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science has long been married to mathematics. Generally it has been for the better. Especially since the days of Galileo and Newton, math has nurtured science. Rigorous mathematical methods have secured science’s fidelity to fact and conferred a timeless reliability to its findings.

a mutant form of math has deflected science’s heart from the modes of calculation that had long served so faithfully. Science was seduced by statistics, the math rooted in the same principles that guarantee profits for Las Vegas casinos. Supposedly, the proper use of statistics makes relying on scientific results a safe bet. But in practice, widespread misuse of statistical methods makes science more like a crapshoot.

science’s dirtiest secret: The “scientific method” of testing hypotheses by statistical analysis stands on a flimsy foundation. Statistical tests are supposed to guide scientists in judging whether an experimental result reflects some real effect or is merely a random fluke, but the standard methods mix mutually inconsistent philosophies and offer no meaningful basis for making such decisions. Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous, and tests of medical dangers or treatments are often contradictory and confusing.

Another example illustrating the central dogma is the French optical telegraph.

The telegraph was an optical communication system with stations consisting of large movable pointers mounted on the tops of sixty-foot towers. Each station was manned by an operator who could read a message transmitted by a neighboring station and transmit the same message to the next station in the transmission line.

The distance between neighbors was about seven miles. Along the transmission lines, optical messages in France could travel faster than drum messages in Africa. When Napoleon took charge of the French Republic in 1799, he ordered the completion of the optical telegraph system to link all the major cities of France from Calais and Paris to Toulon and onward to Milan. The telegraph became, as Claude Chappe had intended, an important instrument of national power. Napoleon made sure that it was not available to private users.

Scientists these days tend to keep up a polite fiction that all science is equal. Except for the work of the misguided opponent whose arguments we happen to be refuting at the time, we speak as though every scientist's field and methods of study are as good as every other scientist's and perhaps a little better. This keeps us all cordial when it comes to recommending each other for government grants.

Why should there be such rapid advances in some fields and not in others? I think the usual explanations that we tend to think of - such as the tractability of the subject, or the quality or education of the men drawn into it, or the size of research contracts - are important but inadequate. I have begun to believe that the primary factor in scientific advance is an intellectual one. These rapidly moving fields are fields where a particular method of doing scientific research is systematically used and taught, an accumulative method of inductive inference that is so effective that I think it should be given the name of "strong inference." I believe it is important to examine this method, its use and history and rationale, and to see whether other groups and individuals might learn to adopt it profitably in their own scientific and intellectual work. In its separate elements, strong inference is just the simple and old-fashioned method of inductive inference that goes back to Francis Bacon. The steps are familiar to every college student and are practiced, off and on, by every scientist. The difference comes in their systematic application. Strong inference consists of applying the following steps to every problem in science, formally and explicitly and regularly: Devising alternative hypotheses; Devising a crucial experiment (or several of them), with alternative possible outcomes, each of which will, as nearly is possible, exclude one or more of the hypotheses; Carrying out the experiment so as to get a clean result; Recycling the procedure, making subhypotheses or sequential hypotheses to refine the possibilities that remain, and so on.

On any new problem, of course, inductive inference is not as simple and certain as deduction, because it involves reaching out into the unknown. Steps 1 and 2 require intellectual inventions, which must be cleverly chosen so that hypothesis, experiment, outcome, and exclusion will be related in a rigorous syllogism; and the question of how to generate such inventions is one which has been extensively discussed elsewhere (2, 3). What the formal schema reminds us to do is to try to make these inventions, to take the next step, to proceed to the next fork, without dawdling or getting tied up in irrelevancies.

British sociologist Harry Collins asked a scientist who specializes in gravitational waves to answer seven questions about the physics of these waves. Collins, who has made an amateur study of this field for more than 30 years but has never actually practiced it, also answered the questions himself. Then he submitted both sets of answers to a panel of judges who are themselves gravitational-wave researchers. The judges couldn't tell the impostor from one of their own. Collins argues that he is therefore as qualified as anyone to discuss this field, even though he can't conduct experiments in it.

The journal Nature predicted that the experiment would have a broad impact, writing that Collins could help settle the "science wars of the 1990s," "when sociologists launched what scientists saw as attacks on the very nature of science, and scientists responded in kind," accusing the sociologists of misunderstanding science. More generally, it could affect "the argument about whether an outsider, such as an anthropologist, can properly understand another group, such as a remote rural community." With this comment, Nature seemed to be saying that if a sociologist can understand physics, then anyone can understand anything.

It will be interesting to see if Collins' results can indeed be repeated in different situations. Meanwhile, his experiment is plenty interesting in itself. Just one of the judges succeeded in distinguishing Collins' answers from those of the trained experts. One threw up his hands. And the other seven declared Collins the physicist. He didn't simply do as well as the trained specialist—he did better, even though the test questions demanded technical answers. One sample answer from Collins gives you the flavor: "Since gravitational waves change the shape of spacetime and radio waves do not, the effect on an interferometer of radio waves can only be to mimic the effects of a gravitational wave, not reproduce them." (More details can be found in this paper Collins wrote with his collaborators.)

a very natural way for atheists to react to religious claims: to ask for evidence, and reject these claims in the absence of it. Many of the several hundred comments that followed two earlier Stone posts “Philosophy and Faith” and “On Dawkins’s Atheism: A Response,” both by Gary Gutting, took this stance. Certainly this is the way that today’s “new atheists”  tend to approach religion. According to their view, religions — by this they mean basically Christianity, Judaism and Islam and I will follow them in this — are largely in the business of making claims about the universe that are a bit like scientific hypotheses. In other words, they are claims — like the claim that God created the world — that are supported by evidence, that are proved by arguments and tested against our experience of the world. And against the evidence, these hypotheses do not seem to fare well.

But is this the right way to think about religion? Here I want to suggest that it is not, and to try and locate what seem to me some significant differences between science and religion

To begin with, scientific explanation is a very specific and technical kind of knowledge. It requires patience, pedantry, a narrowing of focus and (in the case of the most profound scientific theories) considerable mathematical knowledge and ability. No-one can understand quantum theory — by any account, the most successful physical theory there has ever been — unless they grasp the underlying mathematics. Anyone who says otherwise is fooling themselves.

Regarding the “hide the decline” email, Jones has explained that when he used the word “trick”, he simply meant “a mathematical approach brought to bear to solve a problem”. The inquiry made the following criticism of the resulting graph (its emphasis): [T]he figure supplied for the WMO Report was misleading. We do not find that it is misleading to curtail reconstructions at some point per se, or to splice data, but we believe that both of these procedures should have been made plain — ideally in the figure but certainly clearly described in either the caption or the text. [1.3.2] But this was one isolated instance that occurred more than a decade ago. The Review did not find anything wrong with the overall picture painted about divergence (or uncertainties generally) in the literature and in IPCC reports. The Review notes that the WMO report in question “does not have the status or importance of the IPCC reports”, and concludes that divergence “is not hidden” and “the subject is openly and extensively discussed in the literature, including CRU papers.” [1.3.2]

As for the treatment of uncertainty in the AR4’s paleoclimate chapter, the Review concludes that the central Figure 6.10 is not misleading, that “[t]he variation within and between lines, as well as the depiction of uncertainty is quite apparent to any reader”, that “there has been no exclusion of other published temperature reconstructions which would show a very different picture”, and that “[t]he general discussion of sources of uncertainty in the text is extensive, including reference to divergence”. [7.3.1]

Regarding CRU’s selections of tree ring series, the Review does not presume to say whether one series is better than another, though it does point out that CRU have responded to the accusation that Briffa misused the Yamal data on their website. The Review found no evidence that CRU scientists knowingly promoted non-representative series or that their input cast doubt on the IPCC’s conclusions. The much-maligned Yamal series was included in only 4 of the 12 temperature reconstructions in the AR4 (and not at all in the TAR).

history of voting math comes mainly in two chunks: the period of the French Revolution, when some members of France’s Academy of Sciences tried to deduce a rational way of conducting elections, and the nineteen-fifties onward, when economists and game theorists set out to show that this was impossible

The first mathematical account of vote-splitting was given by Jean-Charles de Borda, a French mathematician and a naval hero of the American Revolutionary War. Borda concocted examples in which one knows the order in which each voter would rank the candidates in an election, and then showed how easily the will of the majority could be frustrated in an ordinary vote. Borda’s main suggestion was to require voters to rank candidates, rather than just choose one favorite, so that a winner could be calculated by counting points awarded according to the rankings. The key idea was to find a way of taking lower preferences, as well as first preferences, into account.Unfortunately, this method may fail to elect the majority’s favorite—it could, in theory, elect someone who was nobody’s favorite. It is also easy to manipulate by strategic voting.

If the candidate who is your second preference is a strong challenger to your first preference, you may be able to help your favorite by putting the challenger last. Borda’s response was to say that his system was intended only for honest men.

Most people think of the term in the context of production of goods and services: more efficient means more valuable output is wrung from a given bundle of real resources (which is good) or that fewer real resources are burned up to produce a given output (which is also good).

In economics, efficiency is also used to evaluate alternative distributions of an available set of goods and services among members of society. In this context, I distinguished in last week’s post between changes in public policies (reallocations of economic welfare) that make some people feel better off and none feel worse off and those that make some people feel better off but others feel worse off.

consider whether economists should ever become advocates for a revaluation of China’s currency, the renminbi — or, alternatively, for imposing higher tariffs on Chinese imports. Such a policy would tend to improve the lot of shareholders and employees of manufacturers competing with Chinese imports. Yet it would make American consumers of Chinese goods worse off. If the renminbi were significantly and artificially undervalued against the United States dollar, relative to a free-market exchange rate without government intervention, that would be tantamount to China running a giant, perennial sale on Chinese goods sold to the United States. If you’re an American consumer, what’s not to like about that? So why are so many economists advocating an end to this sale?

Earlier models, Kleinberg explains, indicated the danger of what economists call information cascades. “If you have a few crucial ingredients — namely, that people are making decisions in order, that they can observe the past actions of other people but they can’t know what those people actually knew — then you have the potential for information cascades to occur, in which large groups of people abandon whatever private information they have and actually, for perfectly rational reasons, follow the crowd,”

Plucking out of line most of the vaguely Middle Eastern-looking men at the airport for heightened screening is no more effective at catching terrorists than randomly sampling everyone. It may even be less effective. Press stumbled across this counterintuitive concept — sometimes the best way to find something is not to weight it by probability — in the unrelated context of computational biology. The parallels to airport security struck him when a friend mentioned he was constantly being pulled out of line at the airport.

Racial profiling, in other words, doesn’t work because it devotes heightened resources to innocent people — and then devotes those resources to them repeatedly even after they’ve been cleared as innocent the first time. The actual terrorists, meanwhile, may sneak through while Transportation Security Administration agents are focusing their limited attention on the wrong passengers.

Press tested the theory in a series of probability equations (the ambitious can check his math here and here).

in the magazine article Joshua mentions several studies of “folk morality,” i.e. of how ordinary people think about moral problems. The results are fascinating. It turns out that people’s views are correlated with personality traits, with subjects who score high on “openness to experience” being reliably more relativists than objectivists about morality (I am not using the latter term in the infamous Randyan meaning here, but as Knobe does, to indicate the idea that morality has objective bases).

Other studies show that people who are capable of considering multiple options in solving mathematical puzzles also tend to be moral relativists, and — in a study co-authored by Knobe himself — the very same situation (infanticide) was judged along a sliding scale from objectivism to relativism depending on whether the hypothetical scenario involved a fellow American (presumably sharing our same general moral values), the member of an imaginary Amazonian tribe (for which infanticide was acceptable), and an alien from the planet Pentar (belonging to a race whose only goal in life is to turn everything into equilateral pentagons, and killing individuals that might get in the way of that lofty objective is a duty). Oh, and related research also shows that young children tend to be objectivists, while young adults are usually relativists — but that later in life one’s primordial objectivism apparently experiences a comeback.

This is all very interesting social science, but is it philosophy? Granted, the differences between various disciplines are often not clear cut, and of course whenever people engage in truly inter-disciplinary work we should simply applaud the effort and encourage further work. But I do wonder in what sense, if any, the kinds of results that Joshua and his colleagues find have much to do with moral philosophy.

I apologise for this long overdue article to highlight the erroneous insinuations by my fellow KRC writer’s post, UBS: Singapore has Third World Living Standards.

The Satay Club post’s title was “UBS: Singapore has Russian Standard of Living”. The Original UBS report was even less suggestive, and in fact hardly made any value judgment at all. The original UBS report just presented a whole list of statistics, according to whichever esoteric mathematical calculation they used

As my JC economics teacher quipped, “If you abuse the statistics long enough, it will confess.” On one hand, UBS has not suggested that Singapore has third world living standards. On the other hand, I think it is justified to question how my KRC writer has managed to conclude from these statistics that Singapore has “Third World Living Standards”.

For many scientists, "basic research" means "fundamental" or "pure" research conducted without consideration of practical applications. At the same time, policy makers see "basic research" as that which leads to societal benefits including economic growth and jobs.

The mechanism that has allowed such divergent views to coexist is of course the so-called "linear model" of innovation, which holds that investments in "basic research" are but the first step in a sequence that progresses through applied research, development, and application. As recently explained in a major report of the US National Academy of Sciences: "[B]asic research ... has the potential to be transformational to maintain the flow of new ideas that fuel the economy, provide security, and enhance the quality of life" (Rising Above the Gathering Storm).

A closer look at the actual history of Google reveals how history becomes mythology. The 1994 NSF project that funded the scientific work underpinning the search engine that became Google (as we know it today) was conducted from the start with commercialization in mind: "The technology developed in this project will provide the 'glue' that will make this worldwide collection usable as a unified entity, in a scalable and economically viable fashion." In this case, the scientist following his curiosity had at least one eye simultaneously on commercialization.

The USPSTF recently issued an even sharper warning about the prostate-specific antigen test for prostate cancer, after concluding that the test’s harms outweigh its benefits. Chest X-rays for lung cancer and Pap tests for cervical cancer have received similar, albeit less definitive, criticism.CommentsView/Create comment on this paragraphThe next step in the reevaluation of cancer screening was taken last year, when researchers at the Dartmouth Institute for Health Policy announced that the costs of screening for breast cancer were often minimized, and that the benefits were much exaggerated. Indeed, even a mammogram (almost 40 million are given annually in the US) that detects a cancer does not necessarily save a life.CommentsView/Create comment on this paragraphThe Dartmouth researchers found that, of the estimated 138,000 breast cancers detected annually in the US, the test did not help 120,000-134,000 of the afflicted women. The cancers either were growing so slowly that they did not pose a problem, or they would have been treated successfully if discovered clinically later (or they were so aggressive that little could be done).

Efficiency is the seemingly value-free standard economists use when they make the case for particular policies — say, free trade, more liberal immigration policies, cap-and-trade policies on environmental pollution, the all-volunteer army or congestion tolls. The concept of efficiency is used to justify a reliance on free-market principles, rather than the government, to organize the health care sector, or to make recommendations on taxation, government spending and monetary policy. All of these public policies have one thing in common: They create winners and losers among members of society.

can it be said that a more efficient resource allocation is better than a less efficient one, given the changes in the distribution of welfare among members of society that these allocations imply?

Suppose a restructuring of the economy has the effect of increasing the growth of average gross domestic product per capita, but that the benefits of that growth accrue disproportionately disproportionately to a minority of citizens, while others are worse off as a result, as appears to have been the case in the United States in the last several decades. Can economists judge this to be a good thing?

the "data" from which the economic calculus starts are never for the whole society "given" to a single mind which could work out the implications and can never be so given.

The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess.

The economic problem of society

a journal's impact factor for a given year is the average number of citations received by papers published in the journal during the two preceding years. Letters to the editor, editorials, book reviews, and other non-papers are excluded from the impact factor calculation.

Review papers that don't necessarily contain new scientific knowledge yet provide useful overviews garner lots of citations. Five of the top 10 perennially highest-impact-factor journals, including the top four, are review journals.

Now suppose you're a journal editor or publisher. In these tough financial times, cash-strapped libraries use impact factors to determine which subscriptions to keep and which to cancel. How would you raise your journal's impact factor? Publishing fewer and better papers is one method. Or you could run more review articles. But, as a paper posted recently on arXiv describes, there's another option: You can manipulate the impact factor by publishing your own papers that cite your own journal.

Andrew Lo and Mark Mueller at MIT have a paper called “WARNING: Physics Envy May Be Hazardous to Your Wealth,” also available as a video.

inability to recognize radical UNCERTAINTY is what leads to excessive confidence in mathematical models of reality, and then on to bad policy and prediction. 

key concept of the paper is to define a continuum of uncertainty from the less radical to the more radical. You get into trouble when you think there is a higher level of certainty than there really is. 1. Complete Certainty 2.  Risk without Uncertainty (randomness when you know the exact probability distribution) 3. Fully Reducible Uncertainty (known set of outcomes, known model, and lots of data, fits assumptions for classical statistical techniques, so you can get arbitrarily close to Type 2). 4. Partially Reducible Uncertainty (“model uncertainty”: “we are in a casino that may or may not be honest, and the rules tend to change from time to time without notice.”) 5: Irreducible Uncertainty:  Complete Ignorance (consult a priest or astrologer) Physics Envy in Development leads you to think you are in Type 2 or Type 3, when you are really in Type 4. This feeds the futile search for the Grand Unifying Theory of Development.

Sam Harris's reinvention of Utilitarianism/Consequentialism has charmed many, and in my efforts to show people how pure Utilitarianism/Consequentialism fails (in the process encountering people who seem never to have read anything Harris has written or read on the subject, since I have been challenged to show where Harris has proposed Science as the foundation of our moral system, or that one can derive moral facts from facts about the world), "liberal utilitarianism" has been thrown at me as a way to resolve the problems with pure Utilitarianism/Consequentialism.

Liberal utilitarianism is not a position that one often encounters. I suspect this is because most philosophers recognise that unless one bites some big bullets, it is incoherent, being beholden to two separate moral theories, which brings many problems when they clash. It is much easier to stick to one foundation of morality.

utilitarians typically must claim that ‘the value of liberty. .. is wholly dependent on its contribution to utility. But if that is the case’, he asks, ‘how can the “right” to liberty be absolute and indefeasible when the consequences of exercising the right will surely vary with changing social circumstances?’ (1991, p. 213). His answer is that it cannot be, unless external moral considerations are imported into pure maximizing utilitarianism to guarantee the desired Millian result. In his view, the absolute barrier that Mill extcts against all forms of coercion really seems to require a non-utilitarian justification, even if ‘utilitarianism’ might somehow be defined or enlarged to subsume the requisite form of reasoning. Thus, ‘Mill is a consistent liberal’, he says, ‘whose view is inconsistent with hedonistic or preference utilitarianism’ (ibid., p. 236)...