Entropy

Maybe it's just me but I found this book not very helpful. The easy stuff is repeated often (Bayes's theorem is quoted every few pages) but when a difficulty arises it is glossed over. Maybe it gets better: I decided not to finish the book.

Sivia shows in the first part of his compact book (189 pages) very nice examples (such as the lighthouse problem, signal amplitudes in presence of background noise, etc) how the Bayesian theory works out. The kangaroo problem and monkey argument come up to explain the maximum entropy theory. Further on in the book examples are given in the area of DSP (digital signal processing) and on experimental design, added with references to Sivia's Bayesian applications in molecular spectroscopy, neutron scattering - and powder diffrication analysis. As an applied statistician within the area of hydrological engineering (flood frequency analysis), it was very fruitful to read Sivia's book to fresh up the way of thinking... I highly recommend the book to other applied statisticians!

Mathematics looks like a pile of abstract facts, axioms and theoremsto most people. It is hard to imagine that in some branches of mathematics, there are unsettled controversies about the meanings of basic notions like probability. Statistics is one of these branches, where professional researchers and lecturers can be divided into some sort of "schools of thought".

This small book of 189 pages is a tutorial introduction into statistics. It addresses senior undergraduates and research students in science and engineering. If symbols like integrals, factorials or notions like Eigenvalues do frighten you, you should first complete some courses on calculus and algebra before reading this book. Contrary to "classic" text books on statistics, this book employs the so called Bayesian understanding of probability. While the classic understanding of probability sees each probability as a long-run relative frequency, the Bayesian school sees it as a degree-of-belief (or plausibility). This may sound like a minor disagreement, but it leads to very different ways of solving problems.

Throughout the book, the author explains seven examples of increasing complexity to the reader and solves the problems. Especially in the first two chapters, he simplifies his favourite applications of probability theory in order to explain basic concepts like probability, the error-bar, correlation, and marginal distributions. Each of the graphical panels is explained in detail to make it easier to understand the intuitive meaning of concepts like the probability density function. Often, the author also mentions common misconceptions and vividly explains the consequences of such misunderstandings.

Having read this book, you will be able to employ probability theory in scientific and engineering work. For example in estimation of a parameter like a scattering angle. While these results are often very useful in practice, you should be warned that the Bayesian approach might annoy some representatives of the orthodox statistical guild.

Nevertheless, the book is a good tutorial which is worth reading.

Stories revolving around time travel are difficult to review. The Entropy Effect is an exciting novel to read, and it captures the feel of Star Trek, but in the end, the story is rendered meaningless because it takes place in a timeline that has to be corrected. I suppose you could compare this work to the Deep Space Nine: Millennium Saga, though I preferred that series immensely. Still, The Entropy Effect is a fast-paced story that keeps your attention, and if you enjoy stories about time travel and alternate timelines, it's probably worth your time.

Different versions of the "evil scientist" antagonist are traveling through time doing both evil and good, trying to both harm and to protect. It is up to Kirk & Co. (mostly Spock) to set things right. Although there are some problems with the story - most notably a bad characterization of Mr. Scott (I doubt he would be so quick to take sides against Kirk & Co.) - it does have its moments. In particular, the interplay between Spock and McCoy, the subplot involving Mr. Sulu, the characterizations of the security personnel and the Captain Hunter character.

This story is a classic time paradox in the true spirit of Classic Star Trek. Strange events occur on the starship USS Enterprise which result in a crazed Professor killing Captain James T. Kirk! First Officer Spock investigates this tragedy & uncovers an experiment that threatens to unravel the very fabric of the universe. He must, therefore, put his own life at stake to save the universe, & his friend, Captain Kirk, by travelling through time using the same experiment, attempting to repair, & prevent, the damage from occuring!

I believe the approach of this book is far too basic. The first 100 pages keep repeating the laws of Newton and the conservation of energy. It covers a lot of thermodynamic history - maybe a little too much. The last parts of the book with more application is the best. Too much text and too few formulae, you almost wonder who the book is intended for - partly complex reasoning and no maths or formulae... But it does explain entropy well

This book is truly a gift to thosewho desire to understand in depth the making of that which exists. The thinking and aggressive searchfor understanding behind this workhas brought the laws of entropy toits most basic level. Knowing thatthe breakup of order does not designate disorder but instead order to a higher degree, seems tobe the rudimental step in discovery. The question seems to merely be what phase of order is one looking at and through what psychological belief patterns is one viewing the order? Martin Goldstein and Inge F. Goldstein takes one through the phases of development with simplicity and ease. Knowing that order is the framework by which visualization takes place and that disorder fragments vision until the loss ofvisual effect becomes total, surely gives one a different way by which to understand an environment and its connecting forces. Does change in its most elementary meaning then bring about disorder to an ordered system? Perhaps ordered systemscan expand connecting additional knowledge to itself or expand and break apart, all governed according to the forces feeding it. Martin and Inge have certainlybegun a cycle of reconsiderations and reevaluations of one's basic pattern of thinking.

I recommend this book to anyone who is taking an undergraduate course in stat mech. I also recommend it to beginning GRADUATE students of stat mech. I used it for my own graduate coursework and I found it to be extremely helpful.

This book provides a clean, uncluttered presentation of the principles of stat mech; does not lose sight of the physical reasons behind the mathematical manipulations; and most helpful of all, contains a good set of problems WITH SOLUTIONS! It has been more helpful to me in my graduate work than any graduate-level book!

In a next edition, maybe the authors can include a gentle introduction to the new renormalization group theory of phase transitions, and also increase the number and depth of problems.

If you plan on studying stat mech, get this book.

of mathematical equations from information theory with little or no physical substance. One of the authors (Brooks) appears to be a misplaced mathematician who formally became a zoologist. It should be remembered that General Relativity was first submitted for publication by a mathematician (Hilbert) ahead of a physicist (Einstein) by a matter of weeks (but essentially by theft from Einstein, being a former mentor of Einstein)and dismissed in favour of the physicist as lacking any physical insights.

The late Volkenstein succintly criticized the book in his outstanding book "Physical Approaches to Biological Evolution"
as follows:

"As useless as the book cited above is the book 'Evolution as Entropy'by Brooks and Wiley. The basic proposition in this work is that speciation is controlled by the stochastic premises of the second law of thermodynamics. One may only regret that in the 43 years since the publication of Schrodinger's work [the book 'What is Life?'] a book has appeared whose authors do not understand the role of the second law of thermodynamics in living nature...the authors are concerned only with the amount of information and, hence, with entropy. But, by confining oneself to these concepts alone, one can hardly say anything about evolution...in the world of living things the quality or value of information is often of decisive importance...No appropriate methods have yet been worked out for estimation of the quality of information...

The problem of the origin of valuable information is very important to biology. It can be expressed by the formula:

V = log(P/P0)
where P and P0 are respectively the probabilites of achieving a 'purpose' before and after the information is received.

As we have seen, interesting results can be obtained with the aid of the tentative definition of information value as the indispensability, non-redundancy of information. However, the transition from static information theory, in which time does not figure, to dynamic information theory, which includes reception and memorizing and, hence, time and semantics has not yet been realized in physics.

The molecular theory of orgasmic evolution has not yet been united with the synergistic approaches and its development is beset with formidable difficulties... The key problem of evolutionary theory is the relationship between genotype and phenotype studied at different levels...As we have seen, this problem is missing in systems that are studied in the Eigen theory."

Professor Berry, an distinguished research scientist and highly esteemed instructor at the University of Chicago has used the material of this book in courses for undergraduates in the humanities and social sciences. I believe that this indicates him to be an exceptionally charismatic instructor because this is a moderately rigorous text, doing an excellent job of introducing the subject to science majors. However,from my 33 years of teaching bright chemistry and humanities majors, I believe that it would be disastrous for anyone not devoted to science -- or enrolled in a course where he or she MUST conquer the material -- to be able to complete three chapters. Much more is required of the reader before he or she reaches the 170 page mark and begins to see glimmers of entropy and thermodynamics. An excellent book, but not for everyman.