This museum, located at Andrássy út 60 in Budapest, was used by both the Arrow Cross Militia (i.e. the Hungarian fascists during WWII) and the ÁVH (the secret police from the Communist era.) Specially-constructed (and diabolical) torture cells in the basement probably made it convenient to keep from one regime to the next.
This book reflects upon the various elements that any Theory of Everything (ToE) would have to reconcile. A ToE is the holy grail of physics, a theory that would unify the various forces to explain the nature of the universe as we experience it. There have been many attempts to achieve a ToE, but it remains elusive. There is the mathematically beautiful and elegant string theory that suffers that one drawback of having no experimental support. There are those who have given up on a ToE in the sense that the term is normally used, suggesting that the desired degree of unification isn’t possible and that the desire to think it must be is just wishful thinking.
Probably the most useful piece of information about this book for one considering reading it is its readability. As works of popular science go, it’s more challenging that most (but not as difficult as, for example, Hawking’s “A Brief History of Time.”) [I have little doubt that those who read physics textbooks will find it a walk in the park.] It has few equations, and the mathematics it does present is elementary. However, it does explore quite complicated ideas. The book uses graphics to assist, mostly diagrams, but many of these require thoughtful consideration in their own right.
The organization of the book is based on an eightfold way (no relation to the Buddhist eightfold path) – that is, eight ingredients with which a ToE must be consistent. The nine chapters of the book begin with a brief opening chapter that sets up the rest of the book by discussing what a ToE would really explain (“everything” isn’t necessarily the answer in a strict meaning of that word), what the eight components are, how pre-scientific ToE’s operated, as well as introducing the recurring concept of algorithmic compressibility. (The importance of compressibility lies in the idea that in order to make the equations describing the universe more concise it’s necessary that the data describing the universe be “compressible” – i.e. have some underlying order.)
After the intro chapter, the eight subsequent chapters are logically arranged into the aforementioned eightfold way. These are: 1.) laws, 2.) initial conditions, 3.) the nature of forces and particles, 4.) the constants of nature, 5.) symmetries and the breaking thereof, 6.) organizing principles, 7.) Bias and selection effects, and 8.) to what extent mathematics is integral to the universe. Some of these elements (e.g. the laws and constants) we are told couldn’t vary by much and allow us to still exist. So, the question addressed in the book isn’t only how can science get to a theory that explains the existence of a stable(-ish) universe, but further one that can support complex and intelligent life. The chapters on symmetry breaking and selection effects are particularly relevant to this discussion.
One of the most interesting discussions is the last. Chapter nine, entitled: “Is ‘pi’ really in the sky?” discusses the question of how fundamental mathematics is to the universe. It’s long been a topic of scientific intrigue that there seems to be no particular reason for mathematics to be as effective as it is at describing the way the universe works. The discussion has resulted in a wide range of replies from those who say the success of mathematics is more illusory and limited than it appears to be, to those who believe the universe not only is written in mathematics but is math (see: the work of Max Tegmark.) That is, some say that there are parts of a stable universe that must be orderly enough to be described mathematically and those are the only parts we truly understand as of yet. Others say mathematics is the bedrock of the universe.
I enjoyed this book, and found the organizational approach helped a great deal in thinking about the problem. I doubt I grasped everything the author was trying to convey, but it was a book piled high with food for thought for anyone interested in thinking about the nature of the universe. If you’re interested in the grand-scale questions, I’d recommend this book. That said, there are more readable takes on the subject out there if one is looking for light pop science fare.
Quantum mechanics is so mystifying and baffling that I even misunderstood the title of Philip Ball’s book on the subject at first. I thought “Beyond Weird” was being used as is in, “twelve miles outside of Weird, almost all the way to ‘Incomprehensibly-bizarre-burg,’ is where one finds quantum theory.” About two-thirds of the way through the book, I realized that what he meant was that it’s time to move beyond thinking of the subject as one that – while it works well for the technologist’s practical purposes — is impossible to make any sense of with the human mind. [Perhaps the author wants to move “Beyond Weird” because the popular descriptions of quantum mechanics paint a picture that’s hard for the average reader to differentiate from magic – i.e. things popping in and out of existence inexplicably, things seeming to be in two irreconcilably different states at once, particles interacting instantaneously across light-years, etc. It all sounds like the stuff of a Harry Potter novel.] Who knows, maybe Ball meant “beyond weird” in both ways, like a quantum object is said to be both particle and a wave. (Though Ball weakly rejects that notion as untrue, though stating that sometimes it might as well be true.)
What is weird about the quantum world? To oversimplify, one can think of three interconnected conundrums. The first set of challenges I’ll group together as measurement problems. This includes both the fact that observing evidence of a quantum object cannot be done without influencing the nature of that evidence, and the fact that measuring one characteristic may limit the accuracy with which one can measure another. The second challenge, which derives from the first, is often called wave-particle duality, and it’s the fact that evidence of the same entity or object may sometimes suggest it’s more particle-like and other times that it behaves in a more wave-like fashion. [As is famously observed in double-slit experiments.] A third counter-intuitive fact is quantum entanglement, which is observed when one quantum object is observed and another that has become entangled with it instantaneously displays a corresponding measure. [The reader will note that, even after reading the book, I’m sure that I’m not describing these ideas in nearly sufficient precision to make them truly accurate. And still I’m writing convoluted sentences in attempt to give it my best shot to accuracy. And that’s just how confusing the topic is.]
Because the world behaves oddly at a quantum scale when compared to the world we see (the one that is governed by classical physics,) many paradigms have been established to try to convey what is happening to non-specialists. These models are necessarily oversimplifications. A lot of what Ball does is to try to wring a tiny bit more clarity out of what goes on at the quantum scale by describing in greater detail what is true, false, or under contention about what we “see” in quantum objects. This is how Ball comes up with chapter titles such as: “Quantum objects are neither wave nor particle, (but sometimes they might as well be.” Or, “Quantum particles aren’t in two states at once (but sometimes they might as well be.)” The first half of the book is mostly spent trying to clean up the public perception of quantum mechanics a little. Completely clarifying the subject isn’t yet possible. If it was, the value of such a volume would be minimal.
In the second half of the book, Ball gets into the influence of quantum mechanics on technology (and, in particular, tries to give the lay-reader some concept of what is being talked about when technologists talk of quantum computing.) He also explores some of the theories that are being pursued in the halls of academia to try to make sense of the parts of quantum mechanics that we can’t yet wrap our heads around. This includes the many-worlds interpretation in which each [“decision”] event results in a schism of the universe, such that Schrodinger’s — much misunderstood — cat isn’t in a super-position of alive and dead, but is alive in one branch universe and dead in the other. The book ends with a chapter entitled, “Can we get to the bottom of it?” There is hope that once we are able to look at the subject from the right angle, it will all clear up. Humans do have difficulty making sense of scales that are smaller or bigger than those of our daily experience, as well as time scales shorter than we can notice or longer than we live. We are viewing the world through frames, and those frames create – in a sense – blinders. Some scientists hope that one day we’ll be free of whatever frame (e.g. inability to experience all dimensions of space, time, or space-time) is limiting our capacity to understand the quantum.
As one would expect of this type of book, there are graphics, notes, and a bibliography.
My primary interest in quantum mechanics involves its implications (if any) for consciousness, and this is not a subject that Ball gets into in much detail beyond discussing Eugene Wigner’s views on the subject and touching on the ideas of David Bohm. Wigner was a Nobel Prize-winning scientist who believed that consciousness caused wave-form collapse. It should be noted that there are many scientists who feel that there is no need to think consciousness exerts any influence outside the skull of the conscious one. However, it remains an open question, and it’s not clear whether those who reject it have much better ideas or just have a knee-jerk reaction to that which might halt the onward march of the Copernican revolutionary norm. Though ideas at the interaction of consciousness and the quantum are not explored in great detail in Ball’s book, I still found it of use for edging a little closer to what goes on at a quantum scale than past popular science books have gotten me.
I’d recommend this book for the non-physicist who wants a little better grasp on quantum theory. It’s readable and helps separate wheat from chaff with respect to popular models of quantum mechanics.
Werner Heisenberg famously said, “Not only is the Universe stranger than we think, it is stranger than we can think.”
5.) Ancestor Simulation: The idea that we could be in a simulation isn’t only a staple of science fiction–e.g. The Matrix. It’s been given serious thought by thinkers who aren’t exactly on the lunatic fringe–most famously inventor /entrepreneur Elon Musk. The core of the argument goes like this. 1.) We are getting better and better at making simulations ourselves. 2.) At some point we will achieve a simulation indistinguishable from reality. 3.) If 2 is true, then it’s vastly more likely that we are already simulations because if it can be done, it probably already has been done many times over. (Thus, we’re more likely to be in one of the simulations than so-called “base reality.”)
4.) Mathematical Universe Hypothesis: Max Tegmark proposes that the universe may be–at its core–a mathematical structure, making us self-aware substructures. This may sound like a different way of stating the preceding hypothesis, but not necessarily. The simulation hypothesis suggests certain motivations of a simulation creator. MUH doesn’t require a creator or an objective. It could be the nature of reality at it’s most basic.
3.) A Holographic Universe: This idea sprang from thinking about what happens to the information when something falls into a black hole. The idea being that the information is trapped on the outside of the event horizon–i.e. information for a three dimensional entity stored in two dimensions. As physicists pondered this, some concluded that it might be that we are a projection of data, or–alternatively–much of what we see when we look out into space is.
2.) One of Myriad Universes: The idea that our universe is one of many (or an infinite number of) universes comes in several flavors and is a prediction of several theories widely given credence. In some versions, all the universes have different sets of laws and constants such that many flash in and out of existence and only a small proportion are capable of hosting life (but the math of infinity is weird and a small proportion of the infinite may also be infinite. I don’t know, I’m not a mathematician and the infinite never mattered in economics because ground zero is that everything is limited but desires.) This answers the Goldilocks zone issue nicely–i.e. we couldn’t exist if the equations and constants that govern our universe were very much different, but if there are many universes with many sets of laws then we just happen to be in one of the ones we can be in–hence, credulity remains unstrained. Other versions propose universes with the same laws such that there could be an infinite number of you living out lives that may be slightly different than yours (or–for that matter–in which you might be the Supreme Galactic Overlord.)
1.) Time is slowing: A couple Spanish physicists have suggested that the universe might not be expanding at an accelerating rate (as is the consensus view in physics,) but rather time may be slowing. This slowing would be anticipated to continue until one final moment is captured frozen in time–note: said point would be long after the Sun swallows the Earth.
In this book, physicist Max Tegmark makes an argument for the possibility of a reality in which the universe is a mathematical structure a theory that predicts a Level IV multiverse (i.e. one in which various universes all have different physical laws and aren’t spread out across one infinite space [i.e. not “side-by-side.”]) Nobel Laureate Eugene Wigner wrote a famous paper entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” The article describes one of the great mysteries of science, namely, how come mathematics describes our universe so well and with such high precision. Tegmark’s answer is because the universe is fundamentally mathematical—or at least he suspects it could be.
The first chapter serves as an introduction, setting the stage by considering the core question with which the book is concerned, “What is reality?” The book then proceeds in three parts. The first, Chapters 2 through 6, discuss the universe at the scale of the cosmos. Chapters two and three consider space and time and answer such questions as how big is the universe and where did everything come from. Chapter 4 explores many examples of mathematics’ “unreasonable effectiveness” in explaining our universe with respect to expansion and background radiation and the like (a more extensive discussion is in Ch. 10.) The fifth chapter investigates the big bang and our universe’s inflation. The last chapter in part one introduces the idea of multiverses and how the idea of multiple universes acts as an alternative explanation to prevailing notions in quantum physics (e.g. collapsing wave functions)—and, specifically, Tegmark describes the details of the first two of four models of the multiverse (i.e. the ones in which parallel universes are out there spread out across and infinite space), leaving the other two for the latter parts of the book.
Part two takes readers from the cosmological scale to the quantum scale, reflecting upon the nature of reality at the smallest scales—i.e. where the world gets weird. Chapter 7 is entitled “Cosmic Legos” and, as such, it describes the building blocks of our world as well as the oddities, anomalies, and counter-intuitive characteristics of the quantum realm. Chapter 8 brings in the Level III approach to multiverses and explains how it negates the need for waveform collapse that mainstream physics requires we accept (i.e. instead of a random outcome upon observation, both [or multiple] outcomes transpire as universes split.)
The final part is where Tegmark dives into his own theory. The first two parts having outlined what we know about the universe, and some of the major remaining mysteries left unexplained or unsubstantiated by current theories, Tegmark now makes his argument for why the Mathematical Universe Hypothesis (MUH) is at least as effective at explaining reality as any out there, and how it might eliminate some daunting mysteries.
Chapter 9 goes back to the topic of the first chapter, namely the nature of reality and the differences between our subjective internal reality, objective external reality, and a middling consensus reality. Chapter 10 also elaborates on the nature of reality, but this time by exploring mathematical and physical reality. Here he elaborates on how the universe behaves mathematically and explains the nature of mathematical structures—which is important as he is arguing the universe and everything in it may be one. Chapter 11 is entitled, “Is Time and Illusion?” and it proposes there is a block of space-time and our experience of time is an artifact of how we ride our world lines through it—in this view we are braids in space-time of the most complex kind observed. A lot of this chapter is about what we are and are not. Chapter 12 explains the Level IV multiverse (different laws for each universe) and what it does for us that the others do not. Chapter 13 is a bit different. It describes how we might destroy ourselves or die out, but that, it seems, is mostly a set up for a pep talk. You see, Tegmark has hypothesized a universe in which one might feel random and inconsequential, and so he wants to ensure the reader that that isn’t the case so that we don’t decide to plop down and watch the world burn.
While this book is about 4/5ths pop science physics book, the other 1/5th is a memoir of Tegmark’s trials and tribulations in coloring outside the lines with his science. All and all, I think this serves the book. The author avoids coming off as whiny in the way that scientists often do when writing about their challenges in obtaining funding and / or navigating a path to tenure that is sufficiently novel but not so heterodox as to be scandalous. There’s just enough to give you the feeling that he’s suffered for his science without making him seem ungrateful or like he has a martyr complex.
Graphics are presented throughout (photos, computer renderings, graphs, diagrams, etc.), and are essential because the book deals in complex concepts that aren’t easily translated from mathematics through text description and into a layman’s visualization. The book has endnotes to expand and clarify on points, some of which are mathematical—though not all. It also has recommended reading section to help the reader expand their understanding of the subject.
I enjoyed this book and found it to be loaded with food-for-thought. If Tegmark’s vision of the universe does prove to be meritorious, it will change our approach to the world. And, if not, it will make good fodder for sci-fi.
Why is there a universe, and why is it as it is? This is the question addressed by “The Grand Design.” These questions have been taken up in many ways by many disciplines in addition to science (e.g. mythology, religion, and philosophy), and science, itself, is continuously attempting to hone in on an explanation that is consistent with observed reality. Hawking and Mlodinow suggest that, for now, the leading contender is M-theory.
The authors advocate for M-theory, but also for the [relevant] notion of model-dependent realism. M-theory predicts that quantum fluctuations are causing a continuous spawning of new universes—each with its own laws of nature (or lack thereof.) Most of the bubble universes in this frothy multiverse don’t have staying power, but a few—like ours—are governed by laws that not only allow them to blossom, but also to spawn life. Besides the existence of a multiverse of universes governed by differing sets of laws, there are some other predictions of the M-theory model that remain to be proven. These include the existence of eleven dimensions, most of which are curled up and must be curled up in a certain way according to a set of laws and conditions. The theory also predicts that there will exist “objects” of various dimensionality up to nine. [Whether we will ever be able to test any of these predictions remains unclear.]
What’s this model-dependent realism bit? This is the idea that what we know of reality exists through models that connect observations to a set of rules. Within the limited space for which we have observations, there is no requirement that there be a solitary model or mapping between rules and observations. Because of this, there may be multiple theories. Physics has been long looking for a grand unified theory (GUT) or a Theory of Everything (TOE) that explains all the laws of the universe in one fell swoop. Hawking suggests that such a solitary theory may not be found given our limitations, and that we may have to exploit different theories for different situations. This belief is important because M-theory isn’t a unified theory but a grouping of theories that each work well in certain domains. Needless to say, this isn’t a particularly satisfying notion for the many physicists who are hoping for a more satisfying level of elegance.
The book consists of eight chapters. The first, entitled “The Mystery of Being,” is a brief description of the central question and an outline of why M-theory is proposed as the answer. Chapter two gives an overview of our evolving understanding of the laws that govern the universe, and sets up the important idea that the configuration of the universe is contingent upon the form of the laws governing it. The third chapter is where the authors argue for model-dependent realism, while discussing the arguments of realists and anti-realists as well. Chapter four describes alternate histories and the idea that the probability of an observation is dependent upon all possible histories that could have led to said observations. This bit of quantum strangeness is crucial to reconciling the central question. The next chapter describes the forces seen in our universe and considers attempts to unify the four forces (i.e. gravity, electromagnetism, the weak nuclear force, and the strong nuclear force) in a single theory that explains it all—a ToE. Chapter six discusses our universe with particular respect to its steady expansion that has allowed galaxies and solar systems to form. Chapter seven goes further, exploring the nature of a universe that could support the development and evolution of life. There are a wide variety of precise conditions needed to produce intelligent life. We live in a narrow band with respect to our distance from our star in which our type of life could be created. If the orbit of the sun was more elliptical or our axis wasn’t stabilized by a moon, we couldn’t be—and those features require laws that support them. The authors also examine how the chemistry of our universe is conducive to the development of complex life. The final chapter uses a discussion of a primitive computer game called “the game of life” to show how a model shapes reality as we know it. This grid-based game has only a few rules, and yet if there are more than a few pixels at the beginning, it becomes impossible for us to predict an outcome. With the complexity we see in our universe, this situation is vastly greater.
The book contains many graphics, mostly color, to clarify ideas that are difficult to comprehend via verbal description, or sometimes just to add levity. The only ancillary matter is a brief glossary of terms that come up in the book. There are no notes and no bibliography.
I found this book to be thought-provoking. However, I don’t know why it had the feel of a sales pitch. It repeats the theme of “M-theory is the best game in town” ad nauseam. This repetition draws attention to itself because the book fails to directly challenge those who critique M-theory in any depth or detail. It also fails to take on the question of how it is that M-theory might be taken from a purely theoretical construct to one that can be tested. (It makes falsifiable claims, but does that matter if we may never have a capacity to test those claims?) Those aspects wouldn’t be necessary if the book wasn’t making a pitch. [It felt like the book may have wanted to convince its pop-sci readers that–while they would only have a foggy idea of the why M-theory might have merit at the end of the book–they should remember that it’s the best–so that no funding gets cut from M-theory research and delivered to other lines of inquiry. In other words, the take-away sometimes feels like: “Stephen Hawking is super-smart, and he says ‘vote M-theory.’”]
I would recommend this book for those interested in the big picture of our universe’s existence, but as a neophyte it has made me want to read Woit’s “Not Even Wrong” or Smolin’s “The Trouble with Physics” just so that I’ll know what the critics are saying.
There are a lot of “The Science of…” books out there using science fiction as a means to explain science. It’s easy to see the appeal for both readers and writers. For one thing, it makes complex and technical subjects approachable and palatable. For another, it provides a series of examples with which most readers will already be familiar. Triggering memories of a beloved book can’t hurt sales.
This “Science of” book is a little different in that it uses a work of absurdist humor as its muse. [In the unlikely event that you’re unfamiliar with Douglas Adams’ “The Hitchhiker’s Guide” series, you can access a review here.]One may wonder whether the book delves into this absurdity by contemplating the efficiency of infinite improbability drives (faster than light engines that run on unlikelihood) or the value of melancholy robots. It does and it doesn’t. For the most part, it relates the wildest creations of Adam’s mind to the nearest core notion that has scientific merit. [Though it does have a chapter on babel fish (an ichthyologically-based universal translator), but that’s a technology that’s already in the works—just not in fish form, but rather a phone ap.]
For the most part, the book explores science and technologies that are popular themes in the pop science literature. These include: the existence of intelligent extraterrestrial life, artificial intelligence, the end of the world, the beginning of the world, time travel, teleportation, cows that don’t mind being eaten (presumed to take the form of lab-grown meat, and not talking cows who crave flame-broiling), the simulation hypothesis (as related to Adams’ Total Perspective Vortex), parallel worlds, improbability (only tangentially related to the infinite impossibility drive, i.e. focused on understanding extremely unlikely events), and the answer to the ultimate question. There is also a chapter that I would argue is more in the realm of philosophy (or theology, depending upon your stance) than science, and that’s the question of the existence of a god or gods. (This isn’t to say that the question of whether god is necessary to explain the existence of the universe and our existence in it isn’t a question for science. It is. But Hanlon mostly critiques the numerous arguments for why there must be a god, and it’s easy to see why because they provide a lot of quality comic fodder.)
The book contains no graphics, but they aren’t missed. It has a brief “further reading” section of other popular science books, but it isn’t annotated in the manner of a scholarly work. It is well-researched and highly readable, not only because it hitches its wagon to Adams’ work but also because it’s filled with interesting tidbits of information and its own humor. The book was published in 2005, and so it’s a little old, but most of the technologies it explores are so advanced that the book has aged well. (But if you want the latest on a particular aspect of science fiction-cum-science, you may want to look at a more recent book.)
I’d recommend this book for fans of “The Hitchhiker’s Guide to the Galaxy,” and those interested in popular science generally. (Having read the five books of Adams’ “Hitchhiker’s Guide” trilogy will make the book more entertaining—though it’s not essential to make sense of it.)
Consciousness remains a great mystery. While it has increasingly begun to look like consciousness is an output part of the brain, intriguing questions remain unanswered, and some of these unknowns are hard to reconcile with a materialist model (materialism says all phenomena are born out of matter.) It isn’t just pseudo-scientists and cranks that have a problem with the materialist approach. Major names in physics have pointed out that everything is not accounted for by a model that imagines consciousness as the computational product of the brain. Rosenblum and Kuttner address one such hiccup, the so-called Quantum Enigma that lends its name to the book. In brief, the quantum enigma reflects the fact that physical reality is created by observation. This may seem hard to believe, because it’s only been observed at the levels of the really small—i.e. primarily the atomic and subatomic, though the authors propose that there is theoretically nothing to limit the phenomenon to that level and experiments are being conducted at molecular level.
Rosenblum and Kuttner remind us that while the quantum world behaves oddly, quantum theory is exceptionally successful in scientific terms. Meaning that it has been validated by every single experimental inquiry, and the knowledge gained from quantum mechanics has made possible many of the advanced technologies that shape our world (laser, transistor, CCD, and MRI.) The oddness of Quantum Mechanics can be seen in several issues. One is the two-slit experiment in which atoms and photons behave like either a particle or a wave. Another is quantum entanglement, in which two atoms that have interacted become “wired” together such that changes in one are instantaneously reflected in the other—even if they have been separated by great distances.
The book is a bit repetitive, but perhaps this is necessary. People seem to have trouble grasping the nuances of the arguments being made, and this can lead to some wrong conclusions. For example, some people have leapt to the conclusion that ESP is supported by quantum entanglement, but the evidence doesn’t support the idea that one’s thoughts can control anything. Observation causes some physical reality to coalesce, but one has no influence over what reality displays itself. (In other words, with observation the wave function collapses and some state of being comes into existence from what was a field of probabilities.) Randomness remains. Physicists tell us that this is the problem with the idea of using quantum entanglement for instantaneous communications across light-years of space. A further example of a nuance that is hard to grasp is the notion that quantum probability doesn’t describe the likelihood an atom is a certain place, but rather it describes the likelihood you’ll find it there (and that that is a distinction with a difference.)
One may be wondering how consciousness is central the issue. If a non-intelligent entity observed, would the wave forms collapse? Consciousness doesn’t necessarily equate to intelligence as we know it. Consciousness can be thought of as merely the ability to observe and recognize significance in what is observed. So a thermostat is a very primitive form of consciousness. However, the authors do outline why a robotic observer wouldn’t end the controversy.
I found “Quantum Enigma” to be readable despite the challenging subject being explained. The authors to a good job of both describing the relevant phenomenon in terms the average person could understand (Ch.2 though which doesn’t reflect reality) before going on to explain the experiments in which the phenomena is actually observed (i.e. Ch. 7.) The authors use simple line drawings as graphics as necessary as well as staged dialogues to help make the concept clear by anticipating objections and dealing with them as they come.
I’d recommend the book for those interested in the unresolved questions of science with respect to Quantum Mechanics. In particular, there is the issue of consciousness—though it might not seem as central to the book’s discussion as the subtitle would lead one to believe. The last few chapters do deal in consciousness, though in a way that creates more questions than they answer. (It often feels like another summation of the strangeness of quantum mechanics, but that may be because the issues regarding consciousness remain so unclear. Furthermore, a lot of background is necessary to make sense of these complicated issues.)