Davies is . . . → Read More: Book Review: “Why Beliefs Matter: Reflections on the Nature of Science”]]> In his book Why Beliefs Matter: Reflections on the Nature of science, noted British mathematician E. Brian Davies surveys the sweeping landscape of modern philosophy of science and mathematics, with considerable skill and numerous thoughtful insights. Its closest analogue would be John Barrow’s 1992 book Pi in the Sky: Counting, Thinking and Being.

Davies is certainly qualified to write this book. He has published works in spectral theory, operator theory, quantum mechanics, and the philosophy of science. He served as the President of the London Mathematical Society from 2008-2009.

Some of Davies’ most intriguing comments relate to the nature of mathematics, which constitutes the whole of Chapter 3 and portions of several other chapters. After surveying the various philosophical schools of mathematics (constructivism, formalism, Godel’s result, etc), Davies focuses on Platonism, which he defines as the notion that “theorems are supposed to be true statements about timeless entities, and to be true whether or not they have ever been or will ever be formulated by human beings, and whether or not they have proofs.”

Davies points out that Platonism is implicitly assumed by many mathematicians. Famed mathematician Paul Erdos frequently referred to “God’s book” of the best possible proofs of all theorems. Roger Penrose argued that individual mathematicians can communicate because “each one [has] a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly.” Similarly, French mathematician Alain Connes declared

I maintain that mathematics has an object that is just as real as that of the sciences I mentioned above, but this object is not material, and it is located in neither space nor time. Nevertheless the object has an existence that is every bit as solid as external reality, and mathematicians bump up against it in somewhat the same way as one bumps into a material object in external reality.

But Davies is not so sure. He notes that “To assert that Platonism is obviously correct, and that to deny it is simply ridiculous, is to commit oneself to a quasi-religious world-view.” Davies adds that Platonism “diminishes the status of numerical analysis” and “has delayed the development of topics that focus on quantitative results rather than mere existence.” Producing efficient algorithms to discover mathematical objects might not be as glamorous as proving the existence of solutions of new problems, “but it is arguably just as important and certainly just as hard.” Further, Davies argues that Platonism “depersonalizes mathematics” and “diminishes the respect that we should have for the astonishing creativity of the most able mathematicians.”

Davies summarizes his discussion of Platonism in these terms:

Platonism is attractive to many pure mathematicians, but unsupported intuition is a bad basis for deciding about truth. … Platonism just replaces one mystery by another. Instead of wondering about how we are able to understand mathematics, one has to wonder how the Platonic realm can exert any influence on the physical world.

So what exactly is mathematics? After extended discussion, Davies in the end can offer no firm answers. Why, for example, do we believe in the consistency of mathematics (since we know from Godel’s theorem that this is an unattainable objective)? Davies answers in these pragmatic terms:

The answer is simply intuition. Over two thousand years of formal mathematics have revealed some important misconceptions, but these have been rectified and we feel confident that we can patch up any further problems that we might encounter in the future. There is no way of proving that this confidence is justified, but we have no choice but to rely provisionally on hard-won insights in every other sphere of investigation, and mathematics is no different.

He concludes:

The key to mathematical progress has been the possibility of recording our successes so that they may be transmitted to our descendants. After walking for over two thousand years down this one-way road, we have progressed a considerable distance. Every generation starts further down the road, and builds a new section using tools that are themselves becoming more efficient. We do not know where it will lead, but it is clear that we are not yet near the end.

Some additional observations on Davies’ book may be found in a thoughtful review by Gerald B. Folland in the April 2012 issue of the Notices of the American Mathematical Society.

A highly rewarding (and more technical) book to read in conjunction with Davies’ book is Jeremy Gray’s remarkable Plato’s Ghost: The Modernist Transformation of Mathematics. As described at Princeton University Press,

Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method–debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.

Both books resonate with Math Drudge’s commitment to thoughtful experimental mathematics.

Here is an excerpt from a review written by John D. Cook and published by the Mathematical Association of America . . . → Read More: Borwein’s book Convex Functions selected as Outstanding Academic Title]]> The new book Convex Functions by Jonathan M. Borwein and Jon D. Vanderwerff has been selected as one of the “Outstanding Academic Titles” for 2011 by Choice, the American Library Association’s library book review journal.

Here is an excerpt from a review written by John D. Cook and published by the Mathematical Association of America in their Mathematical Sciences Digital Library:

When mathematicians say a function is “nonlinear” they often mean that it is not necessarily linear. In this sense “nonlinear” is not an assumption but rather the absence of an assumption. To make progress in studying a nonlinear problem, we have to make some assumption about how a function departs from linearity. We have to replace an assumption of linearity with a weaker assumption that still retains enough structure to allow us to prove theorems. Often that weaker assumption is convexity. In large-scale optimization, for example, convexity is just the right assumption in order to retain many of the benefits of the linear theory while greatly increasing its scope of application. The study of convex functions has become more popular as nonlinear problems have become more popular and researchers realize they need to assume a particular kind of nonlinearity. …

Convex Functions tells a story from beginning to end. It starts with examples of convex functions in order to motivate the reader. It then progresses further and further into the theory, introducing special cases before proceeding to more general theory. The book closes with a retrospective, revisiting the differences between convex functions over finite and infinite dimensional spaces. The authors introduce a small amount of redundancy to make the book easier to read.

For example, in . . . → Read More: Merchants of Doubt]]> In a previous blog post, we addressed the perplexing phenomenon that whereas the scientific community years ago reached a strong consensus regarding the fact of global warming and the very likely human contribution to global warming, the public continues to believe that there is significant uncertainty and disagreement in the scientific community.

For example, in a recent poll, only 56% of Americans agreed that there is solid evidence of warming, and only 32% agreed that this warming can mostly be attributed to human actions. Similar results were found in 2009. For details, see 2010 Pew poll; 2009 Pew poll. Similarly, in the U.K., skepticism about global warming appears on the rise, according to a BBC News poll.

Many have noticed parallels with previous instances of public denial of scientific findings, beginning in the 1960s with denials that tobacco usage was harmful, continuing in the 1970s and 1980s with the deleterious effects of second-hand smoke, acid rain, ozone depletion and its cause in human usage of chlorofluorocarbons (CFCs), and, ultimately, global warming.

In a thoroughly researched recent book, Merchants of Doubt, authors Naomi Oreskes and Erik M. Conway point out that not only are there similarities between these “denialist” movements, but in fact that the same small group of people led the charge in each instance! The chief culprits are Fred Singer (former Director of the U.S. National Weather Satellite System), Fred Seitz (a solid-state physicist who had worked on various weapons programs, including the Manhattan Project), Robert Jastrow (a physicist involved in the Manhattan project) and Bill Nierenberg (a nuclear physicist and former Director of the Scripps Institution of Oceanography).

Each of these men were strongly pro-science and pro-technology, but also shared a distaste for environmentalism, which they felt was part of a slippery slope that would lead the U.S. to Soviet-style communism. In most cases they believed that the world of science had become corrupted with left-wing politics, and they strove to turn back the tide. They willingly accepted money from right-wing institutes and industrial sources, including tobacco companies and energy companies.

Unfortunately, in many cases they resorted to tactics utterly unbecoming of good scientists, including allowing their sponsors’ agendas to dictate their scientific conclusions, distorting scientific analysis and findings, and ignoring the strong consensus of other scientists. Sadly, they have been widely and repeatedly quoted by the press, which is always eager to entertain “opposing” viewpoints, even when those “opposing” viewpoints have long ago been refuted in the scientific literature.

Near the end of the book (pg. 262-265), the authors have some sobering advice for scientists. Here they address the question, “If the skeptical arguments pursued by our protagonists [Singer, Seitz, Jastrow, etc.] were not about science — if they were politics camouflaged as science — then why didn’t scientists recognize this, and say something? Why did the scientific community stand by while this was happening?”

In some cases, the authors conclude, individuals were reluctant to speak out by themselves, since they were a part of a large team. In other cases, pressures of project deadlines left little time for addressing nonsense in the news media. But in other cases, prominent individual scientists had been attacked by the denialists and their political allies, both in the press and even in congressional hearings. Some scientists even received death threats. Most of these scientists then reacted as predicted — they ceased making public comments. As the authors note, “Intimidation works.”

It is all too easy to just ignore such difficulties. Unfortunately, as the authors conclude, “garbage doesn’t just go away.” All scientists need to speak up more to address nonsense and pseudo-science. What’s more, “We all need a better understanding of what science really is, how to recognize real science when we see it, and how to separate it from the garbage.”

One article of interest along this line is a recent NY Times Op-ed piece by Gary Cutting. Cutting concludes:

[O]nce we have accepted the authority of a particular scientific discipline, we cannot consistently reject its conclusions. To adapt Schopenhauer’s famous remark about causality, science is not a taxi-cab that we can get in and out of whenever we like. Once we board the train of climate science, there is no alternative to taking it wherever it may go.

In this book, Brown recounts the rise of what is now known as the “postmodern interpretations of science” (PIS) or “sociology of scientific knowledge” (SSK) movement. In addition to pioneers Karl Popper and Thomas Kuhn (the . . . → Read More: Are science and mathematics socially constructed?]]> Richard C. Brown, Are Science and Mathematics Socially Constructed?: A Mathematician Encounters Postmodern Interpretations of Science, World Scientific, 2009.

In this book, Brown recounts the rise of what is now known as the “postmodern interpretations of science” (PIS) or “sociology of scientific knowledge” (SSK) movement. In addition to pioneers Karl Popper and Thomas Kuhn (the latter of whom Brown personally knew), the author describes the contributions of Berkeley philosopher Paul Feyerabend; Harry Collins and Trevor Pinch at Bath University; Steve Woolgar at Brunel; Michel Callon and Bruno Latour in Paris; a group of scholars at the University of Edinburgh; and numerous others.

Brown emphasizes that many of these writers start with a premise that is basically sound (and with which the present reviewer fully agrees): both science in general and mathematics in particular are unavoidably human enterprises, and are subject to all the varieties of human weakness. There are numerous instances of major errors in mathematical proofs (for example, in the original proof of Fermat’s Last Theorem by Andrew Wiles). Some scientific “discoveries”, such as “N”-rays and “cold fusion”, proved short-lived and vacuous (although some still hold hope that some form of cold fusion will prove real). Other scientific discoveries were founded or bolstered by experimental evidence that was later found to be flawed (such as the original observations of the bending of light around the sun, in tests of general relativity). In some instances, it appears that new theories initially prevailed as much because of the persuasiveness and personality of a leading researcher as the scientific merits of the claims. In this sense, mathematics and science are indeed “socially constructed”.

Some SSK writers, such as Karl Popper (who emphasized the value of highly falsifiable theories) and Thomas Kuhn (who analyzed the phenomenon of paradigm shift) have been quite influential and accepted, and their teachings (with some notable exceptions) have become part of the scientific enterprise. But many of the more recent SSK writers go further. They argue that claims of mathematics and science are strongly determined by the ideology and economic class of the actors, and in many, if not most, cases not because of compelling logic or experimental evidence. Thus nature cannot be interpreted independently of the theories and conceptual paradigms that scientists bring to their tasks. As a consequence, the vaunted objectivity of science, and the claimed progress of science through the years, are illusions, and science is merely an ideology on a par with various religions, the myths of native cultures, astrology, and even the “creation science” and “intelligent design” theories advanced by modern-day evangelicals.

Many of these writers emphasize the downside of technology and argue that mathematics and science are tools of western corporate capitalism and have been employed in the repression of women and minorities. SSK scholar Sandra Harding once described Newton’s Principia as a “rape manual”. Many have a rather low opinion of the scientific enterprise. SSK scholar Andrew Ross contemptuously dedicated one of his books to “all the science teachers I did not have; it could only have been written without them”.

Latour and Woolgar argue that laboratory procedures, experimental results and scientific theories should be regarded as rituals, no different from the rituals of some tribal shaman; they may be reported and analyzed, but certainly should not be believed by the “anthropologist”. They also argue, for instance, that the Thyrotropin Releasing Factor (TRF) hormone was “constructed” by Guillemin’s laboratory in 1977; that Robert Koch “constructed” the tuberculosis bacillus in 1882 — it had no real existence prior to that date; and, similarly, Pasteur’s microorganisms did not exist in a strict sense before Pasteur “discovered” them.

Until the 1990s, few mathematicians or scientists were even aware of the SSK movement, even though articles of the SSK genre were widely published in some leading humanities and social studies journals. During that decade, some scientists (Gross, Levitt and others) launched a counter-offensive. They highlighted errors of scientific fact and common sense, noted passages of meaningless technical jargon, and accused the SSK community of greatly exaggerating various scientific controversies. The resulting “science wars” came to a head in 1996 when NYU physicist Alan Sokal wrote the parody “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”. Sokal’s article included approving quotes from the writings of SSK scholars, profuse usage of erudite scientific jargon and flawed references to scientific theories, all wrapped in leftist political rhetoric. One sample paragraph is the following:

“In this way the infinite-dimensional invariance group erodes the distinction between the observer and observed; the pi of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone.”

Note, in addition to the gratuitous technical jargon, Sokal’s assertion that pi and G are not constants! In spite of these flaws (deliberately inserted by Sokal so that any knowledgeable scientist could spot them), the article was accepted and published in Social Text, a leading postmodern science studies journal (in fact in a special issue devoted to the “science wars”). When shortly afterward he exposed the hoax, the episode drew worldwide attention, including front-page coverage in the New York Times. Sokal emphasized that he composed the hoax out of a sincere attempt to steer the SSK community, many of whose ideals he shares, away from nonsense and irrelevance: “Theorizing about the social construction of reality‚ won’t help us find an effective treatment for AIDS or devise strategies for preventing global warming. Nor can we combat false ideas in history, sociology, economics, and politics if we reject the notions of truth and falsity.”

In the present book under review, mathematician Richard C. Brown briefly summarizes the history of the “science wars”, although he does not attempt to rehash these debates, referring the reader to books by Gross and Levitt, Sokal and Bricmont, and others. Instead, Brown’s objective, as stated in the Preface, is to examine in some detail the philosophical and political genesis of the SSK movement, and then discuss how these debates relate to the field of research mathematics. His account is often deeply personal, for example when he gives a first-hand account of the political clashes (which resulted in at least one death) at the Mathematical Research Center at the University of Wisconsin-Madison during the early 1970s.

Brown’s most interesting and most useful material is his discussion of how these issues relate to mathematics. This material begins in Chapter 10, which he appropriately titles, “The Deconstruction of Mathematics”, followed by chapters on “Epistemic Issues” and “The Fallibility of Conventionalism and Fallibilism”. Here he points out some significant errors of reasoning in some of the SSK literature, such as when philosopher Paul Ernest denies that mathematical proof “has the absolute and extra-human basis of certainty presumed by absolutism”. Brown points out, for instance, that Ernest evidently does not clearly distinguish between mathematics as a formal game based on axioms and mathematics as a tool that permits approximate applications in the real world. In any event, Brown points out that few, if any, professional mathematicians truly hold an “absolutist” view in Ernest’s sense — the results of mathematics are not necessarily tied to the real world, and the mathematical literature has numerous mistakes (Brown acknowledges that two of his own papers were later found to have significant errors). Brown further points out that the proof of a mathematical proposition from certain axioms can be “absolutely” valid, whether or not the axioms are consistent. In summary, he observes: “The fearmongering, therefore, concerning mathematics of supporters of SSK seems an exaggeration, and considering the real contradictions within their system, calling mathematics ‘fallible’ on the basis of Godel’s theorems is especially ill-conceived”. [pg. 234]. Brown concludes,

“Whatever the philosophical problems about the status of mathematical ‘truth’, settled areas of mathematics — the pureed kind found in undergraduate or graduate level textbooks as distinct from the frontier — appear more certain than the claims of almost any other human discipline, including the hard sciences such as physics or chemistry.” [pg. 235]….

“Like Ol’ Man River, mathematics just keeps rolling along and produces at an accelerating rate ’200,000 mathematical theorems of the traditional handcrafted variety … annually’. [quoting Davis and Hersh's book The Mathematical Experience, pg. 24]. Although sometimes proofs can be mistaken — sometimes spectacularly — and it is a matter of contention as to what exactly a ‘proof’ is — there is absolutely no doubt that the bulk of this output is correct (though probably uninteresting) mathematics.” [pg. 239].

In this reviewer’s view, Brown has made a valuable contribution to the philosophy of mathematics with this book. Even readers quite familiar with the “science wars” will find many new insights here into the history of these movements and their potential to further influence the scientific enterprise. The book is decidedly even-handed, offering as close to an objective view of both sides as one could hope for in a single book, even though the author, towards the end, clearly points out some of the weaknesses in the SSK reasoning. And Brown’s analysis of the interplay of these issues with mathematical research is very well done, and commands careful analysis. All of this is crafted very skillfully. It is clear that Brown has a real talent for writing to a general audience, which is unfortunately rare among practicing research mathematicians. The book is well worth the purchase price.

Both of the present bloggers have enjoyed Barrow’s previous works. Bailey was so enthralled with Barrow and Tipler’s 1988 book The Anthropic Cosmological Principle that he read every word of its 736 pages multiple times. Borwein (with his brother Peter) wrote a favorable review . . . → Read More: John D. Barrow’s “New Theories of Everything”]]> John D. Barrow, New Theories of Everything, Oxford University Press, 2007.

Both of the present bloggers have enjoyed Barrow’s previous works. Bailey was so enthralled with Barrow and Tipler’s 1988 book The Anthropic Cosmological Principle that he read every word of its 736 pages multiple times. Borwein (with his brother Peter) wrote a favorable review of Barrow’s 1992 book Pi in the Sky for the publication Science.

Barrow’s latest book, New Theories of Everything, does not disappoint. In this wide-ranging work, Barrow examines the notion of viewing science as the search for algorithmic compression of observed data. In other words, the best scientific theory is the one that explains the most data precisely in as crisp a manner as possible.

Barrow examines this proposition from many different angles, including physics, cosmology, mathematics, mathematical logic, computer science, biology, history, philosophy and religion. This material is so well organized, and so lucidly written, that readers are bound to learn many things of interest, no matter what their backgrounds. Advanced knowledge of these fields is not required (although it will help).

Here are a few excerpts from this fascinating work:

[pg 11] On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting – the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic [pg 12] behind the Universe’s properties that can be written down in finite form by human beings.

[pg 52] [quoting Freeman Dyson] Godel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we got into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.

[pg 113] [quoting Albert Einstein] however, we select from nature a complex [of phenomena] using the criterion of simplicity, in no case will its theoretical treatment turn out to be forever appropriate. … But I do not doubt that the day will come when that description [the general theory of relativity], too, will have to yield to another one, for reasons which at present we do not yet surmise. I believe that this process of deepening the theory has no limits.

[pg 121] There is no reason why life has to evolve in the Universe. Such complex step-by-step processes are not predictable because of their very sensitive dependence upon the starting conditions and upon subtle interactions between the evolving state and the ambient environment. All we can assert with confidence is a negative: if the constants of Nature were not within one percent or so of their observed values, then the basic buildings blocks of life would not exist in sufficient profusion in the Universe. Moreover, changes like this would affect the very stability of the elements and prevent the existence of the required elements rather than merely suppress their abundance.

[pg 138] Somehow the breathless world that we witness seems far removed from the timeless laws of Nature which govern the elementary particles and forces of Nature. The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws.

[pg 222] That is, the physicist likes to learn from particular illustrations of a general abstract concept. The mathematician, on the other hand, often eschews the particular in pursuit of the most abstract and general formulation possible. Although the mathematician may think from, or through, particular concrete examples in coming to appreciate the likely truth of very general statements, he will hide all those intuitive steps when he comes to present the conclusions of his thinking to outsiders. It presents the results of research as a hierarchy of definitions, theorems and proofs after the manner of Euclid; this minimizes unnecessary words but very effectively disguises the natural train of thought that led to the original results.

[pg 231] In practice, the intelligibility of the world amounts to the fact that we find it to be algorithmically compressible. We can replace sequences of facts and observational data by abbreviated statements which contain the same information content. These abbreviations we often call “laws of Nature.” If the world were not algorithmically compressible, then there would exist no simple laws of nature. Instead of using the law of gravitation to compute the orbits of the planets at whatever time in history we want to know them, we would have to keep precise records of the positions of the planets at all past times; yet this would still not help us one iota in predicting where they would be at any time in the future. This world is potentially and actually intelligible because at some level it is extensively algorithmically compressible. At root, this is why mathematics can work as a description of the physical world. It is the most [pg 232] expedient language that we have found in which to express those algorithmic compressions.

Carl Sagan, in his 1995 book The Demon-Haunted World issued this sober warning:

We’ve arranged a global civilization in which most crucial elements profoundly depend on science and technology. We have also . . . → Read More: Unscientific America]]> Review/synopsis of Unscientific America: How Scientific Illiteracy Threatens Our Future, by Chris Mooney and Sheril Kirschenbaum, Basic Books, NY, 2009:

Carl Sagan, in his 1995 book The Demon-Haunted World issued this sober warning:

We’ve arranged a global civilization in which most crucial elements profoundly depend on science and technology. We have also arranged things so that almost no one understands science and technology. This is a prescription for disaster. We might get away with it for a while, but sooner or later this combustible mixture of ignorance and power is going to blow up in our faces.

As Mooney and Kirschenbaum observe, “At present we’re marching steadily toward that outcome.”

The authors note that on the plus side, Americans are surrounded by technology and see first-hand the fruits of scientific research. The Internet and other information technologies have made it much easier to disseminate accurate scientific information. But this same technology also makes it possible to disseminate all sorts of nonsense, and to amplify the fallacy-ridden writings of the creation science and global warming denial communities.

In other arenas, the authors lament that only minor progress has been made. Long gone are the glory days of Sagan’s “Cosmos” series on PBS. Nowadays Hollywood and network TV mostly avoid scientists and scientific themes, and when they do deal with a scientific theme or scientific undercurrent, they prefer paranormal topics (UFOs, time travel, etc) and frequently depict scientists as villains, geeks, and jerks. There are a few bright spots — Numbers, a few of the CSI epsiodes and others — but by and large the Hollywood/TV picture is pretty discouraging.

Mooney and Kirschenbaum criticize writers such as Sam Harris, Christopher Hitchens, Richard Dawkins and Daniel Dennett for going out of their way to attack religious belief and believers. In the authors’ opinion,

If the goal is to create an America more friendly toward science and reason, the combativeness of the New Atheists is strongly counterproductive. If anything, they work in ironic combination with their dire enemies, the anti-science conservative Christians who populate the creation science and intelligent design movements, to ensure we’ll continue to be polarized over subjects like the teaching of evolution when we don’t have to be.

One of the more interesting parts of this book is the authors’ account of how Carl Sagan, who arguably was the most successful communicator of science in history, was himself snubbed by the scientific establishment for his efforts. His 1992 nomination to the National Academy of Sciences was rejected, mainly on grounds of his public endeavors. The message was clear to any current or aspiring scientist: engage the public at the peril of your career.

To address these problems, Mooney and Kirschenbaum call for nothing less than a fundamental restructuring of the scientific establishment. First of all, scientists themselves must squarely face the abysmal job they have done in communicating their research to the public. They cannot rely on advanced technology such as Internet blogs here, since these same technologies are just as effective in spreading nonsense. Instead, training in and encouragement for the dissemination of results to the public must be incorporated into the curriculum of every scientific field.

Mooney and Kirschenbaum further argue that society must rethink the financial reward system for those who pursue scientific careers. As a recent blog entry cited in the book laments, “Had I to do it over again, I would not choose a PhD, at least not a general science degree. I would have gone to medical or law school, or perhaps a PhD in public health (a very rapidly growing field). At least after training in these programs your skill set is clearly defined, and you can be confident that you will have a job post-graduation”.

In their conclusion, the authors quote C.P. Snow, “We require a common culture in which science is an essential component. Otherwise we shall never see the possibilities, either for evil or good.”

See also Chris Mooney’s recent essay at HuffingtonPost.com.