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Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States)
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Heller als tausend Sonnen. Das Schicksal der Atomforscher.
Heller als tausend Sonnen. Das Schicksal der Atomforscher.
von Robert Jungk
  Broschiert

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5.0 von 5 Sternen Light from a different direction!, 16. Juli 2006
Recently, in theatres in London and New York, carried the dramatic play "Copenhagen," by the British playwright Michael Frayn, revisiting one theme from this now old book. Since translated from it's original German. The play centers around a detail, also in the book; a visit in September 1941 by the then young German physicist Werner Heisenberg to his mentor and dear friend Niels Bohr in Nazi-occupied Denmark. So a detail in a bigger picture, but still a key detail!

The wider subject of Robert Jungk's book is a biographical sketch of the pioneers in nuclear physics, the individual scientist who built the atomic bomb (the time before Hiroshima and Nagasaki), or whose theories were instrumental. The debate about history, nuclear science, and its implications of the reality of the nuclear bomb started after World War II. Back then nuclear scientists worked on both sides of this conflict. Now with hindsight of the Cold War, nuclear proliferation have taken centre stage, but back in 1956 when Robert Jungk's book first appeared, World War II was still casting a big shadow on events and on the debate about nuclear deterrence. In my opinion Robert Jungk's book was one of the first serious attempts at a general account on what was clearly a watershed in history, a series of events that are shaping our lives even today. Since 1956, Robert Jungk's book was reprinted many times, and many more related books appeared.

Jungk's book paints an interesting vivid portrait of such scientists as Robert Oppenheimer, Werner Heisenberg, Niels Bohr, and other leading physicists at the time, and on both sides of that conflict.

What is interesting now is to view Robert Jungk's book in the light of Michael Frayn's play, and especially in light of newly released papers on the Niels Bohr archives in 2002, following the wide attention given to Michael Frayn's version of the 1941 meeting in Copenhagen. The 2002 addition to Niels Bohr's archives is a deposit comprising documents either dictated or written by Niels Bohr referring to what was said at the fateful 1941 meeting.

Michael Frayn's play makes it clear that the two Bohr and Heisenberg were very close both scientifically and personally, and that the 1941 meeting changed all of that. Both men were devastated!

Heisenberg was a leading scientific advisor to the German government in post WWII Europe; and yet he spent the rest of his life attempting to put his spin on his war work; his work on a nuclear bomb for Hitler, or perhaps rather denying these efforts. Niels Bohr who died in 1962 had been extraordinarily tight lipped about his meeting with Heisenberg in 1941. So while the newly released letters supplement and confirm previously published statements of Bohr's recollections of the meeting, especially those of his son, Aage Bohr, this part of the story is not well known, and especially not to Robert Jungk. The letters are from Niels Bohr to Heisenberg, and they are interesting for many reasons, not least of which is that they were never mailed, and so their contents were never known to Heisenbrg. Quoting from one of Bohr's letters to Heisenberg: "--- I think that I owe it to you to tell you that I am greatly amazed to see how much your memory has deceived you in your letter to the author [Robert Jungk] of the book ["Heller als Tausend Sonnen"],---." Review by Palle Jorgensen, July 2006.


The Curious Incident of the Dog in the Night-time: Adapted for Audio, Partly Dramatised, Complete Story
The Curious Incident of the Dog in the Night-time: Adapted for Audio, Partly Dramatised, Complete Story
von Mark Haddon
  Audio CD

5.0 von 5 Sternen He is just like the rest of us!, 11. März 2006
It is simple, and yet deep. It is hilarious and a little sad too.
While the subject of autism touched many of us a decade ago through Dustin Hoffman in the movie “Rainman”, autism is many faceted. As a medical condition, it is poorly understood; a fact that is brought home in the book. I was told that autistic individuals lack a sense of empathy. And yet the author, an autistic 15-year-old boy abounds with empathy! He says that he relates better to animals than to people, is frightened by loud sounds, especially by touch, is overwhelmed by specific kinds of speech and sensations, notices smells, colors, manners and appearances more than personal traits that may touch the rest of us. He takes in visual sensations more than verbal ones. And he picks out part of the world around us that I for one tend to miss. His little book enriched my life for this reason and many others. And my friends who read it had similar reactions.
Just like we are all unique, one should not expect that autism is a one-dimensional human condition. Autistic individuals are like you and me!
The book is autobiographical and yet it concerns us all. It is both poetic and poignant. It is suspenseful, but above all, this little book is different and truly original: A delight to read. I read it in a plane going south. A page turner! Couldn’t put it down! While it is a mystery, or a detective story with suspense and surprising twists, it is also a sweet mix of deductive logic and emotional complexities. And my plane ride had two legs, so I read the book twice. When I returned home the next week, I checked amazon and found that it’s a runaway bestseller.
The book is penned by a teen age boy who is autistic in some sense. He is mathematically gifted but socially helpless. To find out exactly how, read the book. And I won’t give away the plot or the ending!
The book is probably not meant to be hilarious, but perhaps this made it all the more fun. Actually, I never knew if I should laugh or cry!
Christopher Boone, the autistic 15-year-old narrator reveals that he is from a broken home. That is part of the story. He is uniquely observant and honest. Not because he is better than the rest of us, he says, but because he is unable to lie! At times his narrative reminded me of Albert Camus’s “The Stranger”. Christopher’s uniquely honest narrative is helped by a photographic memory: He remembers spoken sentences to the letter!
Initially, I came across a review of it in a math journal. Why a math journal? It is believed that mathematicians are a bit crazy too. Aren’t we all!? And that is perhaps why many of us can relate to it: We recognize a little of ourselves in it. (Reviewed by Palle Jorgensen, March 2006.)


A Mathematician's Apology (Canto)
A Mathematician's Apology (Canto)
von G. H. Hardy
  Taschenbuch

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5.0 von 5 Sternen a reviewer's apology, 23. Oktober 2005
I believe that the two biggest compliments a math author can get are first to have Graham Greene write: "the best account of what it was like to be a creative artist". And the second is to see his/her book open with an engaging Foreword by C. P. Snow. This little book by G.H. Hardy is deserving of both! And it is for good reasons that it has been reprinted many times over!
More than sixty-six years ago G. H. Hardy so eloquently apologized to the World for mathematics. You might say that no apology is needed, but many of my calculus students beg to disagree!
Back then in the shadow of one World War, and in the approach to a second, Hardy, a pacifist, and the Platonic puritan he was clearly had in mind pure mathematics. -- (And at the time, some parts of applied math had been used in an unpopular war.)
Now reflecting on this many years later, I couldn't help wonder if in the mean time the winds could have changed; wondering whether perhaps now a math author who trespasses into engineering topics and other applied domains might not be expected to apologize; --- at least if he/she has in mind math students as his primary audience. Aside from this, Hardy's lovely little book has over the years become a paradigm for math apologies, and any apologetic mathematician ought to at least mention Hardy in her credits.
Review by Palle Jorgensen, October 2005.


Approaching Quantum Computing
Approaching Quantum Computing
von Dan C. Marinescu
  Taschenbuch
Preis: EUR 160,99

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5.0 von 5 Sternen a new topic in cs and math, 3. Oktober 2005
Rezension bezieht sich auf: Approaching Quantum Computing (Taschenbuch)
In planning a course on quantum computing, an instructor would want to cover the significant highpoints in the subject: Shor's factoring algorithm, Grover's search algorithm, Deutsch's problem, the hidden subgroup problem. I for one found that this book does precisely that. Students will want an accessible and attractive presentation. This book is beautifully presented, nicely organized, and pedagogically presented with motivation, clear explanations, and well chosen exercises.
While the subject has a variety of facets, physics, math, computer science, this book emphasizes the last two. In a highly interdisciplinary subject, each author (or team of authors) must make selections. In selecting what to cover, the authors had the classroom and students in mind.
More precisely the subject here is presented in the form of quantum gates, channels, and circuits. Yet, quantum physics and the foundations are not neglected.
The graphic presentation (figures and diagrams) is done in a way to aid learning, and I expect that this book will be the preferred text in courses in the subject for some time to come.
Advanced undergraduates will be able to follow the logical progression of subjects. Several special features in the book help: Exercises, an extensive and instructive glossary, historical insight, motivation, appendices (including key math topics, e.g., modular arithmetic and Hadamard transforms which perhaps may not be widely known), and circuit diagrams illustrating at the same time matrix factorization and the complexity of circuits.
Contents: 1. History and background, 2. Rudiments of quantum physics as it is needed, 3. Qubits and computer science rewritten in the form of quantum gates, 4. The key quantum algorithms (Shor, Grover, Simon) and the highpoints in the subject, 5. Entanglement, decoherence, error-correcting codes, Bell, dense coding, EPR, reversible computation, thermodynamic entropy, and more.
Highly recommended!


Lise Meitner and the Dawn of the Nuclear Age
Lise Meitner and the Dawn of the Nuclear Age
von Patricia Rife
  Gebundene Ausgabe
Preis: EUR 41,56

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5.0 von 5 Sternen rewards in physics, 2. Oktober 2005
While there has been a recent renewed interest in the life of Lise Meitner, and a number of biographies have appeared, this I believe is the first one to focus on physics, as opposed to personalities. I may add that the authors do weave together an entangled web of scientists, their thoughts (through correspondence), their ambitions, and their (in many cases) flawed judgments. And the narrative is captivating! The main author is himself a pioneer in physics.
Lise Meitner was born in Vienna in 1878, and she started her career in the turbulent times of the First World War, at a time when Germany was a clear leader in physics research, in the Golden Era of physics. Yet, Lise Meitner was the first woman German scientist; first PhD in physics. When she started her studies, German universities were almost entirely closed to women; and especially so in the sciences.
The authors bring to life the turbulent events in modern history which shaped Lise Meitner's career. A central theme in the book is the physics community's reaction to the first use by the USA of a fission bomb over Japan in 1945.
In Berlin, building on a decade of research by Meintner and Otto Hahn, in 1938, the three Lise Meitner, Hahn, and Fritz Strassmann discovered nuclear fission. The Nobel Prize went to Hahn alone, and Lise Meitner has until recently been largely forgotten. In this interesting book, the authors examine why. Readers may find that the reasons are different from what we might have guessed.
Many of the German scientists in the 1930ties were Jewish, or partly Jewish, and they were dismissed by Hitler in 1933, or in the years up to the war. The year before the outbreak of war in 1939 was the last chance to escape, and the entire physics community dispersed as German scientists had to flee, --- some chose to escape. A small number went to neutral Sweden, and others who had left earlier ended up in the USA, and became leaders in the Manhattan project, the secret Los Alamos team of scientists, led by Oppenheimer, the team which built the first atomic bomb. There were some German scientists, Otto Hahn among them who didn't have to flee. They included Lise Meitner's research collaborators, Hahn, and Strassmann, plus Max von Laue, Werner Heisenberg. At the end of the war, their relationships resumed, and an examination (in the book) of private letters reveals some fascinating new insight. Palle Jorgensen, October 2005.


Lise Meitner: A Life in Physics (California Studies in the History of Science, Vol 13)
Lise Meitner: A Life in Physics (California Studies in the History of Science, Vol 13)
von Ruth Lewin Sime
  Gebundene Ausgabe

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5.0 von 5 Sternen a turbulent time, 2. Oktober 2005
The times of Lise Meitner spans two World Wars, and the ensuing Cold War between the two super powers of the East and the West. Lise Meitner's career also spans some of the most fascinating developments of modern physics. As it happened, this includes the beginning of the nuclear age; and it continues with the age of nuclear weapons and nuclear energy resulting from pioneering and basic research into nuclear fission, started by the two Meitner and Otto Hahn.
Lise Meitner was born in Vienna in 1878, and she started her career in the turbulent times of the First World War, at a time when Germany was a clear leader in physics research, in the Golden Era of physics. Yet, Lise Meitner was the first woman German scientist. When she started her studies, German universities were almost entirely closed to women; and especially so in the sciences.
The author Ruth Sime paints a personal and a compassionate portrait of Lise Meitner, her life and her times; and she vividly brings to life the tragic events in our modern history which shaped Lise Meitner's turbulent career. A central theme in the book is the physics community's reaction to the first use by the USA of a fission bomb over Japan in 1945, (in fact it was two nuclear bombs, one was a Uranium bomb, and the other Plutonium.)
In Berlin, building on a decade of research by Meintner and Otto Hahn, in 1938, the three Lise Meitner, Hahn, and Fritz Strassmann discovered nuclear fission. The Nobel Prize went to Hahn alone, and Lise Meitner has been largely forgotten. The book weaves together the individuals, their thoughts (through correspondence), their ambitions, and their flawed judgments.
A part of the story is the ensuing events following the discovery of fission; events that were shaped largely by others than Lise Meitner. During the Second World War, Lise Meitner was a refugee in neutral Sweden. Since she was part Jewish, she had to flee for her life; flee what became Hitler's extermination machine. The racial laws began in the Third Reich with Hitler's dismissal in 1933 of university faculty with Jewish family tree, and it progressed to what we now know as the Holocaust.
Many of the German scientists in the 1930ties were Jewish, or partly Jewish, and they were dismissed by Hitler in 1933, or in the years up to the war. The year before the outbreak of war in 1939 was the last chance to escape, and the entire physics community dispersed as German scientists had to flee, --- some chose to escape. A small number went to neutral Sweden, and others who had left earlier ended up in the USA, and became leaders in the Manhattan project, the secret Los Alamos team of scientists, led by Oppenheimer, the team which built the first atomic bomb. There were some German scientists, Otto Hahn among them who didn't have to flee. They included Lise Meitner's research collaborators, Hahn, and Strassmann, plus Max von Laue, Werner Heisenberg, and of course others. Lise Meitner never married, but was close to Otto Hahn before and after the War. And at high noon, Hahn helped Meintner to escape to Niels Bohr's Copenhagen, and then to neutral Sweden when Denmark became occupied by the Third Reich.
Those of the German physicists who stayed behind were faced with a Faustian choice, knowing Hitler's evil regime and the diabolic potential of the nuclear bomb, what does a scientist do? Does he stay in Hitler's Germany even if he doesn't have to? The second half of the book is about how Lise Meitner and her colleagues judged the physics community's reaction to the Faustian choice it had faced during the ten years of the Third Reich, and which it still was facing during the Cold War. It includes personal correspondence. One letter from Lise Meitner to Otto Hahn touched me. In it Lise Meitner was addressing those of her colleagues who had stayed behind in Germany and had worked on nuclear physics for Hitler, at least in one form or the other. They were her friends and colleagues from youth, and yet she felt compelled to point out what seems to be striking moral flaws: When the war ended in 1945, few of Lise Meitner's former colleagues express any regrets, and appeared instead to ponder the question of why the USA beat the Germany team of scientists in building a fission bomb. What is especially touching is to observe how it pains Lise Meitner to have to spell out this fact to her friends; friends she remained close to for her entire life. And in this ambivalent relationship lies yet another Faustian choice.
It is perhaps ironic that the theme of the Faustian choice has a prominent place in German literature, from the medieval "Faustus" tale to Goethe, Weber's Freischuetz, to Martin Luther's Protestantism, and to Thomas Mann's Doctor Faustus (Mann's moral despair over his country's complacent embrace of Nazism).
Palle Jorgnesen, September 2005.


Signal Processing With Fractals: A Wavelet-Based Approach (Prentice-Hall Signal Processing Series)
Signal Processing With Fractals: A Wavelet-Based Approach (Prentice-Hall Signal Processing Series)
von Gregory Wornell
  Lehrbuch

5.0 von 5 Sternen signals/math/engineering, 25. Juli 2005
Observations of signals, time series in telecommunication, or pictures in medical imaging reveal selfsimilarity, i.e., the signal/picture looks the same as the scale varies. Hence, the name "fractal" ! Pictures in the Intro make this scale-similarity visually apparent. But it is made precise in mathematical statistics, and the book further makes the connection to the engineering of signal/image processing. That's a main point of the book!
Selfsimilar processes are stochastic processes that are invariant in distribution under suitable scaling of time and/or space. Fractional Brownian motion or Brownian sheets are the best known of these. They were found by Kolmogorov long ago, but made popular by Mandelbrot and Ness in 1968. We now speak of 1/f processes. More recent use of wavelet bases in telecommunication and in stochastic integration has revived interest. Other even more recent applications include finance.
While the underlying idea behind all of this is quite simple, and can be traced back to Kolmogorov in the 1930ties, it is only recently, with the advent of wavelet methods, that the *computational* power has been better appreciated. The idea is analogous to that of random Fourier series: Instead of treating the Fourier coefficients as random variables, it is now wavelet coefficients that are analyzed statistically. Since wavelets have computational advantages, it is not surprising that the engineering applications abound. This little book is well written, and should be attractive both to members of the math community and to engineers.
Mathematicians will be pleased to note that wavelet analysis now brings *Hilbert space theoretic features* of the subject back to the fore. Amusingly, this was in fact a dominant feature which motivated both A. N. Kolmogorov and Norbert Wiener in the early days; e.g., curves in Hilbert space.
The author is an authority in the field, and his book brings out beautifully the highpoints of the subject. I further expect that the book will go over well in the classroom; nice summaries at the end of each chapter! (Exercises would have helped though!) The book will help bridge mathematical analysis, probability, and engineering. Engineers may like that proofs are relegated to later in the book. Mathematicians will be pleased with having the proofs, and with the clarity of their presentation. Reviewed by Palle Jorgensen, July, 2005.


The Fabric of Reality: Towards a Theory of Everything (Penguin Science)
The Fabric of Reality: Towards a Theory of Everything (Penguin Science)
von David Deutsch
  Taschenbuch
Preis: EUR 10,99

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5.0 von 5 Sternen quantum computers, 5. Juli 2005
The book was published in 1997, and a lot has happened since then. Yet the foundations retain their permanence, and David Deutsch's captivating writing is as fresh as ever. Despite the availability of newer books, for the layman/woman, now almost 10 years later, I would still rank this book at the top. There is a lot in the book; and yet, the ideas are presented in a clear and engaging way. The author is a pioneer, a giant in modern physics; he was and is a driving force in new discoveries in the subject. Yet he has his personal way of explaining physical reality. His view is not shared by all scientists, one should admit. However, there is agreement about the scientific conclusions. The first chapter in the book stresses *explanation*, our understanding of the reason for things. There are other views of science, e.g., instrumentalism: predicting the outcome of experiments.
The author's view on quantum theory is based his idea about parallel universes. While fascination, the reader should be aware that there are alternative theories for explaining quantum phenomena. An important concept in quantum theory and quantum computation is "decoherence", and it is explained (ch 9) in terms of different (parallel) universes. In ch 9 about quantum computers, it might have been only fair to mention that there are such other current views on decoherence; but this is a minor complaint.
Presentation: I love that each chapter concludes with a section on terminology and a summary.
As a subject theoretical computer science started with Alan Turing and John von Neumann in the 1940ties: Classical computation follows the model of Turing,-- strings of bits, i.e., 0s and 1s; and a mathematical model which is now called the Turing machine.
Instead of bits, why not two-level quantum systems, e.g., models built from electrons or photons? Such an analogues model for computation based on two-level quantum systems, and a quantum version of Turing's machine was suggested in the 1980ties by R.P. Feynman. The form it now has owes much to the author himself, David Deutsch. But it wasn't until Peter Shor's qubit-factoring algorithm in the late 1990ties (not covered in the book) that the subject really took off, and really caught the attention of the mainstream science community, and of the general public: The 'unbreakable' codes might be breakable after all !
That there is a polynomial factoring algorithm, as Shor showed, shook up the encryption community, for obvious reasons, and created headlines in the news. Ideas in the quantum realm, and not part of classical thinking, include superposition of (quantum) states, the EPR paradox (1935), and (quantum) coherence. Although these concepts are at the foundation of quantum theory, they make a drastic change in our whole theoretical framework of computation: Now one passes from the familiar classical notion of bit-registers to that of qubit-registers, and the laws of quantum mechanics take over. Mathematical physicists and computer scientists must revisit the old masters: Bohr, Einstein, Heisenberg, Pauli, and Dirac. In passing from logic gates to quantum gates (unitary matrices), the concept of switching-networks from traditional computer science now changes drastically. The changes introduce brand new scientific challenges, and new truly exciting opportunities. I believe that this book does justice to this, and that it is still a fascinating and thought provoking invitation to some of the most intriguing trends in modern physics.
Review by Palle Jorgensen, July 2005.


Hitler's Scientists: Science, War, and the Devil's Pact
Hitler's Scientists: Science, War, and the Devil's Pact
von John Cornwell
  Taschenbuch
Preis: EUR 15,49

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5.0 von 5 Sternen Ethics and science., 29. Mai 2005
Don't get distracted by the title! When I noticed it while browsing in the book store in an airport, I was at first worried that this would another one of these overly opinionated books, more interested in imposing a view on me the poor reader than in good writing, and in letting me make up my own mind. I started reading in the plane, and was pleased to find that the author manages to paint a captivating portrait of a group of German scientists who were faced with a Faustian choice; Fritz Haber (poison gas), Werner von Braun (rockets), Werner Heisenberg (atomic bomb), Otto Hahn (fission), Max von Laue (nuclear physics) to mention only a few. For the most part, the book reads like a novel, and with his superb writing, the author Cornwell brings the characters to life. Many of the German scientists in the 1930ties were Jewish, or partly Jewish, and they were dismissed by Hitler in 1933, or the years up to the war. Many of them emigrated, and others ended up in concentration camps. Some ( Albert Einstein, John von Neumann, Hans Bethe, and more) went to the USA, and became the core of the team, the Manhattan Project who built the first atomic bomb, the one used by the US government against Japan in 1945.
The bigger picture in Cornwell's book is the role of ethics in science. By weaving together the individuals, their thoughts, their ambitions, and their flawed judgments, Cornwell is not excusing anyone, but rather, he is helping us understand that we all must take responsibility for our actions. We can perhaps understand how present day scientists, and in fact all of us are faced with Faustian choices of our own.
I liked this one of Cornwell's books a lot better than his perhaps better known one, `Hitler's Pope'. It had me hooked from the start, and I couldn't put it down. Cornwell is not just relying on old historical sources. Since Michael Frayn's play `Copenhagen' a few years ago about the meeting in Copenhagen in the fall of 1941 between Werner Heisenberg and Niels Bohr, new documents have been made available from Bohr's archives which help us understand Heisenberg's motives better. Cornwell displays a remarkable judgment in making use of them
My reading of Heisenberg: If you accept a dinner invitation with the Devil, it is best to eat with a tea spoon. While Heisenberg, a humanist at heart may have understood this, at least initially, he soon found himself, perhaps as a result of blind ambition, eating at the trough with both hands deep into the stew, all the way up to his elbows.
It is perhaps ironic that the theme of the Faustian choice has a prominent place in German literature, from the medieval "Faustus" tale to Goethe, Weber's Freischuetz, to Martin Luther's Protestantism, and to Thomas Mann's Doctor Faustus (Mann's moral despair over his country's complacent embrace of Nazism).
In fact the theme of Cornwell's novel is universal, and it is as timely now as it was 60 years ago, and even 300 years ago. Review by Palle Jorgensen, May 2005.


The Road to Reality: A Complete Guide to the Laws of the Universe
The Road to Reality: A Complete Guide to the Laws of the Universe
von Roger Penrose
  Gebundene Ausgabe

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5.0 von 5 Sternen A panorama of science., 26. Februar 2005
It's a delicate balance for book: Encyclopedic vs well focused on a unifying theme!
Penrose succeeds admirably. It's not boring! Books like this are few and far between. Indeed, there are preciously few authors who manage to successfully guide beginning students into serious scientific topics; and even fewer who can see the big picture, and do it all. And then keeping our attention through more than 1000 pages! Penrose's book is inspiring, informative, exciting; and at the same time it's honest about what math and physics are. It is modest when modesty is called for. You are not cheated. You do get the equations (not just hand waving!), but you are gently prepared in advance, so you will want the mathematical formulae. Penrose's book is likely to help high school students getting started in science; and to inspire and inform us all. There is something for everyone: for the beginning student in math or in physics, for the educated layman/woman (perhaps the students' parents), for graduate students, for teachers, for scientists, for researchers; and the list goes on.
It is one of the very few books of this scope that is not intimidating. Not in the least!
I can't begin to do justice to this terrific book. Get it, and judge for yourself. I will also not give away the ending, other than saying that the title of the book is a good hint. And you will be able to form your own take, and your own ideas on the conclusion. Like with all good and subtle endings, they can be understood and appreciated at several levels.
I came across Penrose's book in my bookstore by accident, and I was at first apprehensive: The more than 1000 pages, and the 3.3 pounds are enough to intimidate anyone. But when I started to read, I found myself unable to put it down. And I didn't: Bought it; and I had several days of enjoyable reading. I am not likely to put it away to collect dust either. It is the kind of book you will want to keep using, and to return to.
It will not surprise that one of Penrose's unifying themes is the compelling and pleasing geometric images that underlie both the mathematics (roughly one third of the book: modern geometry, Riemann surfaces, complex functions, Fourier analysis, visions of infinity), and the physics: Cosmology (the big bang, black holes), gravity, thermodynamics, relativity (classical and modern: loop quantum gravity, twisters), and quantum theory (wave-particle duality, atomic spectra, coherence, measurements).
The pictures: In fact, this semester, I was just teaching a graduate course, and I had a hard time presenting of Riemann surfaces in an attractive way. It's a subject that typically comes across as intimidating in many of the classical books: Take Herman Weyl's book, for example. I also found it refreshing to see that Roger Penrose gave the many illustrations his own personal and artistic touch; as opposed to having flashy pictures generated by the latest in color-graphics and special effects. I think readers will relate better to Penrose's own illustrations: They isolate and highlight the core ideas and they are not intimidating: We sense that we ourselves would have been able to make similar pencil sketches. Or at least we are encouraged to try!
The common theme in the pictures serves to bring to life the underlying and fundamental ideas;--- another attractive feature of the book! It is otherwise easy to get lost in some of the equations, and in the encyclopedic panorama of topics. Review by Palle Jorgensen, February 2005.


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