Both traditional creationists and intelligent design scholars have invoked probability arguments in criticisms of biological evolution. They argue that certain features of biology are so fantastically improbable that they could never have been produced by a purely natural, “random” process, even assuming the billions of years of history asserted by geologists and astronomers. They often equate the hypothesis of evolution to the absurd suggestion that monkeys randomly typing at a typewriter could compose a selection from the works of Shakepeare.

One creationist-intelligent design argument goes like this: the human alpha-globin molecule, a component of hemoglobin that performs a key oxygen transfer function, is a protein chain based on a sequence of 141 amino acids. There are 20 different amino acids common in living systems, so the number of potential chains of length 141 is 20¹⁴¹, which is roughly 10¹⁸³ (i.e., a one followed by 183 zeroes). These writers argue that this figure is so enormous that even after billions of years of random molecular trials, involving all the biochemical material on the ancient earth’s surface, no human alpha-globin protein molecule would ever appear, and thus the hypothesis that human alpha-globin arose by an evolutionary process is decisively refuted [Foster1991, pg. 79-83; Hoyle1981, pg. 1-20; Lennox2009, pg. 163-173].

Fallacies in the creationist probability arguments

One fallacy in this particular argument, common to many others of this genre, is that it ignores the fact that a large class of alpha-globin molecules can perform the essential oxygen transfer function, so that the computation of the probability of a single instance is misleadingly remote. Indeed, most of the 141 amino acids in alpha-globin can be changed without altering the key oxygen transfer function, as can be seen by noting the great variety in alpha-globin molecules across the animal kingdom (see DNA). When one revises the calculation above, based on only 25 locations essential for the oxygen transport function (which is a generous over-estimate), one obtains 10³³ fundamentally different chains, a huge figure but vastly smaller than 10¹⁸³, and small enough to neutralize the probability-based argument against evolution [Bailey2000].

But even after this revision, the calculation still suffers from the fatal fallacy of presuming that a structure such as human alpha-globin arose by a single all-at-once random trial event (which, after all, is the creationist theory, not the scientific theory, of its origin). Instead, available evidence from hundreds of published studies on the topic suggests that alpha-globin and other proteins arose as the end product of a long sequence of intermediate steps, each of which was biologically useful in an earlier context [Hardison2001]. Thus any simplistic probability calculation (whether it is arguing for or against some aspect of evolution) that does not take into account the step-by-step process by which the structure came to be is not meaningful and can easily mislead [Bailey2000; Musgrave1998].

What’s more, such calculations completely ignore the atomic-level biochemical processes involved, which often exhibit strong affinities for certain types of highly ordered structures. For example, self-catalyzing biomolecules such as RNA are being investigated in research into the origin of life — see Origin. Also, molecular self-assembly occurs in DNA molecule duplication every time a cell divides. If we were to compute the chances of the formation of a human DNA molecule during meiosis, using a simple-minded probability calculation similar to that mentioned above, the result would be something on the order of one in 10^{1,000,000,000}, which is far, far beyond the possibility of completely “random” assemblage. Yet this process occurs millions of times every day in the human body.

Those familiar with probability theory will recognize that one central difficulty with these creationist arguments stems from the fact that in any probability calculation, one must first very carefully define the ensemble space. As noted above, it makes no sense to consider, as an ensemble, all possible random assemblages of atoms into a protein chain, since that is not the scientific hypothesis of how alpha-globin and other biomolecular structures came to be. Instead, the only valid ensemble for this analysis is the set of all possible outcomes of an eons-long string of biomolecular processes, encompassing proteins, organisms, species and environments. But at present we have no possible way of even enumerating such an ensemble, much less determining the probability of any particular scenario or class of scenarios in this ensemble. Perhaps at some time in the far distant future, a super-powerful computer could simulate with convincing fidelity the multi-billion-year biological history of the earth, in the same way that scientists today attempt to simulate (in a much more modest scope) the earth’s climate. Then, after thousands of such simulations have been performed, we might obtain some meaningful statistics on the chances involved in the formation of some class of biological structures such as alpha-globin. Until that time, all such probability calculations are essentially meaningless.

Along this line, it is also important to keep in mind that the process of natural biological evolution is not really a “random” process. Yes, mutations are “random” events, but the all-important process of natural selection, acting under the pressure of an extremely competitive landscape involving thousands of other species as well as numerous complicated environmental pressures, is anything but random. This strongly directional nature of natural selection, which is the essence of evolution, by itself invalidates simple-minded probability calculations.

Snowflakes

Some of the difficulties with creationist probability arguments can be illustrated by considering snowflakes. Bentley and Humphrey’s book Snow Crystals includes over 2000 high-resolution black-and-white photos of real snowflakes, each with intricate yet highly regular patterns that are almost perfectly six-way symmetric [Bentley1962]. A good online source with numerous high-resolution photographs has been compiled by Kenneth Libbrecht [Libbrecht2012]. Three photos from the Bentley-Hymphrey collection are shown below. By employing a reckoning based on six-way symmetry, one can calculate the chances that one of these structures can form “at random” as roughly one part in 10²⁵⁰⁰. This probability figure is even more extreme (far more extreme, in fact) than those that have appeared in the creationist-intelligent design literature. So is this proof that each individual snowflake has been designed by a supernatural intelligent entity? Obviously not.

The fallacy here, once again, is presuming an all-at-once random assembly of molecules. Instead, snowflakes, like biological organisms, are formed as the product of a long series of steps acting under well-known physical laws, and the outcomes of such processes very sensitively depend on the starting conditions and numerous environmental parameters. It is thus folly to presume that one can correctly reckon the chances of a given outcome by means of superficial probability calculations [Bailey2000].

Virus/E. coli experiment

A recently announced experimental result underscores the futility in attempting to argue against evolution on the basis of probability calculations. In January 2012, a research team led by Richard Lenski at Michigan State University demonstrated how colonies of viruses were able to evolve a new trait in as little as 15 days. The researchers studied a virus, known as “lambda,” which infects only the bacterium E. coli. They engineered a strain of E. coli that had almost none of the molecules that this virus normally attaches to, then released them into the virus colony. In 24 of 96 separate experimental lines, the viruses evolved a strain that enabled them able to attach to E. coli, using a new molecule (a channel in E. coli known as “OmpF”) that they had never before been observed to utilize. All of the successful runs utilized essentially the same set of four mutations. Justin Meyer, a member of the research team, estimated that the chance of all four mutations arising “at random” is roughly one in 10²⁷ (one thousand trillion trillion). Yet these lambda viruses acquired all four mutations in a matter of weeks [Zimmer2012].

Dembski’s information theory arguments

Intelligent design writer William Dembski invokes both probability and information theory (the mathematical theory of information content in data) in his arguments against Darwinism [e.g., Dembski2002]. However, mathematicians who have examined Dembski’s works have identified major flaws his reasoning [Elsberry2011]. For a detailed discussion of Dembski’s theories, see Information theory.

Conclusions

In short, the many arguments against evolution based on probability or information theory that have been published in the creationist-intelligent design literature exhibit serious fallacies:

1. They presume that the biomolecular structure came into existence through a single chance assemblage of atoms, rather than as the result of a long series of intermediate steps, each useful in a previous biological context.
2. They ignore numerous well-known physical laws and processes at the atomic level, by which remarkably rich structures can form naturally, not by chance.
3. They apply faulty mathematical reasoning, such as by ignoring the fact that a very wide range of molecular structures could perform a similar function.
4. They ignore the fact that biological evolution is not a “random” process — mutations may be random, but natural selection is far from random.
5. They attempt to invoke advanced mathematical concepts (e.g., information theory), but derive highly questionable results and misapply these results in ways that render the conclusions invalid in an evolutionary biology context.

Perhaps such failings are to be expected, since the field of probability is notorious for fallacies, and sometimes even persons with impressive-sounding credentials can fool themselves in this arena [Saini2009].

In any event, it is clear that it is extremely unwise to base one’s religious faith on probability arguments. Why look to probability to “prove” God, particularly when there are very serious questions as to whether such reasoning is valid? One is reminded of a passage in the New Testament (1 Cor. 14:8): “For if the trumpet gives an uncertain sound, who shall prepare himself for the battle?”

See Probability, Information theory and English text for additional details.

First of all, with respect to eyewitness records, it must be kept in mind that many other aspects of our physical world are truly beyond the realms of our senses:

• The planets and moons of our solar system are much too far away for humans to examine first-hand, although humans may travel to Mars in 20 years or so.
• For distant stars and their planets, we rely completely on powerful telescopes and exotic techniques such as measuring subtle changes in the light from a distant star (indicating that a planet has passed between us and the star). And galaxies are so much further away that there is, at present, no foreseeable technology to permit humans or our spacecraft to study these objects close-up and first-hand.
• Atoms and molecules are much, much too small for any human to examine first-hand. Thus we rely on exotic equipment such as electron microscopes and atomic-force microscopes to “see” them.
• Chemical reactions cannot yet be observed at the atomic-molecular level, at least not in any way that truly displays everything that is actually happening.
• The nucleus of an atom is far, far smaller than anything that can be seen, even with exotic equipment such as atomic-force microscopes.

In other words, each of the above aspects of our physical world can only be studied via empirical evidence that is certainly very far from anything that we can directly sense. Yet few, if any, persons nowadays seriously doubt that the sun and the planets of our solar system really do exist at roughly the distances scientists claim them to be, or that stars and galaxies populate the universe thousands or millions of light-years away, or that there really are structures known as molecules, atoms and nuclear particles, with roughly the sizes and possessing the properties that scientists assert for them.

In addition, there are a number of ways that scientists can peer into the past with considerable confidence. To begin with, radiometric dating permits scientists to measures dates of fossil layers and the like, based on measurements of the prevalence of certain radioactive isotopes that can be found in many rocks. This technique has been refined and polished over several decades, and in the process has become very reliable. What’s more, measurements of rates of radioactivity are now on very solid ground.

There is one additional type of scientific time machine that enables us to directly study the distant past, and which also permits scientists to gain considerable confidence in the multi-million-year ages asserted by geologists for the fossil layers: viewing distant stars and galaxies is, in a very literal sense, a “time machine.” For example, when we view the Pinwheel Galaxy, which is 21 million light-years away, the image we see is a record of events that occurred 21 million years ago. Quasar 3C253 is 2.5 billion light-years away, so that the light we see today was generated 2.5 billion years ago.

In August 2011, scientists discovered a Type 1A supernova in the Pinwheel Galaxy — one of the closest every observed, and, as it turns out, definitely the most carefully studied. It was first discovered by Lawrence Berkeley Laboratory scientist Peter Nugent (a colleague of the present author), using the Palomar Transient Factory (PTF), a remotely-controlled telescope facility near San Diego, California. Because this supernova was discovered only 11 hours after it exploded (from the earth’s time frame), scientists were able to study its behavior in unprecedented detail, and several major findings resulted [Preuss2011]:

1. The light intensity spectrum, from the earliest moments of discovery to the present (it is still being observed as of this writing), has been more accurately measured than with any previous supernova observation.
2. The early light intensity and spectrum measurements enabled the scientists to rule out several alternative models of supernovas, including red giant stars to double-white-dwarf systems, and confirm the progenitor star was definitely a carbon-oxygen white dwarf, and its companion was a main sequence star.
3. Initial measurements of oxygen ejected from the star found some traveling much faster than expected, but subsequent analysis explained this by determining that the oxygen was not evenly distributed when the dwarf exploded.
4. A tremendous amount of mixing had occurred, with some radioactive nickel mixed all the way to the photosphere (the outer region that generates the light that we observe).
5. In general, the sequence of radioactive decay, which produces most of the light we observe, was confirmed: nickel-56 decays to cobalt-56 and finally to iron-56, all in accordance with long-standing theoretical models and past empirical observations.

So the most carefully studied Type 1A supernova in history confirmed that the fundamental physical laws in play when this supernova exploded 21 million years ago are indistinguishable from those laws we measure in earth-bound laboratories today. Among these laws are the laws of radioactive decay, as well as fundamentals of quantum mechanics and general relativity. For these and other reasons, scientists have very good reasons to be entirely confident in the established old-earth picture of geology and evolution.

In summary, the large telescopes that scientists use to observe these distant galaxies are, in a very literal sense, “time machines.” And the fact that scientists can make ever-more-sensitive and comprehensive measurements of very distant astronomical objects, and in the process confirm, to exquisite precision, many the most sophisticated predictions of basic universal laws, is moot but overwhelming testimony to the reliability of these laws over cosmic time.

For additional discussion, see Radiometric dating, Reliability, Theory, Uniformitarian, Distance and Deceiver.

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.

In this study, among self-identified evangelical Protestant ministers, 48% “strongly agree” or “somewhat agree” that the earth is only 6000 years old. 79% of these pastors “strongly disagree” or “somewhat disagree” that God used evolution to create human beings.

These findings are directly relevant to the continuing challenge of religious movements to retain their youth. In his new book You Lost Me: Why Young Christians are Leaving Church and Rethinking Church, author David Kinnaman lists six principal reasons for disaffection of youth [Barna article]:

1. Churches seem overprotective.
2. Teens’ and twentysomethings’ experience of Christianity is shallow.
3. Churches come across as antagonistic to science.
4. Young Christians’ church experiences related to sexuality are often simplistic, judgmental.
5. They wrestle with the exclusive nature of Christianity.
6. The church feels unfriendly to those who doubt.

Note in particular item #3 above: Many youth are “falling away” from Christian belief due to a perceived tension between science and religion. In some additional analysis of this issue in the study above, 29% of Christian young adults feel that “churches are out of step with the scientific world we live in”. Another 25% perceive that “Christianity is anti-science”. And 23% reported they have been “turned off” by the creation-versus-evolution debate. Such tension is particularly acute for those students in scientific majors, and those whose professional work is in a science-related sector of the economy.

Karl Giberson, an evangelical author who has studied science and religion, reports that this certainly rings true in his experience. He reports that many evangelical youth grow up in a “parallel culture” that is often at odds with modern science. Many of these youth have been shown anti-science material, such as the writings and presentation materials offered by Ken Ham of Answers in Genesis [AIG website].

One of Ham’s oft-emphasized counterpoints to the scientific assertion, say, that life first appeared on earth roughly four billion years ago is “Were you there?”. Unfortunately, as Giberson notes, “many bright evangelical young people are, fortunately, not impressed with the suggestion that only ‘eyewitnesses’ can speak about the past.” Giberson adds,

The dismissive and even hostile approach to science taken by evangelical leaders like Ken Ham accounts for the Barna finding above. In the name of protecting Christianity from a secularism perceived as corrosive to the faith, the creationists are unwittingly driving the best and brightest evangelicals out of the church — or at least into the arms of the compromising Episcopalians, whom they despise. What remains after their exodus is an even more intellectually impoverished parallel culture, with even fewer resources to think about complex issues.

Additional details are in a recent article by Karl Giberson at Huffington Post, from which some of the material above has been adapted: [HuffPost article]. Additional details are available in the following articles on this site:

1. Is the scientific picture of an earth and biological species formed over several billion years in conflict with the Judeo-Christian Bible?
2. What do major religious leaders and denominations say about the “war” between science and religion?
3. What do leading scientists and scientific societies say about the “war” between science and religion?
4. What do major theologians say about the “war” between science and religion?
5. Have creationist writers uncovered significant technical issues that draw into question established theories of geology and evolution?
6. Have intelligent design writers uncovered significant technical issues that draw into question the established theories of geology and evolution?
   ]]> http://www.sciencemeetsreligion.org/blog/2011/11/creationism-and-religious-activity-of-youth/feed/ 0 http://www.sciencemeetsreligion.org/blog/2011/11/mathematics-and-scientific-fraud/ http://www.sciencemeetsreligion.org/blog/2011/11/mathematics-and-scientific-fraud/#comments Fri, 04 Nov 2011 00:55:13 +0000 David H Bailey http://www.sciencemeetsreligion.org/blog/?p=815 From time to time, the scientific community is rocked with cases of scientific fraud. Needless to say, such incidents do not help instill confidence in the public mind that is already predisposed to be skeptical of inconvenient scientific findings, including biological evolution and global warming.

   One notable case of fraud came to light in 2002, . . . → Read More: Mathematics and scientific fraud]]> From time to time, the scientific community is rocked with cases of scientific fraud. Needless to say, such incidents do not help instill confidence in the public mind that is already predisposed to be skeptical of inconvenient scientific findings, including biological evolution and global warming.

   One notable case of fraud came to light in 2002, when Bell Labs researcher Hendrik Schon, once described as a “rising star” in the field of nanoelectronics, was accused of fraud by a review panel consisting of several prominent scientists, including physicist Malcom Beasley of Stanford University [Samuel2002]. Most of the 25 papers in question were published in prestigious journals such as Science, Nature and Applied Physics Letters.

   A 2008, Science article started:

   The only two peer-reviewed scientific papers showing that electromagnetic fields (EMFs) from cell phones can cause DNA breakage are at the center of a misconduct controversy at the Medical University of Vienna (MUV). Critics had argued that the data looked too good to be real, and in May a university investigation agreed, concluding that data in both studies had been fabricated and that the papers should be retracted [Vogel2008].

   In November 2011, Netherlands psychologist Diederik Stapel was accused of publishing “several dozen” articles with falsified data. Stapel’s papers were certainly provocative. One claimed that disordered environments such as littered streets make people more prone to stereotyping and discrimination [Stapel2011]. After being challenged in an “editorial expression of concern” in Science, Stapel confessed that the allegations were largely correct [Carey2011].

   How could such frauds have happened? Firstly, scientific investigation is premised on open enquiry and treating every new result as a potential fraud is both antithetical and destructive. In general, false findings such as the cell phone case are easier to uncover  than “prettifying” — which in some cases comes from enthusiastic assistants “cleaning” the data to assist the case. It is said that other monks knew Brother Mendel liked to see pretty plots of peas and would weed strays of the wrong colour.

   Jonathan Schooler of the University of California, Santa Barbara, says that “the big problem is that the culture is such that researchers spin their work in a way that tells a prettier story than what they really found.” This culture is certainly cultivated by media reports in which every advance must be a breakthrough. In Stapel’s case, he was able to operate for so long because he was “lord of the data,” the only person who saw the data. What’s more, he did not make this data available for other researchers, a practice that Jelte Wicherts of the University of Amsterdam termed “a violation of ethics rules established in the field” [Carey2011].

   It is worth examining the role of mathematics in general, and statistics in particular, in the disclosure of these frauds. In the case of Stapel’s work, researchers found “anomalies in this material, including suspiciously large experimental effects and a lack of ‘outliers’ in the data” [Aldous2011].  A lack of outliers and unlikely distributions are tell-tale signs of poorly constructed artificial data (see http://en.wikipedia.org/wiki/Benford’s_law).

   Even setting aside outright fraud, statistical sloppiness pervades some fields. This is especially true in clinical medical research and in the social sciences where many of the researchers are poorly trained quantitatively. In a 2011 analysis published by Hekte Wicherts and Marjan Bakker of the University of Amsterdam, about half of 281 psychology journal papers they examined contained some statistical error, and that about 15 percent had at least one error that would have changed the reported finding, “almost always in opposition to the authors’ hypothesis” [Carey2011].

   There is even at least one instance of statistical methods being used to detect a problem in a mathematical result. In 1872, Augustus De Morgan noted (in a posthumously published collection) that the digit 7 occurred too few times in the expansion of pi to 606 digits published in 1853 by Shanks (Shanks later extended his calculation to 707 digits, but these were not yet available; and he did not correct the earlier digits). De Morgan wrote, “It is 45 to 1 against the number of 7s being as distant from the probable value (say 61) as 44 on one side or 78 on the other. There must be a reason why the number 7 is thus deprived of its fair share in the structure.” Indeed, in 1945 Ferguson, in one of the first machine-assisted calculations, found that Shanks’ expansion was in error after the first 527 digits, evidently because he omitted two terms in the expansion.

   However, as George Marsaglia recently noted, De Morgan’s analysis was somewhat faulty. Rather than singling out 7s, he should have assessed the chances that the least-frequent digit would appear 44 or fewer times among 606 digits. As it turns out, there is a roughly 10% chance of this occurring, so that the statistical case for error is not as compelling as De Morgan thought [Marsaglia2005].

   Let us emphasize that such scientifc fraud is the exception not the rule. Our cursory search of Science’s archive showed about half-a-dozen headline cases in the past ten years. Business, politics or law would not fair as well.

   In any event, it is clear that: (a) more care needs to be taken in using statistical methods in scientific and mathematical research; and (b) statistical methods can and should, to a greater extent, be used to detect fraud and manipulation of data (deliberate or not). Perhaps the considerable attention drawn to the recent incidents will lead to more rigorous analyses, and more circumspect behavior by scientists. We shall see.

   This was also posted (co-authored with Jonathan M. Borwein) at Experimental math blog.

   References

   1. [Aldous2011] Peter Aldous, “Psychologist admits faking data in dozens of studies”, New Scientist, 2 Nov 2011, available at Online article.
   2. [Carey2011] Benedict Carey, “Fraud Case Seen as a Red Flag for Psychology Research,” New York Times, 2 Nov 2011, available at Online article.
   3. [Marsaglia2005] George Marsaglia, “On the Randomness of Pi and Other Decimal Expansions,” available at Online article.
   4. [Samuel2002] Eugenie Samuel, “Rising star of electronics found to have fabricated his ground-breaking results,” New Scientist, 5 Oct 2002, available at Online article.
   5. [Stapel2011] Diederik A. Stapel and Siegwart Lindenberg, “Coping with Chaos: How Disordered Contexts Promote Stereotyping and Discrimination,” Science, 8 Apr 2011, available at Online article.
   6. [Vogel2008] Gretchen Vogel, “Fraud Charges Cast Doubt on Claims of DNA Damage From Cell Phone Lines, Science 29 August 2008, vol. 321 no. 5893 pp. 1144-1145, available at Online article
   ]]> http://www.sciencemeetsreligion.org/blog/2011/11/mathematics-and-scientific-fraud/feed/ 0 http://www.sciencemeetsreligion.org/blog/2011/09/how-do-scientists-measure-distances-to-stars-and-galaxies/ http://www.sciencemeetsreligion.org/blog/2011/09/how-do-scientists-measure-distances-to-stars-and-galaxies/#comments Wed, 28 Sep 2011 20:53:10 +0000 David H Bailey http://www.sciencemeetsreligion.org/blog/?p=792 Many of us know that the sun is approximately 150 million km or 93 million miles away, a distance that is known as the “astronomical unit” (AU). Neptune, the most distant planet, is 30 AU from the sun, or some 44.8 billion km (27.9 billion mi). The Voyager 2 spacecraft, launched in 1977, reached . . . → Read More: How do scientists measure distances to stars and galaxies?]]> Introduction

   Many of us know that the sun is approximately 150 million km or 93 million miles away, a distance that is known as the “astronomical unit” (AU). Neptune, the most distant planet, is 30 AU from the sun, or some 44.8 billion km (27.9 billion mi). The Voyager 2 spacecraft, launched in 1977, reached Jupiter just two years later, but did not reach Neptune until 1989.

   The nearest stars, Alpha Centauri A-B and Proxima Centauri, are roughly 1000 times more distant, roughly 4.3 light-years away (one light-year is the distance that light travels in a Julian year of 365.25 days, namely 9.461 trillion km or 5.879 trillion mi). The Milky Way galaxy consists of some 300 billion stars in a spiral-shaped conglomerate roughly 100,000 light-years across.

   The Andromeda Galaxy, which can be seen with many home telescopes, is 2.54 million light-years away. There are hundreds of billions of galaxies in the observable universe. As of the present date, the most distant observed galaxy is some 13.2 billion light-years away, so it was formed not long after the big bang, 13.75 billion years ago (plus or minus 0.011 billion). An interesting online tool, which one can use to determine first-hand the age of the universe from known data, is available at [WMAP tool].

   The scope of the universe is perhaps best illustrated by an example given by Australian astrophysicist Geraint Lewis. He noted that if the entire Milky Way galaxy is represented by a small coin, roughly one cm across, then the Andromeda galaxy would be another small coin roughly 25 cm (10 in) away. The observable universe would then extend for 5 km (3 mi) in every direction, encompassing some 300 billion galaxies [Lewis2011].

   How can scientists measure or calculate these enormous distances with any confidence?

   Parallax

   First, it is useful to keep in mind that sophisticated mathematics and technology are often not needed to obtain at least a rough estimate of astronomical distances. Eratosthenes (276-196BC) measured circumference of Earth to within 50 miles of present value by comparing the angular altitude of the Sun at midday on same day at Syene (Aswan) and Alexandria. Subsequently, the distance to the moon was determined to within 1% of our modern value by Hipparchus (160-125 B.C.), by comparing the radius of curvature of the earth’s shadow with the radius of the moon during a lunar eclipse. From the observed ratio the size of the moon could be inferred, since the size of the earth was already known from the work of Eratosthenes, and this then yielded its distance.

   One technique used in modern times is known as parallax, which was first used by German astronomer Friedrich Wilhelm Bessel in 1838. Parallax is not sophisticated — in fact your eyes use parallax to produce the perception of 3-D vision. If you cover one eye and note the position of a nearby object, compared with more distant objects, the nearby object “moves” when you view it with the other eye. This is parallax.

   The same principle is used in astronomy. As the earth travels around the sun in its orbit, relatively close stars are observed to move slightly, with respect to “fixed” stars that are much more distant. In most cases, this movement is very slight, only a fraction of a second of arc, but reasonably accurate distance measurements can nonetheless be made for stars up to about 1000 light-years away.

   Standard candles

   For more distant objects such as galaxies, parallax measurements cannot be used because the angular motion as the earth orbits the sun is much too small to be measured even with the best telescopes. Instead, astronomers rely on what are known as “standard candles.” Since, according to elementary geometry, light flux falls off as the square of the distance, by measuring the actual brightness observed on earth using a powerful telescope, astronomers can calculate the distance to the object.

   One type of “standard candle,” which has been used since the 1920s, is the class of Cepheid variable stars (stars that periodically vary in brightness), for which there is a known relation between the period and its absolute luminosity. There are some difficulties with such measurements, but most of the issues have now been worked out satisfactorily, and distances determined using this scheme are believed accurate to within about 7% for more nearby galaxies, and 15-20% for the most distant galaxies.

   Type Ia Supernovas

   In recent years the most widely used standard candles are what are known as Type Ia supernovas. These occur in a binary star system when a white dwarf star starts to attract matter from a larger red dwarf star. As the white dwarf gains more and more matter, eventually the star becomes unstable and undergoes a runaway nuclear fusion reaction, producing an extremely bright event that may briefly outshine an entire galaxy. Because this process is well understood, and can occur only within a very narrow range of total mass, the absolute luminosity Type Ia supernovas is very predictable, varying only slightly according to the shape of the supernova’s rise-fall curve. The uncertainty in these measurements is typically 5%.

   In August 2011, worldwide attention was focused on a Type Ia supernova that exploded in the Pinwheel Galaxy (known as M101), a beautiful spiral galaxy located just above the handle of the Big Dipper in the Northern Hemisphere. This is the closest supernova to the earth since the 1987 supernova, which was visible in the Southern Hemisphere.

   The cosmic distance ladder

   These and other techniques for astronomical measurements, collectively known as the “cosmic distance ladder,” are described in an excellent Wikipedia article [Ladder2011].

   One advantage of the numerous distance-measuring schemes in use, which overlap over a range of distances from nearby to very distant, is that astronomers can calibrate and corroborate their measurements with multiple approaches. Such calibrations and corroborations thus lend an additional measure of reliability to these schemes.

   Summary

   In short, distances to astronomical objects have been measured with a high degree of reliability, using calculations that mostly employ only high school mathematics. Thus the overall conclusion of a universe consisting of billions of galaxies, most of them many millions or even billions of light-years away, is now considered beyond reasonable doubt.

   However, these distances do cause consternation for some, since as we peer millions of light-years into space, we are also peering millions of years into the past. Some creationists, for instance, have theorized that about 4000 BCE a Creator placed quadrillions of photons in space enroute to earth, with patterns suggestive of supernova explosions and other events millions of years ago [Boardman1973, pg. 26].

   Needless to say, most observers reject this “God the Great Deceiver” theology. Kenneth Miller of Brown University, for example, blasted this notion in these terms [Miller1999, pg. 80]:

   Their version of God is one who has filled the universe with so much bogus evidence that the tools of science can give us nothing more than a phony version of reality. In other words, their God has negated science by rigging the universe with fiction and deception. To embrace that God, we must reject science and worship deception itself.

   This article, co-authored with Jonathan Borwein, is also posted at Math Drudge blog. An abbreviated version will soon appear at The Conversation. For additional details, see Distance.

   References

   1. [Boardman1973] William W. Boardman, Robert F. Koontz and Henry M. Morris, Science and Creation, Creation-Science Research Center, San Diego, CA, 1973.
   2. [Miller1999] Kenneth R. Miller, Finding Darwin’s God: A Scientist’s Search for Common Ground Between God and Evolution, Cliff Street Books, New York, 1999.
   ]]> http://www.sciencemeetsreligion.org/blog/2011/09/how-do-scientists-measure-distances-to-stars-and-galaxies/feed/ 0 http://www.sciencemeetsreligion.org/blog/2011/09/where-is-everybody/ http://www.sciencemeetsreligion.org/blog/2011/09/where-is-everybody/#comments Sat, 10 Sep 2011 14:37:46 +0000 David H Bailey http://www.sciencemeetsreligion.org/blog/?p=770 During a lunch in the summer of 1950, physicists Enrico Fermi, Edward Teller and Herbert York were chatting about a recent New Yorker cartoon depicting aliens abducting trash cans in flying saucers. Suddenly, Fermi suddenly blurted out, “Where is everybody?”

   Behind Fermi’s question was this line of reasoning: Since there are likely many other . . . → Read More: Where is everybody?]]> Introduction

   During a lunch in the summer of 1950, physicists Enrico Fermi, Edward Teller and Herbert York were chatting about a recent New Yorker cartoon depicting aliens abducting trash cans in flying saucers. Suddenly, Fermi suddenly blurted out, “Where is everybody?”

   Behind Fermi’s question was this line of reasoning: Since there are likely many other technological civilizations in the Milky Way galaxy, and since in a few tens of thousand of years at most they could have explored or even colonized many distant planets, why don’t we see any evidence of even a single extraterrestrial civilization?

   Clearly the question of whether other civilizations exist is one of the most important questions of modern science. Any discovery of a distant civilization, say by analysis of microwave data, would certainly rank as among the most significant and far-reaching of all scientific discoveries.

   The Drake equation

   At one of the first conferences to study the possibility of extraterrestrial intelligent civilizations, Frank Drake (1930 — ) sketched out what now is commonly known as the Drake equation, which estimates the number of civilizations in the Milky Way galaxy with which we could potentially communicate:

   N = R^* f_p n_e f_l f_i f_c L

   where

   N = number of civilizations in our galaxy that can communicate
   R^* = average rate of star formation per year in galaxy
   f_p = fraction of those stars that have planets
   n_e = average number of planets that can support life, per star that has planets
   f_l = fraction of the above that eventually develop life
   f_i = fraction of the above that eventually develop intelligent life
   f_c = fraction of civilizations that develop technology that signals existence into space
   L = length of time such civilizations release detectable signals into space.

   The values used by Drake in 1960 were R = 10, f_p = 0.5, n_e = 2, f_l = 1, f_i = 0.01, f_c = 0.01, L = 10,000, so that N = 10 x 0.5 x 2 x 1 x 0.01 x 0.01 x 10,000 = 10.  That is, he estimated that ten such civilizations were out somewhere in the Milky Way.

   In the wake of these analyses, scientists proposed the Search for Extraterrestrial Intelligence (SETI) project, to search the skies for radio transmissions from distant civilizations in a region of the electromagnetic spectrum thought to be best suited for interstellar communication. But after 50 years of searching, using increasingly powerful equipment, nothing has been found. So where is everybody?

   Proposed solutions to Fermi’s paradox

   Numerous scientists have examined Fermi’s paradox and have proposed solutions. Here is a brief listing of some of the proposed solutions, and common rejoinders:

   1. They are here, or at least are observing us, but are under strict orders not to disclose their existence. Common rejoinder: This explanation (often termed the “zookeeper’s theory”) is preferred by some scientists including, for instance, the late astronomer Carl Sagan. But it falls prey to the inescapable fact that it just takes one member of an extraterrestrial society to break the pact of silence.
   2. They have been here and planted seeds of life, or perhaps left messages in DNA. Common rejoinder: The notion that life began on earth from bacterial spores or the like that originated elsewhere, known as the “panspermia” theory, only pushes the problem of the origin of life to some other star system.  More controversially, Francis Crick has suggested “directed panspermia,” but few scientists take his theory seriously.  With regards to DNA, scientists see no evidence in DNA sequences of anything artificial.
   3. They exist, but are too far away. Common rejoinder: Once a civilization is sufficiently advanced, it could send probes to distant stars, which could scout out suitable planets, land, and then construct additional copies of themselves, using the latest software beamed from earth. In this way the entire Milky Way galaxy could be explored within at most a few million years.
   4. They exist, but have lost interest in interstellar communication and/or transportation. Common rejoinder: As with item #1, this explanation requires that each and every member of these civilizations forever lacks interest in communication and transportation. And all it takes is one exception, and this “solution” falls.
   5. They are calling, but we do not recognize the signal. Common rejoinder: This may be, but this explanation doesn’t apply to signals that are sent with the direct purpose of communicating to nascent technological societies. And as with item #1, it is hard to see how a galactic society could enforce a global ban on such targeted communications.
   6. Civilizations like us invariably self-destruct. Common rejoinder: This contingency is already figured into the Drake equation in the L term (the average length of a civilization). In any event, from our experience we have survived at least 100 years of technological adolescence, and have managed not yet to destroy ourselves in a nuclear or biological apocalypse. Besides, soon we will colonize the Moon and Mars, and our long-term survival will no longer rely solely on planet Earth.
   7. The earth is a unique planet in fostering a long-lived biological regime that ultimately results in the emergence of intelligent life. Common rejoinder: Such arguments may have some merit, but the latest studies, in particular the detections of extrasolar planets (see below), point in the opposite direction, namely that environments like ours appear to be quite common.
   8. We are alone, at least within the realm of the Milky Way galaxy. Some scientists in this camp further conclude that we are alone in the entire observable universe. Common rejoinder: This conclusion flies in the face of the “principle of mediocrity,” namely the presumption, popular since the time of Copernicus, that there is nothing special about the human society or environment.

   Numerous other proposed solutions and rejoinders are given in [Webb2002].

   Extrasolar planets

   Two key terms in the Drake equation are f_p (the fraction of stars that have planets) and n_e (the average number of planets that can support life, per star that has planets). Scientists once thought that stable planetary systems in general, and earth-like planets in particular, were a rarity.

   A breakthrough came in September 2010, when Steven S. Vogt of the University of California, Santa Cruz, and R. Paul Butler, of the Carnegie Institution in Washington, discovered evidence of a planet only three or four times the mass of earth orbiting in the “habitable zone” of a star (i.e., at a distance from a star where water could exist) about 20 light-years away from earth. As Butler noted, “This is really the first Goldilocks planet.”

   More recently, NASA deployed the Kepler spacecraft, which searches for planets circulating other stars by measuring small fluctuations in their light reaching earth. In some of the initial findings, announced in February 2011, 1325 planets have been found orbiting around the 150,000 stars surveyed. Of these planets, 68 are earth-sized, and most appear to be in the habitable region around their respective stars. Extrapolation from this data suggests that as many as 10% of all stars in the Milky Way may have earth-sized planets orbiting them [Hooper2011]. A separate team of scientists, using a telescope in Chile and a different detection technique (radial velocity), recently announced the discovery of 50 new planets orbiting distant stars, several of which are approximately the earth’s mass and near the habitable zone around their respective stars [Vastag2011a].

   We should add, however, that many Kepler sightings in particular remain to be ‘confirmed.’ Thus one might legitimately wonder how mathematically robust are the underlying determinations of velocity, imaging, transiting, timing, micro-lensing, etc.?

   Conclusion

   In short, among the factors in the Drake equation, two that have proven amenable to experimental study have been found to have reasonable values, although not quite as optimistic as Drake and his colleagues first estimated.

   With every new research finding in the area of extrasolar planets and possible extraterrestrial living organisms, the mystery of Fermi’s paradox deepens. Indeed, “Where is everybody?” has emerged as one of the most significant scientific questions of our time.

   Astronomer Paul Davies concludes his latest book on the topic by stating his own assessment: “my answer is that we are probably the only intelligent beings in the observable universe and I would not be very surprised if the solar system contains the only life in the observable universe.” Nonetheless, Davies reflects, “I can think of no more thrilling a discovery than coming across clear evidence for extraterrestrial intelligence.” [Davies2010, pg. 207-208].

   This article, which was co-authored by the editor and Jonathan Borwein, is also posted at Experimental math blog. An abbreviated version is posted at The Conversation. For additional details, see Fermi.

   References

   1. [Davies2010] Paul Davies, The Eerie Silence: Renewing Our Search for Alien Intelligence, Houghton Mifflin Harcourt, New York, 2010.
   2. [Hooper2011] Rowan Hooper, “Exoplanet explosion sparks philosophical debate,” New Scientist, 21 Feb 2011, available at Online article.
   3. [Vastag2011a] Brian Vastag, “New ‘super-Earth’ that is 36 light-years away might hold water, astronomers say,” Washington Post, 12 Sep 2011, available at Online article.
   4. [Webb2002] Stephen Webb, If the Universe Is Teeming with Aliens… Where Is Everybody? Fifty Solutions to Fermi’s Paradox and the Problem of Extraterrestrial Life, Copernicus Books, New York, 2002.
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