Posts filed under 'Book review'
There are, as everybody knows, a recent number of books seeking to either demonstrate, scientifically, that God does not exist, or to show that the love of religion is the root of all evil. Some familiar names: Daniel Dennet, Richard Dawkins, Stephen Weinberg, Victor Stenger, Christopher Hitchens, and even John Allen Paulos. All proclaim that the weight of scientific evidence is either completely or heavily on the side of the non existence of God.
The question is, of course: Has the authority of eminent scientists enabled them to prove their case? Berlinski says, “Not even close.” Not only have they not come close, Berlinski goes further and shows how easily they are persuaded by weak or demonstrably false arguments, and the extraordinary lengths that some scientists will go, in the sense of believing bizarre theories, to avoid ceding any ground to the “religionists.” Their distaste of religion has also lead them to say some rather stupid things. For example, Berlinski quotes the eminent biologist Emile Zuckerkandl as saying that if God exists, He would represent “something like a pathology of the state of being.” An enjoyable, sputtering rant by that author published in the peer-reviewed journal Gene is summarized later in the book.
Incidentally, before we get too far, it is worth mentioning that like most (all?) books in this genre, Berlinski does not attempt a definition of who or what God is—and neither do those on the other side. I haven’t one to offer, either. This curiosity can very well mean that everybody is talking at cross purposes. But since nobody delineates or bounds God, I can’t say much more than this, except that it should be borne in mind when reading any of these books.
A non-Enlightened disease
Berlinski puts the claim that religion is bad for you in perspective. Some anti-religion authors won’t settle for anything less than damning religion in all its stripes, disallowing, even, the crumb of comfort given to people when their loved ones die. Even Carl Sagan, in his Demon-Haunted World allowed this kind of solace, without recognizing that since, I must point out, everybody dies, this is an enormous amount of comfort to go around that would be denied mankind if religion were absent. But you never hear of our authors breaking open Mill to assist in calculating the utility of comforts versus torments of religion.
Many scientists feel that religion, while still a cancerous growth, is benign and only mostly harmful, and not immediately deadly. Sort of like smoking, which the more Enlightened among us would like to ban. Presumably, those who would prohibit smoking are same people who would support legalizing assisted suicide. Which happened in Holland in 1984 (and where a partial smoking ban does exist). Since then, about three percent of all deaths in that country are assisted, of which the government admits that about one-fourth are “involuntary.” We call that involuntary method of exiting “murder” here in the States, but Europeans are often considered more Enlightened, so they might be one step ahead of us in legal definitions.
Arguments for assisted suicide are usually intentionally religion-free. Thus, the point of the Holland example, of course, is that the world would not necessarily become a more moral, or safer place, if religion were to disappear. More proof is given by Berlinski in the form of a table, ordered by number of “excess”, or untimely, twentieth-century deaths due to non- or even anti-religious behavior. Leading the pack are of course the two World Wars, but not far behind in the body count are mankind’s experiments with various communist utopias. Since one of the top arguments used by those who would wish to bar religion is that the religious can be cruel and have killed, the evidence that the non-religious can be cruel and have killed in equal or larger number only proves that there will always be a class of people who adore pain, misery, and bloodshed, irrespective of creed.
The disease religion is also seen as congenital, in the sense that people have religion on the brain, literally. Somehow, we are assured, the brain has genetically encoded religion into itself, and that if we’d just grow up and recognize this, we would become Enlightened (or brightened, these days). This is one of the sillier arguments put forth by scientists. If religion is genetically encoded, then it cannot be overcome, unless some of us, the superior ones naturally, have somehow managed to escape expressing those particular genes that activate, say, the praying response. Look for one of those fMRI studies that “proves” this, soon.
Berlinski shows that because some scientists cannot countenance religious arguments of any kind, they refuse to accept any evidence that is any way tainted by religion. This leads to the fallacy that one should not listen to arguments against, say, stem cell research or abortion because they are religious. You will surely certainly recognize this ploy when you meet it.
Scientific ontology
Everybody already knows that physics, and its offshoots, has done brilliantly at explaining more and more of the universe. But it cannot keep doing so forever. At some point, meta-physics must enter into the discussion. This is because, no matter what physical laws we have identified, we will never have explained through observation why these particular laws and not some other are in force, nor can we answer what the laws mean. It is obvious that it is here that God can slip in and offer the needed explanations. Some scientists are therefore anxious to fill in these gap with…something, anything but God. Or, if that cannot be accomplished, then to prove that God does not exist.
Dawkins, in his The God Delusion offers a particularly weak argument. His first premise is that the universe is improbable. And we can stop right there, because that is a nonsensical statement, so his argument fails. Any thing or statement cannot be improbable. A thing can only be improbable with respect to something else. Further, a thing can be improbable with respect to one set of evidence and entirely probable with respect to other evidence. So, in Dawkin’s case, the universe is improbable with respect to what?
Weak Anthropic evidence is sometimes offered, in the guise of certain physical constants having particular values, in the sense that if these constants did not have these values, then human life would be impossible (which is not the same as saying the universe is impossible, but let that pass). Now the burden is on those who tout this evidence to show that this is the best evidence with which to measure the improbability of the universe. And there are many hints that it is not the best evidence. It is, after all, by its very name, suspiciously self indulgent and human centered evidence. Why would the universe care if humans, or other sentient beings, evolved enough to notice that they might not have evolved had the universe been arranged differently anyway? Besides, to say that things might have been different and humans might not have evolved is just a tautology, and therefore of no interest.
Still, accept it if you like, so that we can move to Dawkins’s second premise, which is that God Himself is improbable. Again, the statement is nonsensical: improbable with respect to what? Dawkins suggests that God must be more improbable than the universe, which again makes no sense. Anyway, improbable is not impossible, as Dawkins often argues with respect to evolution by natural selection, arguments he has apparently forgotten. Still, Dawkins moves to his conclusion that God is so improbable that He doesn’t exist, and advises people to accept some recent conjectures in cosmology that seem to do away with the need to explain why the universe, or universes, are the way they are.
These are the Landscape and multiverse hypotheses, put forward by various authors to help them cope with the insolubilities of quantum mechanics and cosmology. These are attempts to shift the questions of “Why?” one step back. That they do not answer them, I would have thought obvious. Even pushing the grand questions a little deeper down is enough to please some people. Berlinski, a mathematical physicist, covers these speculations well, without any math, and gives pointers to books where we might learn more. See especially his very clever “Catechism of Quantum Cosmology.” Briefly, however, the solutions offered posit an uncountable number of alternate universes that are coming into and out of creation always. There are no mechanisms to observe these other universes directly or indirectly. Even if we could, these theories might answer some questions of quantum mechanics and gravity, but they never answer why it is infinities of universes instead of just one. The theories are also mind-boggling complex, and by no means are they consistent with one another. Nobody even knows what the full scope of these ideas are.
Berlinski quotes Dawkins, who is nevertheless satisfied, as saying, “The key difference between the radically extravagant God hypothesis and the apparently extravagant multiverse hypothesis, is one of statistical improbability.” Presumably, he means that God is more improbable. He never says how much more. Infinities, of universes or anything else, are a dangerous thing. More foolishness has been generated by jumping to infinity than by any other reason (see chapter 15 of Jaynes’s remarkable Probability Theory for appropriate words of admonition).
Argument from design
It has long been convincing to many that the wonderful biological complexity that is everywhere in evidence must have had a designer. How else, Darwin himself wondered, can one explain the human eye? This argument is less convincing than it once was, because of the success of modern biology and genetics, and the seeming success of evolution by natural selection.
(It is just as well to point out here that I accept that evolution accounts for some or most of the observed biological variation on Earth, and that the mechanism driving it is natural selection, or something like it.)
Wait a minute. Did he just say seeming success? He did. Which brings us back to Dawkins, the best-known anti-religion author. Was there ever a man who published so much nonsense that was taken so seriously by the scientific community? Nobody else even comes close. Just mentioning the word memes proves my point. Is not believing in God a meme? Berlinski doesn’t discuss memes, but does offer some well known criticisms of “selfish” genes—incidentally, the best are due to the philosopher’s Mary Midgley (Evolution as a Religion) and David Stove (Darwinian Fairytales; if you haven’t read either of these books, please do so, especially Stove’s, before you comment).
Not all biologists are satisfied with present-day theory. Berlinski writes
[Darwinian] theory is what is always was: It is unpersuasive. Among evolutionary biologists, these matters are well known. In the privacy of the Susan B. Anthony faculty lounge, they often tell one another with relief that it is a very good thing the public has no idea what the research literature really suggest.
“Darwin?” a Nobel laureate in biology once remarked to me over his bifocals. “That’s just the party line.”
There are still gaps in the evolutionary record. Nobody knows how life original arose, and nobody knows how species originate. Some fill these gaps with God. Scientists argue that the gaps will be filled in eventually. Berlinski says that this assumption is “both intellectually primitive and morally abhorrent—primitive because it reflects a phlegmatic absence of curiosity, and abhorrent because it assigns to intellectual future a degree of authority alien to human experience” because filling gaps “has created [new] gaps all over again.”
The answer
The best summation on the side of (non-apoplectic) scientists is probably from Richard Feynman, who said, “Today we cannot see whether Schrödinger’s equation [which describes the time evolution of physical systems] contains frogs, musical composers, or morality. We cannot say whether something beyond it like God is needed , or not. And so we can all hold strong opinions either way.”
To say whether or not God exists is the hardest question in the world; yet it is the one people find easiest to answer, and everybody seems delighted to meet an argument, however weak, that agrees with their desires. This leads very smart people to say exceptionally stupid things.
My own surmise is that any proof—for or against—is impossible. And so any belief you have is based entirely on faith.
April 14th, 2008
Gerd Gigerenzer, Simon and Schuster, New York, 310 pp., ISBN 0-7432-0556-1, $25.00
Should healthy women get regular mammograms to screen for breast cancer?
The surprising answer, according to this wonderful new book by psychology professor Gerd Gigerenzer, is, at least for most women, probably not.
Deciding whether to have a mammogram or other medical screening (the book examines several) requires people to calculate the risk that is inherent is taking these tests. This risk is usually poorly known or communicated and, because of this, people can make the wrong decisions and suffer unnecessarily.
What risk, you might ask, is there for an asymptommatic woman in having a mammogram? To answer that, look at what could happen.
The mammogram could correctly indicate no cancer, in which case the woman goes away happy. It could also correctly indicate true cancer, in which case the woman goes away sad and must consider treatment.
Are these all the possibilities? Not quite. The test could also indicate that no cancer is present when it is really there—the test could miss the cancer. This gives false hope and causes a delay in treatment.
But also scary and far more likely is that the test could indicate that cancer is present when it is not. This outcome is called a false positive, and it is Gigerenzer’s contention that the presence of these false positives are ignored or minimized by both the medical profession and by interest groups whose existence is predicated on advocating frequent mammograms (or other disease screenings, such as for prostate cancer or AIDS).
Doctors like to provide an “illusion of certainty” when, in fact, there is always uncertainty in any test. Doctors and test advocates seem to be unaware of this uncertainty, they have different goals than do the patients who will receive the tests, and they ignore the costs of false positives.
How is the uncertainty of a test calculated? Here is the standard example, given in every introductory statistics book, that does the job. This example, using numbers from Gigerenzer, might look confusing, but read through it because its complexity is central to understanding the his thesis.
If the base rate probability of breast cancer is 0.8% (the rate of cancer in women in the entire country), and the sensitivity (ability to diagnose the cancer when it is truly there) and specificity (ability to diagnose no cancer when it is truly not there) of the examination for cancer is 90% and 93%, then given that someone tests positive for cancer, what is the true probability that this person actually has cancer?
To answer the question requires a tool called Bayes Rule. Gigerenzer has shown here, and in other research, that this tool is unnatural and difficult to use and that people consistently poorly estimate the answer. Can you guess what the answer is?
Most people incorrectly guess 90% or higher, but the correct answer is only 9%, that is, only 1 woman out of every 11 who tests positive for breast cancer actually has the disease, while the remaining 10 do not.
If people instead get the same question with the background information in the form of frequencies instead of probabilities they do much better. The same example with frequencies is this: If out of every 1000 women 77 have breast cancer, and that 7 of these 77 who test positive actually have the disease, then given that someone tests positive for cancer what is the true probability that this person actually has cancer?
The answer now jumps out—7 out of 77—and is even obvious, which is Gigerenzer’s point. Providing diagnostic information in the form of frequencies benefits both patient and doctor because both will have a better understanding of the true risk.
What are the costs of false positives? For breast cancer, there are several. Emotional turmoil is the most obvious: testing positive for a dread disease can be debilitating and the increased stress can influence the health of the patient negatively. There is also the pain of undergoing unnecessary treatment, such as mastectomies and lumpectomies. Obviously, there is also a monetary cost.
Mammograms can show a noninvasive cancer called ductal carcinoma in situ, which is predominately nonfatal and needs no treatment, but is initially seen as a guess of cancer. There is also evidence that the radiation from the mammogram increases the risk of true breast cancer!
These costs are typically ignored and doctors and advocates usually do not acknowledge the fact the false positives are possible. Doctors suggest many tests to be on the safe side—but what is the safe side for them is not necessarily the safe side for you. Better for the doctor to have asked for a test and found nothing than to have not asked for the test and miss a tumor, thus risking malpractice.
This asymmetry shows that the goals of patients and doctors are not the same. The same is true for advocacy groups. Gigerenzer studies brochures from these (breast cancer awareness) groups in Germany and the U.S. and found that most do not mention the possibility of a false positive, nor the costs associated with one.
Ignoring the negative costs of testing makes it easier to frighten women into having mammograms, and he stresses that, “exaggerated fears of breast cancer may serve certain interest groups, but not the interests of women.”
Mammograms are only one topic explored in this book. Others include prostate screenings “where there is no evidence that screening reduces mortality”, AIDS counseling, wife battering, and DNA fingerprinting.
Studies of AIDS advocacy group’s brochures revealed the same as in the breast cancer case: the possibility of false positives for screenings and the costs associated with these mistakes were ignored or minimized.
Gigerenzer even shows how attorney Alan Dershowitz made fundamental mistakes calculating the probable guilt of O.J. Simpson, mistakes that would have been obvious had Dershowitz used frequencies instead of probabilities.
The book closes with tongue-in-cheek examples of how to cheat people by exploiting their probabilistic innumeracy, and includes several fun problems.
Gigerenzer stresses that students have a high motivation to learn statistics but that it is typically poorly taught. He shows that people’s difficulties with numbers can be overcome and that it is in our best interest to become numerate.
January 1st, 2008
The Future of Everything by David Orrell. Thunder’s Mouth Press, New York.
I wanted to like this book, which was supposed to be an examination of how well scientists made predictions—my special area of interest—but I couldn’t. It wasn’t just Orrell’s occasional use of juvenile and gratuitous political witticisms: for example, at one point in his historical review of ancient Greek-prediction making, Orrell sarcastically assures us that the “White House” would not, as dumb as its occupants are, stoop so low as to rely on the advice gained from examining animal entrails. It also wasn’t that the book lacked detailed explanations of the three fields he criticizes—weather and climate forecasts, economic forecasts, and health predictions. Nor was it that Orrell was sloppy in some of his historical research: for example, he repeats the standard, but false, view that Malthus predicted mankind would overpopulate the world (more on this below).
No. What is ultimately dissatisfying about this book is that Orrell wants it two ways. He uses the first half of the book warning us that we are, and have been over our entire history, too confident in our forecasts, that we are unaware of the amount of error in our models, and that we should expect the unexpected. Then he uses the second half of the book to warn us that, based on these same forecasts and models, we are heading toward a crisis, and that if we are not careful, the end is near. He softens the doom and gloom by adding an unsatisfactory “maybe” to it all. He cannot make up his mind and make a clear statement.
Now, it might be that the most dire predictions of climate models, economic forecasts, and emergent disease predictions are true and should be believed. But it cannot also be true that the models that produced these guesses are bad and untrustworthy, as he assures us they are. So, which is it? Are scientists too confident in their predictions, given their less-than-stellar history at predicting the future? Almost certainly. For example, we recall Lev Landau, saying of cosmologists, “They are often wrong, but never in doubt.” Could this also apply to climatologists and economists? If so, how is it we should believe Orrell when he says we should prepare for the worst?
To solve that conundrum, Orrell approvingly quotes Warren Buffet who, using an analogy of Pascal’s wager, says it’s safer to bet global warming is real. Pascal argued that if God exists you’d better believe in him because the consequences of not believing are too grim to contemplate; but if He does not exist, you do not sacrifice much by believing anyway. This argument is generally acknowledged as unconvincing—almost certainly Orrell himself does not hold with it, as he shows no sign of devoutness. Orrell does, sometimes, allow himself to say that people are too sure of themselves and their predictions. To which I say, Amen.
You now need to understand that weather and climate models both require a set of observations of the present weather or climate before they can run. These are called initial conditions, and the better we can observe them, the better the forecasts can be. Ideally, we would be able to measure the state of the atmosphere at every single point, see every molecule, from the earth’s surface, way up to where the solar wind impacts on the magnetosphere. Obviously, this is impossible, so there is tremendous uncertainty in the forecasts just because we cannot perfectly measure the initial conditions. There is a second source of uncertainty in forecasts, and that is model error. No climate model accurately models the real atmosphere. Moreover, it is impossible that they can do so. Approximations, many of them crude and no better than educated guesses, are made for many physical phenomena: for example, the way clouds behave. So some of the error in forecasts is due to model error and some due to uncertainty in the initial conditions.
Orrell makes the claim that most of the error in weather forecasts is due to model error. Maybe so—though this is far from agreed upon—but he goes further to say that these weather models do not have much, or any skill. (Skill means that the model’s forecast is better than just guessing that the future will be like the past.) This is certainly false. Orrell is vague about this: at times it looks like he is saying something uncontroversial, like long-range (on the order of a week) weather forecasts do not have skill. Who disagrees with that? Perhaps some private forecasting companies providing these predictions—but that is another matter. But often, Orrell appears to lump all, short- and long-term, weather forecasts in the same category and hints they are all error filled. This is simply not true. Meteorologists do a very good job forecasting weather out to about three or four days ahead. Climatologists, of course, do a very poor job of even forecasting “past” weather; i.e., most climate models can not even reproduce past known states of the atmosphere with any degree of skill.
Lovelock’s Gaia hypothesis is lovingly detailed in Orrell’s warning that we had better treat Mother Nature nicely. This curious—OK, ridiculous—idea treats the earth itself as a finely tuned, self-regulating organism. Orrell warmly quotes some “environmentalists” as saying that Gaia treats humans as a “cancer”, and that it sometimes purposely causes epidemics, which are its way of keeping humans in check and curing the cancer. Good grief.
Of course, the Gaia idea is invoked only after humans come on the scene. The earth is only in its ideal state right before humans industrialized. But where was Gaia when those poor, mindless and apolitical, anaerobic bacteria swam in the oceans so many eons ago? The finely tuned earth-organism must have decided these bacteria were a cancer too, as the oxygen dumped as their waste product poisoned these poor creatures and killed them off. So too have other species come and gone before humans came down out of the trees. Belief in Gaia in this sense is no better than those who also believe that the climate we now have is the one, the one that is perfect and would always exist (and didn’t it always exist?) if only it weren’t for us people, and in the particular the Bush “Administration.”
But again, Orrell is wishy-washy. He assures us that Gaia is “just another story” (though by his tone, he indicates it’s a good one). His big-splash conclusion is that models should not be used as forecasts per se, that they should only be guides to give us “insight”. Well, a guide is just another word for a forecast, particularly if the guide is used to make a decision. Making a decision is nothing but making a guess and a bet on the future. So, once again, he tries to have it both ways.
A note on Malthus. What he argued was that humans, and indeed any species, reproduced to the limit imposed upon them by the availability of food. If the food supply increased, the population would increase. Both would also fall together. What Malthus said was that humans are in *equilibrium* with their environment. He never said that people would overpopulate and destroy the earth. He was, though, in a sense, an early eugenicist and did worry that a March of the Morons could happen if somebody didn’t do something about the poor; but that is a story for another day.
December 17th, 2007
This is a lovely, lovely book and I can’t believe it has taken me this long to find and read it (November 2005: I was lead to this book via Jaynes, who was the author that also recommended Stove). Cox, a physicist, builds the foundations of logical probability using Boolean algebra and just two axioms, which are so concise and intuitive that I repeat them here:
1. “The probability of an inference on given evidence determines the probability of its contradictory on the same evidence.”
2. “The probability on given evidence that both of two inferences are true is determined by their separate probabilities, one on the given evidence, the other on this evidence with the additional assumption that the first inference is true.”
Cox then begins to build. He shows that probability can be, should be, and is represented by logic; he shows the type of function probability is, the relation of uncertainty and entropy, and what expectation is. He ends with deriving Lapace’s rule of succession, and argues when this rule is valid and when it is invalid. And he does it all in only 96 pages!. This is one of the rare books that I also recommend you read each footnote. If you have any interest in probability or statistics, you have a moral obligation to read this book.
December 6th, 2007
Is deductive logic empirical? No. Is inductive logic also empirical? No. Is induction justified and, if so, is it just an extension of logic? Yes.
These are Stove’s conclusions as he takes Hume (and current-day relativists,such as Popper) to task and shows that, yes, induction is rational. He also shows that the common belief that ordinary logical is formal is a myth. Knowledge of the validness of certain arguements must come from intution, as Carnap argued, and Stove proves. He shows that certain forms of logical arguments do not always give valid conclusions, and that all arguments must be judged individually. In his words, “Cases Rule”.
This is another in a series of books that I think are largely unknown by most statisticians and probabilists, especially those who tend toward so-called pure mathematics. But this book, like those by Jaynes and Cox, argue the case for logical, as opposed to subjective, probability forcefully and conclusively. They deserve to be more widely read because, I believe, they have a great deal to say on the foundations of our field.
October 6th, 2007
