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jkauzlar (Joe Kauzlarich) writes "You've had a long, tedious day at work. You have some money in the bank and decide that you need to spend some of it on yourself rather than hand it over to the Man. Therefore, being a nerd, you go straight to the bookstore after work. You don't see anything exciting in the new releases for science fiction; you look at the new pop-science books, but nothing jumps out at you from the shelf- but wait... what's this massive new book by the acclaimed physicist Roger Penrose, The Road to Reality? The subtitle seems a bit presumptuous: 'A Complete Guide to the Laws of the Universe.' You pick up the heavy volume to inspect its contents ..." Read on for the rest of Kauzlarich's review. The Road to Reality: A Complete Guide to the Laws of the Universe author Roger Penrose pages 1136 publisher Knopf rating 10 reviewer Joe Kauzlarich ISBN 0679454438 summary General audience introduction to modern physics

Flipping through the eleven-hundred pages, you notice the gratuitous inclusion of mathematical formulae and the chapter titles on the page headers -- "Quantum algebra, geometry, and spin," "Gravity's role in quantum state reduction," "Calculus on manifolds" -- suggest a far more exclusive audience than yourself, a lowly paper-pusher with a four-year degree. "But then, what's this doing in the popular new releases?" you ask yourself, "Shouldn't it be hidden away in the darkened corner of the store's physics section?" But that's where you're wrong, you realize, glancing through the author's preface; this book is for you: Penrose has, it seems, composed a mathematical physics book for the general audience -- and not merely an introductory one, but one that takes you to the frontiers of modern theory.

The trouble with the common popular-science books that propose to illustrate modern physical theories is in their implicit premise of avoiding mathematical notation and concept in favor of plain English. This works to an extent, but ultimately breaks down when the nature of the subject matter itself is mathematical. Indeed, after reading the wonderful Dancing Wu Li Masters, the reader is no more prepared to plunge into a textbook on modern physics or to comprehend even the titles of the latest mathematical physics papers on Arxiv.org. Physicists know about the fundamental particles or the nature of space only through the mathematics that model the phenomena. Which is not to say that such English language renderings are useless, but they skillfully devise to distance themselves from what physicists actually do, as well as to reenforce readers' natural aversion to numbers and formulae.

Penrose's approach is not to dive head-first into the most strenuous material or to assume a proper background for the comprehension of advanced physics; instead, the first several chapters are devoted to building the necessary mathematical subtext for the remaining bulk of the book. The volume's length is not, as is often the case, a result of lengthy diversions or pedantry (needless complexity); Penrose keeps his eye on the ball throughout, consistently informing the reader how the topic at hand is related to the over-arching theme and infusing the more well-known pedagogy with creative insight, so that even a talented math major may learn from the introductory chapters on number systems or geometry. What's more, the careful organization of the disparate topics permits a fluid drift from one to the next. The effect is a single cohesive book and not a collection of notes or essays.

With 390 illustrations and a generous supply of endnotes and bibliography entries, it's clear that Penrose didn't consider the work completed with the text alone. The inclusion of short problems within the footnotes hints to the reader what concepts are important to understand. The usual footnote-commentary is withheld for the endnotes at the end of each chapter.

It's probable that the name "Roger Penrose" might excite some memories you may have of his previous works, published over a decade ago, both of which explore the mind-brain relationship. At least one of these (Shadows of the Mind -- the other is the more popular The Emperor's New Mind) proposes a quantum theoretical explanation for consciousness which was perhaps too liberal to have been taken seriously by neurologists. Penrose's efforts in quantum theory have, however, been more successful than those in neurology: in 1988 he was awarded the Wolf Prize, one of the very highest honors in mathematics (perhaps second only to the Fields Medal), along with Stephen Hawking, and has made invaluable contributions to quantum physics for the past several decades, proving himself to be one of the finest scientific minds of our day. In consequence to his stature, it's certainly a treat for laypeople that Penrose has donated the time and energy to the creation of a monumental expository work for general consumption.

Whereas the average pop-science journalist reaches upwards to accrue a book's material, Penrose's acknowledged expertise on the subject forces him back towards the ground again. If you think about it, I suppose this is as difficult a task, since much of what Penrose describes he's known for forty or fifty years (he was born in 1931). He apologizes in the final chapter for the necessity of handpicking among the dozen or so "theories of everything," sometimes according to his own professional biases. Today's leading theory, "String Theory" along with the theory of "Loop Quantum Gravity," and the little known "Twister Theory," are all covered in the later chapters; the first portion of the book builds the mathematical foundations for the succeeding chapters, which give an indepth treatment of quantum physics and quantum field theory. These topics are followed by the previously described "theories of everything."

A glance at the table of contents may make or break your purchasing decision; chances are, if you find the mysteries of the terms somehow galvanizing, then you'll enjoy the book. On the other hand, if the eclectic terms frighten you, you should perhaps look at the preface (where Penrose gives solace to anxious readers), or it may be best to avoid the book altogether.

As I mentioned earlier, little has been done for the general audience to explore the wide expanse between physics and mathematics. The Road to Reality is, in this respect, a virtually pioneering effort, and given its size, scope and quality, I would venture to guess it will remain the de facto text in its area for many decades to come, and may safely be placed on your bookshelf next to E.T. Bell's Men of Mathematics, Douglas Hofstadter's Gödel, Escher, Bach, or Benjamin Yandell's recent (*highly* recommended) The Honor's Class: Hilbert's Problem's and Their Solvers.

I am fortunate to have had some mathematics education and so am familiar with the basic principles of complex numbers, calculus, and geometry, making the first several chapters, while still insightful, less toilsome than it might've been. I suspect that the average bright high school graduate would have no trouble with Penrose's quick treatment of these concepts. I would recommend the reader have at least some familiarity with the basic terms of mathematics and physics (i.e. when Penrose mentions "set" you know he's referring to a particular mathematical structure) or the book could overwhelm you quickly. Additionally, readers would be at an advantage having read "English-based" modern physics books such as The Dancing Wu Li Masters, Michio Kaku's Hyperspace, Brian Greene's The Elegant Universe or a similar book about 20th century quantum physics. Either way, it's safe to say that despite the virtuosic readability of the text, it's still going to take an intellectual commitment on the part of the reader to reap all of the available knowledge."

You can purchase The Road to Reality: A Complete Guide to the Laws of the Universe from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

aaron240 asks: "When Google published the GLAT (Google Labs Aptitude Test) the Unix question was intriguing. They asked an open-ended question about what is wrong with Unix and how you might fix it. Rob Pike touched on the question in his Slashdot interview from October. What insightful answers did the rest of Slashdot give when they applied to work at Google? To repeat the actual question, 'What's broken with Unix? How would you fix it?'"

jkauzlar writes "Popular mathematics books don't come along often and when they do, they're only occasionally worth the read. John Derbyshire, a controversy-stirring political propagandist by day, and mathematician-enthusiast by night, has composed what may turn to out to be one of the classics of mathematical literature for the lay-person." Read on for the rest of jkauzlar's review. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics author John Derbyshire pages 422 publisher Plume rating 9/10 reviewer jkauzlar ISBN 0452285259 summary History of the attempt to prove the Riemann Hypothesis

Bernhard Riemann came to the University of Goettingen in 1846 at the age of 19, originally to study theology. The University, however, was home to Carl Friedrich Gauss, "the greatest mathematician of his age and possibly of any age," and the impressionable young Riemann, succumbing to the privilege of Gauss's presence and following his already blossoming interest in mathematics, refocused his studies on the area in which he would soon attain distinct immortality. As early as 1851 he was impressing even Gauss with the results of his doctoral dissertation and in 1859 was appointed a corresponding member of the Berlin Academy. To this honor, Riemann responded with his most famous paper, entitled "On the number of prime numbers less than a given quantity," containing therein what became known as the Riemann Hypothesis.

At the heart of the RH is the Zeta function which, in its basic form, looks like this: Z(s)=1 + 1/2^s + 1/3^s + 1/4^s + ... and which, through some simple algebraic manipulation as demonstrated by the mathematically gifted journalist Derbyshire, can be given in the form (1 - 2^-s)^-1 * (1 - 3^-s)^-1 * (1 - 5^-s)^-1 * (1 - 7^-s)^-1 * ... And it is in this second form which Derbyshire calls "The Golden Key" where the non-mathematician gets the first glimpse of the Zeta function's relationship with prime numbers.

But where this Golden Key appears as this "novel's" turning point--its central conflict-- it is not until Prime Obsession's climax when the Key is at last turned and the Zeta function's true relationship to the prime counting function pi(x)--the number of primes less than a given x--is at last made clear. Along the way, from the introduction of the Zeta function to the final explanation of its relevance to prime numbers (the turning of the Key), Derbyshire enlightens us with clear, mostly English language descriptions of the mathematics involved, as well as plentiful anecdotes that give readers a sense of the life and work of the major figures in the history surrounding the RH from Euler, Gauss and Dedekind in the late 18th century through Riemann's 1859 paper, and from 1859 onward to recent advancements in the '80s and '90s.

The Riemann Hypothesis states that "all nontrivial zeros of the Zeta function have real part one-half." Understanding the statement of the hypothesis is Derbyshire's first mission for the reader. In short, most functions with a dependent variable, say f(x)=x^2-2x+1, have a value for which if you replace x with this value, the function returns zero. In the example given, it is at the value x=1 where f(x)=0. The Zeta function has an infinite number of these zeroes and an infinite number of these is "non-trivial." The non-trivial zeroes come from complex number values. Riemann's guess, his hypothesis, is that the real part of each of these non-trivial zeroes is equal to one-half. The imaginary part can be anything.

Derbyshire explains all of the mathematics in very readable language. It's unlikely that anyone who did well in high school mathematics will not be able to follow Derbyshire's mathematics (and it's unlikely that those who didn't do well will pick up a 400-page book on this topic). The Zeta function is explored from a number of angles--numerically, graphically, algebraically, statistically, and there's even a link between the non-trivial zeroes of the Zeta function and quantum physics! By a larger margin, however, Prime Obsession's intrigue lies in Derbyshire's expositions on Riemann, Hilbert, Turing, Gauss, et al, as well as those modern mathematicians he's interviewed personally. The line between the mathematical half of the book and the historical is clearly defined; the odd-numbered chapters are devoted to the former, the even to the latter.

Those fans and foes of Derbyshire's most public line of work as a journalist/editorial writer for National Review will be comforted to know all political polemics have been set aside. John Derbyshire gives a virtuoso performance as an informed journalist and maintains his stance as a personable and careful guide through a sometimes difficult terrain. Anyone with some interest in the topic will find it hard to put down Derbyshire's book once begun. If we are lucky (hint, hint, JD) perhaps Derbyshire's next book will cover the newly-proven Poincare Conjecture ...

You can purchase Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, carefully read the book review guidelines, then visit the submission page.

jkauzlar writes "Have you ever read a math book that was able to carry you through its proofs, heart racing, and make your skin tingle upon reaching its philosophically astounding conclusion? Rarely have I encountered such a book, but among those that I have found (such as the books written by Ian Stewart or Douglas Hofstadter), Gregory Chaitin's 'Metamath! The Quest for Omega' is a favorite. Chaitin takes the reader on a thrilling race through the history of computability research to arrive at the discovery of his own number, Omega." Read on for the rest of jkauzlar's review. MetaMath! The Quest for Omega author Gregory Chaitin pages 157 publisher Self-published e-book rating Excellent! reviewer Joe Kauzlarich ISBN n/a summary Limits of computability

Chaitin's goal is the casual reader's comprehension of an irreducible, uncomputable, and truly random real number. He doesn't actually find one of these numbers, of which there are an indenumerably infinite supply, but he comes as close as a person can to actually referring to it.

Does this sound mysterious (and a little weird)? It is! But this ties in to just the sort of problem mathematicians have been working on for the past hundred or so years. You may be familiar with Goedel's Incompleteness Theorem, in which he proves that no formal axiomatic system (FAS) is powerful enough to prove all of the true statements its notation can express. For a long time, many people were wondering if Fermat's Last Theorem could be one of these statements (although it was finally (and famously) proven by Andrew Wiles about a decade ago). This is the type of "metamathematical" problem Chaitin attacks with his arsenal of complexity and information theory.

Key to understanding the book's premise is understanding the problems involved in defining a truly random number. Chaitin works in binary, so it is easy to find a random number by flipping a coin multiple times, although defining what a random number is supposed to look like (without circularly using the word 'random') is impossible. If you can define exactly what it should look like, then you can use that definition to create (or compress (see below)) a random number. It would not, then, be random.

The next key word is 'reducibility' (or 'compressibility'). If a number is random then it cannot be reduced or compressed into a smaller equation or algorithm. The digits of pi appear to be random, but they are reducible. This entire infinitely long real number can be expressed with just a few symbols- 4*sum_(k=1)^n(((-1)^(k+1))/(2k-1)). The same is true with 'e' or the golden ratio. You might be aware of the distinction between denumerable and nondenumberable infinities-- Chaitin explains this in his book; in short, there are (at least) two kinds of infinite sets, those that map directly to the integers (e.g. the rationals) and those that don't (e.g. the reals). It has been shown that all computer programs may be mapped to integers and hence are denumerable. Any number that can be generated by a computer program (pi, e, etc) therefore is denumerable. For Chaitin's random real number to be truly random, we must look only at real numbers that are indenumerable (cannot be calculated-- otherwise it would be compressible).

Here is where we run into problems-- we can't possibly generate a random real number and we can't even define what it looks like! Chaitin discusses the philosophical arguments for the very existence of such a number, and in the end uses Turing's Halting Program idea to show that a random real number can exist-- and the random real number vaguely referenced in this way, he calls Omega, the halting probability. The probability that an arbitrary program halts is the random real number that Chaitin had been searching for.

But this is not giving away the ending by any means. In fact he tells us this before even embarking upon his journey. What is remarkable about the book is that, in plain English, and using ideas that a non-mathematician like myself can understand, in only 157 pages, Chaitin can explain the grandest ideas on the cutting edge of mathematics. "As you have no doubt noticed," began Chaitin's conclusion, "this is really a book on philosophy, not just a math book. And as Leibniz says... math and philosophy are inseparable."

Although the book can be read quickly and painlessly (there are only a few simple equations in the book), the insights it contains are profound and likely to stick in your brain for some time. Furthermore Chaitin's enthusiastic style is contagious and will leave you on the edge of your seat. He floats through dozens of interesting anecdotes about the great mathematicians-- Leibniz, Newton, Turing, Godel and others--, the process of mathematical discovery from the vantage-point of an actual mathematician, insights into the mind of a working mathematician, and the craft of mathematics, interjecting his own educated thoughts on all of these matters. His style is aimed towards those whose education in mathematics extends only a little past high school and the ideas are simply followed (don't worry if you can't follow my own explanations above; I'm not nearly as skilled an expositer as Chaitin!)

This book is available for free on Chaitin's own website (so why not give it a try?) and also at ArXiv.org. Slashdot welcomes readers' book reviews -- to see your own review here, carefully read the book review guidelines, then visit the submission page.

jkauzlar writes "When thinking about a software product's architecture there are two viewpoints to consider: the marketecture (or the marketing architecture) and the tarchitecture (the technical architecture). Oftentimes an architecture is designed without consideration of the market toward which the product is directed and even a technically superior product can fail against competitors with an inferior product, but who understand the market a lot better." This book tries to remind programmers (and managers) about maintaining the right balance of these things; read on for the rest of jkauzlar's review. Beyond Software Architecture author Luke Hohmann pages 314 publisher Addison-Welsey rating 5 out of 5 reviewer Joe Kauzlarich ISBN 0201775948 summary A software architect's guide to designing software with the market and end-user in mind

Overview Beyond Software Architecture explains how to bridge the gap between the marketecture and tarchitecture- how to create a product that not only performs well, but which also appeals to the market. It is part of the Addison-Wesley Professional Series line of books (also containing notable titles like Design Patterns, Refactoring, and Patterns of Enterprise Architecture) but this latest installment in the series is (thankfully) paperback, so it comes at a paperback price ($39.99 USD).

I am a software developer with no marketing background who works in small development teams, usually in an open-source development atmosphere. I was excited to find this book because it told me what I need to consider for my projects to help them reach the intended user. There is a lot of helpful information in this book, and at times it almost seems to suggest more work than I can handle, but I think it will ultimately pay off to be able to use the knowledge gained.

Table of Contents Forwards by Martin Fowler and Guy Kawasaki
1. Software Architecture
2. Product Development Primer
3. The Difference between Marketecture and Tarchitecture
4. Business and License Model Symbiosis
5. Technology In-Licensing
6. Portability
7. Deployment Architecture
8. Integration and Extension
9. Brand and Brand Elements
10. Usability
11. Installation
12. Upgrade
13. Configuration
14. Logs
15. Release Management
16. Security
Appendix A. Release Checklist
Appendix B. A Pattern Language for Strategic Product Management

Organization by chapter: Chapters 1-3 set up the rest of the book, defining the scope of the book as well as concepts and key terms used throughout the book. They describe a product development cycle, the players involved, etc.

The remaining chapters each focus on a particular aspect of a software product and how it relates to both the customer and the product's architecture. Catalogs of alternatives are available for each topic along with caveats for each alternative.

For example, in Chapter 6, "Portability," the advantages and disadvantages of creating a portable application are discussed. If most of your customers are using Windows and your code is written in C++, then the cost of supporting Solaris as well may be the difference between a product's financial success and failure. The chapter reminds us that guaranteeing support for 6 operating systems and 4 database backends and 3 browsers means that we have to support and provide quality assurance for 6x4x3=72 combinations of products. Then it describes a process of eliminating or prioritizing combinations of platform support. The chapter goes on to describe ways in which a product's architecture can affect its portability and how best to write software to be portable.

Related to this is a discussion of how supporting particular platforms ties your release cycles into the release cycles of products you support-- another problem that can financially doom a project. Another point from Chapter 6 that I found interesting was what it means to support a platform-- the customer expects you to take advantage of the platform's features. Many cross-platform products are written to be identical on each platform they support, which means they probably ignore platform dependent libraries or features that can enhance performance or usability. This creates a potential place where competitors can gain an edge.

So you see each chapter goes into great length and detail to cover the nuances of its topic, and it is extensive enough that it can be overwhelming and even discouraging.

Who should read this book Anyone involved in software architecture or design, particularly project managers, whether in a very small group or a large corporate atmosphere. Open source developers are notoriously technically proficient, and often are not marketing-savvy. Oftentimes you have to be technically proficient to even install and use an open-source product. Ordinary developers who do not participate in architecture might benefit from reading this book in order to understand the decisions being made by the architects.

Why someone should read this book Many software industry professionals are not marketing experts and may even view the marketing department as their enemy. This book helps bridge that gap between marketing and project management, helping the two parties work together to create more effective, usable, or profitable software. Similarly, open-source developers usually architect and market their own software. Tactics described in this book could help OS developers create software that lasts longer, is more extensible, and more usable.

What this book is and is not. This is a general, and not technology-specific, guide to designing software and while doing so, keeping a marketing perspective in mind. It describes what things a software architect should remember when designing a product.

It is not a guide to marketing software. It does not recommend particular solutions for particular problems. It does not tell you what you should do, only what the consequences of your choices may be.

What I would like to see A similar book that concentrates on the open-source aspects of the topics included in this book and how and how not to use open source tools (like Freshmeat, Sourceforge, Bugzilla, CVS) for marketing and maintaining successful open-source projects.

Recommendation Buy this book if you have benefited from Design Patterns, Refactoring or Patterns of Enterprise Architecture. This book is a welcome addition to a line of books that has consistently contributed to the standard knowledge base of the software architecture discipline.

You can purchase Beyond Software Architecture from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.