (b) what makes thought meaningful are the ways those neural circuits are connected to the body and characterize embodied experience; (c) so-called abstract ideas are embodied in this way as well, as is language. Experimental results in embodied cognition are seen not only as confirming NTTL but also explained via NTTL, mostly via the neural theory of conceptual metaphor. Left behind more than three decades ago is the old idea that cognition uses the abstract manipulation of disembodied symbols that are meaningless in themselves but that somehow constitute internal "representations of external reality" without serious mediation by the body and brain. This article uniquely explains the connections between embodied cognition results since that time and results from cognitive linguistics, experimental psychology, computational modeling, and neuroscience.

Writing, Remembering and Embodiment: Australian Literary Responses to the First World War

This paper is part of a larger project exploring Australian literary responses to the Great War of 1914-1918. It draws on theories of embodiment, mourning, ritual and the recuperative potential of writing, together with a brief discussion of selected exemplars, to suggest that literary works of the period contain and lay bare a suite of creative, corporeal and social impulses, including resurrection, placation or stilling of ghosts, and formation of an empathic and duty-bound community.

A Framework for Hierarchical Perception–Action Learning Utilizing Fuzzy Reasoning

Perception-action (P-A) learning is an approach to cognitive system building that seeks to reduce the complexity associated with conventional environment-representation/action-planning approaches. Instead, actions are directly mapped onto the perceptual transitions that they bring about, eliminating the need for intermediate representation and significantly reducing training requirements. We here set out a very general learning framework for cognitive systems in which online learning of the P-A mapping may be conducted within a symbolic processing context, so that complex contextual reasoning can influence the P-A mapping. In utilizing a variational calculus approach to define a suitable objective function, the P-A mapping can be treated as an online learning problem via gradient descent using partial derivatives. Our central theoretical result is to demonstrate top-down modulation of low-level perceptual confidences via the Jacobian of the higher levels of a subsumptive P-A hierarchy. Thus, the separation of the Jacobian as a multiplying factor between levels within the objective function naturally enables the integration of abstract symbolic manipulation in the form of fuzzy deductive logic into the P-A mapping learning. We experimentally demonstrate that the resulting framework achieves significantly better accuracy than using P-A learning without top-down modulation. We also demonstrate that it permits novel forms of context-dependent multilevel P-A mapping, applying the mechanism in the context of an intelligent driver assistance system.

Computation is Symbol Manipulation

Computation can be seen as symbol manipulation Indeed, a computation is a sequence of simple, well-defined steps that can lead to the solution of a problem. The problem itself must be defined exactly and unambiguously, and each step in the computation that solves the problem must be described in very specific terms.

Chunking or not chunking? How do we find words in artificial language learning?

Chunking or Not Chunking? How Do We Find Words in Artificial Language Learning? Ana Franco (afranco@ulb.ac.be) Arnaud Destrebecqz (adestre@ulb.ac.be) Cognition, Consciousness and Computation Group Universite libre de Bruxelles, 50 ave. F.-D. Roosevelt, B1050 BELGIUM Abstract What is the nature of the representations acquired in implicit statistical learning? Recent results in the field of language learning have shown that adults and infants are able to find the words of an artificial language when exposed to a continuous auditory sequence consisting in a random ordering of these words. Such performance can only be based on processing the transitional probabilities between sequence elements. Two different kinds of mechanisms may account for these data: Participants either parse the sequence into smaller chunks corresponding to the words of the artificial language, or they become progressively sensitive to the actual values of the transitional probabilities. The two accounts are difficult to differentiate because they tend to make similar predictions in similar experimental settings. In this study, we present two experiments aimed at disentangling these two theories. In these experiments, participants had to learn two sets of pseudo-linguistic regularities (L1 and L2) presented in the context of a Serial Reaction Time (SRT) task. L1 and L2 were either unrelated, or the intra- words transitions of L1 became the inter-words transitions of L2. The two models make opposite predictions in these two situations. Our results indicate that the nature of the representations depends on the learning conditions. When cues are presented to facilitate parsing of the sequence, participants learned the words of the artificial language. However, when no cues were provided, their performance was strongly influenced by the actual values of the transitional probabilities. Keywords: implicit statistical learning; SRN; chunking; serial reaction time task Introduction A central issue in implicit learning research concerns the nature of the acquired knowledge. Does it reflect the abstract rules on which the training material is based or the surface features of the material, such as the frequencies of individual elements or chunks? According to some theorists, cognition can be viewed as rule-based symbol manipulation (Pinker & Price, 1988). From this perspective, learning would consist in the formation of new abstract, algebra-like rules. According to another theoretical position, information processing is essentially based on associative processes. In this view, learning would not depend on rule acquisition but on mechanisms capable of extracting the statistical regularities present in the environment (e.g., Elman, 1990). Over the last few years, a series of experimental results have provided new insights into the question of the nature of the representations involved in implicit learning. Research on language acquisition has shown that 8-months old infants are sensitive to statistical information (Jusczyk et al., 1994; Saffran, Aslin, & Newport, 1996; Saffran, Johnson, Aslin, & Newport, 1999) and capable of learning distributional relationships between linguistic units (Gomez & Gerken, 1999; Jusczyk, Houston, & Newsome, 1999; Saffran, Aslin, & Newport, 1996; Perruchet & Desaulty, 2008) presented in the continuous speech stream formed by an artificial language. Other studies have indicated that adults are also capable of extracting statistical regularities, and that these mechanisms are not restricted to linguistic material but also apply to auditory non-linguistic stimuli (Saffran, Johnson, Aslin, & Newport, 1999) or to visual stimuli (Fiser & Aslin, 2002). In the same way, implicit sequence learning studies have indicated that human learners are good at detecting the statistical regularities present in a serial reaction time (SRT) task. Altogether, these data suggest that statistical learning depends on associative learning mechanisms rather than on the existence of a “rule abstractor device” (Perruchet, Tyler, Galland, & Peereman, 2004). However, different models have been proposed to account for the data. According to the Simple Recurrent Network model (Elman, 1990; Cleeremans, & McClelland, 1991; Cleeremans, 1993), learning is based on the development of associations between the temporal context in which the successive elements occur and possible successors. Over training, the network learns to provide the best prediction of the next target in a given context, based on the transitional probabilities between the different sequence elements. On the other hand, chunking models, such as PARSER, consider learning as an attention-based parsing process that results in the formation of distinctive, unitary, rigid representations or chunks (Perruchet & Vinter, 1998). Thus, both models are based on processing statistical regularities, but only PARSER leads to the formation of “word-like” units. Although the representations assumed by these two classes of models are quite different, contrasting their assumptions is made difficult by the fact that they tend to make similar experimental predictions. For instance, in a typical artificial language learning experiment, participants are exposed to a continuous stream of plurisyllabic non-words (e.g., BATUBI, DUTABA…) presented in a random order, such that transitional probabilities between syllables are stronger intra-word

MASA : a library for verification using manufactured and analytical solutions

In this paper we introduce the Manufactured Analytical Solution Abstraction ( MASA ) library for applying the method of manufactured solutions to the verification of software used for solving a large class of problems stemming from numerical methods in mathematical physics including nonlinear equations, systems of algebraic equations, and ordinary and partial differential equations. We discuss the process of scientific software verification, manufactured solution generation using symbolic manipulation with computer algebra systems such as Maple™ or SymPy, and automatic differentiation for forcing function evaluation. We discuss a hierarchic methodology that can be used to alleviate the combinatorial complexity in generating symbolic manufactured solutions for systems of equations based on complex physics. Finally, we detail the essential features and examples of the Application Programming Interface behind MASA , an open source library designed to act as a central repository for manufactured and analytical solutions over a diverse range of problems.

Discussion paper: how much of commonsense and legal reasoning is formalizable? A review of conceptual obstacles

Fifty years of effort in artificial intelligence (AI) and the formalization of legal reasoning have produced both successes and failures. Considerable success in organizing and displaying evidence and its interrelationships has been accompanied by failure to achieve the original ambition of AI as applied to law: fully automated legal decision-making. The obstacles to formalizing legal reasoning have proved to be the same ones that make the formalization of commonsense reasoning so difficult, and are most evident where legal reasoning has to meld with the vast web of ordinary human knowledge of the world. Underlying many of the problems is the mismatch between the discreteness of symbol manipulation and the continuous nature of imprecise natural language, of degrees of similarity and analogy, and of probabilities.

Enumeration of Rosenberg-type hypercompositional structures defined by binary relations

Every binary relation ρ on a set H,(card(H)>1) can define a hypercomposition and thus endow H with a hypercompositional structure. In this paper, binary relations are represented by Boolean matrices. With their help, the hypercompositional structures (hypergroupoids, hypergroups, join hypergroups) that emerge with the use of the Rosenberg’s hyperoperation are characterized, constructed and enumerated using symbolic manipulation packages. Moreover, the hyperoperation given by x∘x={z∈H|(z,x)∈ρ} and x∘y=x∘x∪y∘y is introduced and connected to Rosenberg’s hyperoperation, which assigns to every (x,y) the set of all z such that either (x,z)∈ρ or (y,z)∈ρ.

Imperial Politics and Symbolics in Ancient Japan: The Tenmu Dynasty, 650-800 (review)

Reviewed by: Imperial Politics and Symbolics in Ancient Japan: The Tenmu Dynasty, 650-800 Samuel C. Morse Imperial Politics and Symbolics in Ancient Japan: The Tenmu Dynasty, 650-800 by Herman Ooms. Honolulu: University of Hawai'i Press, 2009. Pp. xxi + 353. $50.00. For political drama, few periods in Japanese history can match that of the Tenmu dynasty. The lineage was founded when Emperor Tenmu, then known as Prince Ōama, came to power after defeating Prince Otomo, his son-in-law and the consort's brother, in a bloody civil war in 672. It concluded when Tenmu's last direct descendant who had claims on the throne, Prince Osabe, was killed with his mother, Princess Inoue, in 775, after a year and a half of house arrest. Their deaths eliminated the last potential rivals of Prince Yamabe, a descendant of Emperor Tenji, Tenmu's brother, who took the throne in 781 as Emperor Kanmu. Between these two events, as Herman Ooms writes in this fascinating and densely detailed book, were "assassinations, plots, poisonings . . . black magic, bewitching, several large-scale armed rebellions, and many hundred banishments" (p. 12). This chaos, Ooms rightly argues, came about because of the unsettled questions of succession. The dynasty put on record a number of firsts: "the first recorded non-adult crown prince and the only female crown princess ever, the succession backtracking, from son to mother, and the first abdication" (pp. 12-13). In fact, although Ooms does not delve into it in great detail, one of the prime reasons the Tenmu dynasty ended so abruptly was Emperor Shomu's decision, orchestrated by his Fujiwara consort, Komyo, to make their daughter Princess Abe, heir designate, and then to abdicate on her behalf. Although the Tenmu dynasty ultimately failed to control imperial succession, during its almost one hundred and fifty years a number of the most distinctive aspects of Japanese kingship were established. These include legitimizing the dynasty through an association with the Sun Goddess Amaterasu; the establishment of a bureaucratic state based on Chinese legal codes; the fashioning of Yamato into an "empire" (tenka) that was for the first time ruled by a "heavenly sovereign," or "emperor" (tennō); the establishment of the first capital as a locus of rule; and the extension of political authority beyond the Yamato region (pp. 3-4). These innovations, as well as the shift away [End Page 159] from basing succession exclusively on double royals (princes with two royal parents), are the true focus of Ooms's excellent monograph. Ooms does not provide his readers with a narrative history. The text does not describe the specific details of the Jinshin Rebellion that brought Tenmu to power. Nor does it explain a great deal about the actual planning and establishment of the Fujiwara and Heijō capitals, the smallpox epidemic of 737, or Emperor Shōmu's peregrinations—all topics that appear in more conventional histories of the period. Rather, as Ooms writes in his introduction, "politics and symbolics" are the subject of his study (p. xvi). He is interested in exploring the "adoption or manipulation of symbols, a practice with symbols and parallel to politics, both related to the acquisition or exercise of power, status, or authority" (p. xvi). Thus, he builds an understanding of the period thematically. Although the book begins with Tenmu and Empress Jitō and ends with Kanmu who firmly reestablished the lineage of Tenji, ten separate topics are introduced, revisited, and revisited yet again, and only slowly and somewhat indirectly does the reader progress through the one hundred and fifty years that are the subject of the volume. This thematic approach has its benefits since it frees Ooms from being overly biographical and tied to a chronological sequence. Moreover, it allows him to explore each topic, summarized by single-word chapter titles, in full detail. But it can also make the book somewhat difficult to follow. The complexity of the events is probably the reason Ooms (or perhaps his editors) provide a tear-out guide with ruler lineages and plots for the reader to use as a bookmark. Acknowledging the scholarship of Shinkawa Tokio among others throughout the volume, Ooms emphasizes the central role Daoist practices...