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Algebraic Cobordism (Springer Monographs in Mathematics)
Algebraic Cobordism (Springer Monographs in Mathematics)
by Marc Levine
Edition: Hardcover
Price: $119.00
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3.0 out of 5 stars Rigorous but difficult, January 31, 2016
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This book is written in the Bourbaki style of modern mathematical exposition and so readers should not be expected to find fundamental insights or intuitive hints that will give them a better understanding of the origins and relevance of algebraic cobordism. Readers of this book will have to bring with them a solid understanding of algebraic geometry at the level of the theory of schemes, and an in-depth knowledge of classical cobordism theory as is found in the works of the mathematician Daniel Quillen or the book by Robert Stong.

Therefore an understanding the theory of algebraic cobordism will be in the light of Daniel Quillen’s work on the complex oriented cobordism group MU, but generalized in the context of algebraic geometry. The paper by Quillen entitled “Elementary proofs of some results of cobordism theory using Steenrod operations” is widely quoted in the book and should be studied before tackling some of the difficult constructions in the book.

Key to Quillen’s work was in the universality of the ‘formal group law’ and in the explicit use of a set of generators and relations for complex oriented cobordism. Complex cobordism is a universal contravariant functor on smooth manifolds and has a first Chern class for complex line bundles which satisfies the universal formal group law. Cobordism classes are generated by proper complex oriented maps, with two such maps giving the same cobordism class if they are fibers of a proper complex oriented map (the orientation coming from the virtual normal bundles of the smooth map). For smooth manifolds, pull-backs of generators are meaningful because of Thom’s tranversality theorem, and will be proper complex oriented maps between smooth manifolds. If f: W -> Y is such a smooth proper map between smooth manifolds, then f needs to factor through a closed immersion of W in C(N) X Y and there needs to be a complex structure on the normal bundle of W in C(N) X Y, where C(N) is complex N-space. Also, the codimension of f must be equal to dim Y - dim W.

So what is different about algebraic cobordism and Quillen complex cobordism? One difference is that role of the formal group law and the first Chern classes. The other difference has its origins in the “rigid” nature of algebraic geometry, namely in the difficulty of constructing pull-backs along morphisms between smooth schemes, i.e. two such morphisms cannot be arranged to be transversal. If smooth schemes are taken to be representatives of classes in algebraic cobordism, the challenge then is to construct these pull-backs. Further, in ordinary complex cobordism, the unoriented cobordism ring has one generator for every degree not of the form 2^(k-1) and therefore is a “large” ring. The oriented complex cobordism ring is generated over the rational numbers by complex projective spaces. Cobordism rings are related to cohomology theories via the notion of a spectrum, and in particular the Thom spectra can be used to define cohomology theories. The fact that algebraic cobordism is a universal cohomology theory for algebraic varieties immediately implies a connection with the theory of motives, and the authors acknowledge this connection. Both the Chow ring and motivic cohomology should have some connection with the theory of algebraic cobordism in this regard.

But it is cohomology theories that are oriented that are main focus of this book since an orientation on a ring cohomology theory gives rise to a “good” theory for projective push-forwards. One of the main points is to view the first Chern class of the tensor product of two line bundles not as the sum of the individual bundles but rather as a formal group law of the underlying oriented cohomology theory. The pull-backs, projective push-forwards, and the projective bundle formula will then determine the value of the first Chern class and the formal group law. Pull-back and push-forward morphisms are therefore needed to obtain first Chern classes, and how these different constructions are “entangled” with each other is modeled by the Borel-Moore functor, and these considerations are dealt with early on in the book.

The (oriented) Borel-Moore functor is an additive functor that maps from an admissible subcategory of finite type k-schemes to graded Abelian groups that satisfies certain axioms that codify how smooth equi-dimensional morphisms (pull-backs), projective morphisms (push-forwards) and first Chern classes of line bundles are entangled with each other (the reviewer is using the word “entangled” to reflect the fact the properties of commutativity between the pull-backs and push-forwards, and how the first Chern classes behave with respect to these maps). Cobordism cycles for k-schemes X of finite type are then defined in terms of a projective morphism and a finite collection of line bundles. Isomorphism classes C(X) of cobordism cycles and the free abelian group Z(X) on these classes gives a graded abelian group, the group of cobordism cycles on X. Push-forward maps for projective morphisms and pull-backs for smooth equi-dimensional morphisms of relative dimension d are defined straightforward in terms of Z(X), as is a notion of a first Chern class homomorphism. These constructions are encapsulated into a functor Z* from any admissible subcategory of the k-schemes to the category of graded abelian groups which is shown to be a (universal) oriented Borel-Moore functor. All of this is done over an arbitrary field. The authors generalize this to the case where there is an external product on Z*, and define a set of ‘standard cycles’ on oriented Borel-Moore functors with products. They then show how to construct a new oriented Borel-Moore functor by “modding out” a set of homogeneous elements.

By adding three additional axioms to the definition of an oriented Borel-Moore functor, the authors make another connection with the theory of motives by defining an oriented Borel-Moore functor of ‘geometric type’. The Chow group, asserted to be motivic in nature by some mathematicians is shown to be of geometric type. The authors also show, with some degree of clarity but a high degree of rigor that algebraic cobordism has connections to ordinary intersection theory via a formulation and proof of a moving lemma. This allows them to show that the algebraic cobordism is a universal Borel-Moore homology theory for k-schemes of finite type.

Gauge/Gravity Duality: Foundations and Applications
Gauge/Gravity Duality: Foundations and Applications
by Martin Ammon
Edition: Hardcover
Price: $73.46
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2 of 2 people found the following review helpful
4.0 out of 5 stars A good start, January 16, 2016
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Any methodology for solving difficult problems in string theory or quantum field theory that seems to show some promise is always welcomed by practitioners in these two areas. Historically, most of the emphasis has been in perturbative calculations, which cannot be used for problems that involved strong coupling, such as quantum chromodynamics or the general bound state problem in quantum field theory.

This book outlines an interesting approach to these types of problems that is based on a paper that was written by Juan Malcadena in 1998 and which has instigated a considerable amount of research since then. Marketed (with some justification) as a technique for studying strongly coupled field theories, the AdS/CFT correspondence is described as a map relating gravitational theories on asymptotically Anti-de Sitter spacetimes to conformal field theories. Those readers who want to familiarize themselves with this approach, and the more general methodology that is designated as ‘gauge/gravity duality’, will find the presentation adequate, as long as they are very familiar with superstring theory, supergravity, the mathematical formalism of general relativity, quantum chromodynamics, and of course conformal field theories in their different guises. The authors do give and overview of some of this background in the first four chapters, but readers who are not familiar with this material may find it heavy-going and too terse.

Some readers may be skeptical regarding the claim that N = 4 super Yang-Mills theory in 3 + 1 dimensions is “dynamically equivalent” to type IIB superstring theory on AdS(5) X S(5). The authors define this dynamical equivalence to mean that both theories describe the same physics from two different perspectives, but since experimental evidence is what determines the viability of physical theories, this claim seems extravagant at the present time. The reviewer prefers viewing this correspondence in terms of “tools of calculation” for performing difficult derivations in one side of the correspondence by mapping it to the other. In addition, some readers may be disappointed to learn that most of the calculations in the opening sections are done in the weak coupling limit on the string theory side. These readers, the reviewer being one of them, have expectations that the AdS/CFT correspondence is used to study non-perturbative phenomena, and therefore any talk about doing perturbation calculations is somewhat of a disappointment.

The authors though are apparently aware of some of the current skepticism regarding the applicability of gauge/gravity duality and therefore spend a few chapters on how it can function as a calculation tool in areas such as quantum chromodynamics (QCD) and condensed matter. In fact, two entire chapters are spent on QCD, with emphasis on how gauge/gravity duality can be applied to the confinement problem and to chiral symmetry breaking, in spite of the fact that QCD has no underlying supersymmetry. After studying these chapters, readers who need a more in-depth treatment will be prepared to consult the references or more advanced works on the subject.

Analyticity (New Problems of Philosophy)
Analyticity (New Problems of Philosophy)
by Cory Juhl
Edition: Paperback
Price: $41.95
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3.0 out of 5 stars Musings on a classification algorithm, November 26, 2015
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Texts and monographs in philosophy can be difficult to read and understand not because the complexity of their contents but rather because of the context in which they are presented. This context is set by the historical background and problem sets which the texts were written to address. If readers of these texts do not have a knowledge of this history they may not be able to appreciate the sometimes lengthy argumentation that can be found in them. With few exceptions, authors of philosophical texts assume that their readers have such a background, and therefore do not bother to motivate the subject matter at hand. Readers who have a sincere desire to understand certain trends in philosophical thought but who are time-constrained may therefore by stymied in their efforts because of this lack of historical motivation.

This book is an exception because it does offer such a motivation. The authors could have restricted their discussion to their solution of the problem of analyticity that they outline in the last chapter of the book, with the assumption that readers have the background to understand the solution. Instead, they dramatically improve the didactic quality of the book by discussing how the problem of analyticity arose and why it was (and is) deemed important by a large number of professional philosophers. Even if readers disagree with some of the details of the presentation and the proposed solution, they can still walk away with a better appreciation of the subject matter. The reviewer therefore found the clarity of the writing exceptional and therefore this review will concentrate on the details of the problem of the analytic-synthetic distinction as brought out in the book.

At least for the reviewer, what immediately comes to mind is that the problem of the analytic-synthetic distinction can be reduced to that of a classification algorithm, similar to algorithms that are very prevalent in the field of machine learning and mathematical linguistics. This is especially true for the elaborations of the analytic-synthetic distinction due to David Hume and Immanuel Kant. The issue from this standpoint is therefore of finding a methodology/algorithm that will successfully demarcate analytic statements from synthetic ones. One can straightforwardly apply this conception as one progresses through the book. It is of course not the intent or belief of the authors or of professional philosophers that the problem of the analytic-synthetic distinction be viewed as a problem in classification theory in machine learning/mathematical linguistics, but all through the book the dialog is dominated by the need to classify statements according to some specialized criteria.

From the standpoint of elementary mathematics it is also important to note how naive some philosophers are when it comes to simple arithmetic. For example, it is brought out in the book how Immanuel Kant accepted the analyticity of some statements like for example 7 + 5 = 12, forgetting that even in his time it was perfectly acceptable to conclude that 7 + 5 can also be 0, if one views this from the vantage point of telling time (clock arithmetic: 7 + 5 = 0 (mod 12), 12 + 12 = 12 (mod 12), and so on). Kant may have therefore exhibited more scrutiny in dealing with the supposed analyticity of arithmetic statements such as these by a mere reflection on the telling of time. A more contemporary inquirer with a broader knowledge of mathematics may conclude that mathematical statements should in fact be classified as more synthetic rather than analytic, due the context dependence of mathematical statements (modular arithmetic being one of many examples in this regard). In other words, mathematical statements are not as “analytic” as Kant thought since one must always check in which context the statements are being made. The statement 7 + 5 = 12 is certainly true in the context of the integers but it is also true that 7 + 5 = 0 in the context of the integers modulo 12. In addition, Kant and those using this example to discuss analyticity assume that such statements are made in non-noisy environments where pure communication is possible. But over a noisy radio channel for example a radio receiver may receive the statement 7 + 5 = 1, with the “2” in the 12 being corrupted by the noise. Only after error correction is performed at the receiver to recover 7 + 5 = 12 will argumentation about its analyticity arise again.

The reviewer is always struck not only from a study of this book but that of others as to the degree that the Godel incompleteness theorems are viewed as “devastating” for the foundations of mathematics. It is certainly true that the construction of true sentences that are not provable in a formal system is based on rigorous argumentation and therefore should be accepted. However one can easily view such statements as “outliers” because they normally do not arise in the construction of mathematical concepts and theories. In addition, the Godel incompleteness theorems arise in a context that is strictly formal, and this context bears no resemblance to the informal methods and use of ordinary language that characterize the construction of proofs in modern mathematical practice. Indeed, it would be extremely difficult to reduce for example the proof of Fermat’s last theorem to a collection of formal statements of the kind that you find in the context of the incompleteness theorems. The field of automated theorem proving for example has been stymied by the difficulty in modeling the way in which mathematicians construct proofs, which is definitely not formal, and makes heavy use of ordinary language, which itself has also defied formalization. Also, the methodology of science has never been reduced to a formal system to the best knowledge of the reviewer. Such a reduction would make the field of automated scientific discovery a more viable and powerful one. The authors do a good job however of explaining how the Godel results were instrumental in moving Carnap away from his contention of a universal logic that forms the foundation of all of science and mathematics. But here again, Carnap could have argued that the Godel statements are outliers that could be excised from the formal system of interest, with not much harm done, other than perhaps diminishing one’s emotional confidence in formal systems.

Maybe if philosophers would actually work in a scientific laboratory they would appreciate more what the subject of experimental science is all about and thus be able to write about the foundations and philosophy of science more effectively. In the discussion of Carnap’s P-rules in this book, an example of the gas law is given wherein a conclusion is drawn that the volume of a gas will decrease to a certain value depending on given changes in temperature and pressure. Not observing that value is considered to be a counterexample to the Carnap P-rules, but no discussion at all is delegated to the ever present measurement error that accompanies actual experiments. The value predicted (taken to be 2500 cc in the example discussed) is different from that observed (taken to be 2300 cc). But the equipment used in making measurements of volume may not be fine enough to distinguish these numbers. The possibility of “mistaken observations” is briefly referred to in the discussion along with the need for testing the equipment to make sure it is working properly, and thus one could perhaps extend the Carnap P-rules, but this is not discussed in the book, and in fact is usually omitted entirely in discussions of philosophy of science (Karl Popper being a notable exception in this regard). Not only that making sure equipment is “working properly” addresses primarily the occurrence of systematic error in experiments.

The assertion of the reviewer that discussions on analyticity can be reduced to a search for a classification algorithm is brought out in the authors’ discussion of Carnap’s shift to a semantic approach to the problem, wherein the “analytic truths” of a language were to be identified on a case-by-case basis. This would involve enumerating these cases, or the language rules that enabled construction of analytic sentences. Also, the authors speak of Carnap’s need to distinguish between analytic statements for formulating rules of a language and “synthetic” statements which have a truth value that arises from “extra-linguistic matters of fact”. Such a classification would be language dependent of course, but nevertheless amenable to modern symbolic programming languages that are designed explicitly to deal with textual processing and the consequent classification of grammatical constructions. Whether such algorithms are part of Carnap’s notion of philosophical activity as “language engineering” (as the authors refer to it) is perhaps speculative however, and will probably be rejected as being too “pragmatic”. Pragmatism is considered by many philosophers to be a sign that one has given up on philosophy, in that appeals to common sense are sometimes made, and this is considered to be an abomination to the entire philosophical enterprise. Carnap aggravated things even more by his insistence that metaphysical conceptions be eliminated entirely from language, in order to uncover the meaningful ones of science, and in using “expediency and fruitfulness” to adopt certain linguistic frameworks. Willard Quine too, whose reaction to Carnap is developed in detail in the book, could also be considered by many philosophers to have retreated into what some philosophers have called “vulgar pragmatism” because of his “radical naturalism”. As the authors discuss, Quine wanted to embed the results of empirical science into philosophy itself, believing that such an embedding would bring out the “best theory of the world”.

Much space, in fact most of the book, is devoted to the Quinean objections to analyticity , but the authors thankfully do not want their book to be merely an historical overview. The last chapter is devoted to giving a “positive account” to the discussion of analyticity that is not simply a collection of refutations of the notion of analyticity. Some virtues of their discussion include the fact that they are not hesitant to use terms such as “implausible”, and “outweighed” to answer objections and to use analogies to illustrate some of the main points of their solution. One part of their discussion that could stand a little more illumination is when they discussion the notion of a French bachelor or “frenchelor” that they have used in various parts of the book. Such a contraction is very meaningful from the standpoint of information compression in information networks because of the savings in bandwidth. Hence the term “frenchelor” could have some utility, despite the authors’ claim to the contrary that it has no interesting role to play in scientific theory. These kinds of contractions take place frequently in information compression, and are therefore meaningful in that context. It is not necessary to “stipulate” or endow them with any meaning over and above that context.

The authors elaborate on their solution to the analytic/synthetic distinction by introducing the notions of “analyticity*” and “T-analyticity.” It is here where the entire discussion can be summarized as a search for an algorithm to classify which statements are to be regarded as analytic* and when that is done to further segment the collection of analytic* statements that will assist in applying analyticity* to mathematics. This is readily apparent in their introduction of a “coordinate rule” for stipulation sentences for example. This move is very reminiscent of what is done in certain areas of artificial intelligence, particularly those that engage in representing common sense reasoning and language processing.

In defining analytic* statements it is not clear, at least for the reviewer, what the authors mean by “empirically indefeasible” in this discussion (and in other parts of the book). An elaboration of the meaning of this phrase seems warranted. Along these same lines the authors also make the astounding claim that mathematicians “typically ignore empirical data in their normal activity”. This claim is completely unsupported by any statistical sampling of the pool of mathematicians. There are scores of mathematicians, particularly those working in the fields of statistics and artificial intelligence, who routinely must deal with empirical data and revise their theories based on the nature and quality of this data. Philosophers of mathematics and philosophers of science should take time off and actually work in laboratories, think tanks, or applied research centers before they theorize about how mathematicians and scientists actually proceed in practice.

The authors give a fairly convincing case in how using the notion of analyticity* can be used to counter some of the objections to analyticity, but after studying carefully the overall discussion in the last chapter it was difficult for the reviewer to grasp the actual relevance of it for the area of mathematics. The last paragraph of the chapter attempts to offer some value for what they have done in the context of the goal of obtaining “intelligible schemes” for guiding our practices. No explicit examples are given however of how a certain area of mathematics or indeed any other quantitative field of endeavor would benefit from the notions developed in this book, interesting as they are. One field that immediately comes to mind is that of ‘anomaly detection’ in machine learning, wherein a gargantuan effort is spent on finding “novel possibilities” and “unforeseen patterns” that the authors refer to in the last sentence of the book. Those working in this field will certainly agree with the authors of the desirability for intelligent guidance using these possibilities and patterns.

From Colony to Superpower: U.S. Foreign Relations Since 1776 (Oxford History of the United States)
From Colony to Superpower: U.S. Foreign Relations Since 1776 (Oxford History of the United States)
by George C. Herring
Edition: Hardcover
Price: $25.82
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1 of 1 people found the following review helpful
5.0 out of 5 stars Exceptional, October 7, 2015
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Studying this book gives ample justification for the belief that the United States is an empire that is built upon the ashes of old empires. However unlike the empires of the past, the United States has through subtleness and tact caused many of its citizens to believe that empire-building is not only historically and economically justified, but also the morally proper thing to do. Even the use of military force, which has been used over and over again in US imperial adventures, is viewed as an ethical imperative, even “healthy to a nation”, as Henry Cabot Lodge is quoted as saying in this book. Other empires in history have been deemed “evil” for carrying out the same sort of actions that the US has indulged itself in for the last 200 years, and is continuing to do, albeit under the guise of “security” rather than under the banner of “extending civilization to lesser peoples abroad”.

This book however is not a study in the psychology of mass hysteria, xenophobia and jingoism, but rather a detailed account of the policy-makers/plunderers who attempted to maneuver events to their benefit throughout American history. This story is not a pretty one, but readers who desire the raw, naked truth about US foreign policy will find sound scholarship in between the covers of this book. There is much more waiting to be uncovered when it comes to this aspect of US history, but the author gives a fairly unbiased account, and one that does not show any signs of being seduced by the doctrine of American exceptionalism or sycophancy to any political party.

After finishing this book one can conclude with fairness that there does not seem to be any country in the world that has not been touched by US foreign policy. But even though the violence the US has deployed to attain its goals does not compare perhaps with other nations, many countries that showed promise for development and self-determination were decimated by the decisions made by weak-minded, ethically austere American government officials. Countries like Cuba, Chile, Haiti, Guatemala, and Vietnam come to the immediate forefront in the carnage, terror, and body count they experienced as the result of misguided US foreign policies, but there are many other places that have found themselves under the yoke of these policies. Newcomers to the history of American foreign policy may be surprised to hear for example of US presence in the Russian revolution, the US invasion of Mexico, or the attempts to force Japan into opening up its markets.

The attempted control of the “weak and semi-barbarous people” delineated in this book has not only lead to disasters for the peoples trampled upon, but also for the United States. Using a pistol rather than rational persuasion has been viewed as the more intelligent alternative, and like other empires in the past, the United States is now feeling the burden of its loyalty to this alternative. It remains to be seen of course what country in the world will attempt to build upon the ashes of the American empire.
Comment Comment (1) | Permalink | Most recent comment: Jan 10, 2016 4:13 PM PST

The Hindus: An Alternative History
The Hindus: An Alternative History
by Wendy Doniger
Edition: Paperback
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5 of 8 people found the following review helpful
5.0 out of 5 stars An alternative history as well as a refreshing alternative to the West, August 31, 2015
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At least from the standpoint of the reviewer who before reading this work was essentially ignorant of the history of India, its study assisted to some degree in answering the following questions concerning Indian history and culture:
1. Why do many Western intellectuals who have an aversion for religion find themselves being sympathetic to Hinduism and Indian culture in general?
2. Why does the practice of Hinduism not instill the raising of large armies that cross borders to forcibly proselytize this religion on others who do not practice its tenets, such as commonly the case for Western religions such as Islam and Christianity?
3. Are Brahmins the rich, uppity individuals they are frequently imputed to be by those individuals (such as the reviewer) who have concentrated disdain for the caste system of India?
4. Indeed, what is really the origin of the caste system and are the members of each caste comfortable with their status or do they consider it burdensome and unfair?
5. What is really the origin of vegetarianism and what is the extent of bovine worship in India?
6. When historically did the concept of karma arise, and what motivated it as a belief structure in the minds of Hindus?
7. Does the Hindu religion have a proliferation of different sects as is the case for Western religions or is there a Hindu canon?

The author does a fine job of answering these questions in this sizeable but interesting (and entertaining) book. There is no doubt that the author has some bias in her approach to the reporting of Indian history, but she is aware of this bias and reveals her agenda early on in the book. This involves setting the record straight on the role of women and “Pariahs” in developing Hinduism, and in revealing to what extent Brahmins were always sycophants to the ruling classes in India. The author however does not pull any punches when it comes to the Brahmins, who she describes as “misogynists” and “class-bound.”
That Hindus can engage in violent intolerance is brought out throughout the book, and readers who imagine Hindus via the Hollywood-Gandhi-Johnny Quest point of view will probably be surprised by this. But the breaking down of reader prejudices about Hindus is perhaps the best reason for studying this book, and those readers who decide to finish it will be amply rewarded for their discipline, even though it is not burdensome to study it, thanks to the rich and sometimes biting dialog throughout the book.

That being said, the author does not throw eggs at the reader or at Hindus, in spite of her having some thrown at her, as she alludes to early on in the book. But she does concentrate her attention on what she refers to as the “history of marginalized” Hindus, and not the “mainstream” ones. Her focus in this regard readily explains the subtitle of the book, and for those readers, such as the reviewer, who do not agree with the usual axiom that history = a history of kings and rulers, this approach is refreshing and one that should be emulated throughout the history profession.

But the preservation of history through writing (and coinage) is typically done by kings and rulers, who of course emphasize their own contributions (if they be called that), and not those of the culture at large. So where does an historian go, particularly one who is concentrating on a part of the world where the oral tradition is predominant, to find information on the “history of the marginalized”? The author elaborates on this question in some detail, and points to texts such as the Upanishads as her starting point. And of course, the storytelling and myths, which proliferate throughout Indian history, must be distinguished from the history itself. The study of the impact of ideas goes hand in hand with the history of the ideas, but the former is harder to prove than the latter, and care must be taken not to impute the motivations for taking certain actions solely because ideas were part of the Zeitgeist of the time.

The caste system was “regulated” by religion, the author argues, and if true this is not a surprise, since social hierarchies throughout history have been invented, manipulated, and “regulated” by religion. Kings, tyrants, and every form of despot have found religion convenient and useful for their ends, and they usually find willing supplicants to assist with their strategies and goals. In this respect, Hinduism has much in common with other religions, even though Western intellectuals typically impute to it a level of wisdom not found in Western religions.

There are many surprises in store in this book for the reader not familiar with Hindu history:
- The concept of reincarnation has its origins in the ancient Greeks, not the Hindus.
- People from Africa were the first to settle India.
- There is a flood myth in Hinduism, but it did does not have much intersection with the Biblical myth: only a fish to warn the “Indian Adam” Manu about a upcoming flood, and Manu builds a ship to save himself (all other creatures perished).
- Hinduism, at least in the Upanishads, has a kind of “triadic” metaphysics: three “qualities of matter”, and only the numbers one and two appear (there is a third called “plural” that stands for all those numbers above the number three).
- Loosely speaking, one may say that the “is-ought” problem of Western ethical philosophy is encapsulated in the Dharma, “which is the way things are and the way they ought to be.”
- Just as in the Old Testament of the Bible, absurdly long lifetimes of people were part of the Ramayana, and the cities that Rama ruled are an analog of Eden, where “no one died at the wrong time”, “no living creatures got sick”, and no violation of dharma occurred.
- India had its violent leaders, with Ashoka of northern India, characterized as both a brute and a repentant sinner after he viewed the carnage of march on Kalinga.
- Hindus are forbidden by dharma to have contact with dogs, the latter of which are compared in the Mahabharata to “upwardly mobile Pariahs”.
- The god Shiva is a gambler, according to the Artha-shastra texts, and also cheats at it (such lively gods deserve worship more than the Western ones).
- Alcoholism and various other vices are viewed in the Mahabharata, not as “diseases” but as coming “outside the individual”.
- Women are considered as “addictions” in the Dharma-Shastras, and should be “watched very carefully.”
- Lest the Western reader believe that the Hindus are always compliant to social hierarchies, the author points to the bhakti movement as protesting against “Brahmin exclusivity.”
- The somewhat lengthy discussion of the Tantra sheds light on the actual rituals that were practiced, and that some in the West consider abhorrent or unsanitary.
- Readers will gain a deep appreciation of the current tensions between Hindus and Muslims, and historically between Buddists, Jainas, and Hindus.

The British deservedly take some potshots from the author, and she includes some commentary on Hindus in the United States. The reader may walk away with the impression that those currently in the United States are faring well, but it remains to be seen whether Hinduism, even as the rich tapestry of ideas and practices that the author describes it in the book, will evolve as quickly as the Western religions under the onslaught of science and secularism. But if Hinduism survives pretty much in its current form, there is not much for those hostile to religion to fret about. Its history and the conduct of its practitioners lend credence to the idea that polytheism has a much calmer effect on the human psyche. It seems that when there are many gods and they sometimes fight amongst themselves, their worshippers act in the opposite manner. There seems to be no provocation from these gods for their worshippers to act violently. There seems to be no incentive for these worshippers to cross borders and engage in forced conversion.
Comment Comments (4) | Permalink | Most recent comment: Dec 18, 2015 11:42 AM PST

Electronic Warfare Receivers and Receiving Systems (Artech House Electronic Warfare Library)
Electronic Warfare Receivers and Receiving Systems (Artech House Electronic Warfare Library)
Price: $143.20

2 of 2 people found the following review helpful
4.0 out of 5 stars Very helpful and comprehensive, May 25, 2015
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The biggest challenge to writing any book on electronic warfare (EW) is to give an in-depth review of the important concepts and developments without divulging classified information. This book, sizable as it is, gives the reader who is or is intending to work in the area of electronic warfare relevant information while still remaining unclassified. All of the topics discussed can be found in the open literature but the author has saved readers a lot of browsing and search time by including the most important ones. Readers requiring more specialized or in-depth discussion may find that this type of information is not publicly available. Due to its size, there is a lot in this book to absorb, but no doubt readers who decide to commit to its study will not read it in its entirety but will instead topics of interest to them.

Radio receivers of course are noisy entities, and the different noise contributions to receiver electronics are revealed quantitatively in this book, using primarily only elementary mathematical tools, instead of using the full theory of stochastic processes. That the level of mathematical details is kept at an elementary level will help readers who are interested primarily in the practical implementation of radio receivers in an EW environment. Readers who want a more sophisticated mathematical/theoretical treatment will have to consult another monograph or the research literature (which is relatively sparse because of security constraints).

The first chapter is more of a bread-and-butter topic and definition list that covers the important metrics and performance parameters of EW receivers. EW network designers and EW network performance engineers frequently use these metrics, especially those who must configure military tactical networks so they they adhere here to performance requirements in an EW environment. The challenge of course in making a network function in such an environment is being able to distinguish friendly from un-friendly jamming/interference. In this regard, another very helpful feature of this book is that the author devotes considerable discussion on the difficulties in measuring the important quantities of interest, one example being the bandwidth. The author uses signal-to-noise ratio (SNR) instead of the SINR (signal-to-interference noise ratio) to frame the concept of receiver sensitivity. The SINR model of interference has been gaining in popularity in recent years, due mainly to is connection with network performance optimization and network capacity, both of which are very important considerations for networks in EW environments.

The author also includes a discussion of random modulation in the book, which is somewhat atypical and helpful to readers who are interested in how randomness can be used in radio communications. Contrary to what one’s intuition might indicate, the deliberate incorporation of randomness can greatly assist in optimizing radio communication performance. The discussion on random modulation could be viewed as the most complex in the book from a mathematical standpoint.

Although still not widely used in military tactical networks, but definitely coming in the future, is that of cellular technology. The issue of how to place base stations is the main inhibitor in implementing this kind of technology in military tactical networks, but whatever eventual decisions are made will no doubt have to respect some of the considerations that the author includes in this book, particularly in this discussion of CDMA. When studying this part of the book, it is interesting to learn for example that uplinks in cellular networks require power control of 1 dB in accuracy and about 1 kbps of control data. Measurement error may prohibit such an accuracy in real networks, but even if this is dealt with, it goes beyond saying that power control in tactical networks is very important from the standpoint of EW network coordination and scheduling.

At least from the standpoint of the reviewer, who needed to learn these topics, the most important parts of the book dealt with the different stages of radio receiver electronics, and how each can essentially act as a noise source and the degree to which RF amplifiers determine the receiver sensitivity. Network designers, engineers, and analysts need to have an appreciation of the different factors contributing to noise in EW receivers, and this book will definitely assist them in gaining the necessary insight.

Survival and Event History Analysis: A Process Point of View (Statistics for Biology and Health)
Survival and Event History Analysis: A Process Point of View (Statistics for Biology and Health)
by Odd O. Aalen
Edition: Hardcover
Price: $112.67
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2 of 2 people found the following review helpful
5.0 out of 5 stars Both explains and expounds, April 10, 2015
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Survival and Event History Analysis

Survival analysis and the theory of competing risks have found extensive application in the financial and medical fields, and the literature on these applications is vast. For analysts who want to apply these techniques to these fields, broaden their application to others, or who need a rigorous understanding of them, assimilating this literature can be an arduous task. There are many books that have appeared in the last two decades that are very helpful in acquiring the needed understanding, but this one is unusual in that it is able to articulate on both the theoretical and the applied, and do so in a way that does not trivialize the subject. Readers will find an inclusion of many examples drawn mostly from the authors’ geographic location, and also discussions of the mathematical formalism that makes it intuitively clear why some of the formalisms are deployed.

For example, of utmost importance in survival analysis is that of censored data, and it only takes the author 2 pages to begin discussing how to handle this kind of data, wherein they motivate the difference between survival analysis and ordinary statistical analysis when it comes to censoring data. They then move right into the definition of the hazard rate, which is is rather straightforward, but newcomers to the field may confuse it with an ordinary probability, but it is not since it can essentially be any nonnegative function even though it is defined as a conditional probability. Some texts have referred to it as a “probability rate”. The authors give many examples that illustrate the many complexities that the hazard rate can exhibit, and of crucial importance in some of these examples is the actual shape of the hazard rate. The reviewer can attest to a few applications (such as in data networks) where it is also of interest to compare the shape or slope of the hazard rate as the observation time increases.

Some of the more widely used survival models are discussed, such as the Cox proportional hazard model, and additive regression models. The reason for the popularity of these models lies in the use of observable variables or covariates to model differences between individuals. The authors show how to extend these models to take into account unobservable heterogeneities between individuals by using frailty models, wherein the hazard rate of an individual is changed by simply multiplying by a frailty variable. The topic of informative censoring is not discussed in the book, but readers who are at the level of sophistication to be able to appreciate this topic can find ample discussion of it in the literature. Multistate models can be used for the case that individuals can experience more than one type of event, which are better known as ‘competing risks’. The authors show how to modify the hazard rate to take into account competing risks, and caution the reader in remembering the difference between the cumulative incidence function and the cumulative cause-specific hazard.

This book sets itself from others on the subject in its coverage on stochastic processes and their connection with event history analysis. An excellent motivation for martingales is given that makes their understanding readily apparent to readers who may have only encountered formal definitions in their prior exposure to the research literature. This is readily apparent in the authors’ discussion of sigma algebras of events and the notion of adaptation to the time evolution of families of these sigma algebras. The authors’ discussion is very lucid as compared to what a reader might find by perusing other literature on this topic, in particular in the area of financial modeling. Along these same lines, the martingale property is shown to be resilient to some transformations that act on processes with this property. The authors discuss the concept of an ‘optional stopping time’ as an illustration of this, in that the martingale property is left intact under optional stopping. Most importantly, they connect optional stopping with censoring, and set the analyst’s mind at ease in showing that the martingale property will remain intact and therefore unbiased estimates can occur.

Another stumbling block to those learning it for the first time, due in part to the formal nature of most treatments of it in the research literature, is that of the ‘Doob decomposition’. The authors explain this as essentially a decomposition of an arbitrary stochastic process into one that is dependent on the past, and one that reflects what is novel or unanticipated if compared to past experience. To experts in probability theory and the theory of stochastic processes such a description may seem trivial or imprecise, but for those who really want to understand the subject, and do so outside the constraints of formal reasoning, the authors’ “intuitive discussion” is very helpful and considerably shortens the time to learn the important ideas.

Of fundamental importance in applying survival analysis are the nonparametric estimators of the cumulative hazard rate going by the names of the Nelson-Aelen and Kaplan-Meier estimators. These two techniques are widely used, sometimes in contexts where they should not be, but they do give “back-of-the-envelope” estimates that can serve as a guide in lieu of more refined approaches. The authors, interestingly, view the Nelson-Aelen estimator as the more fundamental of the two techniques, and so begin with it. They also show that the estimator for the variance of the Nelson-Aalen estimator is approximately normal distributed and so one can speak meaningfully about confidence intervals and percentiles. The properties of the Kaplan-Meier estimator, which of the two is the most familiar to analysts, is shown also to be approximately normally distributed for large samples, and interestingly shown in one of the exercises to be equal to 1 – (empirical cumulative distribution function) when there is no censoring. The reviewer has successfully applied both of these techniques to packet drops in data networks, an area that has not yet seen significant application of survival analysis.

Dereliction of Duty: Johnson, McNamara, the Joint Chiefs of Staff, and the Lies That Led to Vietnam
Dereliction of Duty: Johnson, McNamara, the Joint Chiefs of Staff, and the Lies That Led to Vietnam
by H.R. McMaster
Edition: Paperback
Price: $16.14
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4 of 4 people found the following review helpful
5.0 out of 5 stars A history of twisted thought and the Coppola Four-Star Clowns, February 28, 2015
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For those of age during the Vietnam war, there is no doubt that objectivity is difficult as to why America got involved and eventually pulled out. The view of those who fought the war is usually quite different from those who instigated it and were responsible for its disastrous outcome. It takes courage to go into battle and fight for a cause that through the detestable bureaucratic legislation called the draft one is forced to fight for. It takes just as much courage to voluntarily fight in a war that has been marketed as being necessary, unavoidable, and winnable. This book gives further evidence that the disaster of the Vietnam war was not the result of those who fought it, but rather with the DC clowns who feigned competence in military matters and those who remained silent or acquiesced in the horrible circus of political maneuvering.

There are some who may hold to the premise that Lyndon Johnson and his closest advisors showed real guts in attempting to fight against the Vietnamese Communist threat and to “save American face”. But it does not take any intestinal fortitude or keen intellect to indulge in the deceit and verbal machinations that are delineated in meticulous detail in this book. For those readers who want the raw, naked truth about Vietnam, this book is highly recommended, and its study will reveal that the author has definitely done his homework.

Having its origin in the National Security Act of 1947, the Joint Chiefs of Staff (JCS) during the Vietnam war is portrayed in this book as more of a collection of “technicians for planners” than a body of individuals who carefully thought out strategies and tactics. Some readers may be shocked as to what little influence the JCS had on actual policy decisions during the buildup of the war and its actual execution in the years that followed. One can only wonder whether this was the result of tacit agreement with those policies or rather from an excess of veneration for the Presidency and his cabinet officers. The author seems to argue for a superposition of both of these, and frequently the JCS is accused of placating the president.

Robert McNamara is rightfully portrayed as an evil demon in this book, as a government bureaucrat who cannot engage in self-criticism and smug in the certainty of his analysis and assessments of progress in the war. McNamara’s dwelling at the time was definitely a cesspool of apodictic certainty as is well brought out in this book, especially in the manner in which he interacted with the president and the JCS.

Johnson failed along with his vision of the Great Society. The JCS failed. Robert McNamara and Cyrus Vance failed. The only success of that time was the drive to end the debacle of the Vietnam war. This book is a microscopic view of these failures, and the biggest lesson to take away from the study of this book is an appreciation of just how removed from reality a government bureaucracy can be, and how uncritical adulation for a president or an idea can result in horrible destruction and heartache.

Gauge/String Duality, Hot QCD and Heavy Ion Collisions
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
by David Mateos
Edition: Hardcover
Price: $105.00
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1 of 1 people found the following review helpful
4.0 out of 5 stars A good overview, January 10, 2015
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In an article on quantum chromodynamics (QCD) in the year 1978 the physicists W. Marciano and H. Pagels and writing in particular on the Schwinger-Dyson equations for QCD, they stated that “ultimately we will have to face up to solving these equations or some equivalent problem.” These authors were of course cognizant of the fact that to understand QCD will take approaches very different than what had been done in other quantum field theories, such as quantum electrodynamics, the latter of which can be tackled successfully using perturbation theory. Of course, the property of asymptotic freedom in QCD allows one to do perturbation calculations at high enough energy, and useful insights may be obtained from these equations, but if one is to understand non-perturbative phenomena, such as bound states, then one has to make use of techniques outside the context of perturbation theory.

As the content of this book illustrates with great clarity, much has happened in the field since 1978, not only in the discovery of non-perturbative techniques such as lattice gauge theory and the AdS/CFT correspondence, but also in the experimental techniques such as heavy ion collisions. Indeed all these developments have been interesting and no doubt will continue to give surprising results in the years ahead.

For those interested in non-perturbative quantum field theory, either as a profession or from the standpoint of a spectator, there is much to be gained from studying this book. The authors keep the physics to the forefront, and despite the fact that they frequently have to refer the reader to the research literature for details on calculations, this book should not be viewed as a literature survey. And even though the authors clearly want to advertise the virtues of using the AdS/CFT correspondence to understand QCD, they do not hesitate to point out the problems in using this correspondence. They also discuss in great detail some of the gaps in understanding in the experiments dealing with heavy ion collisions (and do a through job of motivating the experimental situation in the first two chapters of the book).

Some of the discussions/results that the reader may find interesting or surprising include:

1. The breakdown of the eikonal formalism in describing parton energy loss in heavy ion collisions (due to the partons themselves being created in the collisions and suffering energy loss in the medium created). The resulting ‘jet quenching” of partons as they move through dense matter is a challenge to theorists and is to be contrasted with the perturbation theory calculation that can be done for parton showers in a vacuum. The authors describe a simple jet quenching model in Chapter 2, and refer the reader to the literature for estimates based on Monte Carlo simulations.

2. The phenomenon (ala the Matsui/Satz model) of ‘color screening’ in preventing meson production in the hot quark-gluon plasma, and approaches to estimating the screening length for the quark-antiquark force.

3. Although their vacuum solutions are very different, QCD and N = 4 Super Yang-Mills theory have similar properties above the critical temperature Tc, which is defined to be the crossover temperature from a hadron gas to a quark-gluon plasma. QCD is no longer confining above Tc. The authors give a comprehensive list of their similarities and differences at nonzero temperatures. Most interesting is that the authors show that the ratio between the shear viscosity and the entropy density does not depend on the number of degrees of freedom, the latter of which are not equal for these two theories. And even though SUSY is not present in QCD, at finite temperature the difference between bosons and fermions can be ignored. However the interplay between the number of flavors and the number of colors remains important. Readers hungry for a research problem using gauge/string duality can try extending the methods in this book to the case where the number of colors are comparable to the number of flavors.

4. The absence of quasiparticles in the strongly coupled N = 4 SYM plasma. The quasiparticle picture has of course dominated applications of quantum field theory to condensed matter and many-body systems. This paradigm finally goes away when there is strong coupling between the constituents of the system.

5. The authors show that thermodynamic quantities do not vary much between weakly and strongly coupled non-Abelian gauge theory plasmas.

6. The extensive discussion on the physics of holographic mesons (quarkonium mesons), given much needed understanding of the properties of (strongly coupled) hot QCD.

The book therefore gives a good update on what techniques are available for studying non-perturbative QCD. With further work and possibly even more exotic mathematical techniques, researchers may be closing in on the major unsolved problem of quantum field theory. In the same article in 1978, Marciano and Pagels remark that “no one has ever proven the existence of a single bound state let alone the confinement property in any relativistic, 3 + 1 dimensional quantum field theory”.

God and the Multiverse: Humanity's Expanding View of the Cosmos
God and the Multiverse: Humanity's Expanding View of the Cosmos
by Victor J. Stenger
Edition: Hardcover
Price: $22.49
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3 of 3 people found the following review helpful
4.0 out of 5 stars Finely tuned to physics, November 16, 2014
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The conducting and reporting of scientific research requires a degree of intellectual honesty, both personal and public, that is usually not required in religion and politics. Typically, the goal of the latter two is control, both personal and public, and any counterexamples found to its dogmas or beliefs are usually dealt with by force, censorship, or marketing hype. False professionalism, namely the feigning of intellectual competence, is characteristic of many who inhabit these areas, and evidence or supporting data is usually thought of as a necessary evil instead of a guide for decisions or revisions of thought. There are only a few examples that the reviewer is aware of where sound, scientific and constructive inquiry takes place in the fields of religion and politics.

This book, with its dramatic and beautifully designed cover, is not of course free of marketing hype, but within its pages one will find a highly interesting and informative account of the physics and astronomy behind some of the new conceptions that are beginning to be hotly debated among physicists and astronomers. It also serves as a counterweight to those assertions made by religious apologists who want to use astrophysical research to support their beliefs as to the divine origin of the things that be. Both the author and the religionists he quotes are biased, but the author is aware of his biases and freely admits them, knowing full well that a privileged apodictic point of view is not possible in science (or even desired).

Along these lines, the author describes himself as being an instrumentalist, and promotes instrumentalism as the view that the models built by scientists don't correspond exactly to reality. His opinion on the reality of quantum fields in the book is a clear example of his stance on the "ontological status" of scientific models. He is careful to distance himself though from some religious apologists who want to label him and others as subscribing to what is called "ontological pluralism", which as the name implies assets that there are many independent "valid" realities. Some readers, even of a purely scientific persuasion, may object to the instrumentalist "worldview", and might be tempted, because of its emphasis on empirical results, to classify it as yet another manifestation of positivism, the latter of which has become almost a dirty word in some professional circles in the philosophy of science.

One should not view the contents of this book as promoting an instrumentalist worldview however, and there are many surprising scientific facts that will be encountered between its covers, even for readers with a solid background in physics or astronomy. One example of this is the discussion of the entropy at the Planck time, and another is the discussion (albeit brief) on the ACDM model. And as is always the case in rational discussion of physical models, charts and data abound. For readers who are pressed for time and are not able to consult the original literature, these are welcome additions.

One could argue perhaps that the author has wasted page space in attempting to refute or even address the arguments of religionists such as William Lane Craig and Robin Collins that the author feels he has to deal with in this book, even if they appear to be "physics savvy" as the author describes them. These individuals, as well as physicists who are interested in this problem, need to show that life, even if based strictly on carbon chemistry, would be impossible without the "fine-tuning" hypothesis. To show this would require a solution of the bound state problem in quantum field theory, which to this date is the major unsolved problem in quantum field theory. But the reviewer has not found any written record that fine-tuning religious apologists are interested in solving physics problems of this kind, difficult as they are and requiring massive commitments of time and resources. As it stands, and the author gives several examples showing the weaknesses of their assertions, colloquially speaking their arguments are to be viewed as a slice of bread lying in a bowl of milk. When picked up for examination, it falls to pieces.

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