What are scientific 'revolutions'? Part II: Qualitative paradigm adjustments

As we described yesterday, when scientists are doing what Thomas Kuhn referred to as 'normal' science, we are working within a given theoretical framework--or 'paradigm' as he called it--and using new technologies, data, and approaches to refine our understanding of Nature in terms of that framework. In biology now, normal science is couched within the evolutionary framework, the acceptance of descent with modification from a common ancestor.  We might tweak our views about the importance of natural selection vs drift, say, but that doesn't change the paradigm.

But there are energetic, and sometimes fierce discussions about just how we should go about doing our work. These discussions often involve the basic statistical methods on which our inferences lie.  We've talked about the statistical aspects of life science in numerous past posts. Today, I want to write about an aspect that relates to notions of 'revolution' in science, or what Kuhn called paradigm shifts.  What follows is my own view, not necessarily that of anybody else (including the late Kuhn).

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For many if not most aspects of modern science, we express basic truths mathematically in terms of some parameters.  These include values such as Newton's gravitational constant and any number of basically fixed values for atomic properties and interactions.  Such parameters of Nature are not known with perfect precision, but they are assumed to have some universally fixed value, which is estimated by various methods.  The better the method or data, the closer the estimate is held to be, relative to the true value.  Good science is assumed to approach such values asymptotically, even if we can never reach that value without any error or misestimation.

This is not the same as showing that the value is 'true', or that the underlying theory that asserts there is such a value is true.  Most statistical tests evaluate data relative to some assumed truth or property of truth, or some optimizing criterion given our assumptions about what's going on, but many scientists think that viewing results this way is a conceptual mistake.  They argue that our knowledge leads only to some degree of confidence, a subjective feeling, about an interpretation of Nature. Using approaches generally referred to as 'Bayesian', it's argued that all we can really do is refine our choice of properties of nature that we have most confidence in.  They rarely use the terms 'belief' or 'faith' in the preferred explanation, because 'confidence' carries a stronger sense of an acceptance that can be systematically changed.  The difference between Bayesian approaches and purely subjective hunches about Nature is that Bayesian approaches have a rigorous and in that sense highly objective format.

This comes from a famous rearrangement of a basic fact of probabilities, credited to Thomas Bayes. It is a rearrangement of basic laws of probability, and it goes like this:

     p(Hypothesis|Evidence) = p(Evidence|Hypothesis) p(Hypothesis) / p(Evidence)

This says that the probability of some Hypothesis we may be interested in is equal to the probability of that evidence E if the Hypothesis were truly true, times the probability that we have in mind for the Hypothesis, all divided by the overall probability of the Evidence; that is, there must be a lot of ways that the Evidence might arise (or we'd already know our Hypothesis was true!), so you sum up the probaiblity of the data if H is true (weighted by your prior probability that it is, and separately the probability of the data if an alternative to H is true weighted by the probability of its not being true. It's somewhat elusive, but here's an oversimplified example:

Suppose we believe that a coin is fair. But there's a chance that it isn't.  In advance of doing any coin-flipping, we might express our lack of knowledge by saying the chance that the coin is fair is, say, 50%, since we have no way to actually know if it is or isn't.  But now we flip the coin some number of times.  If it's fair, the probability of it coming up Heads equals 50%, or p(H) = 0.5 per flip.  But suppose we observe 60% Heads.  A fair coin could yield such results and we can calculate the probability of that happening.  But an unfair coin could also generate such a result.

For simplicity, let's say we observe HHHTT.  For a fair coin, with p(H) = 1/2, the probability of this result is (1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = 0.0312, but if the coin is unfair in a way that yields 60% Heads, the probability of this result is (0.6)(0.6)(0.6)(0.4)(0.4) = 0.035.  Using the formula above, the probability that the coin is fair actually drops from 50% to about 31%: we're less confident about the coin's fairness. If we kept flipping and getting such results, that value would continue dropping, as we became less confident that it's fair and increasingly confident that its true probability of Heads was 0.6 instead of 0.5.  We might also ask if the probability of it being fair is, say, zero, or 1/8, or 0.122467--that is, we can test any value between zero (no chance it's fair) to 1.0 (completely sure it's fair).

The basic idea is that we have some prior reason, or probability (p(H)) that the Hypothesis is true and we gather some new Evidence to evaluate that probability, and we adjust it in light of the new Evidence.  The adjusted value is called the posterior (to the new data) probability of the Hypothesis, and Bayes' theorem provides a way to make that adjustment.  Since we assume that something must be true, Bayes' formula provides a systematic way to change what we believe about competing explanations.  That is, our prior probability is less than 1.0 (certainty of our Hypothesis) which implies that there are other hypotheses that might be true instead.  The use of Bayes' theorem adjusts our confidence in our specified Hypothesis, but doesn't say or show that it is true.  Advocates of a Bayesian approach argue that this is the reality we must accept, and that Bayesian approaches tell us how to get a best estimate based on current knowledge.  It's always possible that we're not approaching truth in any absolute sense.  

A key aspect of the Bayesian view of knowledge is that the explanation is about the probability of the data arising if our preferred explanation is true, accepting that it might or might not be.  It assigns quantitative criteria for alternative explanations whose relative probability can be expressed--that is, the set of possible hypotheses each have a probability (a value between zero and 1),  and their sum exhausts all possibilities (just as Heads and Tails exhaust the possible flip outcomes, or a coin must either be fair or not-fair).

OK, OK so what does this have to do with scientific 'revolutions'?
The basic idea of Bayesian analysis is that it provides a technically rigorous way to express subjective confidence in a scientific context.  It provides a means to use increasing amounts of data to adjust the level of confidence we assign to competing hypotheses, and identify the Hypothesis that we prefer.

This is a good way to express confidence rather than a yes-no illusion of ultimate truth, and has found widespread use.  However, its use does depend on whether the various aspects of experiments and hypothesis can adequately be expressed in probabilistic terms that accurately reflect how the real world is--and, for example, important causal components may be missing, or the range of possibilities may not be expressible in terms of probability distributions.

I am by no means an expert, but a leading proponent of Bayesian approaches, the late ET Jaynes, said this in his classical text on the subject (Probability Theory, Cambridge Press, 2003):

Before Bayesian methods can be used, a problem must be developed beyond the 'exploratory phase' to the point where he it has enough structure to determine all the needed apparatus (a model, sample space, hypothesis space prior probabilities, sampling distribution).

This captures the relevant point for me here, in the context of the idea of scientific revolutions or paradigm shifts.  I acknowledge that in my personal view, and this is about philosophy of inference, such terms should be used only for what is perhaps their original reference, the major and stunning changes like the Darwinian revolution, and not the more pedestrian applications of everyday scientific life that are nonetheless casually referred to as revolutions.

These issues are (hotly) debated, but I feel we should make a distinction between scientific refinement and scientific revolutions.  To me, Bayesian analysis is a systematic way to refine a numerical estimate of the relative probability of an idea about Nature compared to other ideas that could be correct.  The prior probability of the best of these alternatives should asymptotically with increased amounts of data (as schematically shown in the figure below), unless something's wrong with the  conceptualization of the problem.  I think this is conceptually very different from having a given scientific 'paradigm' replace another with which it is incommensurable.   

Where it's useful, Bayesian analysis is about altered ideas among what are clearly commensurable hypotheses--based on different values of the same parameters. Usually, the alternative hypotheses are not very different, in fact, so that for example, a coin has some bias in its probability of Heads, ranging from no-chance to fair (50%) to inevitable; but assuming such things as that the flips are all done the same way and the results generated by flipping are probabilistic by nature.

In my view, Bayesian analysis is a good way to work through issues within a given theoretical framework, or paradigm, and it has many strong and persuasive advocates.  But is not a way to achieve a scientific revolution nor does it reflect one.  Sometimes the idea is used rather casually, as if formal Bayesian analysis can adjudicate between truly incomparable ideas; there, to me, we simply must rely on our subjective evaluations. One can't, of course, predict when or even whether a truly revolutionary change--a paradigm shift, if you will--will occur, or even if such is needed.

Ptolemaic epicycles added accuracy to the predictions of planetary motion, at the price of being cumbersome.  One could have applied Bayesian analysis to the problem at the time, had the method been available.  The Copernican revolution changed the basic structure of the underlying notion of what was going on.  One might perhaps construct Bayesian analysis that would evaluate the differences by somehow expressing planetary positions in probabilistic terms in both systems and allow one to pick a preference, but I think this would be rather forced--and, most importantly, a post hoc way to evaluate things (that is, only after we have both models to compare).  In fact, in this case one wouldn't really say one view was true and the other not--they are different ways of describing the same motions of bodies moving around in space relative to each other, and the decision of how to model that is essentially one of mathematical convenience.

I think the situation is much clearer in biology.  Creationist ideas about when and where species were created or how they related to each other in terms of what was called the Great Chain of Being, could have been adjusted by Bayesian approaches as, for example, the dates of fossils being discovered could refine estimates of when God created the species involved.  But Bayesian analysis is inappropriate for deciding whether creationism or evolution is the best hypothesis for accounting for life's diversity in the first place.  The choice in both approaches would be a subjective one, but without artificial contortions the two hypotheses are not probabilistic alternatives in a very meaningful sense. That's what incommensurability, which applies in this case I think, implies.  You can't very meaningfully assign a 'probability' to whether creationism or evolution is true, even if the evidence is overwhelmingly in favor of the latter.

Current approaches
These posts express my view of the subject of scientific theory, after decades of working in science during periods of huge changes in knowledge and technology.  I don't think that scientific revolutions are changes in prior probabilities, even if they may reflect them, but are more and different from that.  From this viewpoint, advocates for Bayesian analysis in genomics are refining, but not challenging the basic explanatory framework at all.  One often hears talk of paradigm shifts and use of similar 'revolution' rhetoric, but basically what is happening is just scaling up our current "normal science", because we know how to do that, not necessarily because it's a satisfactory paradigm about life.  And there are many reasons why that is what people normally do, more or less as Kuhn described.  I don't think our basic understanding of the logic of evolution or genetics has changed since I was a graduate student decades ago, even if our definition of a gene, or modes of gene frequency change, or our understanding of mechanisms have been augmented in major ways.

It is of course possible that our current theory of, say genomic causes of disease, is truly true, and what we need to do is refine its precision.  This is, after all, what the great Big Data advocacy asserts: we are on the right track and if you just give us more and more DNA sequence data we'll get there, at least asymptotically.  Some advocate Bayesian approaches to this task, while others use a variety of different statistical criteria for making inferences.

Is this attitude right for what we know of genomics and evolution?  Or is there reason to think that current "normal science" is pushing up against a limit and only a true conceptual revolution, one essentially incommensurate with, or not expressible in the terms of, our current models? In past posts, we've suggested numerous reasons why we think current modes of thought are inadequate.

It's all too easy to speak of scientific revolutions (or to claim, with excitement, that one is in the midst of creating one if only s/he can have bigger grants, which is in fact how this is usually expressed).  It's much harder to find the path to a real conceptual revolution.

What are scientific 'revolutions'? Part I: Qualitative paradigm shifts

How do we know what we think we know?  And how do we know how close we are to the 'truth'? These are fundamental questions in life, and especially in science where we expect to be in pursuit of the truth that we assume exists.  We build our work upon an accepted body of trusted knowledge, one that we first spend many years learning, and then even more years contributing to.  But there are always facts that don't quite fit the existing paradigm -- or don't fit at all -- and these can be wrong, or they can make a revolution.

In 1962, Thomas Kuhn published The Structure of Scientific Revolutions.  He built on his earlier work in the history and philosophy of science, The Copernican Revolution (1957) which analyzed  the way the sun-centered Copernican view of planetary motion replaced the long-standing Ptolemaic earth-centered view as an example of how scientific understanding of the world can change.  

In a nutshell, Kuhn says that scientists at any given time usually work within a model or theory, or paradigm as he referred to it, that explains their findings.  This paradigm guides what we do every day as we work away at what Kuhn called "normal science".  There are always unexplained or even apparently contradictory facts that don't easily fit into our working theory, but we do our very best in normal science to fit, or shoe-horn, these anomalies into our current paradigm.  Occasionally, when the lack of fit becomes too great, a 'revolution,' essentially a new theory, is proposed, usually based on a new finding or a new way of synthesizing the data that does a better job of accounting for the anomalies in question (even if it may do less or less well for some known facts).

The new theory dramatically and at one fell swoop accounts for hosts of facts that hadn't fit into the previous working paradigm, including the apparent anomalies.  A key point we'll discuss below is that the new view is not just a quantitative improvement in, say, measurement accuracy or something like that.  It's not technology. Instead, a defining characteristic is that the new view is "incommensurate" with the view it replaced: you cannot express the new view in terms of its predecessor.  It is quickly adopted by the profession in what Kuhn coined a "paradigm shift", which becomes the tool of a new phase of 'normal science'.  This was what he called a scientific 'revolution'.

Motion of Sun, Earth, and Mars according to heliocentrism (left) and to geocentrism (right), before the Copernican-Galilean-Newtonian revolution. Note the retrograde motion of Mars on the right. Yellow dot, Sun; blue, Earth; red, Mars.
(In order to get a smooth animation, it is assumed that the period of revolution of Mars is exactly 2 years, instead of the actual value, 1.88 years). The orbits are assumed to be circular, in the heliocentric case. Source: Wikipedia, Copernican Revolution

The view that the earth was part of the solar system fundamentally changed the way planetary motion was accounted for.  In the older Ptolemaic system, movements that were supposed to be perfect circles in the perfect spheres of the heavens, did not fit astronomical observations. So occasional little circles of movement (called epicycles) were invoked to explain observations and make predictions more accurate and consistent. But if the sun were viewed as the system's center, then one could account for the motions with ellipses and no epicycles. Refinements were to come along with Newton and Kepler, and Tycho Brahe then showed that geocentric mathematics could also work, with a "geo-heliocentric" system in which the Sun and Moon orbit the Earth (see Wikipedia: Tycho Brahe); but in which the other planets go around the Sun.

However, there have been other examples that reflect the basic Kuhnian idea: Darwin's evolutionary theory replaced one of special creation of the earth's species; quantum theory and relativity added truly revolutionary ideas about space, time and even causal determinism; plate tectonics (continental drift) replaced a diversity of ad hoc accounts for geological forms and changes, and so on.  The basic notions of normal science, working paradigms, and essentially incommensurable replacement of one theory by another may be criticized in detail, but Kuhn's way of explaining the dynamics of science has much to recommend it.

The phrase "paradigm shift" has become canonized in modern science parlance.  It glamorizes the genius (Copernicus, Einstein, Darwin) who was responsible for the change of view, often neglecting others who had roughly the same idea or whose work triggered the iconic figure's work.  And for that reason, and because scientists are mainly middle class drudges who need to feel important, we throw the phrase around rather loosely (often referring to our own work!).  We speak of scientific revolutions now rather casually as if they are occurring, whenever some new finding or technology comes along.  But is that justified?

Generalizations about classical 'paradigm shifts' and revolutions in science
We were lead to write about this because of comments on our recent post on the faith component of science having to do with how we in science view what we think we know.  This and the following post tomorrow are reflections about this, and not intended as an argument with the commenter.

A key relevant question is how we decide that what we assert today is better than what we said yesterday.  If it is different, but not better, then where can we find a sense that we know more, or are closer to the truth?  What if there is no single truth that we hope science is asymptotically approaching--with each new discovery getting closer to a perfect understanding?

At least one aspect of the answer lies in the idea of incommensurability between 'paradigms' as opposed to accuracy within a given paradigm.  Here, I'll focus on genetics and evolution, fields I know at least something substantial about.

Prior to Darwin, in Western culture the prevailing view of life was that species had been individually created by God for His own reasons.  Species might change under husbandry and so on, but they were basically static (though they might become extinct, again for some reason in God's plan), but they didn't morph one into another.  After Darwin, species were viewed as the result of a historical physical process, evolution taking place over time due to physical constraints (natural selection).  In a Darwinian view one cannot measure the nature or arrival of species in terms of events of special creation.  Humans cannot be viewed as specially created at the Beginning with the rest of life created for our use.  Evolution is not just a quantitative description of special creation.  The two views are incommensurable.

In the new 'paradigm', everything changed.  Species and their traits are viewed in terms of historical usage history, context-specific factors that affect what forms could succeed better than other forms relative to each other at the time, not in any external Creator's eye.  Evolution was truly a revolutionary change in the understanding of global diversity in life.  It has had at least as much impact as any other revolutionary conceptual change in any science.  But is it more 'true' or has it given us the truth about life?

Of course, even if the process of speciation is an historical one that takes place gradually by Darwinian means, each species must arise at some specific time.  Is this so different?  Yes!  It's different first because the definition of 'species' is a human-imposed cultural one and because the many processes that could lead populations to be mating-incompatible (the usual definition of 'species') may arise by single events (mutations in chromosome regions required for mating, for example) but they were historical, random changes in DNA, etc.  They were not guided from without with any purpose.  And generally, diversity accumulates along with mating incompatibility, gradually.

And what about natural selection?  It is the theoretically accepted origin of complex traits in living species.  It is a gradual process even if each life or death or conception may be discrete events in time and place.  And, after Darwin, we have had to add chance (genetic drift) into the picture of how genomic structures and what they cause have changed over time.  But such additions modify, but do not at all overthrow the idea of evolution.  They introduce no paradigm shift.

Nor does the discovery that chromosomes contain more than just protein-coding DNA sequence--they have regulatory sequences, sequences involved in DNA's own packaging, and so on.  The idea of gene regulation, or of genes being made of discrete, interrupted sequence regions (coding exons, introns, etc) added new theoretical elements to biology, but they are entirely commensurable with prior views that were non-specific as to just what genes 'are'.  The discovery of the base-pairing nature of DNA and its use of a code for protein sequence and other functions added to our understanding of life, and produced a new theory of genetic causation.  But that theory didn't replace some earlier specific theory about what genes were.  None of this in any serious way was a paradigm shift, even though these discoveries were of momentous importance to our understanding of life.

And then there's the origin of 'life'.  Mustn't that, too, have had a moment of creation?  Biochemists will have to assert that the possibility has always existed since the beginning of the cosmos, but that only when the right ingredients (molecules, pH, temperature, etc.) existed at the same time and place did life start.  It may have had countless molecular origins, but here on earth at least only one such led to life as we know it today.  That is, in a sense, a theory of a moment of occurrence--though not of 'creation'.  So in our modern view it's part of the historical process that is life.

So, biology has had its scientific revolution, and one that shook the earth in very Kuhnian terms. But whether we are closer to the 'truth' about what life is, is itself a rather vague or even unanswerable question.  As technology advances, we could be getting a better and better understanding, and a more complete explanation of the essential nature of life.  Or, forces at work within organisms might be discovered which will lead to fundamentally different kinds of understanding of life.  How can we ever know unless or until that happens?

One way to rephrase this question is to ask whether we can know how 'close' we are to understanding the truth.  We can compare origin theories from many different cultures, including our own Biblical one, but we can't really concoct a quantitative measure of how true they are even relative to each other.  In a sense, all have zero truth except evolution, but that's not very useful, because we have no way to know what new idea may come along to challenge the one that we now believe to be true.  Of course, some people, even some otherwise scientists, accept religious explanations and will simply not acknowledge what I've been saying because they have an incommensurable truth that cannot be compared in this way to evolution other than by forced contortions such as that the Bible should be taken metaphorically and the like.  Or others have a mystical view of universal unity and reincarnation etc. which, like Biblical explanations, cannot really be compared because it doesn't attempt to explain the same things.

But there is another very different way to view scientific progress, typically referred to by the term 'Bayesian', which is often implicitly equated with 'revolutions' or 'paradigm shifts', as a systematic rather than episodic way for scientific truth to become known.  We'll discuss that tomorrow.

Every scientist since yesterday.....

One objective of science is to unlock Nature's 'secrets', and there is a natural hunger to be among those who see most deeply what others have not seen before. That's why our culture properly respects our Newtons and Darwins (and why there are priority squabbles). But (and as priority squabbles show), we have to lobby and promote our ideas to get them both recognized and accepted.

When we do that, especially if there has been financial investment in our ideas, we naturally tend to be defensive about them. We can easily back ourselves into a conceptual corner in doing so. Being wrong is not what our ethos is all about. Defending dated ideas is not good for science, but it is largely the way science actually works, until a better idea forces earlier ones off the stage. This was a central point in Thomas Kuhn's analysis of scientific 'revolutions' (like the Darwinian one of which we're the beneficiaries).

But being wrong and having only imperfect knowledge is part of the game. As put in a cogent quote in a very fine recent biography of Ernst Haeckel by Robert Richards (The Tragic Sense of Life, 2009, U Chicago Press), 'every scientist since yesterday' has been wrong. If there's a lesson here for all of us, it would--or at least should--be to be more humble in promoting our favorite ideas. They are all wrong, in one way or another.

Unfortunately, imperfection is the gap that opponents of science itself often use as a wedge to dislodge an understanding of the world from its empirical foundations. In this case, I've been barraged with a listserv of messages from a group of people (mainly scientists of various kinds) who support a theological interpretation of life by hammering away at the imperfections, and excessive claims, of evolutionary biologists. They use various arguments, but mainly the false syllogism that because evolutionary biologists don't know everything, they must be wrong about evolution....and therefore some God-based explanation must be right.

In genetics and evolution there are many unknowns, and we tend to minimize them (except those that help us in a grant application), and overstate or oversimplify our own particular worldviews. We are doubtlessly wrong in many ways, but it is not true that every scientist since yesterday was completely wrong, and there can be little doubt that we understand Nature much better today than we did yesterday.

Life is a tough subject to study, and we should be more careful about what we don't know and the range of plausible explanations for our phenomena. But it is also true that what we don't know is not evidence for some specific alternative theory, religious or otherwise. Scientific theories may always be underdetermined--more than one explanation being consistent with the available facts, but there is nonetheless likely to be some truth out there, and it must be compatible with those same facts. We should do our best not to shun or exclude alternative ideas, while at the same time defending the nature of science as an imperfect attempt to understand Nature that needs to have a coherent operating framework.

It is, in fact, remarkable that blobs of protoplasm, called 'humans', could have evolved to have even the level of ability to understand Nature that we have. Since every scientist since yesterday has been wrong in one way or another, the Aristotelian kind of argument that we evolved to have a correct intuitive understanding of Nature does not account for our species' abilities. Indeed, we evolved by doing what we needed to do, so it is likely that we would have cognition at least consistent with the relevant subset of the nature of Nature. Beyond that is the remarkable fact that, fallible though we are, the evolution of general problem-solving ability has led us to go so deeply beyond the specifics of our past survival challenges.