Posts Tagged Philosophy of Science

Data without theory is lame

Just over eight years ago Chris Anderson of Wired announced with typical Silicon Valley humility that big data had made the scientific method obsolete. Seemingly innocent of any training in science, Anderson explained that correlation is enough; we can stop looking for models.

Anderson came to mind as I wrote my previous post on Richard Feynman’s philosophy of science and his strong preference for the criterion of explanatory power over the criterion of predictive success in theory choice. By Anderson’s lights, theory isn’t needed at all for inference. Anderson didn’t see his atheoretical approach as non-scientific; he saw it as science without theory.

Anderson wrote:

“…the big target here isn’t advertising, though. It’s science. The scientific method is built around testable hypotheses. These models, for the most part, are systems visualized in the minds of scientists. The models are then tested, and experiments confirm or falsify theoretical models of how the world works. This is the way science has worked for hundreds of years… There is now a better way. Petabytes allow us to say: ‘Correlation is enough.’… Correlation supersedes causation, and science can advance even without coherent models, unified theories, or really any mechanistic explanation at all.”

Anderson wrote that at the dawn of the big data era – now known as machine learning. Most interesting to me, he said not only is it unnecessary to seek causation from correlation, but correlation supersedes causation. Would David Hume, causation’s great foe, have embraced this claim? I somehow think not. Call it irrational data exuberance. Or driving while looking only into the rear view mirror. Extrapolation can come in handy; but it rarely catches black swans.

Philosophers of science concern themselves with the concept of under-determination of theory by data. More than one theory can fit any set of data. Two empirically equivalent theories can be logically incompatible, as Feynman explains in the video clip. But if we remove theory from the picture, and predict straight from the data, we face an equivalent dilemma we might call under-determination of rules by data. Economic forecasters and stock analysts have large collections of rules they test against data sets to pick a best fit on any given market day. Finding a rule that matches the latest historical data is often called fitting the rule on the data. There is no notion of causation, just correlation. As Nassim Nicholas Taleb describes in his writings, this approach can make you look really smart for a time. Then things change, for no apparent reason, because the rule contains no mechanism and no explanation, just like Anderson said.

In Bobby Henderson’s famous Pastafarian Open Letter to Kansas School Board, he noted the strong inverse correlation between global average temperature and the number of seafaring pirates over the last 200 years. The conclusion is obvious; we need more pirates.

Data without theory is lame - The Multidisciplinarian blog

My recent correlation-only research finds positive correlation (r = 0.92) between Google searches on “physics” an “social problems.” It’s just too hard to resist seeking an explanation. And, as positivist philosopher Carl Hempel stressed, explanation is in bed with causality; so I crave causality too. So which is it? Does a user’s interest in physics cause interest in social problems or the other way around? Given a correlation, most of us are hard-coded to try to explain it – does a cause b, does b cause a, does hidden variable c cause both, or is it a mere coincidence?

Big data is a tremendous opportunity for theory-building; it need not supersede explanation and causation. As Sean Carroll paraphrased Kant in The Big Picture:

“Theory without data is blind. Data without theory is lame.”

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[edit 7/28: a lighter continuation of this topic here]

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Happy is he who gets to know the causes of things – Virgil

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Can Science Survive?

galileo
In my last post I ended with the question of whether science in the pure sense can withstand science in the corporate, institutional, and academic senses. Here’s a bit more on the matter.

Ronald Reagan, pandering to a church group in Dallas, famously said about evolution, “Well, it is a theory. It is a scientific theory only.” (George Bush, often “quoted” as saying this, did not.) Reagan was likely ignorant of the distinction between two uses of the word, theory. On the street, “theory” means an unsettled conjecture. In science a theory – gravitation for example – is a body of ideas that explains observations and makes predictions. Reagan’s statement fueled years of appeals to teach creationism in public schools, using titles like creation science and intelligent design. While the push for creation science is usually pinned on southern evangelicals, it was UC Berkeley law professor Phillip E Johnson who brought us intelligent design.

Arkansas was a forerunner in mandating equal time for creation science. But its Act 590 of 1981 (Balanced Treatment for Creation-Science and Evolution-Science Act) was shut down a year later by McLean v. Arkansas Board of Education. Judge William Overton made philosophy of science proud with his set of demarcation criteria. Science, said Overton:

  • is guided by natural law
  • is explanatory by reference to natural law
  • is testable against the empirical world
  • holds tentative conclusions
  • is falsifiable

For earlier thoughts on each of Overton’s five points, see, respectively, Isaac Newton, Adelard of Bath, Francis Bacon, Thomas Huxley, and Karl Popper.

In the late 20th century, religious fundamentalists were just one facet of hostility toward science. Science was also under attack on the political and social fronts, as well an intellectual or epistemic front.

President Eisenhower, on leaving office in 1960, gave his famous “military industrial complex” speech warning of the “danger that public policy could itself become the captive of a scientific technological elite.” At about the same time the growing anti-establishment movements – perhaps centered around Vietnam war protests –  vilified science for selling out to corrupt politicians, military leaders and corporations. The ethics of science and scientists were under attack.

Also at the same time, independently, an intellectual critique of science emerged claiming that scientific knowledge necessarily contained hidden values and judgments not based in either objective observation (see Francis Bacon) or logical deduction (See Rene Descartes). French philosophers and literary critics Michel Foucault and Jacques Derrida argued – nontrivially in my view – that objectivity and value-neutrality simply cannot exist; all knowledge has embedded ideology and cultural bias. Sociologists of science ( the “strong program”) were quick to agree.

This intellectual opposition to the methodological validity of science, spurred by the political hostility to the content of science, ultimately erupted as the science wars of the 1990s. To many observers, two battles yielded a decisive victory for science against its critics. The first was publication of Higher Superstition by Gross and Levitt in 1994. The second was a hoax in which Alan Sokal submitted a paper claiming that quantum gravity was a social construct along with other postmodern nonsense to a journal of cultural studies. After it was accepted and published, Sokal revealed the hoax and wrote a book denouncing sociology of science and postmodernism.

Sadly, Sokal’s book, while full of entertaining examples of the worst of postmodern critique of science, really defeats only the most feeble of science’s enemies, revealing a poor grasp of some of the subtler and more valid criticism of science. For example, the postmodernists’ point that experimentation is not exactly the same thing as observation has real consequences, something that many earlier scientists themselves – like Robert Boyle and John Herschel – had wrestled with. Likewise, Higher Superstition, in my view, falls far below what we expect from Gross and Levitt. They deal Bruno Latour a well-deserved thrashing for claiming that science is a completely irrational process, and for the metaphysical conceit of holding that his own ideas on scientific behavior are fact while scientists’ claims about nature are not. But beyond that, Gross and Levitt reveal surprisingly poor knowledge of history and philosophy of science. They think Feyerabend is anti-science, they grossly misread Rorty, and waste time on a lot of strawmen.

Following closely  on the postmodern critique of science were the sociologists pursuing the social science of science. Their findings: it is not objectivity or method that delivers the outcome of science. In fact it is the interests of all scientists except social scientists that govern the output of scientific inquiry. This branch of Science and Technology Studies (STS), led by David Bloor at Edinburgh in the late 70s, overplayed both the underdetermination of theory by evidence and the concept of value-laden theories. These scientists also failed to see the irony of claiming a privileged position on the untenability of privileged positions in science. I.e., it is an absolute truth that there are no absolute truths.

While postmodern critique of science and facile politics in STC studies seem to be having a minor revival, the threats to real science from sociology, literary criticism and anthropology (I don’t mean that all sociology and anthropology are non-scientific) are small. But more subtle and possibly more ruinous threats to science may exist; and they come partly from within.

Modern threats to science seem more related to Eisenhower’s concerns than to the postmodernists. While Ike worried about the influence the US military had over corporations and universities (see the highly nuanced history of James Conant, Harvard President and chair of the National Defense Research Committee), Eisenhower’s concern dealt not with the validity of scientific knowledge but with the influence of values and biases on both the subjects of research and on the conclusions reached therein. Science, when biased enough, becomes bad science, even when scientists don’t fudge the data.

Pharmaceutical research is the present poster child of biased science. Accusations take the form of claims that GlaxoSmithKline knew that Helicobacter pylori caused ulcers – not stress and spicy food – but concealed that knowledge to preserve sales of the blockbuster drugs, Zantac and Tagamet. Analysis of those claims over the past twenty years shows them to be largely unsupported. But it seems naïve to deny that years of pharmaceutical companies’ mailings may have contributed to the premature dismissal by MDs and researchers of the possibility that bacteria could in fact thrive in the stomach’s acid environment. But while Big Pharma may have some tidying up to do, its opponents need to learn what a virus is and how vaccines work.

Pharmaceutical firms generally admit that bias, unconscious and of the selection and confirmation sort – motivated reasoning – is a problem. Amgen scientists recently tried to reproduce results considered landmarks in basic cancer research to study why clinical trials in oncology have such high failure rate. They reported in Nature that they were able to reproduce the original results in only six of 53 studies. A similar team at Bayer reported that only about 25% of published preclinical studies could be reproduced. That the big players publish analyses of bias in their own field suggests that the concept of self-correction in science is at least somewhat valid, even in cut-throat corporate science.

Some see another source of bad pharmaceutical science as the almost religious adherence to the 5% (+- 1.96 sigma) definition of statistical significance, probably traceable to RA Fisher’s 1926 The Arrangement of Field Experiments. The 5% false-positive probability criterion is arbitrary, but is institutionalized. It can be seen as a classic case of subjectivity being perceived as objectivity because of arbitrary precision. Repeat any experiment long enough and you’ll get statistically significant results within that experiment. Pharma firms now aim to prevent such bias by participating in a registration process that requires researchers to publish findings, good, bad or inconclusive.

Academic research should take note. As is often reported, the dependence of publishing on tenure and academic prestige has taken a toll (“publish or perish”). Publishers like dramatic and conclusive findings, so there’s a strong incentive to publish impressive results – too strong. Competitive pressure on 2nd tier publishers leads to their publishing poor or even fraudulent study results. Those publishers select lax reviewers, incapable of or unwilling to dispute authors. Karl Popper’s falsification model of scientific behavior, in this scenario, is a poor match for actual behavior in science. The situation has led to hoaxes like Sokal’s, but within – rather than across – disciplines. Publication of the nonsensical “Fuzzy”, Homogeneous Configurations by Marge Simpson and Edna Krabappel (cartoon character names) by the Journal of Computational Intelligence and Electronic Systems in 2014 is a popular example. Following Alan Sokal’s line of argument, should we declare the discipline of computational intelligence to be pseudoscience on this evidence?

Note that here we’re really using Bruno Latour’s definition of science – what scientists and related parties do with a body of knowledge in a network, rather than simply the body of knowledge. Should scientists be held responsible for what corporations and politicians do with their knowledge? It’s complicated. When does flawed science become bad science. It’s hard to draw the line; but does that mean no line needs to be drawn?

Environmental science, I would argue, is some of the worst science passing for genuine these days. Most of it exists to fill political and ideological roles. The Bush administration pressured scientists to suppress communications on climate change and to remove the terms “global warming” and “climate change” from publications. In 2005 Rick Piltz resigned from the  U.S. Climate Change Science Program claiming that Bush appointee Philip Cooney had personally altered US climate change documents to lessen the strength of their conclusions. In a later congressional hearing, Cooney confirmed having done this. Was this bad science, or just bad politics? Was it bad science for those whose conclusions had been altered not to blow the whistle?

The science of climate advocacy looks equally bad. Lack of scientific rigor in the IPCC is appalling – for reasons far deeper than the hockey stick debate. Given that the IPCC started with the assertion that climate change is anthropogenic and then sought confirming evidence, it is not surprising that the evidence it has accumulated supports the assertion. Compelling climate models, like that of Rick Muller at UC Berkeley, have since given strong support for anthropogenic warming. That gives great support for the anthropogenic warming hypothesis; but gives no support for the IPCC’s scientific practices. Unjustified belief, true or false, is not science.

Climate change advocates, many of whom are credentialed scientists, are particularly prone to a mixing bad science with bad philosophy, as when evidence for anthropogenic warming is presented as confirming the hypothesis that wind and solar power will reverse global warming. Stanford’s Mark Jacobson, a pernicious proponent of such activism, does immeasurable damage to his own stated cause with his descent into the renewables fantasy.

Finally, both major climate factions stoop to tying their entire positions to the proposition that climate change has been measured (or not). That is, both sides are in implicit agreement that if no climate change has occurred, then the whole matter of anthropogenic climate-change risk can be put to bed. As a risk man observing the risk vector’s probability/severity axes – and as someone who buys fire insurance though he has a brick house – I think our science dollars might be better spent on mitigation efforts that stand a chance of being effective rather than on 1) winning a debate about temperature change in recent years, or 2) appeasing romantic ideologues with “alternative” energy schemes.

Science survived Abe Lincoln (rain follows the plow), Ronald Reagan (evolution just a theory) and George Bush (coercion of scientists). It will survive Barack Obama (persecution of deniers) and Jerry Brown and Al Gore (science vs. pronouncements). It will survive big pharma, cold fusion, superluminal neutrinos, Mark Jacobson, Brian Greene, and the Stanford propaganda machine. Science will survive bad science because bad science is part of science, and always has been. As Paul Feyerabend noted, Galileo routinely used propaganda, unfair rhetoric, and arguments he knew were invalid to advance his worldview.

Theory on which no evidence can bear is religion. Theory that is indifferent to evidence is often politics. Granting Bloor, for sake of argument, that all theory is value-laden, and granting Kuhn, for sake of argument, that all observation is theory-laden, science still seems to have an uncanny knack for getting the world right. Planes fly, quantum tunneling makes DVD players work, and vaccines prevent polio. The self-corrective nature of science appears to withstand cranks, frauds, presidents, CEOs, generals and professors. As Carl Sagan Often said, science should withstand vigorous skepticism. Further, science requires skepticism and should welcome it, both from within and from irksome sociologists.

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the multidisciplinarian

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XKCD cartoon courtesy of xkcd.com

 

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The Trouble with Strings

Theoretical physicist Brian Greene is brilliant, charming, and silver-tongued. I’m guessing he’s the only Foundational Questions Institute grant awardee who also appears on the Pinterest Gorgeous Freaking Men page. Greene is the reigning spokesman for string theory, a theoretical framework proposing that one dimensional (also higher dimensions in later variants, e.g., “branes”) objects manifest different vibrational modes to make up all particles and forces of physics’ standard model. Though its proponents now discourage such usage, many call string theory the grand unification, the theory of everything. Since this includes gravity, string theorists also hold that string theory entails the elusive theory of quantum gravity. String theory has gotten a lot of press over the past few decades in theoretical physics and, through academic celebrities like Greene, in popular media.

XKCD

Several critics, some of whom once spent time in string theory research, regard it as not a theory at all. They see it as a mere formalism – a potential theory or family – very, very large family – of potential theories, all of which lack confirmable or falsifiable predictions. Lee Smolin, also brilliant, lacks some of Greene’s other attractions. Smolin is best known for his work in loop quantum gravity – roughly speaking, string theory’s main competitor. Smolin also had the admirable nerve to publicly state that, despite the Sokol hoax affair, sociologists have the right and duty to examine the practice of science. His sensibilities on that issue bring to bear on the practice of string theory.

Columbia University’s Peter Woit, like Smolin, is a highly vocal critic of string theory. Like Greene and Smolin, Woit is wicked sharp, but Woit’s tongue is more venom than silver. His barefisted blog, Not Even Wrong, takes its name from a statement Rudolf Peierls claimed Wolfgang Pauli had made about some grossly flawed theory that made no testable predictions.

The technical details of whether string theory is in fact a theory or whether string theorists have made testable predictions or can, in theory, ever make such predictions is great material that one could spend a few years reading full time. Start with the above mentioned authors and follow their references. Though my qualifications to comment are thin, it seems to me that string theory is at least in principle falsifiable, at least if you accept that failure to detect supersymmetry (required for strings) at the LHC or future accelerators over many attempts to do so.

But for this post I’m more interested in a related topic that Woit often covers – not the content of string theory but its practice and its relationship to society.

Regardless of whether it is a proper theory, through successful evangelism by the likes of Greene, string theory has gotten a grossly disproportionate amount of research funding. Is it the spoiled, attention-grabbing child of physics research? A spoiled child for several decades, says Woit – one that deliberately narrowed the research agenda to exclude rivals. What possibly better theory has never seen the light of day because its creator can’t get a university research position? Does string theory coerce and persuade by irrational methods and sleight of hand, as Feyerabend argued was Galileo’s style? Galileo happened to be right of course – at least on some major points.

Since Galileo’s time, the practice of science and its relationship to government, industry, and academic institutions has changed greatly. Gentleman scientists like Priestly, Boyle, Dalton and Darwin are replaced by foundation-funded university research and narrowly focused corporate science. After Kuhn – or misusing Kuhn – sociologists of science in the 1980s and 90s tried to knock science from its privileged position on the grounds that all science is tainted with cultural values and prejudices. These attacks included claims of white male bias and echoes of Eisenhower’s warnings about the “military industrial complex.”   String theory, since it holds no foreseeable military or industrial promise, would seem to have immunity from such charges of bias. I doubt Democrats like string more than Republicans.

Yet, as seen by Smolin and Woit, in string theory, Kuhn’s “relevant community” became the mob (see Lakatos on Kuhn/mob) – or perhaps a religion not separated from the state. Smolin and Woit point to several cult aspects of the string theory community. They find it to be cohesive, monolithic and high-walled – hard both to enter and to leave. It is hierarchical; a few leaders control the direction of the field while its initiates aim to protect the leaders from dissenting views.  There is an uncommon uniformity of views on open questions; and evidence is interpreted optimistically. On this view, string theorists yield to Bacon’s idols of the tribe, the cave, and the marketplace. Smolin cites the rarity of particle physicists outside of string theory to be invited to its conferences.

In The Trouble with Physics, Smolin details a particular example of community cohesiveness unbecoming to science. Smolin says even he was, for much of two decades, sucked into the belief that string theory had been proved finite. Only when he sought citations for a historical comparison of approaches in particle physics he was writing did he find that what he and everyone else assumed to have been proved long ago had no basis. He questioned peers, finding that they too had ignored vigorous skepticism and merely gone with the flow. As Smolin tells it, everyone “knew” that Stanley Mandelstam (UC Berkeley)  had proved string theory finite in its early days. Yet Mandelstam himself says he did not. I’m aware that there are other takes on the issue of finitude that may soften Smolin’s blow; but, in my view, his point on group cohesiveness and their indignation at being challenged still stand.

A telling example of the tendency for string theory to exclude rivals comes from a 2004 exchange on the sci.physics.strings Google group between Luboš Motl and Wolfgang Lerche of CERN, who does a lot of work on strings and branes. Motl pointed to Leonard Susskind’s then recent embrace of “landscapes,” a concept Susskind had dismissed before it became useful to string theory. To this Lerche replied:

“what I find irritating is that these ideas are out since the mid-80s… this work had been ignored (because it didn’t fit into the philosophy at the time) by the same people who now re-“invent” the landscape, appear in journals in this context and even seem to write books about it.  There had always been proponents of this idea, which is not new by any means.. . . the whole discussion could (and in fact should) have been taken place in 1986/87. The main thing what has changed since then is the mind of certain people, and what you now see is the Stanford propaganda machine working at its fullest.”

Can a science department in a respected institution like Stanford in fairness be called a propaganda machine? See my take on Mark Jacobson’s science for my vote. We now have evidence that science can withstand religion. The question for this century might be whether science, in the purse sense, can withstand science in the corporate, institutional, and academic sense.

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String theory cartoon courtesy of XKCD.

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I just discovered on Woit’s Not Even Wrong a mention of John Horgan’s coverage of Bayesian belief (previous post) applied to string theory. Horgan notes:

“In many cases, estimating the prior is just guesswork, allowing subjective factors to creep into your calculations. You might be guessing the probability of something that–unlike cancer—does not even exist, such as strings, multiverses, inflation or God. You might then cite dubious evidence to support your dubious belief. In this way, Bayes’ theorem can promote pseudoscience and superstition as well as reason.

Embedded in Bayes’ theorem is a moral message: If you aren’t scrupulous in seeking alternative explanations for your evidence, the evidence will just confirm what you already believe.”

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My Trouble with Bayes

The MultidisciplinarianIn past consulting work I’ve wrestled with subjective probability values derived from expert opinion. Subjective probability is an interpretation of probability based on a degree of belief (i.e., hypothetical willingness to bet on a position) as opposed a value derived from measured frequencies of occurrences (related posts: Belief in Probability, More Philosophy for Engineers). Subjective probability is of interest when failure data is sparse or nonexistent, as was the data on catastrophic loss of a space shuttle due to seal failure. Bayesianism is one form of inductive logic aimed at refining subjective beliefs based on Bayes Theorem and the idea of rational coherence of beliefs. A NASA handbook explains Bayesian inference as the process of obtaining a conclusion based on evidence,  “Information about a hypothesis beyond the observable empirical data about that hypothesis is included in the inference.” Easier said than done, for reasons listed below.

Bayes Theorem itself is uncontroversial. It is a mathematical expression relating the probability of A given that B is true to the probability of B given that A is true and the individual probabilities of A and B:

P(A|B) = P(B|A) x P(A) / P(B)

If we’re trying to confirm a hypothesis (H) based on evidence (E), we can substitute H and E for A and B:

P(H|E) = P(E|H) x P(H) / P(E)

To be rationally coherent, you’re not allowed to believe the probability of heads to be .6 while believing the probability of tails to be .5; the sum of chances of all possible outcomes must sum to exactly one. Further, for Bayesians, the logical coherence just mentioned (i.e., avoidance of Dutch book arguments) must hold across time (synchronic coherence) such that once new evidence E on a hypothesis H is found, your believed probability for H given E should equal your prior conditional probability for H given E.

Plenty of good sources explain Bayesian epistemology and practice far better than I could do here. Bayesianism is controversial in science and engineering circles, for some good reasons. Bayesianism’s critics refer to it as a religion. This is unfair. Bayesianism is, however, like most religions, a belief system. My concern for this post is the problems with Bayesianism that I personally encounter in risk analyses. Adherents might rightly claim that problems I encounter with Bayes stem from poor implementation rather than from flaws in the underlying program. Good horse, bad jockey? Perhaps.

Problem 1. Subjectively objective
Bayesianism is an interesting mix of subjectivity and objectivity. It imposes no constraints on the subject of belief and very few constraints on the prior probability values. Hypothesis confirmation, for a Bayesian, is inherently quantitative, but initial hypotheses probabilities and the evaluation of evidence is purely subjective. For Bayesians, evidence E confirms or disconfirms hypothesis H only after we establish how probable H was in the first place. That is, we start with a prior probability for H. After the evidence, confirmation has occurred if the probability of H given E is higher than the prior probability of H, i.e., P(H|E) > P(H). Conversely, E disconfirms H when P(H|E) < P(H). These equations and their math leave business executives impressed with the rigor of objective calculation while directing their attention away from the subjectivity of both the hypothesis and its initial prior.

2. Rational formulation of the prior
Problem 2 follows from the above. Paranoid, crackpot hypotheses can still maintain perfect probabilistic coherence. Excluding crackpots, rational thinkers – more accurately, those with whom we agree – still may have an extremely difficult time distilling their beliefs, observations and observed facts of the world into a prior.

3. Conditionalization and old evidence
This is on everyone’s short list of problems with Bayes. In the simplest interpretation of Bayes, old evidence has zero confirming power. If evidence E was on the books long ago and it suddenly comes to light that H entails E, no change in the value of H follows. This seems odd – to most outsiders anyway. This problem gives rise to the game where we are expected to pretend we never knew about E and then judge how surprising (confirming) E would have been to H had we not know about it. As with the general matter of maintaining logical coherence required for the Bayesian program, it is extremely difficult to detach your knowledge of E from the rest of your knowing about the world. In engineering problem solving, discovering that H implies E is very common.

4. Equating increased probability with hypothesis confirmation.
My having once met Hillary Clinton arguably increases the probability that I may someday be her running mate; but few would agree that it is confirming evidence that I will do so. See Hempel’s raven paradox.

5. Stubborn stains in the priors
Bayesians, often citing success in the business of establishing and adjusting insurance premiums, report that the initial subjectivity (discussed in 1, above) fades away as evidence accumulates. They call this washing-out of priors. The frequentist might respond that with sufficient evidence your belief becomes irrelevant. With historical data (i.e., abundant evidence) they can calculate P of an unwanted event in a frequentist way: P = 1-e to the power -RT, roughly, P=RT for small products of exposure time T and failure rate R (exponential distribution). When our ability to find new evidence is limited, i.e., for modeling unprecedented failures, the prior does not get washed out.

6. The catch-all hypothesis
The denominator of Bayes Theorem, P(E), in practice, must be calculated as the sum of the probability of the evidence given the hypothesis plus the probability of the evidence given not the hypothesis:

P(E) = [P(E|H) x p(H)] + [P(E|~H) x P(~H)]

But ~H (“not H”) is not itself a valid hypothesis. It is a family of hypotheses likely containing what Donald Rumsfeld famously called unknown unknowns. Thus calculating the denominator P(E) forces you to pretend you’ve considered all contributors to ~H. So Bayesians can be lured into a state of false choice. The famous example of such a false choice in the history of science is Newton’s particle theory of light vs. Huygens’ wave theory of light. Hint: they are both wrong.

7. Deference to the loudmouth
This problem is related to no. 1 above, but has a much more corporate, organizational component. It can’t be blamed on Bayesianism but nevertheless plagues Bayesian implementations within teams. In the group formulation of any subjective probability, normal corporate dynamics govern the outcome. The most senior or deepest-voiced actor in the room drives all assignments of subjective probability. Social influence rules and the wisdom of the crowd succumbs to a consensus building exercise, precisely where consensus is unwanted. Seidenfeld, Kadane and Schervish begin “On the Shared Preferences of Two Bayesian Decision Makers” with the scholarly observation that an outstanding challenge for Bayesian decision theory is to extend its norms of rationality from individuals to groups. Their paper might have been illustrated with the famous photo of the exploding Challenger space shuttle. Bayesianism’s tolerance of subjective probabilities combined with organizational dynamics and the shyness of engineers can be a recipe for disaster of the Challenger sort.

All opinions welcome.

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Science, God, and the White House

Back in the 80s I stumbled upon the book, Scientific Proof of the Existence of God Will Soon Be Announced by the White House!, by Franklin Jones, aka Frederick Jenkins, later Da Free John, later Adi Da Samraj. I bought it on the spot. Likely a typical 70s mystic charlatan, Jones nonetheless saw clearly our poor grasp of tools for seeking truth and saw how deep and misguided is our deference to authority. At least that’s how I took it.

Who’d expect a hippie mystic to be a keen philosopher of science. The book’s title, connecting science, church and state, shrewdly wraps four challenging ideas:

  1. That there can be such a thing as scientific proof of anything
  2. That there could be new findings about the existence of God
  3. That evidence for God could be in the realm of science
  4. That government should or could accredit a scientific theory

On the first point, few but the uneducated, TIME magazine, and the FDA think that proof is in the domain of science. Proof is deductive. It belongs to math, logic and analytic philosophy. Science uses evidence and induction to make inferences to the best explanation.

Accepting that strong evidence would suffice as proof, point number 2 is a bit trickier. Evidence of God’s existence can’t be ruled out a priori. God could be observable or detectable; we might see him or his consequences. An almighty god could easily have chosen to regularly show himself or to present unambiguous evidence. But Yahweh, at least in modern times, doesn’t play like that (A wicked and adulterous generation demands a sign but none will be given – Matthew 16:4). While believers often say no evidence would satisfy the atheist, I think a focused team could come up with rules for a demonstration that at least some nonbelievers would accept as sufficient evidence.

Barring any new observations that would constitute evidence, point number 3 is tough to tackle without wading deep into philosophy of science. To see why, consider the theory that God exists. Is it even a candidate for a scientific theory, as one WSJ writer thinks (Science Increasingly Makes the Case for God)? I.e., is it the content of a theory or the way it is handled by its advocates that makes the theory scientific? If the latter, it can be surprisingly hard to draw the line between scientific investigations and philosophical ones. Few scientists admit this line is so blurred, but how do string theorists, who make no confirmable or falsifiable predictions, defend that they are scientists? Their fondness for non-empirical theory confirmation puts them squarely in the ranks of the enlightenment empiricist, Bishop Berkeley of Cloyne (namesake of our fair university) who maintained that matter does not exist. Further, do social scientists make falsifiable predictions, or do they just continually adjust their theory to accommodate disconfirming evidence?

That aside, those who work in the God-theory space somehow just don’t seem to qualify as scientific – even the young-earth creationists trained in biology and geology. Their primary theory doesn’t seem to generate research and secondary theories to confirm or falsify. Their papers are aimed at the public, not peers – and mainly aim at disproving evolution. Can a scientific theory be primarily negative? Could plate-tectonics-is-wrong count as a proper scientific endeavor?

Gould held that God was simply outside the realm of science. But if we accept that the existence of God could be a valid topic of science, is it a good theory? Following Karl Popper, a scientific theory can withstand only a few false predictions. On that view the repeated failures of end-of-days predictions by Harold Camping and Herbert Armstrong might be sufficient to kill the theory of God’s existence. Or does their predictive failures simply exclude them from the community of competent practitioners?

Would NASA engineer, Edgar Whisenant be more credible at making predictions based on the theory of God’s existence? All his predictions of rapture also failed. He was accepted by the relevant community (“…in paradigm choice there is no standard higher than the assent of the relevant community” – Thomas Kuhn) since the Trinity Broadcast Network interrupted its normal programming to help watchers prepare. If a NASA engineer has insufficient scientific clout, how about our first scientist? Isaac Newton predicted, in Observations upon the Prophecies of Daniel and the Apocalypse of St. John, that the end would come in 2000 CE. Maybe Newton’s calculator had the millennium bug.

If we can’t reject the theory for any number of wrong predictions, might there be another basis for rejecting it? Some say absence of a clear mechanism is a good reason to reject theories. In the God theory, no one seems to have proposed a mechanism by which such a God could have arisen. Aquinas’s tortured teleology and Anselm’s ontological arguments still fail on this count. But it seems unfair to dismiss the theory of God’s existence on grounds of no clear mechanism, because we have long tolerated other theories deemed scientific with the same weakness. Gravity, for example.

Does assent of the relevant community grant scientific status to a theory, as Kuhn would have it? If so, who decides which community is the right one? Theologians spend far more time on Armageddon than do biologists and astrophysicists – and theologians are credentialed by their institutions. So why should Hawking and Dawkins get much air time on the matter? Once we’ve identified a relevant community, who gets to participate in its consensus?

This draws in point number 4, above. Should government or the White House have any more claim to a scientific pronouncement than the Council of Bishops? If not, what are we to think of the pronouncements by Al Gore and Jerry Brown that the science of climate is settled? Should they have more clout on the matter than Pope Francis (who, interestingly, has now made similar pronouncements)?

If God is outside the realm of science, should science be outside the jurisdiction of government? What do we make of President Obama’s endorsement of “calling out climate change deniers, one by one”? You don’t have to be Franklin Jones or Da Free John to see signs here of government using the tools of religion (persecution, systematic effort to censure and alienate dissenters) in the name of science. Is it a stretch to see a connection to Jean Bodin, late 16th century French jurist, who argued that only witches deny the existence of witches?

Can you make a meaningful distinction between our government’s pronouncements on the truth or settledness of the climate theory (as opposed to government’s role in addressing it) and the Kremlin’s 1948 pronouncement that only Lamarckian inheritance would be taught, and their call for all geneticists to denounce Mendelian inheritance? Is it scientific behavior for a majority in a relevant community to coerce dissenters?

In trying to draw a distinction between UN and US coercion on climate science and Lysenkoism, some might offer that we (we moderns or we Americans) are somehow different – that only under regimes like Lenin’s and Hitler’s does science get so distorted. In thinking this, it’s probably good to remember that Hitler’s eugenics was born right here, and flourished in the 20th century. It had nearly full academic support in America, including Stanford and Harvard. That is, to use Al Gore’s words, the science was settled. California, always a trendsetter, by the early 1920s, claimed 80% of America’s forced sterilizations. Charles Goethe, founder of Sacramento State University, after visiting Hitler’s Germany in 1934 bragged to a fellow California eugenicist about their program’s influence on Hitler.

If the era of eugenics seems too distant to be relevant to the issue of climate science/politics, consider that living Stanford scientist, Paul Ehrlich, who endorsed compulsory abortion in the 70s, has had a foot in both camps.

As crackpots go, Da Free John was rather harmless.

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“Indeed, it has been concluded that compulsory population-control laws, even including laws requiring compulsory abortion, could be sustained under the existing Constitution if the population crisis became sufficiently severe to endanger the society.” – Ehrlich, Holdren and Ehrlich, EcoScience, 3rd edn, 1977, p. 837

“You will be interested to know that your work has played a powerful part in shaping the opinions of the group of intellectuals who are behind Hitler in this epoch-making program.” – Charles Goethe, letter to Edwin Black, 1934

 

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Fine Tuned Fibs for the Cause

In my last post I compared our self-policing of facts that might chip away at our beliefs about environmental religion to lying for God in medieval and ancient times – something the writer of the epistles seems to boast of doing. Lying for God, on matters of science, may still be with us today.

William Lane Craig argues, in a line of thinking he calls reasonable faith (see his video),  that the apparent fine tuning of the universe allowing life in it to exist can only be explained as the work a designer. For Craig that designer happens to be the God of evangelical Protestantism.

Fine tuning has two different but related meanings in physics. The first deals mainly with theory, the second mainly with observation – something for Descartes, and something for Bacon.

In theory selection, fine tuning refers to how the details of a theory might need to be tweaked to make them fit observations. For example, in Ptolemaic astronomy, as used prior to Copernicus, the model only matched measurements if the planets’ epicycles stayed put in comparison to the straight line connecting the earth and sun and if the periods of the epicycles were exactly one year. Given those restrictions, the Ptolemaic model made good predictions. But why would those particular quantities have such relations? No reason could be found other than that they needed to be that way for the model to work. In Ptolemy’s defense, he did not believe the model represented reality; it merely gave right predictions. But the church believed it; and they forbade the teaching of the Copernican model. Copernicus’s model gave no better predictions; and it didn’t explain the lack of parallax in star positions or why a rotating earth didn’t suffer from great winds. But, Copernicus didn’t rely on fine tuning of his theory. What criterion is most important in theory selection – absence of fine tuning, predictive success, or explanatory power? That’s a topic for another time I guess. Read Paul Feyerabend on the matter if it grabs you.

In modern physics, fine tuning more commonly refers to our observation that many of the measured values that are, to our knowledge, constant across the universe have values that, were they even slightly different, would prevent life from being possible anywhere. Martin Rees, perhaps the first scientist to delve deep into the matter, identified six dimensionless constants (ratios of things we measure in physics, basically) on which life as we know it depends. These include the ratio of electromagnetic strength to the strength of gravity, the ratio of the mass density of the universe to the density required to halt expansion, and the so-called cosmological constant, the ratio of dark energy density in the universe to the density that would be needed to halt its expansion.

Popular examples of such fine tuning include the claim that if the electromagnetism/gravity ratio differed by an almost infinitesimal amount – say 1 part in 10 to the 40th power (1E-40) – things would be very quiet indeed. With a bit more gravity, stars would be too small and would burn out far too fast. Tweaking the other constants makes things even worse. Adjusting the cosmological constant to a few parts in ten to the 120 in either direction would make the universe either expand too fast for galaxies and stars to form or to collapse upon itself just after the big bang. These are unimaginably large/small numbers. A few scientists argue that our thinking is wrong here – again a topic for later. If interested, see Why the Universe Is Not Designed for Us  by Victor J. Stenger.

William Lane Craig accepts that fine tuning exists, giving three possible explanations: physical necessity, chance, or design. Craig rules out necessity because a life-prohibiting universe is easily imaginable. He notes that the probabilities for these incredibly fine-tuned values to occur by chance is ridiculously remote, thus leaving design as the only alternative.

Now I can’t know Craig’s motives or his state of mind, but his argument here is consistent with someone who knows more than he’s telling. That is, Craig is clearly highly intelligent; he has command of analytic philosophy, mathematics and at least a decent knowledge of physics. Yet he starts his fine tuning evangel with an egregious example of privileged hypothesis on top of false choice – just to start. Is he sure the given alternatives are the only live options? And can chance be ruled out in a multiverse model? I.e., in a model with 10 to the 500 instances of what we call our universe, you’re pretty much bound to get a few that look like ours with randomized values for the physical constants.

But we need not start with an exotic option. Did Craig rule out combinations of necessity and chance? Did he challenge the problem statement from the beginning? Many other have – questioning the notion that these measure values aren’t environmental constants at all; perhaps we’ve misconceived an underlying relationship that ties the values together in the same way pi is tied to 3.141592. Part of Stenger’s work is along these lines.

Having given his rationale for preferring the designer hypothesis to an artificially restricted set of alternatives, Craig then takes the leap from designer to the God of evangelical Christianity. That is, Krishna, Zeus, Ahura Mazda and the spaghetti monster are off the table. Craig holds that a being with unlimited cosmic power – who could construct any universe of his choosing – used his infinite powers to fine tune that universe to the precise values of constants that would allow that universe to support galaxies, stars and life. It’s hard for me to believe Craig doesn’t see the contradiction in an argument involving a God of ultimate power being bound by laws of physics. That is, Craig’s God is praiseworthy for essentially outwitting – by a tiny margin – physical laws that are nearly out of his control. This seems a better argument for the religion of the Assyrians than for evangelical Christianity; it recalls Marduk’s narrow defeat over Tiamat.

In Reasonable Faith, Craig deals often with the concept of insincere arguments. Do his religious convictions cause him to be blind to elementary fallacies and contradictions in his own doctrine? Or is he simply lying for the cause?

 

“…unbelief is at root a spiritual, not an intellectual, problem.” – William Lane Craig, Reasonable Faith: Christian Truth and Apologetics, 3rd edn., p.59

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Galileo, Cantor and the Countably Infinite

I recently found my high school algebra book from the classic Dolciani series. In Chapter 1’s exercises, I stumbled upon this innocent question: Determine whether there exists a one-to-one correspondence between the two sets {natural numbers} and {even natural numbers}. At the end of chapter 1 is a short biography of Georg Cantor (d. 1918), crediting him with inventing set theory, an approach toward dealing with the concept of infinity.

I’m going out on a limb here. I’m not a mathematician. I understand that Cantor is generally accepted as being right about infinity and countable sets in the math world; but I think I think his work on on one-to-one correspondence and the countability of infinite sets is flawed.

First, let’s get back to my high school algebra problem. The answer given is that yes, a one-to-one correspondence does exist between natural number and even numbers, and thus they have the same number of elements. The evidence is that the sets can be paired as shown below:

1 <—> 2
2 <—> 4
3 <—> 6

n <—> 2n

This seems a valid demonstration of one-to-one correspondence. In most of math – where deduction rules – a single case of confirming evidence is assumed to exclude all possibility of disconfirming evidence. But this infinity business is not math of that sort. It employs math and takes the general form of mathematical analysis; but some sleight of hand is surely at work. Cantor, in my view, indulged in something rather close to math, but also having a foot in philosophy, and perhaps several more feet (possibly of an infinite number of them) in language and psychology. One might call it multidisciplinary. Behold.

I can with equal validity show the two sets (natural numbers and even numbers) not to have a one-to-one correspondence but a two-to-one correspondence. I do this with the following pairing. Set 1 on the left is the natural numbers. Set 2 on the right is the even numbers:

1      unpaired
2 <—> 2
3      unpaired
4 <—> 4
5      unpaired

2n -1      unpaired
2n <—> 2n

By removing all the unpaired (odd) elements from the set 1, I pair each  remaining member of set 1 with each element of set 2. It seems arguable that if a one to one correspondence exists between part of set one and all of set two, the two whole sets cannot support a one-to-one correspondence. By inspection, the set of even numbers is included within the set of natural numbers and obviously not coextensive with it. Therefore Cantor’s argument, based solely on correspondence, works only by promoting one fact – pairing of terms – while ignoring an equally obvious fact, the matter of inclusion.  Against my argument Cantor seems to dismiss the obvious difficulty by making a sort of mystery-of-faith argument – his concept of infinity entails that a set and a proper subset of it can be the same size.

Let’s dig a bit deeper. First, Cantor’s usage of the one-to-one concept (often called bijection) is heavy handed. It requires that such correspondence be established by starting with sets having their members placed in increasing order. Then it requires the first members of each set to be paired with one another, and so on. There is nothing particularly natural about this way of doing things; Cantor devised it to suit his needs. It got him into enough logical difficulty that he had to devise the concepts of cardinality and ordinality, with problematic definitions. Gottlob Frege and Bertrand Russell had to patch up his definitions. The notion of equipollent sets fell out of this work, along with complications addressed by mental heavy lifters like von Neumann and Tarski, which are out of scope here. Finally, it seems to me that Cantor implies – but fails to state outright – that the existence of a simultaneous two-to-one correspondence (i.e., group each n and n+1 in set 1 with each 2n in set 2 to get a two-to-one correspondence between the two sets) does no damage to the claims that one-to-one correspondence between the two sets makes them equal in size. In other words, Cantor helped himself to an unnaturally restrictive interpretation (i.e., a matter of language) of one-to-one correspondence – one that favored his agenda. Cantor slips a broader meaning of equality on us than the strict numerical equality that math grew up with. Further, his usage of the term – and concept of – “size” requires a special definition.

Cantor’s rule set for the pairing of terms and his special definitions are perfectly valid axioms for mathematical system, but there is nothing within mathematics that justifies these axioms. Believing that the consequences of a system or theory justify its postulates is exactly the same as believing that the usefulness of Euclidean geometry justifies Euclid’s fifth postulate. Euclid knew this wasn’t so, and Proclus tells us Euclid wasn’t alone in that view.

Galileo, who, like Cantor, hurled some heavy-handed arguments when he was in a jam, seems to have had a more grounded sense of the infinite than Cantor. For Galileo, the concrete concept of equality, even when dressed up in fancy clothes like equipollence, does not reconcile with the abstract concept of infinity. Galileo thought concepts like similarity, countability, size and equality just don’t apply to the infinite. By the time of Leibnitz and Newton, infinity had earned a place in math, but as something that could be only approached, but not reached, equaled, measured or compared.

Cantor’s model of infinity may be interesting and useful, but it is a shame that’s it’s taught and reported as fact, e.g., “infinity comes in infinitely many different sizes – a fact discovered by Georg Cantor” (Science News, Jan 8, 2008).

The under-celebrated WVO Quine comes to mind as bearing on this topic. Quine argued that the distinction between analytic and synthetic statements was  false, and that no claim should be immune to empirical falsification. Armed with that idea, I’ll offer that Cantor’s math is subject to scientific examination. Since confirming evidence is always weaker than disconfirming evidence (i.e., Popperian falsifiability) I’d argue the demonstration of inequality of the sets of natural and even numbers (inclusion of one within the other) trumps the demonstration of equal size by correspondence.

Mathematicians who state the equal-size concept as a fact discovered by Cantor have overstepped the boundaries of their discipline. Galileo regarded the natural-even set problem as a true paradox. I agree. Did Cantor resolve this paradox, or did he merely conceal it with language?

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