Wain notes the successful Mathematikum in Giessen, Germany, which opened in 2002 and now attracts 150,000 visitors per year, and the Museum of Mathematics in New York City, which is slated to open . . . → Read More: Researchers seek UK home for mathematics museum]]> Geoff Wain, a mathematics educator at Leeds University, is promoting an initiative to organize a museum of mathematics in the U.K.

Wain notes the successful Mathematikum in Giessen, Germany, which opened in 2002 and now attracts 150,000 visitors per year, and the Museum of Mathematics in New York City, which is slated to open later this year. He asks “Where would you go to find out about mathematics? … There’s absolutely nowhere in this country. It’s very sad.”

Last week Wain and some supporters gathered at King’s College to discuss plans for the museum, which is tentatively known as “MathWorldUK.” They hope to provide something for persons of all ages, with a strong focus on interactivity and hands-on experimentation. Wain notes, “mathematics as a theoretical thing with no concrete side to it is what can kill it off, I think. … Having things you can actually do is really important.”

For additional details see this New Scientist article, from which the above notes were excerpted in part.

Here is an excerpt from a review written by John D. Cook and published by the Mathematical Association of America . . . → Read More: Borweins’ 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.

As the Crafoord Prize website . . . → Read More: Jean Bourgain and Terence Tao receive Crafoord Prize in mathematics]]> The Royal Swedish Academy of Sciences has awarded the 2012 Crafoord Prize to Jean Bourgain (Institute for Advanced Study, Princeton, USA) and Terence Tao (U.C. Los Angeles) “for their brilliant and groundbreaking work in harmonic analysis, partial differential equations, ergodic theory, number theory, combinatorics, functional analysis and theoretical computer science”.

As the Crafoord Prize website explains,

This year´s Crafoord Prize Laureates have solved an impressive number of important problems in mathematics. Their deep mathematical erudition and exceptional problem-solving ability have enabled them to discover many new and fruitful connections and to make fundamental contributions to current research in several branches of mathematics.

On their own and jointly with others, Jean Bourgain and Terence Tao have made important contributions to many fields of mathematics — from number theory to the theory of non-linear waves. The majority of their most fundamental results are in the field of mathematical analysis. They have developed and used the toolbox of analysis in groundbreaking and surprising ways. Their ability to change perspective and view problems from new angles has led to many remarkable insights, attracting a great deal of attention among researchers worldwide.

Bourgain and Tao will receive an award of SEK 4,000,000 (approximately USD 587,752) in a ceremony to be held in Lund, Sweden on 15 May 2012 hosted by the King and Queen of Sweden.

Moore’s Law stems from a seminal 1965 article by Intel founder Gordon Moore. He wrote

The complexity for minimum component costs has increased at a rate of . . . → Read More: Moore’s Law and the future of science and mathematics]]> Introduction

What do iPhones, Twitter, Netflix, cleaner cities, safer cars, state-of-the-art environmental management and modern medical diagnostics have in common? They all are made possible by Moore’s Law.

Moore’s Law stems from a seminal 1965 article by Intel founder Gordon Moore. He wrote

The complexity for minimum component costs has increased at a rate of roughly a factor of two per year. … Certainly over the short term this rate can be expected to continue, if not to increase. Over the longer term, the rate of increase is a bit more uncertain, although there is no reason to believe it will not remain nearly constant for at least 10 years. That means by 1975, the number of components per integrated circuit for minimum cost will be 65,000.

Moore noted that in 1965 engineering advances were enabling a doubling in semiconductor density every 12 months, but this rate was later modified to roughly 18 months. In any event, Moore’s Law has now continued unabated for 45 years, defying several confident predictions that it would soon come to a halt, and represents a sustained exponential rate of progress that is without peer in the history of human technology. Here is a graph of Moore’s Law, shown with the transistor count of various computer processors (courtesy Wikimedia):

Present status of Moore’s Law

At the present time, researchers are struggling to keep Moore’s Law on track. Processor clock rates have stalled, as chip designers have struggled to control energy costs and heat dissipation, but the industry’s response has been straightforward — simply increase the number of processor “cores” on a single chip, together with associated cache memory, so that aggregate performance continues to track or exceed Moore’s Law projections.

The capacity of leading-edge DRAM main memory chips continues to advance apace with Moore’s Law. The current state of the art in computer memory devices is a 3-D design, which will be jointly produced by IBM and Micron Technology, according to a December 2011 announcement from IBM.

At the present time, the best bet for the future of Moore’s Law are nanotubes — submicroscopic tubes of carbon atoms that have remarkable properties. According to a recent NY Times article, Stanford researchers have created prototype electronic devices by first growing billions of carbon nanotubes on a quartz surface, then coating them with an extremely fine layer of gold atoms, then using a piece of tape (literally!) to pick them up and transfer them to a silicon wafer. They believe that commercial devices could be made with these components as early as 2017.

Moore’s Law in science and mathematics

So what does this mean for researchers in science and mathematics?

Plenty, as it turns out. A scientific laboratory typically uses hundreds of high-precision devices that rely crucially on electronic designs, and with each step of Moore’s Law, these devices become ever cheaper and more powerful. One prominent case is DNA sequencers. When scientists first completed sequencing a human genome in 2001, at a cost of several hundred million U.S. dollars, observers were jubilant at the advances in equipment that had made this achievement possible. Today, only ten years later, researchers expect to reduce this cost to only $1000 within two years, according to a recent NY Times report, and genome sequencing may well become a standard part of medical practice. This astounding improvement is even faster than Moore’s Law!

Applied mathematicians have benefited from Moore’s Law in the form of scientific supercomputers, which typically employ hundreds of thousands of state-of-the-art components. These systems are used for tasks such as climate modeling, product design and biological structure calculations. As of the current date (1 Jan 2012), the world’s most powerful system is a Japanese supercomputer that recently ran the industry-standard Linpack benchmark test at over 10 “petaflops,” or, in other words, 10 quadrillion floating-point operations per second.

Here is a graph of the Linpack performance of world’s leading-edge system over the time period 1993-2011 (data courtesy Top 500 site). Note that over this 18-year period, the performance of the world’s #1 system has advanced more than five orders of magnitude. The current #1 system is more powerful than the sum of the world’s top 500 supercomputers just four years ago.

Pure mathematicians have been a relative latecomer to the world of high-performance computing. The present bloggers well remember the era, just a decade or two ago, when the prevailing opinion in the community was that “real mathematicians don’t compute.” But thanks to a new generation of mathematical software tools, not to mention the ingenuity of thousands of young, computer-savvy mathematicians worldwide, remarkable progress has been achieved in this arena as well (see our 2011 AMS Notices article on exploratory experimentation in mathematics).

For example, in 1963 Daniel Shanks, who himself had calculated pi to 100,000 digits, declared that computing one billion digits would be “forever impossible.” Yet this level was reached in 1989. In 1989, famous British physicist Roger Penrose, in the first edition of his best-selling book The Emperor’s New Mind, declared that humankind likely will never know if a string of ten consecutive sevens occurs in the decimal expansion of pi. Yet this was found just eight years later, in 1997.

Computers are certainly being used for more than just computing and analyzing digits of pi. For example, in 2003 the American mathematician Thomas Hales completed a computer-based proof of Kepler’s conjecture, namely the long-hypothesized fact that the simple way the grocer stacks oranges is in fact the optimal packing for equal-diameter spheres. Many other examples could be cited.

Future prospects

What does the future hold? Assuming that Moore’s Law continues unabated at approximately the same rate as the present, and that obstacles in areas such as power management and system software can be overcome, we will see, by the year 2021, large-scale supercomputers that are 1000 times more powerful and capacious than today’s state-of-the-art systems — “exaflops” computers (see NAS Report). Applied mathematicians eagerly await these systems for calculations, such as advanced climate models, that cannot be done on today’s systems.

Pure mathematicians will use these systems as well to intuit patterns, compute integrals, search the space of mathematical identities, and solve intricate symbolic equations. If, as one of us discussed in a recent Conversation article, such facilities can be combined with machine intelligence, such as a variation of the hardware and software that enabled an IBM system to defeat the top human contestants in the North American TV game show Jeopardy! (see NY Times report), we may see a qualitative advance in mathematical discovery and even theory formation. Only time will tell for sure, but it is not a big leap to imagine that within the next ten years tailored and massively more powerful versions of Siri (Apple’s new iPhone assistant) will be an integral part of mathematics, not to mention medicine, law and  just about every other part of human life.

Some observers, such as those in the Singularity movement, are even more expansive, predicting a time just a few decades hence when technology will advance so fast that at the present time we cannot possibly conceive or predict the outcome. The present bloggers do not subscribe to such optimistic projections, but even if more conservative predictions are realized, it is clear that the digital future looks very bright indeed. We will likely look back at the present day with the same technological disdain with which we currently view the 1960s.

One of the most common refrains in news and commentaries, from both the religious right and the secular left, is that modern society is in sharp decline: skyrocketing rates of crime, divorce, teenage sex, teenage births, drug abuse . . . → Read More: The great decline of Western society: What are the facts?]]> [This is a repost of an article that appeared on 21 Dec 2011 at Science Meets Religion.]

One of the most common refrains in news and commentaries, from both the religious right and the secular left, is that modern society is in sharp decline: skyrocketing rates of crime, divorce, teenage sex, teenage births, drug abuse and war (especially in the 20th century). There is also concern that modern society’s focus on science and technology is leading to a widening of the gap in living conditions and educational opportunities between prosperous first-world nations and impoverished third-world nations.

The religious right blames science in general and evolution in particular for these ills. One display at the Creation Museum in Petersburg, Kentucky, warning of the consequences of a scientific worldview, features photos of a nuclear explosion, a collection of skulls from the Holocaust, and what may be a photo of a woman undergoing an abortion. Another exhibit displays news clips about birth control, abortion, divorce, mass murder, stem cells and war.

Not to be out-done, numerous secular writers blame religion. Christopher Hitchens declares that religion is “violent, irrational, intolerant, allied to racism, tribalism, and bigotry, invested in ignorance and hostile to free inquiry, contemptuous of women and coercive toward children” [Hitchens2007, pg. 56]. These writers also note the numerous wars in Europe and elsewhere that have been fought in the name of religion [Atheists]. In a related but strange twist, historians Will and Ariel Durant question whether progress is real [Durant1968], and “critical theorists” blame the Enlightenment and scientific advances of past centuries for the disasters of the 20th century [Pinker2011b, pg. 133].

So what are the facts here? Who is to blame?

There are certainly some aspects of present-day society that qualify as instances of moral decline. For example, while the Internet has been huge benefit to society worldwide, it has unleashed tidal waves of pornography, fraud and “Internet addiction” that show no sign of abating. One other area of general concern in modern society is the rising percentage of children born to unmarried women. In the U.S., this percentage has risen from just 10.7% in 1970 to 18.4% in 1980, to 28% in 1990, to 33.2% in 2000, and to 41% in 2010 [Health2010]. Some have said that high rates of unwed parentage are an inevitable feature of a highly technological, urban, and secular society. But this claim is countered by Japan, which is certainly highly technological, urban and secular, but where only 2% of children are born to unwed mothers [Ventura2009].

But beyond items such as this, it is difficult to identify any clear instances of significant decline in morality or, even more broadly, in overall standards of living. Here are some of the latest statistics:

1. Crime. It is widely believed that crime, from minor burglary to serious violent offenses, is growing worse every year. Yet the facts point in quite the opposite direction. In the U.S., in spite of the worst economic slowdown since the Great Depression, with millions out of work and many others in desperate economic straits, violent crime in 2010 actually declined by 5.5% from the 2009 level, and the 2009 level declined by a similar percentage from the 2008 level. In fact, the 2010 U.S. crime rates are the lowest in 40 years, and are down by more than a factor of two since peaking in 1994 [Oppel2011].
2. Divorce. Another commonly mentioned ill is a soaring rate of divorce. But in the U.S., the divorce rate per thousand people peaked in 1981, and has declined ever since. Indeed, the divorce rate in 2005 (3.6 divorces per 1000 population) was the lowest since 1970. It is true that the marriage rate has also been declining, but even if one computes the number of divorces per married couples, here too the rate has fallen, from a peak of 22.8 divorces per 1,000 married couples in 1979, to only 16.7 in 2005 [Stevenson2007].
3. Teenage sex and birth. A 2010 report from the U.S. National Center for Health Statistics reported that the percentage of American high school students who have had sex (2007 data) is significantly lower than in 1991 (47.8% versus 54.1%) [Parker2009]. Similarly, in 2010 the U.S. teen birth rate fell to 34.3 births per 1000 teens, a record low. This is a nine-point drop from 2009 and a whopping 28-point drop since 1991, when the rate was 62 births per 1000 teens [CDC2011].
4. Abortion. The number of abortions in the U.S. peaked in 1991 at 24 per 1000 U.S. women aged 15-44, but has dropped since then to 16.1 [CDC2008].
5. Teenage alcohol, cigarette and drug use. According to a 2011 report by University of Michigan researchers, only 12.7% of 8th graders reported any alcohol usage in the prior 30 days, which is down by nearly half from the 25.1% level in 1991. Among 10th graders, the figure is down from 42.8% in 1991 to 27.2% in 2011, and among 12th graders, it is down from 54% in 1991 to 40% in 2011. Even more dramatic declines have been seen in cigarette, cocaine and crack usage. One area of concern is marijuana usage: in 2011, 7.2% of 8th graders, 17.6% of 10th graders, and 22.6% of 12th graders reported some usage in the previous 30 days, which figures are roughly the same as in 2003. But even these figures are down from 1997 when these rates peaked [Johnston2011].
6. War. It is widely believed that recent years have seen more violence and deaths due to warfare than ever before. Surely the 20th century, with tens of millions killed in two horrific world wars, must be the worst ever? But if we normalize these statistics by population, then beyond the “blips” of the two world wars there is an unmistakable trend of decline. According to Harvard scholar Steven Pinker, “violence has been in decline over long stretches of time, and we may be living in the most peaceful time in our species’ existence. … [I]t’s a persistent historical development, visible on scales from millennia to years, from the waging of wars and perpetration of genocides to the spanking of children and the treatment of animals.” [Pinker2011a; Pinker2011b]. See also the previous blog.
7. Religious belief and participation. There is a widespread perception that church attendance and religious belief have significantly declined during recent decades. Indeed, according to a 2010 study, Americans 18-29 years of age are less likely to be affiliated with a particular faith than the older generation. But in other ways they remain fairly traditional. Beliefs in life after death, for instance, closely resemble those of the older generation, and more Americans 18-29 engage in daily prayer today than 20 years ago [Pew2010]. Similarly, a 1997 study of American research scientists (physicists, biologists and mathematicians) revealed that 40% of these scientists believe in God, a figure not significantly different than in 1916 [Angier1997].
8. Worldwide living conditions. There is widespread concern that our global economy, while lifting up some, has condemned hundreds of millions of others to extreme poverty, particularly in light of the current worldwide economic recession. But according to the latest U.N. report (2010), its Human Development Index rose in all but three nations (Democratic Republic of the Congo, Zambia and Zimbabwe) from 1970 to 2010. For example, worldwide average income per capita in 2010 was $10,760, which is twice the inflation-adjusted level in 1970. Over this 40-year period, income per capita rose in all but six nations worldwide, with increases averaging 184% in developing countries and 126% in developed countries [UN2010].

With regards to the last item, Matt Ridley asks us to imagine a better-off-than-average family somewhere in Western Europe or Eastern North America in 1800 [Ridley2010, pg. 13]:

The family is gathering around the hearth in the simple timber-framed house. Father reads aloud from the Bible while mother prepares to dish out a stew of beef and onions. The baby boy is being comforted by one of his sisters and the eldest lad is pouring water from a pitcher into the earthenware mugs on the table. His elder sister is feeding the horse in the stable. Outside there is no noise of traffic, there are no drug dealers and neither dioxins nor radioactive fall-out have been found in the cow’s milk. All is tranquil; a bird sings outside the window.

Oh please! Though this is one of the better-off families in the village, father’s Scripture reading is interrupted by a bronchitic cough that presages the pneumonia that will kill him at 53 — not helped by the wood smoke of the fire. (He is lucky: life expectancy even in England was less than 40 in 1800.) The baby will die of the smallpox that is now causing him to cry; his sister will soon be the chattel of a drunken husband. The water the son is pouring tastes of the cows that drink from the brook. Toothache tortures the mother. The neighbour’s lodger is getting the other girl pregnant in the hayshed even now and her child will be sent to an orphanage. The stew is grey and gristly yet meat is a rare change from gruel; there is no fruit or salad at this season. It is eaten with a wooden spoon from a wooden bowl. Candles cost too much, so firelight is all there is to see by. Nobody in the family has ever seen a play, painted a picture or heard a piano. School is a few years of dull Latin taught by a bigoted martinet at the vicarage. Father visited the city once, but the travel cost him a week’s wages and the others have never travelled more than fifteen miles from home. Each daughter owns two wool dresses, two linen shirts and one pair of shoes. Father’s jacket cost him a month’s wages but is now infested with lice. The children sleep two to a bed on straw mattresses on the floor. As for the bird outside the window, tomorrow it will be trapped and eaten by the boy.

Conclusions

In short, there is absolutely no substance to the claim that science in general or evolution in particular is responsible for the perceived declined in morality or living standards. And there is absolutely no substance to the claim that religion is responsible for this perceived decline either. This “decline,” by all objective measures, simply does not exist, certainly not to the extent that it is often pictured in commentary of the left or right. It is a regrettable consequence of the media’s fascination with bad news.

Recently there was an excellent, and much read, article on The Conversation entitled There’s no place for pseudo-scientific chiropractic in Australian universities which made the case against chiropractic “medicine” all too well.

Dodgy doctors are dodgy wherever they . . . → Read More: Chiropractic: crackers now, and crackers way back when]]> [This is a repost of an article that appeared on 23 Dec 2011 in The Conversation].

Recently there was an excellent, and much read, article on The Conversation entitled There’s no place for pseudo-scientific chiropractic in Australian universities which made the case against chiropractic “medicine” all too well.

Dodgy doctors are dodgy wherever they live and are trained. Despite the value of a good and not-too-vigorous back massage (or perhaps some mild acupuncture), neither alternative medicine nor chiropractic make the grade as health sciences.

The article, by John Dwyer of the University of New South Wales, made me reflect that in 1998 Dr Bessie Borwein – whom among her many other attributes is my mother – had been involved in a similar, and largely successful battle to stop such bogus or unvetted programs becoming ensconced in Canadian Universities.

A quick web search reveals several websites – including Wikipedia’s Chiropractic in Canada entry – written largely by the chiropractic community. This makes make it clear that, even now, only one legitimate (if small) university (Trois Riviere in Quebec) hosts a chiropractic program. To put it mildly, there has been very little buy-in from the serious medical and health science community in Canada.

It made me a bit depressed to think a battle won in Canada more than a decade ago is only just being fought now in Australia and elsewhere. Sadly, this is often the case, and often the facts do not change when the dates and places do. Perhaps vehicles such as The Conversation and related modern electronic journalism can reduce the frequency of such events.

So, in that spirit, let me reproduce my mother’s letter – dated April 17, 1998 – when she was an Assistant Dean of Research at the University of Western Ontario – one of Canada’s top medical schools.

Earlier this month, a large group of serious medicos directly criticised a current attempt to set up a programme at Central Queensland University to add to those at RMIT, Macquarie and Murdoch.

All of these institutions presumably chose money over principle. Perhaps my mother’s succinct summary can help them reconsider.

This book is about . . . → Read More: The remarkable decline of violence]]> Many will greet the title of this piece with considerable skepticism — in this day and age how could one possibly talk about a decline in violence? Yet it is true. Harvard psychologist Steven Pinker begins his new book The Better Angels of Our Nature: Why Violence Has Declined as follows:

This book is about what may be the most important thing that has ever happened in human history. Believe it or not – and I know that most people do not – violence has declined over long stretches of time, and today we may be living in the most peaceable era in our species’ existence. The decline, to be sure, has not been smooth; it has not brought violence down to zero; and it is not guaranteed to continue. But it is an unmistakable development, visible on scales from millennia to years, from the waging of wars to the spanking of children.

Pinker is hardly a devout religious believer — his review of biblical violence, for instance, is openly irreverent. But from another point of view, Pinker’s book is deeply inspiring: it is a stunning confirmation of the fundamental good in human nature, a chronicle of how the “better angels of our nature” are slowly overcoming the bad. His work also constitutes a striking refutation of those writers, both from the academic left and the religious right, who have decried our time as irredeemably fallen from the “good old days” (decades, centuries or millennia ago) when the human race was presumably more gentle and civilized.

Pinker’s book is not an easy read. He meticulously documents his claims with extensive charts, graphs and footnotes. He invokes relatively sophisticated concepts such as “power-law distributions” with aplomb. He does not bat an eyelash while describing the revolting instruments of torture and execution used in medieval “Christian” Europe. He documents the violent practices of many native peoples. But he has a clear purpose in all of this: to demonstrate in no uncertain terms the fact that the human society is slowing become more averse to violence. He also attempts to understand this phenomenon, so that we can hasten its progress, although it is clear that he does not have all the answers.

Here are some brief highlights from Pinker’s book:

1. Ancient primitive societies were hardly the Edenic paradises that they are often pictured to be. Careful analyses of skeletons from archaeological sites have confirmed that roughly 15% of these individuals died a violent death. Among more modern pre-state societies, similar analyses show 25% violent death. By contrast, even in medieval Europe, with the bloody wars of religion in the 17th century, the rate of death was only 2%, and this rate fell to less than 1 percent in the 20th (yes, even counting WWI and WWII).
2. In a list of the 21 “Worst Things People Have Done to Each Other,” which ranks the wars and massacres with the highest death tolls, the 20th century indeed is well-represented: WWII tops the list, following closely by the Chinese cultural revolution. But when these episodes are normalized by world population at the time, then WWII drops to #9. Number 1 on the normalized list is the little-known 8th century An Lushan Revolt, which resulted in the loss of 2/3 of the Chinese empire’s population.
3. The “long peace” among major powers since WWII has confounded the predictions of many that large-scale war is inevitable in our time. Pinker emphasizes that perhaps the most interesting post-WWII statistic of all is zero: Zero is the number of times that nuclear weapons have been used in combat; zero is the number of times that the two Cold War superpowers fought each other on the battlefield; zero is the number of times that any of the top 40 great powers have fought each other (since 1953); zero is the number of wars fought between any European nation (prior to this there were an average of two armed conflicts per year going back to at least 1400); zero is the number of developed countries that have expanded their territory by conquering another country; and zero is the number of internationally recognized states that have gone out of existence through conquest.
4. While the modern world, especially in the West, agonizes over even remote chances of harm to today’s children, for much of human history little ones faced a much greater risk: infanticide. Anthropologist Laila Williamson found until very recently, between 10 and 15 percent of all babies were killed shortly after birth. By contrast, in 2007 just 221 infants were killed in the U.S. out of 4.3 million births, which is a reduction from the historical average by a factor of 2000 to 3000.
5. The U.S. crime rate rose during the 1960s, 1970s and 1980s until about 1992, but has declined since then. By 2010, the homicide rate had fallen to just 4.8 per 100,000 residents, down by more than a factor of two from its peak. Other measures of violent crime, and even property crime, have followed in unison. In the wake of the 2008-2011 recession, with millions out of work, losing homes and in desperate economic straits, crime rates have fallen even further, confounding criminologists who had predicted sharp increases.
6. Pinker points out that by today’s standards, even great statesmen of recent history would be considered hopelessly bigoted and violence-happy. Theodore Roosevelt excused the decimation of Native Americans as necessary to prevent the continent from becoming a “game preserve for squalid savages.” Woodrow Wilson blocked black students from Princeton, praised the Ku Klux Klan, and declared that any hyphenated American “carries a dagger that he is ready to plunge into the vitals of this Republic.” Franklin Roosevelt jailed 100,000 U.S. citizens in a concentration camp because they were of the Japanese race. And Winston Churchill declared that the Aryan stock “is bound to triumph,” and that India is “a beastly people with a beastly religion.”

What is behind such changes? One major factor is the rise of large, effective systems of democratic government, which Pinker terms the “Leviathan” effect, named after the title of a book by 17th century philosopher Thomas Hobbes. Others include the Civilizing Effect and the Pacifying Effect, wherein people have begun to see other societies as cooperating partners capable of trade and mutual enrichment, instead of loathsome aliens that must be eliminated. It also seems that society as a whole, perhaps through improved education, is better able to see the world from the eyes of others. Whatever the reason, it is a trend that we should cherish and understand better.

Pinker’s conclusion resonates with both hope and gratitude:

For all the tribulations in our lives, for all the troubles that remain in the world, the decline of violence is an accomplishment we can savor, and an impetus to cherish the forces of civilization and enlightenment that made it possible.

The piece was originally published at the Science-Meets-Religion blog. See also the previous Math Drudge blog.

As a first and very important example, most people presume, as an indisputable fact, that the past century has been the most violent in all . . . → Read More: Innumeracy and public risk]]> Assessing risk is something everyone must do every day.  Yet few are very good at it, and  there are significant consequences to the public’s collective inability to accurately assess risk.

As a first and very important example, most people presume, as an indisputable fact, that the past century has been the most violent in all history — two devastating world wars, the Holocaust, the Rawanda massacre, the September 11 attacks and more — and that we live in a highly dangerous time today.

And yet, as Canadian psychologist (now at Harvard) Steven Pinker has exhaustively documented in his new book The Better Angels of Our Nature: Why Violence Has Declined [Pinker2011b], the opposite is closer to the truth, particularly when normalized by population [Pinker2011a]:

Believe it or not — and I know most people do not — violence has been in decline over long stretches of time, and we may be living in the most peaceful time in our species’ existence. The decline of violence, to be sure, has not been steady; it has not brought violence down to zero (to put it mildly); and it is not guaranteed to continue. But I hope to convince you that it’s a persistent historical development, visible on scales from millennia to years, from the waging of wars and perpetration of genocides to the spanking of children and the treatment of animals.

How could the public perception be so wrong? The news media is partly to blame — good news doesn’t sell much advertising space. But the problem might go even deeper: We may be psychologically disposed to miscalculate risk, perhaps as an evolutionary response to danger. One well-known problem is the “conjunction fallacy” — the common predilection to assign greater probability to a more specialized risk.

For example, Pinker recently presented five scenarios for worldwide calamity on a website and then asked respondents to rate each according to risk. Two of the five were (2): A nuclear weapon will be set off in a war or act of terrorism; and (4) Iran will provide nuclear weapons to a terrorist group that will use one of them against Israel or the United States. Roughly half of the subjects assigned the second scenario more likely than the first, even though the conjunction of two events clearly has lower probability than either event by itself [Pinker2011b, pg. 369].

One indication of our inability to objectively assess risk is the fanatical and often counter-productive measures taken by parents nowadays to protect children. For example, 42 years years ago 67% of U.S. children walked or biked to school, but today only 10% do, in part stemming from a handful of highly publicized abduction incidents. Yet the number of cases of true child abduction by strangers (as opposed to, say, a divorced parent) has dwindled from 200-300 per year in the 1990s to only about 100 in the U.S. today. Even if one assumes that all of these children are harmed (which is not true), this is still only about 1/20 the risk of drowning and 1/40 of the risk of a fatal car accident [Pinker2011b, pg. 444].

Such considerations many not diminish the tragedy of an individual loss, but they do raise questions of priority in prevention. For example, governments worldwide often agonize over marginal levels of additives in certain products (agar in apples in the 1980s and asbestos insulation in well-protected ceilings), while refusing to spend money or legislate for clear social good (smoking in the developing world, gun control, infectious disease control,  needle exchange programs and working conditions in coal mines).

One completely absurd example is the recent surge of opposition in the U.S. (supposedly on health concerns) to “smart meters,” which once an hour send usage statistics to the local electric or natural gas utility [Barringer2011]. Yet the microwave exposure for these meters, even if one is standing just two feet from a smart meter when it broadcasts its data, is 550 times less than standing in front of an active microwave oven, up to 4600 times less than holding a walkie-talkie at your ear, and up to 1100 times less than holding an active cell phone at your ear. It is even less than sitting in a WiFi cyber cafe using a laptop computer [SDGE website].

A much more serious example is the ongoing hysteria, especially in the U.K. and the U.S., over childhood vaccinations. Back in 1998, a study was published in the British medical journal Lancet claiming that vaccination shots with a certain mercury compound may be linked to autism, but other studies showed no such link. But in the meantime, many jumped on the anti-vaccination bandwagon, and several childhood diseases began to re-appear, including measles in England and Wales, and whooping cough in California.  We should note that the rate of autism is probably  increasing (see Conversation article).

Finally, in January 2011, Lancet formally acknowledged that the original study was not only bad science (which had been recognized for years), but further an “elaborate fraud” [NYT2011]. Yet nearly one year later, opposition to vaccination remains strong, and irresponsible politicians such as would-be-US-President Michele Bachmann cynically (or ignorantly?) milk it.

A related example is the worldwide reaction to the Fukushima reactor accident. This was truly a horrible incident, and we do not wish to detract from death and environmental devastation that occurred [Tabuchi2011]. But we question decisions such as that quickly made by Germany to discontinue and dismantle its nuclear program.

Was this decision made after a sober calculation of relative risk, or simply from populist political pressure? We note that this decision inevitably will mean more consumption of fossil fuels, as well as the importation of electricity from France, which is 80% nuclear. Is this a step forward, or a step backward? We note that concern about global warming is, if anything, more acute than ever in light of accelerating carbon consumption [Gillis2011].

This kind of over-reaction — to which many of us are prey — is exacerbated by cynical and exploitive individuals, such as Bill and Michelle Deagle and Jeff Rense, who profit from such fears by peddling bogus medical products, speaking at conspiracy conventions for hefty fees, and charging for elite information. This is just one instance of a large growing and dangerous co-evolution of creationist, climate-denial and other anti-science movements — see Math Drudge blog and Ecker2011.

How do we protect against such misinformation and misperceptions? The complete answers are complex but several things are clear. First of all, science education must be augmented to address the assessment of risk — this should be a standard part of high school mathematics as should be more attention to the information needed to make informed assessment (see Conversation article).  Secondly, the press needs to be significantly more vigilant in critically commenting on dubious claims of public risk — citing literature, consulting real experts, etc. Ideally, we should anticipate scientifically trained and certified scientific journalists. Thirdly, mathematicians and scientists themselves need to recognize their responsibility in helping the public to understand risk. Failure to do so, well, poses a serious risk to society.

References

1. [Barringer2011] Felicity Barringer, “New Electricity Meters Stir Fears,” New York Times, 30 Jan 2011, available at Online article.
2. [Ecker2011] Ulrich Ecker and Stephan Lewandowski, “Why The Guardian’s correction won’t change your mind about Milly Dowler,” The Conversation, 17 Dec 2011, available at Online article.
3. [Gillis2011] Justin Gillis, “Record Jump in Carbon Emissions in 2010, Study Finds,” New York Times, 4 Dec 2011, available at Online article.
4. [NYT2011] [Editorial], “Autism Fraud,” New York Times, 12 Jan 2011, available at Online article.
5. [Pinker2011a] Steven Pinker, “A History of Violence: Edge Master Class 2011,” 27 Sep 2011, available at Online article.
6. [Pinker2011b] Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined, Viking, New York, 2011.
7. [Tabuchi2011] Hiroko Tabuchi and Martin Fackler, “More Radioactive Water Leaks at Japanese Plant,” New York Times, 4 Dec 2011, available at [Tabuchi2011].