As the author of this book, you may want to ignore my rating! I am really writing to simply note that the book will be reprinted late in 2001 or early in 2002 by The Johns Hopkins University Press. I have written a new introduction for the JHUP edition to bring the book up-to-date on all the latest about Heaviside.

Although Dr. Nahin may be a seasoned explorer of ideas involving time travel, his failure to used organized paragraphs and effective examples greatly lowered the value of this how-to book.

Nahin also omitted the concept of parallel universes entirely. (A now popular belief, that as soon as a traveler breaks his own space-time barrier and moves back in time, the universes splits into two identical entities, the original universe where you came from is the one you can never return to. This may sound disheartening, but this is the only conceivable way in which the time traveler would not induce changes in histories, and therefore time paradoxes.)

Books like this deserve to be better.

I'm a layman when it comes to science, but I was interested in the theories of the reality of time travel. I tried another book (that will remain nameless) which didn't work at all for me. It was just way over my head. This one's great! It's got all of the same kind of information that the first one had, but Nahin is so much more understandable and gets his points across in a much more organized way.

He's literally writing for the lay person here-- the book is intended for writers who would like write science fiction, but want to be scientifically updated on the scientifically possible realities of time travel (both to the past and to the future), teleportation (through wormholes, bending of the 4 dimensions, etc.), the special and general theories of relativity and more. His premise is that science fiction could get away with anything even 50 years ago, when most people and most scientists thought time travel to be impossible, but nowadays, you have to be scientifically sound if you don't want to be laughed out of the literary world. True Sci-fi readers will know if you're legit or not, so Nahin is educating them.

I'm not a writer, but because of the nature of his premise, the book is extremely clear and thus much more informative than the first one ever was. This book even answers questions that I was high-and-dry on before (after reading the first book I picked up). Some of the math may be over the layman's head (some of it's over mine!) and more than you care to know, but he includes a lot of thought-provoking information about the paradoxes of time travel and explains things in pictures very well. He colors his book with quotes and anecdotes from all kinds of works of science fiction and from scientists in the past to make the book fun (and sometimes humorous!).

It's a must-read for anyone interested in the possibilities of time travel and a must-MUST-read for anyone interested in writing a book on anything scientific.

I'm a layman when it comes to science, but I was interested in the theories of the reality of time travel. I tried another book (that will remain nameless) which didn't work at all for me. It was just way over my head. This one's great! It's got all of the same kind of information that the first one had, but Nahin is so much more understandable and gets his points across in a much more organized way.

He's literally writing for the lay person-- the book is intended for writers who would like write science fiction, but want to be scientifically updated on the scientifically possible realities of time travel (both to the past and to the future), teleportation (through wormholes, bending of the 4 dimensions, etc.), the special and general theories of relativity and more. His premise is that science fiction could get away with anything even 50 years ago, when most people and most scientists thought time travel to be impossible, but nowadays, you have to be scientifically sound if you don't want to be laughed out of the literary world. True Sci-fi readers will know if you're legit or not, so Nahin is educating them.

I'm not a writer, but because of the nature of his premise, the book is extremely clear and thus much more informative than the first one ever was. This book even answers questions that I was high-and-dry on before (after reading the first book I picked up). Some of the math may be over the layman's head (some of it's over mine!) and more than you care to know, but he includes a lot of thought-provoking information about the paradoxes of time travel and explains things in pictures very well. He colors his book with quotes and anecdotes from all kinds of works of science fiction and from scientists in the past to make the book fun (and sometimes humorous!).

It's a must-read for anyone interested in the possibilities of time travel and a must-MUST-read for anyone interested in writing a book on anything scientific.

This is an excellent book which combines the history, the
mathematics and the physics of radio. It is not a textbook
and you need to know calculus and physics to understand its
technical chapters. It has ten appendices, they explain the
"bottom" material or background needed in the book. However,
the all book is well written and it has an excellent presentation.
I think that the author's opinions about the
radio developers such as Marconi, DeForest and Tesla
are out of place in a book like this. So I gave three starts.

I have been a fan of Paul Nahin's writting since I came across his book an imaginary tale ... In this text he clearly describes the history as well as the EE of radio. It is an excellent book and I especially enjoyed the appendices and matlab and electronics workbench examples.

I've never met a technical book as well-written as this one. Imagine what if Maxwell's Treatise had been written by himself in collaboration with Martin Gardner and ... Bill Bryson! Paul Nahin is a great writer, and I can only imagine how great a teacher he must be. I will buy every single book he writes. Don't be misled: this is a very serious book, and the pleasure of its reading comes from a very sound teaching philosophy (called top-down by Nahin) combined with a knack for history, which gives context to every topic. Look at the table of contents, and you will see that the author means business.

Nahin has a lot of interesting things to say with regard to time travel, but he has a tendency to set up as straw men viewpoints not in agreement with his and let viewpoints that do agree with his slide by when, perhaps, they warrant deeper critical examination. Special derision is reserved for various philosophers and their "fairy tales" and such. The chief respect in which I really enjoyed this book was in the many and varied discussions Nahin engages in with regard to time travel in literature. What he has to say is almost always lucid, interesting and fair, and the examples he rescues from obscurity are invariably intriguing. It's unfortunate that he didn't show such equanimity, again, with regard to opposing philosophically-oriented viewpoints. I have mixed feelings about the book because the recurring tendentiousness can wear on one, but I think the discussion of time travel in literature makes it worth the while.

As I have always been fascinated by the idea of time travel, I very much enjoyed its discussion both in 'strictly scientific' terms and from a philosophical, literary, and, essential, pop-culture perspective.
Sadly, Nahin completely ignores one aspect that features prominently in many modern time travel narratives: the idea of alternate universes / alternate realities and, tied to that, the narrative perspective of sequentiality, which follows the POV of the protagonist of a narrative and projects his continuity against the alterations his actions cause. As a result, a number of time travel stories are missing, while others show flaws/inconsistencies in their interpretations. For instance, Isaac Asimov's The End of Eternity (1955), which deals with the idea of realities literally being 'engineered' through minimum manipulations in the course of history, thus weeding out 'mishaps' like world wars and famines but at the same time stalling natural progress, remains completely unmentioned. On the other hand, Nahin points to the 'flaw' in the end of Back to the Future I that the shopping mall should always have been "Lone Pine Mall" and never "Twin Pines Mall" as it was called in the beginning because taken from a timeline perspective, Marty had already been to 1955 and run over one of the twin pines with the DeLorean when the temporal experiment #1 took place in the parking lot in 1985. However, taken from this perspective, Marty's family should have been healthy and wealthy from the beginning on as well, which would undermine the whole plot idea of changing history (which is, added to that, even expressedly discussed in detail in the also unmentioned Back to the Future II).
Nevertheless, Nahin gives a lot of food for thought on the idea of time travel, and the rather extensive bibliography supplies a very good reference for further individual exploration.

As I have always been fascinated by the idea of time travel, I very much enjoyed its discussion both in 'strictly scientific' terms and from a philosophical, literary, and, essentially, pop-culture perspective.
Sadly, Nahin completely ignores one aspect that features prominently in many modern time travel narratives: the idea of alternate universes / alternate realities and, tied to that, the narrative perspective of sequentiality, which follows the POV of the protagonist and projects his continuity against the alterations his actions cause. As a result, a number of time travel stories are missing, while others show flaws/inconsistencies in their interpretations. For instance, Isaac Asimov's "The End of Eternity" (1955), which deals with the idea of realities literally being 'engineered' through minimum manipulations in the course of history, thus weeding out 'mishaps' like world wars and famines but at the same time stalling natural progress, remains completely unmentioned. On the other hand, Nahin points to the 'flaw' in the end of "Back to the Future" that the shopping mall should always have been 'Lone Pine Mall' and never 'Twin Pines Mall' as it was called in the beginning because taken from a timeline perspective, Marty had already been to 1955 and run over one of the twin pines with the DeLorean when the temporal experiment #1 took place in the parking lot in 1985. However, taken from this perspective, Marty's family should have been healthy and wealthy from the beginning on as well, which would undermine the whole plot idea of changing history (which is, added to that, even expressedly discussed in detail in the also unmentioned "Back to the Future II").
Nevertheless, Nahin gives a lot of food for thought on the idea of time travel, and the rather extensive bibliography supplies a very good reference for further individual study.

To be fair this is one of the better written books on popular mathematics that I have read. Also to be fair he is an electrical engineer who has missed the last century of complex analysis and complex dynamics completely. It would make a good introduction for a college course on the complex plane. The history and proofs are well worth the price as they can't be found together in other books. But a book on imaginary numbers that omits Klein groups, Julia sets and Mandelbrot can't be said to be fair or modern. If he is sending his engineering students into the world thinking that complex analysis ended in 1899, he is doing them a real disservice and preregistering them for failure in a world where chaos and aerodynamics depend on nonlinear equations on the complex plane.

Despite its billing as a history of science book, I would really categorize "An Imaginary Tale" as a supplemental math text with occasional historical color, much as you'll find, for example, in offset boxes of "friendly" freshman calculus treatments. The author largely concedes this in the preface. Granted, the first couple of chapters have a more historical emphasis, but by the end of chapter 3 we've largely left behind the etiology of complex analysis.

However, as long as you are aware of this going in, you'll be treated to an absolutely first-rate trip through the motivation, development and application of complex function theory, including several thoroughly worked out real-world examples. I was delighted by Nahin's painstaking efforts to build intuition about the meaning of complex algebra. If nothing else, drilling in the idea that i is a pi/2 rotation operator in the complex plane would give a conceptual toehold to thousands of high school students who never learn anything about complex algebra beyond formal symbol manipulation. One can easily imagine "An Imaginary Tale" as recommended reading for interested high school seniors, or for undergraduates looking for some background and motivation of ideas they are required to understand.

Make no mistake, when the author says he will not "fall to his knees in dumbstruck horror" at the sight of an integral, you should take him at his word --- this book is packed with integral calculus equations, and you're not going to get much out of it if you're not prepared to follow along with them. But I think Nahin has achieved the right blend of explaining each step versus leaving algebra to the reader (here I disagree somewhat with smlauer@mindspring.com, though I am sympathetic to his point).

I have deducted a star for exactly the reasons Duwayne Anderson and others complained about: (1) we need to have *many* of the results numbered, but unfortunately we only get a box or two in the entire text, and (2) who proofed this thing? I mean, honestly, stating Green's theorem correctly twice and then misprinting it in the section where it's proved? Randomly leaving the circle off of contour integrals? (sqrt(15)i)^2 = 15? It's fun to work the algebra that's left to the reader, but it's *tedious* to work out which results are misprinted and which aren't.

Despite these typographical problems, I can enthusiastically recommend "An Imaginary Tale" to all readers at a moderate level of mathematical sophistication who are curious about the origins, theory and application of complex analysis.

Nahin's text on the history of i is an exciting, comprehensive look into the origins of i and its elementary theoretical applications. It rightfully has been compared to Eli Maor's wonderful book "e: The Story of A Number", which deserves five stars in its own right. I do have to take issue with some of the other reviews posted here. For instance, a few have said that you have to have a "graduate math" background to fully appreciate this book?!? Who are they kidding? Nahin actually *sacrifices* mathematical rigor in order to improve his exposition. Anyone with a real mathematics background knows that complex analysis gets far more complicated than the basic material Nahin presents in his book. To get an idea, you can peruse Walter Rudin's fine text "Real and Complex Analysis". To be fair, I agree with the reviewer who wrote that Nahin should not have omitted material on Klein groups, Julia and Mandelbrot sets. However, I can understand why he did. It is difficult to write on such subjects as groups and fractals to an audience intended to have a (motivated) high school or freshman calculus background. I read this book, understood it, and loved it, long before I had any idea what groups or fractals were. Nahin gives fair warning in the introduction to his book that it is not a "mathematical lightweight". I do think that a solid background in (single variable) calculus, including power series, is crucial to a true appreciation of the book. In particular, one must know these things to value the genius of Euler and others in the section on "Wizard Mathematics". Nahin does tread lightly into other topics, such as differential equations and (advanced) algebra, but to say these are a prerequisite to reading the book is ridiculous. I think even if the reader has never encountered ideas such as the Fundamental Theorem of Algebra before, they serve to enrich, not detract from, the material. In any case, the reader should be pleased to see a leisurely treatment of something so blown out of proportion as FTA, as an understanding of it is basic to anything beyond calculus. Proofs of it are rich in variety, ranging from topology to geometry to complex variables (using the theorem of Liouville and properties of entire functions). One criticism that is entirely justified is the typographical errors that regrettably plague the book. In particular, the theorem of Green, relating double integrals to single contour integrals, a result that is surprising and illuminating. However, the careful reader can usually spot and correct such errors, and he or she should be delighted in their own astuteness, rather than blame the author. He does a wonderful job explaining the conceptual basis of i, and I think this overrides any of the books minor flaws. The book does seem to end rather abruptly, however, and I hope that if the author chooses to revise his work, he will expand upon the material, in particular, a (brief?) treatment of the Residue Theorem, the crowning jewel of complex integration. Perhaps even a section on conformal mapping? I do realize though that this may place the book too far out of reach of his intended audience.

The bottom line: if you want a storybook, this is not for you. If you like mathematics, and have a historical bent, this book will satisfy you. Those with a mathematical background will realize that Nahin has the perfect background to write this book: electrical engineers have a *much better* idea of what's going on with complex variables in terms of getting their hands dirty than mathematicians themselves. This is because most mathematicians insist on strict formalism and rigor, but engineers think more freely, and in any case they are the ones that discovered half of the applications of complex variables. E.g., imagine Laplace transforms even existing without Oliver Heaviside, who was thought to be a fool by the mathematical community in his day!

For those that are curious, I only have a B.A. in math, and no graduate education, though I do pursue math study in my free time. So I think I am in a position to make the above arguments.

The best puzzle books start with problems that are interesting and non trivial, and offer unexpected solutions. They appeal to a crowd with different levels of education and offer a new idea or two to all. They will lead an unsuspecting layman to a new beautiful mathematical subject, and treat a pro with a lighthearted yet technically sound look at the concepts he is already familiar with.

"Dueling idiots" is none of that. To read it you must be more than familiar with probability theory, and at ease with going through rather tedious calculations and using mathlab. Yet all a sophisticated reader finds here is absence of fresh ideas and technical sloppiness.

I am giving it two stars rather than one because it could provide some probability theory buff with a nice set of "real life" applications -- good as an auxiliary text book for an undergraduate probability class e.g. Apart from that, you will find a better puzzle book almost anywhere you look.

There is surely a need for a book like this but sadly this one doesn't do the
job. The author clearly has no idea what's really required. On p 20 he has
the results of five runs of 10,000 simulations to estimate the probability
P(A) of an event A. Now P(A) is known here, so these simulations are just an
ATTEMPT to verify that the program is working correctly. The author merely
notes that "the estimates for P(A) are a bit on the high side." No kidding!
All five runs produced consistently high estimates, and combining the runs
there's only one chance in 87 that the overall estimate would be so high
(ASSUMING the program were working properly). Of course, it's POSSIBLE that
the procedure is correct, that such high estimates just happened by a long
shot, but my email suggesting that the simulations be rerun drew no reponse.
Given this failure to demonstrate that a KNOWN probability can be estimated
properly, goodness only knows how good/bad UNknown probability estimates are.
Little wonder so many bombs are missing their targets in Afghanistan.

Turning to how the random numbers were generated I promptly noticed the table
of autocorrelations on p 184. These are not only bad, the zero-lag
correlation (a variable with itself) is 1.023!!! Given that it should be
nothing but EXACTLY 1 I initially thought this was a social comment on the
age of the generator, but machines were NEVER THAT bad. Rather, you'll find
the reason in the mishmash just above the table.

Indeed, in what little I read, statistical concepts are massacred. Further,
on p 27 there's an expression for pi which is actually mathematical nonsense
(ie, it is incorrect). At that stage I quit reading, it's so painful.

Nonetheless, I'll give the author two stars for TRYING to fill a void. He
just needs someone to correct everything, which is obviously no small task.

Books on probability are often boring. (Remember all those tedious problems involving people obsessed with drawing balls from urns?). In "Duelling Idiots", Nahin actually makes the subject fun by describing offbeat problems with unexpected solutions. If you like solving math puzzles, then this is a great book to look at. If you're teaching a course and want to assign a book that students might actually read, then look no further.