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Certainly a recommended book for the Southeast-Asia enthusiast!
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In describing Russell's theory of types he says, "The paradoxes are avoided by the theory of simple types which is combined with the theory of simple orders - a "ramified hierarchy""
Godel argues that the vicious circle principle is false rather than that classical mathematics is false.
p. 202 "A remark about the relationship between relativity theory and idealistic philosophy (1949a) (Note that this view supports my usual presentations in class on this!)
"The argument runs as follows: Change becomes possible only through the lapse of time. The existence of an objective lapse of time 4, however, means (or, at least, is equivalent to the fact) that reality consists of an infinity of layers of "now"
p. 203 which come into existence successively. But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of "nows", and none of these various systems of layers can claim the prerogative of representing the objective lapse of time. 5"
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"Conscription and Conflict in the Confederacy" did not have to be an interesting book, but it is one because Moore's writing style is assured, easy, understated. He has a keen eye for the pithiest quotes from his sources. And he knows his Latin. His Southerners regarded their battlefield victories with sincere "gratulation," and Moore cannot bring himself to write "conscripted" when he knows Cicero would only have approved "conscribed."
Moore's book is still valued by historians for both parts of its title. The 1996 introduction to the University of South Carolina edition rightly praises the book as still the fundamental introduction to Confederate conscription, as well as a groundbreaking exploration of internal divisions in the CSA. That was a topic which had been given short shrift by the Lost Cause version of the Civil War which prevailed in America at that time.
Moore views Southern conscription as a flawed, but ultimately successful system that kept the Confederacy's will to fight for independence focused in an effective military effort for four hard years. He finds no inherent shame to the Confederate cause in the mere fact of conscription. "President Davis told the Mississippi legislature that there was no more reason to expect voluntary service in the army than voluntary labor upon the public roads or the voluntary payment of taxes," he writes.
Yet he appreciates the challenge of applying a system of compulsory service "among a proud and free people." He writes that the South's general public was "gradually reconciled" to the idea, though "strong opposition" remained.
His assumption that secession was principally about states' rights is no longer shared by most historians. But because Moore felt the South's cause was states' rights, the "conflict" in the book's title is largely that between Davis' central government and state authorities, notably the states'-rights governors Brown and Vance.
The book avoids statistics as much as possible, and the author always alerts his reader, if he delves into numbers, that all the figures are estimates at best, that they are often in dispute, and that surviving Confederate records are very incomplete.
Moore does not compare Southern conscription with the North's parallel messy venture in it, and he makes no attempt to place the CSA's experience in the flow of military history. This is, to me, a serious oversight.
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The author follows the standard Osprey Campaign series format and succinctly summarizes the origins of the campaign, the opposing leaders and the opposing armies in the opening chapters. Oddly, there is no separate section on opposing plans, as there normally is in Osprey titles, although this information is partly addressed in the main campaign narrative. Actually, the issue of opposing plans and objectives is critical for assessing the outcome of the Corunna campaign and Haythornthwaite's omission may have been intentional due to the controversial nature of the outcome. The British expeditionary force was dispatched to Lisbon under General Sir John Moore to support the Spanish in their effort to oppose French domination. Although the willingness of the Spanish to cooperate with the British and the size of the French invasion were poorly understand by the British, Moore marched his army deep into the Iberian hinterland. Nearing Madrid, Moore became aware that the French had crushed organized Spanish resistance and had occupied Madrid. A vast French army of over 200,000 troops under Napoleon was fast approaching the tiny 20,000 man British army. Moore elected to retreat to Corunna, pursued by the French corps of Marshal Soult and Ney. It was a bitter three-week retreat through winter snow and sleet, across extremely rugged and treacherous terrain.
Haythornthwaite naturally focuses on the superb tactical skill of the British rearguard under Lord Paget, which inflicted several rebuffs upon the pursuing French. Yet tactical success was accompanied by a virtual disintegration of morale and discipline within the retreating British army. Over 5,000 British troops were lost in the retreat, many of whom were drunk on looted stores. Since this was the only occasion in the Napoleonic Wars where the French captured substantial numbers of British prisoners, a bit more attention could have been focused on this disintegration. Once Moore reached Corunna and was about to evacuate by sea, the Marshal Soult launched a last-minute attack on the British defenses south of the port. The result was tactically indecisive but Moore was killed in the brief battle. The Royal Navy evacuated the British troops the next day. Of course the real question on the battle is why Soult would launch a one-division probing attack against the British, particularly when he had a 5-1 or better superiority in artillery. A fixing attack on a withdrawing force makes sense, but why did the French not rely more heavily on their artillery advantage (Moore was killed by French artillery)? As the French failed to fix the British force, the battle was a tactical success for the British. However in strategic terms, the Corunna campaign was undoubtedly a British defeat since a British army had been forced to evacuate after losing 6,000 troops and achieving no real successes.
British historians always like to portray hard-fought retreats and withdrawals like Corunna or Dunkirk as victories, and Haythornthwaite is no exception in this account. He suggests that Moore's fighting retreat diverted Napoleon from advancing on Lisbon and thereby gave the British time to regroup in Portugal. This is entirely specious. Napoleon left Spain because of the building crisis in central Europe, with Austria about to re-enter the war. It was the Hapsburg's, not Moore's tiny army, which diverted French attention. Had Austria not begun to mobilize in the winter of 1808/1809, it is quite possible that Napoleon might have remained longer in the Iberian Peninsula. Certainly larger French forces would have been available in the summer of 1809. It is even possible that the great clash between Napoleon and Wellington might have occurred in Portugal in mid-1809, but for the Hapsburgs.
Corunna 1809 is an excellent account of this campaign, and the maps and artwork are superb. However, readers should be aware of the author's pro-British bias in evaluating the results of the campaign. When the dust settled, it was the French army that held Corunna, not the British.
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The author gives a brief introduction to the use of Seiberg-Witten equations in chapter 1, along with a review of the background needed from the theory of vector bundles, differential geometry, and algebraic topology needed to read the book. All of this background is pretty standard, although the appearance of spin structures may not be as familiar to the mathematician-reader, but completely familiar to the physicist reader. Detailed proofs of the main results are not given, but reference to these are quoted. Also, the theory of characteristic classes is outlined only briefly so no insight is given as to why they work so well. In particular, the reason for the vanishing of the second Stiefel-Whitney class as a precondition for the manifold having a spin structure is not given.
In chapter 2, the author goes into the spin geometry of 4-manifolds in more detail. After discussing the role of quaternions in this regard, spin structures are defined. A spin structure on a manifold M, via its cocycle condition, give two complex vector bundles of rank two over M. The complexified tangent bundle can thus be represented in terms of these vector bundles, which are themselves quaternionic line bundles over M. The author also defines spin(c) structures, and shows how, using an almost complex structure, to obtain a canonical spin(c) structure on a complex manifold of complex dimension two. The spin(c) structure also allows a construction of the "virtual vector bundles" W+, W-, and L, for manifolds that do not have a spin structure. These bundles play a central role in the book. Clifford algebra becomes meaningful on the direct sum W of W+ and W-, and spin connections can be defined on W. In particular given a unitary connection on a complex line bundle L over a spin manifold M, one can obtain a connection on the tensor product of W and L. When M is not a spin manifold, this is still possible but one must use the "square" L^2 of L. One can then define the Dirac operator over the sections of this tensor product, which the author does and extends it to one with coefficients in a general vector bundle. The author then discusses, but does not prove, the Atiyah-Singer index theorem and the Hirzebruch signature theorem. These theorems, the author emphasizes, are proved in the context of linear partial differential equations, and give invariants of 4-manifolds.
This sets up the discussion in chapter 3, which deals with the problem of how to find invariants of 4-manifolds if one works in the context of nonlinear partial differential equations. Those familiar with the Donaldson theory, which was done using the (nonlinear!) Yang-Mills equations, will understand the difficulties of this approach. The strategy of the nonlinear approach as outlined by the author is to show that the solution set of a nonlinear PDE is compact and a finite-dimensional compact manifold. The solution set depends on the Riemannian metric, but its cobordism class does not, and this may give a topological invariant. The fact that it is defined in terms of a PDE might give a way of distinguishing smooth structures.
The Seiberg-Witten theory is one method for doing this. The Seiberg-Witten equations are nonlinear, but the nonlinearity is "soft" enough that it can be dealt with. They arise in the context of oriented 4-dimensional Riemannian manifolds with a spin(c) structure and a positive spinor bundle W+ tensored with L. A connection on L^2 and a section of this spinor bundle are chosen to satisfy these equations, which involve the self-dual part of the connection. One also needs to work with the "perturbed" Seiberg Witten equations, where a self-dual two-form is added. The moduli space of the solutions to the perturbed Seiberg-Witten equations is shown to form a compact finite-dimensional manifold. The proof follows essentially from the Weitzenbock formula, the Sobolev embedding theorem, and Rellich's theorem. Sard's theorem shows that the moduli space is smooth and the Fredholm theory shows it is oriented. The Seiberg-Witten invariants are associated to virtual complex line bundles over the 4-manifold, and when the dimension of the self-dual harmonic two-forms is greater than or equal to 2, and the dimension of the moduli space is even. Their definition does involve the Riemannian metric, but changing this metric only alters the moduli space by a cobordism. It is proved that oriented Riemannian manifolds with positive scalar curvature have vanishing Seiberg-Witten invariants. Kahler surfaces are shown to have positive Seiberg-Witten invariants, and the author proves that there is a compact topological manifold with infinitely many distinct smooth structures. Unfortunately though, an explicit example of one of these is not given. Such an example may be very important from the standpoint of physics, for the behavior of dynamical systems or quantum field theories might be very different for different smooth structures.
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Excellent in that it gives a good broad brush picture of Sir John's life and military career but, as pure biography, I found it left too many questions unanswered. As a minor point, there is a brilliant cover on this book (my copy picked up second hand fortunately still had its dust-jacket) of Moore by Lawrence. I have seen the painting myself at the National Army Museum in Chelsea. However, we never learn in the book how Moore came to sit for the painting. Also, we never learn much about his relationship with Lady Hester Stanhope, surely one of the most fascinating female characters of the period. Then, too, we never learn whether Moore's promotions during his career, right up to General, were by merit or purchase. This is a fundamenal point to have omitted, in my view, as knowing the answer tells a lot about the man - both his personal fortune and his personal achievements. Moore came from a lower middle class family; there was no apparent money although in his very early years he had a noble patron in the Duke of Hamilton.
Too many questions for me, an avid reader of biography and a lover of this particular period of history for me to give this 5 stars. However, it was a cracking read, well illustrated and carefully based on the original sources, eg Moore's own journal, Napier and Oman (the foremost 19th c writers on the Peninsular War). A good addition to the little library my husband and I have on this period.
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