Just as much of modern science has become self-serving in striving for status and funding, the theory of how science should be done is similarly afflicted. An assessment of a theory based on ‘degrees of belief’ might be useful if scientists didn’t routinely ignore, minimize or dismiss falsifying evidence and twiddle the countless knobs on their models to fit new data. The most glaring modern example of such behavior is the rejection of stark evidence of intrinsic redshift of quasars. Big bang cosmology is already lifeless by this assessment but ‘belief’ keeps the corpse warm. While we allow the few scientists who judge the data according to their beliefs to control publication, funding and press releases, real science is dead.
On May 7 New Scientist published “Do we need to change the definition of science?” by Robert Matthews.
Karl Popper
“Identified as the defining characteristic of real science by the philosopher Karl Popper more than 70 years ago, falsifiability has long been regarded by many scientists as a trusty weapon for seeing off the menace of pseudoscience.
The late Viennese thinker has been lauded as the greatest philosopher of science by the likes of Nobel prizewinning physicist Steven Weinberg, while Popper’s celebrated book The Logic of Scientific Discovery was described by cosmologist Frank Tipler as ‘the most important book of its century’.
Times change, though. Popper’s definition of science is being sorely tested by the emergence of supposedly scientific ideas which seem to fail it. From attempts to understand the fundamental nature of spacetime to theories purporting to describe events before the big bang, the frontiers of science are sprouting a host of ideas that are seemingly impossible to falsify.”
It is not clear how people could conclude that Popper “identified [falsification] as the defining characteristic of real science” if they actually read The Logic of Scientific Discovery. The book is about the logic associated with the discovery of new ideas; the title is not The Objective Characteristics of a Reified Abstraction. He clearly presents looking for false entailments as a convention. (That’s actually a quote from Popper on p. 37— “convention.”: Falsifiability “will accordingly have to be regarded as a proposal for an agreement or convention.” [Emphasis in original]. That is, an agreement not to “adjust” a theory but to consider any variation as an entirely new theory that must compete with all available alternatives and to admit that the old version was falsified.)
The book is not so much about science as about an attitude—an eagerness to discover and to test new ideas rather than to defend an established dogma against life’s inevitable changes. On the next page, Popper writes:
“Thus I freely admit that in arriving at my proposals I have been guided, in the last analysis, by value judgments and predilections. But I hope that my proposals may be acceptable to those who value not only logical rigour but also freedom from dogmatism; who seek practical applicability, but are even more attracted by the adventure of science, and by discoveries which again and again confront us with new and unexpected questions, challenging us to try out new and hitherto undreamed-of answers.”
The New Scientist article continues:
Much of [Popper’s] appeal rests on the clear-cut logic that seems to underpin the concept of falsifiability. Popper illustrated this through the now-celebrated parable of the black swan.
Suppose a theory proposes that all swans are white. The obvious way to prove the theory is to check that every swan really is white – but there’s a problem. No matter how many white swans you find, you can never be sure there isn’t a black swan lurking somewhere. So you can never prove the theory is true. In contrast, finding one solitary black swan guarantees that the theory is false. This is the unique power of falsification: the ability to disprove a universal statement with just a single example – an ability, Popper pointed out, that flows directly from the theorems of deductive logic.
Comment: Popper’s emphasis is on testing, and he repeats that it’s something scientists decide to do. It doesn’t exist independently in the (passive-voiced) objective world; someone does it (or, more commonly these days, doesn’t do it). Popper’s idea isn’t “sorely tested” by modern theories; modern scientists simply decided not to discover new ideas: There are plenty of black swans swimming in the pond of science; scientists just decided to define them as a different species rather than to look for a new theory that accounts for black swans.
Philosopher Colin Howson of the London School of Economics in the UK “believes it is time to ditch Popper’s notion of capturing the scientific process using deductive logic. Instead, the focus should be on reflecting what scientists actually do: gathering the weight of evidence for rival theories and assessing their relative plausibility.
Howson is a leading advocate for an alternative view of science based not on simplistic true/false logic, but on the far more subtle concept of degrees of belief. At its heart is a fundamental connection between the subjective concept of belief and the cold, hard mathematics of probability…”
Comment: Here is the point of departure from real science, where the perceived probability of a belief being true determines the course of science.
This should sound familiar; after all, it is what scientists do for a living. And it is a view of scientific reasoning with a solid theoretical basis. At its core is a mathematical theorem, which states that any rational belief system obeys the laws of probability – in particular, the laws devised by Thomas Bayes, the 18th-century English mathematician who pioneered the idea of turning probability theory on its head. Unlike Popper’s concept of science, the Bayesian view doesn’t collapse the instant it comes into contact with real life. It relies on the notion of accumulating positive evidence for a theory.
Comment: It is this kind of thinking that has allowed the big bang theory to persist when it should have collapsed the instant it came into contact with real life—the observations that highly redshifted objects (quasars) are connected to low redshift galaxies. In simple terms, redshift is not a measure of an expanding universe. We cannot ‘rewind’ time to a metaphysical ‘creation’ event—the big bang. What has happened is not science. It has been a process of selectively fitting the evidence to a belief in the big bang. Such a belief is not rational and shouldn’t even qualify for the Bayesian test.
“At first glance, it might appear surprising that a trivial mathematical result obtained by an obscure minister over 200 hundred years ago ought still to excite so much interest across so many disciplines, from econometrics to biostatistics, from financial risk analysis to cosmology. Published posthumously thanks to Richard Price in 1763, “An essay towards solving a problem in the doctrine of chances” by the rev. Thomas Bayes (1701(?)–1761) had nothing in it that could herald the growing importance and enormous domain of application that the subject of Bayesian probability theory would acquire more than two centuries afterwards. However, upon reflection there is a very good reason why Bayesian methods are undoubtedly on the rise in this particular historical epoch: the exponential increase in computational power of the last few decades made massive numerical inference feasible for the first time, thus opening the door to the exploitation of the power and flexibility of a rich set of Bayesian tools. Thanks to fast and cheap computing machines, previously unsolvable inference problems became tractable, and algorithms for numerical simulation flourished almost overnight…
Cosmology is perhaps among the latest disciplines to have embraced Bayesian methods, a development mainly driven by the data explosion of the last decade. However, motivated by difficult and computationally intensive inference problems, cosmologists are increasingly coming up with new solutions that add to the richness of a growing Bayesian literature.”
Comment: Trotta’s argument boils down to extolling the virtues of being able to play computer games with the data more effectively in recent times. The aim is to produce computer models that mimic as closely as possible ‘real life.’ However, cosmological models fail unless they introduce imaginary black holes, dark matter and dark energy as ‘fudge factors’ to match appearances. Once again, this is not science, it is computer game playing. Judging by science news reports, cosmologists are increasingly coming up with new science fiction that will certainly add to the richness of the laughter at their ‘literature’ in future. This misuse of Bayesian methodologies is symptomatic of a disconnect from reality in the sciences.
The New Scientist article continues:
Scientists begin with a range of rival explanations about some phenomenon, the observations come in, and then the mathematics of Bayesian inference is used to calculate the weight of evidence gained or lost by each rival theory. Put simply, it does this by comparing the probability of getting the observed results on the basis of each of the rival theories. The theory giving the highest probability is then deemed to have gained most weight of evidence from the data.
Comment: Bayes’s idea of calculating “the probability of getting observed results on the basis of each of the rival theories” may be of some use in comparing small variations on initial beliefs, but it misconceives the situation when different initial beliefs are involved. “Observed results” are interactive with the theories that direct observers about what to observe, how to observe it, what value to put on it, and which way to interpret it. As a good illustration Matthews quotes cosmologist Lawrence Krauss at Case Western Reserve University in Cleveland, Ohio:
“You just can’t tell if a theory really is unfalsifiable.” [Krauss] cites the case of an esoteric consequence of general relativity known as the Einstein ring effect. In a paper published in 1936, Einstein showed that the light from a distant star can be distorted by the gravitational field of an intervening star, producing a bright ring of light around it. It was a spectacular prediction but also, Einstein said, one that astronomers stood ‘no hope of observing’, as the ring would be too small to observe.
For all his genius, Einstein had reckoned without the ingenuity of astronomers, which in 1998 led to the discovery of the first example of a perfect Einstein ring – created not by a star, but by a vast galaxy billions of light years away.
Comment: Clearly the author had no idea that other “results” were possible: multiple active galactic nuclei ejections, plasma torus, etc. The interactivity between theories and observations is present in something as simple as observing an electron: are you looking at a particle with momentum or at a charge comprising an electrical current? Or at something no one has yet imagined?
The Einstein Cross.
In the mid-1980’s, astronomers discovered these four quasars, with redshifts about z = 1.7, buried deep in the heart of a galaxy with a low redshift of z = .04. (The central spot in this image is not the whole galaxy but only the brightest part of the galaxy’s nucleus.) When first discovered, the high redshift quasar in the nucleus of a low redshift galaxy caused a panic. To save the redshift/distance conviction, gravitational lensing had to be invoked despite Fred Hoyle’s calculation that the probability of such a lensing event was less than two chances in a million! And there is little sign of the expected reddening of the quasars’ light if it had passed so deeply through the dusty spiral. A change in brightness of the quasars was observed over a period of three years. Arp’s explanation is that the galaxy has ejected four quasars, which are growing brighter with age as they move farther from the nucleus. The lensing explanation is that the bending of the light varies when individual stars pass in front of the quasar. If the lensing explanation were correct, the quasars should brighten briefly and then fade as the star moves out of alignment.
A cardinal rule before applying the Bayes methodology is to ask whether the situation calls for a probability test. For example, an astronomer obtains an image of a highly redshifted quasar that appears to be in front of a low-redshift galaxy. Other astronomers are unconvinced and demand that he should evaluate the a posteriori probability that the quasar is indeed closer to us than the galaxy. In this case, examining data is not a matter of ‘probabilities’ (neither a priori nor a posteriori). It is simply a question of do you believe the evidence or not. If not, then you must be prepared to say why not. Are you accusing the presenter of the evidence of forgery? Are you saying the quasar is an ‘artifact’ and not really there? To raise probabilistic arguments in cases where the evidence is so confronting is an evasion. It is dishonest.
Probabilities aren’t prices by which you can compare the apples and oranges of different initial beliefs. Probabilities incorporate the very initial beliefs that scientists should be discovering and questioning. The theory that is based on familiar assumptions will always calculate out as more probable than the ones with unfamiliar assumptions. Bayesian probabilities are little more than digitized familiarities. “Secure knowledge” is the enemy of scientific discovery.
The author gets nowhere. “In the end,” he still misses Popper’s point and stays stuck in the conformist peer (reviewed) pressure that has all but stopped progress: “empirical observations…decide if a theory gets taken seriously.” As if people had nothing to do with it. No, scientists decide—to take seriously, to take for granted, or to discover new combinations of data, ideas, and initial beliefs.
It seems that modern scientists will not learn from history. They seem more opposed to unfamiliar theoretical options than in the past, which will only be apparent to scientists of the future. The Bayesian probabilistic evaluation of theories by those who choose which theories to test and the importance of the data merely serves to perpetuate this dysfunctional aspect of science. When the suspect is the judge and jury the verdict is not real science.
With appreciation to Mel Acheson for his contribution.
The late Viennese thinker has been lauded as the greatest philosopher of science by the likes of Nobel prizewinning physicist Steven Weinberg, while Popper’s celebrated book The Logic of Scientific Discovery was described by cosmologist Frank Tipler as ‘the most important book of its century’.
