Tag Archives: book review

Einstein was Right All Along

General relativity has a reputation for being very difficult. I think the reason is that it is very difficult.

Leonard Susskind, General Relativity: The Theoretical Minimum

Two events have left me obsessed with the concept of gravity. Such an obsession is fundamentally unhealthy, I’ll admit it. I will nonetheless explain it to you.

First, let us back up a little. While I have an educational background in science and engineering, higher-level math was never my strength. Thus while Physics 101 was both interesting and fairly easy for me, when it came to further courses in Physics, my sailing was not quite so smooth. Electromagnetism, quantum mechanics, relativity, and light all left the realm where my own intuition could no longer help me along and where my tenuous grasp on matrix math and advanced calculus came around to kick me in the tush.

Despite both coursework and a subsequent lifetime spent reading, through which I’ve sought to understand all of these concepts, my self evaluation is that my understanding remains fairly superficial.

The two events that sent me down the path to insanity took place in 2019. The first was that I viewed the TV show The Expanse, which had become available via streaming. The show’s attempt to get right certain aspects of space travel made it stand out from its science fiction peers and got me thinking about the details. Around about the same time, I read the book The Perfect Theory, which helped me cogitate upon some of these same issues.

It took a few years, but these thoughts ultimately began to consume me. I found an old social media post, from the fall of 2021, where I described waking up at night convinced that I could do the requisite math in my head (and, therefore, must before going back to sleep) to solve complex calculations for orbital mechanics. By 2022, I had mulled on this enough to share with my readers here (in another post).

That now-three-year-old post was framed as a question but I had already begun working on creating some answers. The problem was I could not develop for myself, based on intuition, any answers… and no wonder! From the beginning of his conception of General Relativity, Einstein himself struggled to define experiments that could distinguish between “real” gravity (caused by proximity to a very large, massive object) and “apparent” gravity, caused by an externally-driven acceleration.

Let me catch you up with what has happened, inside my own head, since then.

Once again, a science fiction series has driven me to move on this. Since that last post, I had the opportunity to finish the First Formic War trilogy (now almost 10 years old) by Orson Scott Card. In this set of books, there is extensive use of anti-gravity technology to drive several major plot arcs. The way that technology is used strikes me as wrong; both from the engineering and the physics standpoints. Because I’ve spent so much energy dwelling on this, the wrongness is almost painful to me.

I’ll contrast this to the original Ender’s Game. Like many science fiction works that preceded it, Ender’s world sees mankind having developed some control of gravity. The book (and if you haven’t read it, maybe you should) takes place on a space station where the future officers in a space defense force are trained. Ender notes that, in some cases, the gravity on the station defies physical logic but no explanation is given. To a reader, this is satisfying. Maybe the inter-species space warfare imparted some knowledge upon mankind or maybe it is a result of many decades of technological advancement. The fact that gravity and anti-gravity are common in space sci-fi books and, especially, films makes it easy to accept.

The Formic Wars (starting with the novel Earth Unaware) takes place long before Ender’s Game. In it, we find out that the development of gravitation “lensing” will be an entirely human achievement. Through judicious manipulation of the gravity field in the vicinity of an aircraft, the military will develop a rotorless helicopter with near-infinite lift capacity. At the same time, a private company has developed a gravity laser that can disrupt a local gravitation field so as to eliminate the integrity of solid masses.

The flaw in this has to do with balance. There are concepts such as conservation of energy that can be calculated and could, I suspect, throw a big monkey wrench into this concept. It also attempts a technical explanation without considering the equations for the fields that are being disrupted. Some not-so-simple math, one might think, would explain to me what is so troublesome about this as a near-future technology. Unfortunately, one of my problems, apparent for several years now, is that lack of the required mathematical ability.

Non-fiction, scientific books on the subject of gravitation seem to either either with “imagine you’re floating in space” or “here is the equation for a Lorentzian manifold; you should be thoroughly familiar with this math from your prior course work.” What I really needed was something in between. The good news is that I found that something.

The book General Relativity: The Theoretical Minimum by Leonard Susskind provides a reasonably happy medium between those two extremes. It starts its readers off with a minimum of assumptions about their mathematical background. It suggests that the reader should already have gone through some of the earlier books in his series but I found that, for the most part, that wasn’t necessary. A basic university-level understanding of math (even if decades out of use) plus a couple of internet searches seemed more than sufficient to follow along.

The book goes on to illustrate how a physicist might manipulate advanced math concepts using the shorthand representation for vector and tensor equations. Doing so allows one to evaluate the implications of such equations without actually having to solve them. Susskind does, in fact, encourage the reader to work through the math by hand (for simpler solutions) to aid in understanding but I did not do so. I found I could accept the assertions of the author without having to prove them for myself and was comfortable following along with the abstract notions.

Realize, too, that I was reading this book at night, in bed. The last thing I wanted to do was to get up and start doing lengthy math computations when I really should have been sleeping.

The second big impression General Relativity made on me was about black holes. In particular, it answered the question as to why there is so much focus on black holes in nearly everything I’ve read so far.

Indeed, this book does focus on black holes. Heavily. It introduces early a discussion about “falling into a black hole” with then a promise that you can come back to that after establishing a foundation. The second half of the book (more than half, really) is then dedicated to further analysis of black holes and their effects. Surely there are far more interesting things in this universe than the (admittedly very interesting) black holes?

The answer has to do with the math. One way to untangle the incredible complexity is to find situations where the terms of these equations go to zero. Doing so will allow the solutions to be extracted from otherwise unsolvable differential equations. One way to usefully zero out terms is to imagine the space/time in the vicinity of a mass approaching the infinite and a size approximating a dimensionless point.

Further investigation into the nature of this mathematical “singularity” began producing interesting properties. For example, the mass need not be infinite – just very large, and the size is not “zero1.” This prompted astrophysicists to speculate on how such an entity might come into being.

In 1939, Einstein himself published a paper, “On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses,” attempting to use General Relativity to prove that black holes were a physical impossibility. Within months, Robert Oppenheimer published “On Continued Gravitational Contraction,” using general relativity to prove that they should exist. It would take until 1972 for the effects of a presumed black hole (Cygnus X-1) to be observed, thus proving that the mathematical slight-of-hand, in fact, corresponded to a physical thing.

To me, it is quite remarkable that this “imagine if…” turned out to be something that is real and not particularly uncommon. That, combined with the easy math, goes a long way towards explaining why a book like General Relativity expends so much of itself on Black Holes rather than just General Relativity in general.

So, contrary to my title, we learn that Einstein was initially wrong about Black Holes. In “general” (oh I slay myself), though, his is a story of being right when those around him thought otherwise. When his peers felt that his descriptions of the physical universe were just too strange to be true.

This brings me around to that frequent subject of this site and my ponderings upon the true nature of gravity. If my feel for the state of the science, as rough as that is, is correct – this remains even today a subject for debate.

Specifically, I am thinking about Einstein’s assertion that there is no difference between an object in free fall within a gravitational field and an object outside of any effects of gravitation. In this understanding, it must be the shape of time and space that causes the apparent application of forces rather than the balance between gravity, acceleration, and momentum that makes the Newtonian understanding of gravity.

The alternative to Einstein’s explanation is that gravity is, truly, a “force field” similar to an electromagnetic field. That when an object in orbit which sees its forces balance out to zero, as Newtonian physics would explain, that this doesn’t mean those forces don’t exists. It is instead a convenient mathematical outcome. It’s a fine distinction but, in this this conception, we must consider Einstein’s version something other than the fundamental nature of the universe, as he proposed it. Instead, that fundamental nature has something to do with gravitons or unified fields – things we don’t yet fully understand – and Einstein’s thought experiments are just a nice way to get our minds around this deeper reality.

Dr. Susskind is in this second camp. Similar to my own line of thinking (if I may be so bold as to put myself in a league with a Stanford theoretical physics professor), he has gone further and proposed a thought experiment that would allow one to distinguish between these two concepts. His experiment involves a 2,000 mile tall man.

Imagine, he suggests, an astronaut who is 2,000 miles in height. Our big fella decides to don a spacesuit and engage in some outer space sky-diving, dropping back towards home from an orbital height. Imitating an atmosphere-limited jumper, his body is aligned flat with the earth’s surface, perpendicular to the direction in which he is falling. Encountering a sudden sense of dislocation combined with a momentary blindness, he finds himself unsure as to whether he is floating in the vastness of space or freefalling towards his home planet – two states which Einstein says are identical. But for our very tall spacefarer, they are not. If at some orbital height near the earth, he will be able to determine that “down” has different directions for his head versus his toes. More technically speaking, he will sense some compression as the two ends of his massive body move towards the earth following converging trajectories. If he were all alone in deep space, by contrast, he would feel no such sensation.

While the 2,000 miles of manflesh is necessary to make the differential significant, one might imagine that ability to detect the phenomenon exists (Planck’s insights notwithstanding) for a more reasonably sized body. It should be possible to design an experiment to measure the effect and, proof in hand, show that the nature of gravity is a force field and that Einstein’s thought experiments fail when one strays outside their applicability.

For my own peace of mind, I can’t fully accept Dr. Susskind’s reasoning and I am further comforted that there are others, far better educated than I, who feel similarly. My gut tells me that his 2,000 mile mind experiment glosses over certain realities. When he imagines his man in orbit, isn’t he, at least in some ways, imagining inhabiting the world of Newtonian physics? Might he be neglecting some reality of space-time curvature? Might he be ignoring the difference between a point mass and a distributed mass and the limitations of communication across distances. Can a 2,000 mile tall man even evaluate simultaneity properly so as to determine that he is both in free fall and under a gravitational-induced stress? I’ll even offer (without details) how this thought experiment has some common features with “ladder paradox” in special relativity. Might have similar resolution?

Part of me wants to believe that there it is possible to gain an intuitive understanding of General Relativity; one that does not need to depend on advanced math. General Relativity: The Theoretical Minimum gets me a little bit closer to bringing it all together in a way that, as a mildly committed amateur, enables me to comprehend the nature of the universe. If I found any issues with Dr. Susskind’s presentation, these were minor relative to the value that this book provided to me.

As to Einstein, I previously highlighted the date on which he published his paper on General Relativity. Yet it was on THIS day, November 18th, that he made his discovery. He was looking at a problem with Mercury’s orbit and the fact, since 1859, its perihelion (the point where the planet is closest to the sun) advanced 43 inches2 per century more than physics predicted. While physical explanations were considered (e.g. an invisible moon around Mercury), an alternative was that Newton’s law of gravitation was wrong.

Since 1911, Einstein has realized that empirical validation of this theories would have to come through astronomical observations. In the case of Mercury’s orbit and Newton’s inverse square law, this ε, the discrepancy or error factor, provided an opportunity to put his theories to a test. Applying his theory of gravitation to Mercury’s orbit produced, exactly, the measured orbital advance of 43 inches per century with no additional, unknown factors required. The computations were finalized on November 18th, 1915 and this discovery informed the paper that he submitted on the 25th.

  1. It is a spheres whose dimensions are described by the Schwarzschild radius. The book explains what that means. I will not. ↩︎
  2. The calculation in 1859 was an error of 38″ per century. By 1882, the number was corrected to 42″ per century. ↩︎

Related

In the fall of 1915, after ten years of analysis, Albert Einstein presented his gravitational field equations of general relativity in a series of lectures at the Royal Prussian Academy of Sciences. The final lecture was delivered on November 25th, 104 years ago.

Yet it wasn’t until a month or so ago that I got a bug up my butt about general relativity. I was focused on some of the paradox-like results of the special theory of relativity and was given to understand, without actually understanding, that the general theory of relativity would solve them. Not to dwell in detail on my own psychological shortcomings, but I was starting to obsess about the matter a bit.

Merciful it was that I came across The Perfect Theory: A Century Of Geniuses And The Battle Over General Relativity when I did. In its prologue, author Pedro G. Ferreira explains how he himself (and others he knows in the field) can get bitten by the Einstein bug and how one can feel compelled to spend the remainder of one’s life investigating and exploring general relativity. His book explains the allure and the promise of ongoing research into the fundamental nature of the universe.

The Perfect Theory tells its story through the personalities who formulated, defended, and/or opposed the various theories, starting with Einstein’s work on general relativity. Einstein’s conception of special relativity came, for the most part, while sitting at his desk during his day job and performing thought experiments. He was dismissive of mathematics, colorfully explaining “[O]nce you start calculating you shit yourself up before you know it” and more eloquently dubbing the math “superfluous erudition.” His special relativity was incomplete in that it excluded the effects of gravity and acceleration. Groundbreaking though his formulation of special relativity was, he felt there had to be more to it. Further thought experiments told him that the gravity and acceleration were related (perhaps even identical) but his intuition failed to close the gap between what he felt had to be true and what worked. The solution came from representing space and time as a non-Euclidean continuum, a very complex mathematical proposition. The equations are a thing of beauty but also are beyond the mathematical capabilities of most of us. They have also been incredibly capable of predicting physical phenomena that even Albert Einstein himself didn’t think were possible.

From Einstein, the book walks us through the ensuing century looking at the greatest minds who worked with the implications of Einstein’s field equations. The Perfect Theory reads much like a techno-thriller as it sets up and then resolves conflicts within the scientific world. The science and math themselves obviously play a role and Ferreira has a gift of explaining concepts at an elementary level without trivializing them.

Stephen Hawking famously was told that every formula he included in A Brief History of Time would cut his sales in half. Hawking compromised by including only Einstein’s most famous formula, E = mc2. Ferreira does Hawking one better, including only the notation, not the full formula, of the Einstein Tensor in an elaboration on Richard Feynman’s story about efforts to find a cab to a Relativity conference as told in Surely You’re Joking, Mr. Feynman. The left side of that equation can be written as, Gμν. This is included, not in an attempt to use the mathematics to explain the theory, but to illustrate Feynman’s punch line. Feynman described fellow relativity-conference goers as people “with heads in the air, not reacting to the environment, and mumbling things like gee-mu-nu gee-mu-nu”. Thus, the world of relativity enthusiasts is succinctly summarized.

The most tantalizing tidbit in The Perfect Theory is offered up in the prologue and then returned to at the end. Ferreira predicts that this century will be the century of general relativity, in the same way the last century was dominated by quantum theory. It is his belief we are on the verge of major new discoveries about the nature of gravity and that some of these discoveries will fundamentally change how we look at and interact with the universe. Some additional enthusiasm shines through in his epilogue where he notes the process of identifying and debunking a measurement of gravitational waves that occurred around the time the book was published.

By the end of the book, his exposition begins to lean toward the personal. Ferreira has an academic interest in modified theories of gravity, a focus that is outside the mainstream. He references, as he has elsewhere in the book, the systematic hostility toward unpopular theories and unpopular researchers. In some cases, this resistance means a non-mainstream researcher will be unable to get published or unable to get funding. In the case of modified gravity, he hints that this niche field potentially threatens the livelihood of physicists who have built their careers on Einstein’s theory of gravity. In fact, it wasn’t so long ago that certain aspects of Einstein’s theory were themselves shunned by academia. As a case in point, the term “Big Bang” was actually coined as a pejorative for an idea that, while mathematically sound, was too absurd to be taken as serious science. Today, we recognize it as a factual and scientific description of the origin of our universe. Ferreira shows us a disturbing facet of the machinery that determines what we, as a society and a culture, understand as fundamental truth. I’m quite sure this bias isn’t restricted to his field. In fact, my guess would be that other, more openly-politicized fields exhibit this trend to an even greater degree.

Ferreira’s optimism is infectious. In my personal opinion, if there is to be an explosion of science it may come from a different direction than that which Ferreira implies. One of his anecdotes involves the decision of the United States to defund the Laser Interferometer Space Antenna (LISA), a multi-billion dollar project to use a trio of satellites to measure gravitational waves. To the LISA advocates, we could be buying a “gravitational telescope,” as revolutionary in terms of current technologies as radiotelescopy was to optical telescopes. The ability to see further away and farther back in time would then produce new insights into the origins of the universe. But will the taxpayer spend billions on such a thing? Should he?

Rather than in the abstract, I’d say the key to the impending relativity revolution is found in Ferreira’s own description of the quantum revolution of the past century. It was the engineering applications of quantum theory, primarily to the development of atomic weapons, that brought to it much of the initial focus of interest and funding. By the end of the century, new and practical applications for quantum technology were well within our grasp. My belief is that a true, um, quantum leap forward in general relativity will come from the promise of practical benefit rather than fundamental research.

In one of the last chapters, Ferreira mentions that he has two textbooks on relativity in his office. In part, he is making a point about a changing-of-the-guard in both relativity science and scientists, but I assume he also keeps them because they are informative. I’ve ordered one and perhaps I can return to my philosophical meanderings once I’m capable of doing some simple math. Before I found The Perfect Theory, I had been searching online for a layman’s tutorial on relativity. Among my various meanderings, I stumbled across a simple assertion; one that seems plausible although I don’t know if it really has any merit. The statement was something to the effect that there is no “gravitational force.” An object whose velocity vector is bent (accelerated) by gravitational effects is, in fact, simply traveling a straight line within the curvature of timespace. If I could smarten myself up to the point where I could determine the legitimacy of such a statement, I think I could call that an accomplishment.

Artificial, but Intelligent? Part 2

I just finished reading Practical Game AI Programming: Unleash the power of Artificial Intelligence to your game. My conclusion is there is a lot less to this book than meets the eye.

For someone thinking of purchasing this book, it would be difficult to weigh that decision before committing. The above link to Amazon has (as of this writing) no reviews. I’ve not found any other, independent evaluations of this work. Perhaps you could make a decision simply by studying the synopsis of this book before you buy it. Having done that, it is possible that you’d be prepared for what it offered. Having read the book, and then going back and reading the Amazon summary (which is taken from the publisher’s website), I find that it more or less describes the book’s content. In my case, I picked this book up as part of a Humble Book Bundle, so it was something of an impulse buy. I didn’t dig too hard into the description and instead worked my way through the chapters with my only expectations being based on the title.

Even applying the highest level of pre-purchase scrutiny only gets you so far. The description may indicate that the subject matter is of interest, but it is still a marketing pitch. It gives you no idea of the quality of either the information or the presentation. Furthermore, I think someone got a little carried away with their marketing hype. The description also tosses out some technical terms (e.g. rete algorithm, forward chaining, pruning strategies) perhaps meant to dazzle the potential buyer with AI jargon. The problem is, these terms don’t even appear in the book, much less get demonstrated as a foundation for game programing. I feel that no matter how much upfront research you did before you bought, you’d come away feeling you got less than you bargained for.

What this book is not is an exploration of artificial intelligence as I have discussed that term previously on this website. This is not about machine learning or generic decision-making algorithms or (despite the buzz words) rule-engines. The book mentions applications like Chess only in passing. Instead, the term “AI” is used as a gamer might. It discusses a few tricks that a game programmer can use to make the supposedly-intelligent entities within a game appear to have, well, intelligence when encountered by the player.

The topic that it does cover does, in fact, have some merit. The focus is mostly on simple algorithms and minimal code required to create the impression of intelligent characters within a game. Some of the topics I found genuinely enlightening. The overarching emphasis on simplicity is also something that makes sense for programmers to aspire to. There is no need to program a character to have a complex motivation if you can, with only a few lines of code, program him to appear to have such complex motivation. It is just that I’m not sure that these lessons qualify as “unleashing the power of Artificial Intelligence” by anyone’s definition.

But even before I got that far, my impression started off very bad. The writing in this book is rather poor, in terms of grammar, word usage, and content. In some cases, misused words become so jarring as to make it difficult to read through a page. Elsewhere, there will be several absolutely meaningless sentences strung together, perhaps acknowledging that a broader context is required but not knowing how to express it. At first, I didn’t think I was going to get very far into the book. After a chapter or so, however, reading became easier. Part of it may be my getting used to the “style,” if one can call it that. Part of it may also be that there is more “reaching” in the introductory and concluding sections but less when writing about concrete points.

I can’t say for sure but it is my guess, based on reading through the book, that the author does not use English as his primary language. I sometimes wondered if the text was written first in another language and then translated (or mistranslated, as the case may be) into English. Beyond that, the book also does not seem to have benefited from the work of a competent editor.

The structure of the chapters, for the most part, follows a pattern. A concept is introduced by showcasing some “classic” games with the desired behavior. Then some discussion about the principle is followed by coding example, almost always in Unity‘s C# development environment. This is often accompanied by screenshots of Unity’s graphics, either in development mode or in run-time. Most of the chapters, however, feel “padded.” Screenshots are sometimes repetitious. Presentation of the code is done incrementally, with each new addition requiring the re-printing of all of the sample code shown so far along with the new line or lines added in. By the end of the chapter, adding a concept might consist of two explanatory sentences, 3 screenshots, and two pages of sample code, 90% of which is identical to the sample code several pages earlier in the book. This is not efficient and I don’t think it is useful. It does drive the page count way up.

I want to offer a caveat for my review. This is the first book I’ve read from this publisher. When reading about some of their other titles, it was explained that the books come with sample source code. If you buy the book directly from the publisher’s website (which I did not), the sample code is supposed to be downloaded along with the book text. If you buy from a third party, they provide a way to register your purchase on the publisher’s site to get access to the downloads. I did not try this. If this book does have downloadable samples that can be loaded into Unity, and those samples are well-done, that has a potential for adding significant value over the book on its own.

Back to the chapters. When I start going through the chapters, again it feels like there is some “padding” going on to make the subject matter seem more extensive than it is. The book starts with two chapters on Finite State Machines FSM and how that logic can be used to drive an “AI” character’s reactions to the player. Then the book takes a detour into Unity’s support for a Finite State Machine implementation of animations, which has its own chapter. This is mostly irrelevant to the subject of game AI and also, likely, of little value if you’re not using Unity.

After the animation chapter, we head back into the AI world with a discussion of the A*, and the Theta* variant thereof, pathfinding algorithm. This discussion is accompanied by a manual optimization solution of a simple square-grid based 2D environment, describing each calculation and illustrating each step. I do appreciate the concrete example of the algorithm in action. Many explanations of this topic I’ve found on-line simply show code or pseudo-code and leave it to the “student” to figure it all out. In this case, I think he managed to drive the page count up by and order of magnitude over what would have been sufficient to explain it clearly.

The final chapters show how Unity’s colliders and raycasting can be used to implement both collision avoidance and vision/detection systems. These are two very similar problems involving reacting to other objects in the environment that, themselves, can move around. As I said earlier, there are some useful concepts here, particularly in emphasizing a “keep it simple” design philosophy. If you can use configurable attributes on your development tool’s existing physics system to do something, that’s much preferable to generating your own code base. That goes double if the perception for the end user is indistinguishable, one method from the other. However, I also get the feeling that I’m just being shown some pictures of simple Unity capabilities, rather than “unleashing the power of AI” in any meaningful sense.

A few years back, I was trying to solve a similar problem, but trying to be predictive about the intent of the other object. For example, if I want to plot an intercept vector to a moving target but that target is not, itself, moving at a constant rate or direction, I need a good bit more math than the raycasting and colliders provide out of the box. Given the promise of this book’s subject matter, that might be a problem I’d expect to find, perhaps in the next chapter.

Alas, after discussing the problem of visual detection involving both direction and obstacles, the book calls an end to its journey. With the exception of the A* algorithm, the AI solutions consist almost entirely of Unity 3D geometry calls.

Although the book claims to be written in a way such that each chapter can be applied to a wide range of games, I feel like it narrows its focus as it progresses. The targeted game is, and I struggle with how to describe it so I’ll just pick an example, the heirs to the DOOM legacy. By this, I mean games where the player progresses through a series of “levels” in order to complete the game. What the player encounters through those levels is imagined and created by the designer so as to construct the story of the game. The term AI, then, distinguishes between different kinds of encounters, at least as far as the player perceives them. For example, the player might find herself rushing across a bridge, which starts to collapse when they reach the middle. This requires no “AI.” It is simply programmed in that, when the player reaches a certain point on the bridge, call the “collapseBridge” routine. If she makes it past the bridge and into the next chamber, where there are a bunch of gremlins that want to do her in, the player starts considering the “AI” of those gremlins. Do they react to what the player does, adopting different tactics depending on her tactics? If so, she might praise the “AI.” By the book’s end, the focus is entirely on awareness of and reaction between mobile elements of a game which, by defining the problem as such, is the subset of games in this category.

My harping on the narrow focus of this book goes to the determination of its value. If this book were free or very low cost, you would have to decide whether the poor use of English and the style detract from whatever useful information is presented. The problem with that is the price this book asks. The hardcopy (paperback) of the book is $50.00. The ebook is $31.19 on Amazon, discounted to $28 if you buy directly from the publisher’s site. All of those seem like a lot of money, per my budget. Now, my own price I figure to have been $7. I bought the $8 bundle package over the $1 package purely based on interest in this title. This is the first book in that set I’ve read, so if some of the others are good, I might consider the cost to be even lower. Still, even at $5, I feel like I’ve been cheated a bit by the content of this book.

The bundle contained other books from this same publisher, so I’ll plan to read at least one other before drawing any conclusions about their whole library. Assuming that the quality of this book is, in fact, an outlier, this is still a risk to the publisher’s reputation. When one of your books is overpriced and oversold, the cautious buyer should assume that they are all overpriced and oversold. Looking at the publisher’s site, this book has nothing but positive reviews. It’s really a blemish on the publisher as a whole.

Although I won’t go so far as to say “I wish I hadn’t wasted the time I spent reading this,” I can’t imagine any purchaser for whom this title would be worth the money.