[Paleopsych] Meme 038: When do anomalies begin?
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Wed Jan 26 15:43:36 UTC 2005
Meme 038: When do anomalies begin?
by Alan Lightman and Owen Gingerich
Science, Feb 7, 1992 v255 n5045 p690(6).
[This is one of my all-time favorites.]
An anomaly in science is an observed fact that is difficult to explain in
terms of the existing conceptual framework. Anomalies often point to the
inadequacy of the current theory and herald a new one. It is argued here that
certain scientific anomalies are recognized as anomalies only after they are
given compelling explanations within a new conceptual framework. Before this
recognition, the peculiar facts are taken as givens or are ignored in the old
framework. Such a "retrorecognition" phenomenon reveals not only a significant
feature of the process of scientific discovery but also an important aspect of
IN ANY EXAMINATION OF HOW SCIENTIFIC THEORIES CHANGE over time, "anomalies"
enter the discussion. The word anomaly has a venerable astronomical usage,
going back to the Greek, meaning a celestial motion that deviates from simple
uniformity. In Latin, it frequently designated any deviation from a regular
law of grammar. In English, the word gradually took on the meaning of any
deviation from the expected natural order, well exemplified by the Oxford
English Dictionary's 1873 citation from Charles Darwin: "There is no greater
anomaly in nature than a bird that cannot fly."
Anomalies are particularly helpful in understanding the scientific process,
for they point to the inadequacies of an old model and emphasize the merits of
the new. In these terms, an anomalous fact is one that is unexpected and
difficult to explain within an existing conceptual framework. For example, the
inadequacy of classical electrodynamics in the atomic domain was indicated by
a number of anomalies found in the early 1990s, such as the behavior of
electrons in metals, and the stability and emission of electron shells in
Rutherford's nuclear model of the atom. These phenomena were later given
compelling explanations by the new quantum theory.
In his seminal study of the scientific process, The Structure of Scientific
Revolutions, Thomas Kuhn described scientific discovery as a complex process
in which an "anomalous" fact of nature is recognized and then followed by a
change in conceptual framework (paradigm) that makes the new fact no longer an
anomaly. As Kuhn described it, "Discovery commences with the awareness of
anomaly, that is, with the recognition that nature has somehow violated the
pre-induced expectations that govern normal science" (1, pp. 52-53).
But when do anomalies begin? We will argue that certain scientific anomalies
are recognized only after they are given compelling explanations within a new
conceptual framework. In some cases, an anomalous fact may be unquestioned or
accepted as a given in the old paradigm. In others, the anomaly may be noted
by a small segment of the scientific community but not widely regarded as
important or legitimized until a good explanation is at hand in a new
paradigm. The development of this class of anomalies we call the
"retrorecognition" phenomenon. We will give several examples of
The Flatness Problem
According to the Big Bang model, the leading theory of modern cosmology, the
universe began in an explosion about 10 billion years ago. Since that violent
beginning, the universe has been expanding and cooling. As it expands, its
parts attract each other gravitationally, and that attraction slows down the
expansion. The competition between the outward motion of expansion and the
inward pull of gravity leads to three possibilities. The universe may expand
forever, with its outward motion always overwhelming the inward pull of
gravity. Such a universe is called "open." A second possibility is that the
inward force of gravity is sufficiently strong to halt and reverse the
expansion. Such a universe is called "closed." The final possibility, a "flat"
universe, lies exactly midway between a closed and open universe and is
analogous to a rock thrown upward with precisely the minimum speed that
ensures its escape from the pull of Earth. (In Einstein's theory of gravity,
open and closed universes have curved, non-Euclidean geometries, whereas a
flat universe has a noncurved, Euclidean geometry.)
The Big Bang model allows any of the three possibilities. Which one holds for
our universe depends on the manner in which the cosmic expansion began, or, in
particular, the initial gravity relative to the initial rate of expansion. In
other terms, the fate of the universe was determined by its initial
gravitational energy relative to its initial kinetic energy of expansion. Even
without knowledge of these initial conditions, we can infer the fate of our
universe by comparing its present gravitational energy with its present
kinetic energy of expansion. If the magnitude of the first of these two
energies is greater, the universe is closed, fated to collapse at some time in
the future. If the second is greater, the universe is open, fated to expand
forever. If the magnitudes of the two energies are precisely equal, the
universe is flat. The ratio of magnitudes of the two energies is [omega] =
(gravitational energy)/(kinetic energy). Thus, the universe is closed, flat,
or open depending on whether [omega] is greater than one, equal to one, or
less than one, respectively.
Current measurements of [omega] give it a value of about 0.1 (2). Although the
measurements are difficult and may be revised, cosmologists feel certain that
the value of [omega] lies between 0.1 and 10. As we will see, such a range is
surprisingly close to unity.
Now comes the flatness problem: Whyi is [omega] so close to one so long after
the universe began? It follows from the Big Ban model that, as time goes on,
[omega] differs more and more from one, unless it started out exactly one. In
an open universe, [omega] begins less than one and gets smaller in time; in a
closed universe, [omega] begins bigger than one and gets larger in time. Only
in a flat universe does [omega] begin and remain one. Finding the universe
today with its gravitational energy so closely balanced with its kinetic
energy of expansion is analogous to finding a rock thrown upward from Earth,
far from Earth, still moving outward but at a tiny speed, having neither
fallen back to Earth nor escaped Earth altogether. Such a situation would
require the rock's initial kinetic energy of motion to have been
extraordinarily close to its initial gravitational energy at launch.
The real issue behind the flatness problem is the value of [omega] in the
early universe. Physicists believe that the initial conditions of the cosmos
were set when the universe was about [10.sup.-43] s old, the era of "quantum
gravity." In order for the value of [omega] to lie between 0.1 and 10 today,
10 billion years after the quantum era, after the universe has expanded in
size by a factor of more than [10.sup.30], the initial value of [omega] had to
lie between about 1 + [10.sup.-59] and 1 - [10.sup.-59]. Equivalently, the
kinetic energy of expansion and the gravitational energy of the cosmos had to
be initially balanced to within one part in [10.sup.59]. It is important to
add that the Big Bang model has nothing to say about the initial conditions of
the universe. In particular, the model does not require any special value for
the initial ratio of gravitational energy to kinetic energy. yet to many
scientists today, it seems unlikely that so fine an initial balance, as
required by the observations, could have been merely an accident. Thus, there
is no "natural" explanation for the balance in the Big Bang model. The
extremely close balance of the two energies is an anomaly.
The flatness problem was first raised by Robert Dicke of princeton University
in 1969 . For a number of years afterward, however, few cosmologists
considered the observed value of [omega] a serious anomaly, an observed fact
that required a physical explanation. Some scientists, for example, regarded
the initial value of [omega] as a given or accidental property of our universe
and saw no difficulty with the near flatness of the cosmos; it was perhaps a
philosophical enigma but certainly not a legitimate scientific problem.
Typifying this viewpoint are Margaret Geller of the Harvard-Smithsonian Center
for Astrophysics and Robert Wagoner of Stanford University. According to
Geller, "the flatness problem has always seemed to me like an argument of
religion rather than an argument of science. Because the universe is one
realization. It's one system. So how can you talk about a priori
probabilities?" (4, p. 368). Wagoner says, "I don't think any of these
arguments [for or against the naturalness of [omega] being so close to one]
are relevant because I think they are philosophical. Let observation decide
what [omega] is" (4, p. 181). Other cosmologists paid no attention at all to
the flatness problem, and some briefly considered it but then dismissed it
because they had no good solutions to it.
The attitude of many scientists toward the flatness problem changed after
1981, when Alan Guth of Massachusetts Institute of Technology proposed a
significant addition to the Big Bang model called the inflationary universe
model . According to calculable physical processes described by new "grand
unified" theories of physics, the matter and energy in the infant universe
existed in a peculiar state, behaving as if they had repulsive gravity and
resulting in a very brief period of extremely rapid cosmic expansion. One of
the consequences of the inflationary epoch expansion was that, whatever its
initial value, [omega] would have been driven to a value extremely close to
one. Thus, the inflationary universe model gives a natural solution to the
flatness problem. The inflationary expansion, and the physics underlying it,
provided a mechanism to achieve an extremely close balance between the kinetic
and gravitational energies of the infant universe.
The questionable status of the flatness problem before the inflationary
universe model is evident in Guth's paper, where he devotes an entire appendix
to arguing that the problem is real and significant. According to
astrophysicist Marc Davis of Berkeley, "I have to say that I was so impressed
with the inflationary model because it had promoted the horizon [and flatness]
problems to tractable problems. . . . The reason that the flatness problem
wasn't wholly compelling [before the inflationary model] was that we couldn't
really justify why [omega] started off [near] one in the first place. . . .
Unless you have a dynamical argument, you're arguing about nonphysical
questions" (4, pp. 352 and 354). In the words of physicist Charles Misner at
the University of Maryland, "I just couldn't see how to play with those
equations, and so I didn't come on board thinking [the flatness problem] was
serious until the inflationary models came out. later, I developed a strong
preference for the flat universe, feeling that the Dicke paradox [the flatness
problem] suggested it. The key point for me was that inflation offers an
explanation. . . . What was crucial was that the inflationary universe [model]
provided an example that turned the Dicke paradox into a standard physics
problem" (4, pp.240-241).
Today, Misner and many other cosmologists consider the close balance of
kinetic and gravitational energies to be one of the most significant
observational facts of the universe, whether or not the inflationary universe
model itself survives the test of time. Before the new paradigm of the
inflationary universe model, only a handful of cosmologists considered the
close balance of energies to be a serious anomaly in the standard Big Bang
The Perigee-Opposition Problem
The contemporary reactions to the flatness problem have a fascinating parallel
with a cosmological revolution that took place four and a half centuries ago,
when Nicholas Copernicus (1473-1543) introduced the heliocentric planetary
system. The principal challenge for the astronomers of antiquity and the
Renaissance was to account for the seemingly irregular motions of the planets
among the stars, especially the so-called retrograde motion, in which a planet
appears temporarily to reverse its eastward motion against the background of
stars as seen from Earth. In the sun-centered system of Copernicus, this
phenomenon is easily explained. When the swifter moving Earth bypasses the
slower moving Mars, for example, Mars temporarily appears to move backward.
Precisely the same observed phenomenon was explained 1400 years earlier in the
geocentric system of Claudius Ptolemy (A.D. 140). To account for the
retrograde motion, Ptolemy proposed that each planet moved in a small circle,
called the epicycle, with in turn rode on a larger circle centered on Earth
(Fig. 1A). The compounded circles produced an occasional reverse motion.
But there is more. It is a basic observational fact, known since antiquity,
that retrograde motion occurs only around the time when the sun is in a direct
line with the planet. For the superior planets, Mars, Jupiter, and Saturn, the
sun must lie opposite the planet in the sky, hence the designation
"opposition." In particular, and this was especially obvious for Mars, the
planet was observed to be brightest, and therefore presumably closest to
Earth, during the time of retrogression.
In a sun-centered system, it is a simple geometrical truth that the middle of
the retrograde motion, and the planet's closest approach, must coincide with
opposition, when the sun, Earth, and planet lie in a straight line. But in an
Earth-centered system, such a coincidence is not required by the geometry. A
planet at the moment of opposition could, a priori, lie at any position on its
epicycle (Fig. 1B). (Only at perigee, at the bottom of the epicycle, would the
planet be in retrogression.) Alternatively, in the middle of retrograde
motion, the planet-Earth line and the sun-Earth line could a priori form any
angle at all (Fig. 1C). To explain the observations, Ptolemy had to assume
that each superior planet revolved in its epicycle at just the right rate so
that it reached perigee at the moment of opposition on every orbit (Fig. 1D).
We know that pre-Copernican astronomers were aware of these observational
facts because the Alfonsine planetary tables, made early in the 14th century,
took advantage of the solar connections, even though astronomers rarely
mentioned the fact explicitly. Thus, a striking observational fact that would
later have a completely natural explanation in the heliocentric system of
Copernicus had to be accepted as a given, without explanation, in the
geocentric system of Ptolemy.
For centuries, no one, not even Copernicus, remarked on the oddness of
Ptolemy's tacit assumption regarding perigee and opposition. It was an
astronomer in the generation after Copernicus, Gemma Frisius (1508-1555), who
first recognized the assumption as a problem. Gemma wrote (6, p. 42):
While a first glance the Ptolemaic hypotheses may seem more plausible than
Copernicurs', nevertheless the former are based on not a few absurdities, not
only because the stars are understood to be moved nonuniformly in their
circles, but also because they do not have explanations for the phenomena as
clear as those of Copernicus. For example, Ptolemy assumes that the three
superior planets in opposition--diametrically opposite the sun--are always in
the perigees of their epicycles, that is, a "fact-in-itself." In contrast, the
Copernican hypotheses necessarily infer the same thing, but they demonstrate a
The perigee-opposition phenomenon was recognized as an anomaly in the
Earth-centered framework only after it was given a "reasoned" explanation in
the new sun-centered framework.
The Continental-Fit Problem
As a third example of the retrorecognition phenomenon, consider the remarkable
similarity of shapes of the opposite coasts on the two sides of the Atlantic.
South America and Africa, in particular, are shaped as if they were two
fitting pieces of a jigsaw puzzle. We believe today that the two continents
were once joined and part of a single landmass, which subsequently split and
drifted apart. In such a framework, the good fit of continents on opposite
sides of the Atlantic is easy to explain. However, the fit is without
explanation in the previous conceptual framework, which held that landmasses
could move only vertically.
The remarkable fit of the continents could have been noticed soon after the
Atlantic Ocean had been mapped, certainly by the early 17th century .
Around 1800, the German naturalist and geographer Alexander von Humboldt
(1769-1859) proposed that the lands bordering the Atlantic were once joined.
His suggestion was not taken seriously. Half a century later the French
scientist Antonio Snider-Pellegrini, using fossil evidence as well as the fit
of the shapes, claimed that the continents were once joined. Again, the
proposal, which in this case was accompanied by a rather preposterous
mechanism, was not taken seriously by the majority of scientists. In 1881,
Reverend Osmond Fisher, English scientist and author of perhaps the earliest
textbook on geophysics, discussed a geological mechanism to explain the good
fit of the continents. He was largely ignored. Belief in the fixity of
continents held fast.
In 1912, the German geophysicist Alfred Wegener (1880-1930) analyzed the
situation much more carefully and included geological and fossil evidence to
argue for an ancient continuity of the landmasses, which then broke apart and
drifted away from each other . Wegener called his theory "continental
drift." Although additional evidence for continental drift began accumulating,
the hypothesis was highly controversial until the mid-1960s, when patterns of
magnetism in rocks on the ocean floor became convincing. Then, in the late
1960s, the theory of plate tectonics was developed. This theory, for the first
time, provided a persuasive mechanism by which the continents could move
horizontally, namely, the existence of a series of "plates" on which the
continents sit. The slow, convective flows within Earth's mantle force
neightorinb plates apart, carrying along the continents piggyback. Given the
mechanism provided by the theory of plate tectonics and the evidence for that
theory, the framework of continental drift has become accepted and has
replaced the previous framework of the fixity of continents.
What was for Wegener a clear anomaly in need of a reasoned explanation had
been for the great majority of geologists just a curiosity, scarcely even a
puzzle awaiting a solution. Only after the paradigm changed was the fit of the
continents seen as an anomaly pointing toward a major new way of looking at
the stability of continental arrangements.
The Adaptation-of-Organism Problem
As a fourth example, we turn to biology. For centuries, naturalists have
marveled at the exquisite specificity and adaptation of organisms to their
environment. Camels carry their energy-storing fat all in one place, on their
backs; thus, the rest of their bodies are not blanketed by a thick layer of
fat and so can efficiently cool off in the arid deserts where camels live. The
long necks of giraffes allow the animals to eat from the high trees in their
environment. pandas have a thumb-like sixth digit, which they use for
stripping the leaves off the bamboo shoots in the mountains of western China.
And so on.
Before the mid-19th century, most naturalists and many others took such
adaptation as evidence of a grand design, evidence of an intelligent and
powerful creator, and they explained the situation accordingly. For example,
in his The Wisdom of God Manifested in the Works of the Creation British
naturalist John Ray (1627-1705) wrote "because it is the great design of
providence to maintain and combine every Species, I shall take notice of the
great Care and abundant Provision that is made in securing this End" (9, p.
133). A clear statement of this view can be also found in Jean Jacques
Rousseau's (1712-1778) Profession of Faith of a Savoyard Vicar (10, pp. 259
How much sophistry does it not require to disavow the harmony of created
beings and that admirable order in which all the parts of the system concur to
the preservation of each other? . . . it is impossible for me to conceive that
a system of beings can be so wisely regulated, without the existence of some
intelligent cause which effects such regulation. . . . I believe, therefore,
that the world is governed by a wise and powerful Will.
In this prevailing "creationist" framework, which included belief in the
fixity of species, the perfect adaptation of organisms to their environment
was both natural and expected. However, some organisms are not so adapted.
Charles Darwin (1809-1882), in The Origin of the Species, cited a number of
examples. There are the ducks with feet designed for swimming that do not swim
(11, p. 177):
He who believes that each being is created as we now see it must have
occasionally felt surprise when he has met with an animal having habits and
structure not in agreement. What can be plainer than that the webbed feet of
ducks and geese are formed for swimming? Yet there are upland geese with
webbed feet which rarely go near the water.
There are the many animals that live in dark caves and are blind. Why should
these animals have eyes if they are not needed? The cave rat (Neotoma), for
example, has (blind) eyes that are lustrous and large. There are the birds,
like the 300-pound ostrich or the penguin, that do not fly. Why have wings and
And there are so many perfect habitats that are uninhabited (11, p. 401):
The general absence of frogs, toads, and newts on so many true oceanic islands
cannot be accounted for by their physical conditions: indeed it seems that
islands are peculiarly fitted for these animals; for frogs have been
introduced into madeira, the Azores, and Mauritius, and have multiplied so as
to become a nuisance. . . . But why, on the theory of creation, they should
not have been created there, it would be very difficult to explain.
At the end of the last passage, Darwin pointed out that nonadaptations are
anomalies in the creationist framework. Yet, these anomalies went unrecognized
until Darwin's new theory of adaptation, natural selection. Because natural
selection requires the evolution of organisms, it explains both adaptation and
nonadaptation. Organisms with traits suitable for survival in a particular
environment live to yield offspring, continue their line, and produce a
descendant population adapted to that environment. But organisms continue to
evolve and change habitats, so that a particular trait that was formerly
beneficial, like the webbed feet of upland ducks, may be no longer beneficial,
although still inherited. Traits not important for survival are not as
strongly subject to the forces of natural selection and thus may appear
unsuited to a particular environment at a particular time.
The Equality of Inertial and Gravitational Mass
As our final example, we consider the equality of inertial and gravitational
mass. The first mass resists a body's change in motion whereas the second
determines its gravitational force. It is the equality of these two masses
that causes bodies of different masses or different materials to fall with the
same acceleration in a gravitational field, a long-observed fact. Indeed, in
1592 Galileo wrote in his De Motu (12, p. 48):
The variation of speed in air between balls of gold, lead, copper, porphyr,
and other heavy material is so slight that in a fall of 100 cubits [about 46
m] a ball of gold would surely not outstrip one of copper by as much as four
fingers. Having observed this, I came to the conclusion that in a medium
totally void of resistance all bodies would fall with the same speed.
In Newtonian physics, the inertial mass and gravitational mass are regularly
canceled against each other. Newton himself was perplexed by this
extraordinary equality between quantities that seemed conceptually very
different, and he went to considerable lengths to establish their experimental
equivalence. For example, Newton recognized that a pendulum was a case in
which both types of mass played a role and that the equality of swings of
pendula with different bobs would measure the equality of the two masses to
high accuracy. Referring to his experiments timing the periods of pendula of
different materials, Newton says in his System of the World (13, p. 568):
I tried the thing in gold, silver, lead, glass, sand, common salt, wood,
water, and wheat. I provided two equal wooden boxes. I filled the one with
wood, and suspended an equal weight of gold (exactly as I could) in the center
of oscillation of the other. The boxes, hung by equal threads of 11 feet, made
a couple of pendulums perfectly equal in weight and figure, and equally
exposed to the resistance of the air: and, placing the one by the other, I
observed them to play together forwards and backwards for a long while, with
equal vibrations. And therefore the quantity of matter [inertial mass] in the
gold was to the quantity of matter in the wood as the action of the motive
force [gravitational mass] upon all the gold to the action of the same upon
all the wood; that is, as the weight of the one to the weight of the other.
In his law for the gravitational force, Newton simply equated the inertial and
gravitational masses without anything other than observational justification.
There was no essential reason within the theory itself as to why these two
quite different masses should be equal. They were simply assumed to be so,
much as Ptolemy had assumed that the epicyclic and orbital phases would be
exactly synchronized for the three superior planets or modern cosmologists had
assumed that the value of [omega] started off extremely close to one.
After Newton, the equality of inertial and gravitational mass was verified
with greater and greater accuracy. In the late 19th century, Lorant Eotvos, a
Hungarian baron, announced that his studies with plumb bobs showed that the
acceleration of gravity on different objects could not differ by more than a
few parts in a billion . Despite the extraordinary accuracy with which the
equality of the two masses was verified, scientists continued to accept that
equality as a given, without recognizing it as an anomaly in Newton's theory
It was not until Albert Einstein's new theory of gravity, general relativity,
that a fundamental explanation was given for the equality of inertial and
gravitational mass. Indeed, Einstein saw this equality, which was a part of
his "equivalence principle," as a profound statement about the naure of
gravity, and he constructed his entire theory around it. In the resulting
theory, gravity is understood as a geometrical phenomenon, with the equality
of the two masses a fundamental and necessary part of that picture. General
relativity was an entirely new theory, with new predictions. For example, as a
consequence of the equivalence principle, the bending of light by a
gravitating body may be quantiatively explained. And, for the first time, it
was realized that Newton's theory, and indeed all previous theories, had
failed to account adequately for the equality of inertial and gravitational
mass. As Einstein wrote in 1911, while struggling to develop his new theory of
gravity (15, p. 100),
This experience, of the equal falling of all bodies in the gravitational
field, is one of the most universal which the observation of nature has
yielded; but in spite of that the law has not found any place in the
foundations of our edifice of the physical universe.
Characterization of the Retrorecognition
The five examples given above follow a similar pattern:
1) A fact of nature is observed in the context of an existing explanatory
2) The fact does not have a logical explanation in the existing framework but
is nevertheless unquestioned and ignored, or accepted as a given property of
the world, or simply postulated to be true.
3) A new theory or model is advanced in which the observed fact now has a
compelling and reasoned explanation. At the same time, the fact is
retroactively recognized as an anomaly in the context of the old theory or
We might borrow the language of Gemma Frisius  by referring to facts taken
as givens as "facts-in-themselves" and to facts logically explained as
"reasoned facts." In this language, step 2 involves understanding the observed
fact as a fact-in-itself, whereas in step 3, with the emergence of a new
paradigm, the fact-in-itself is transformed into a reasoned fact. For the
class of anomalies that we are considering, it is only in step 3 that the
anomaly is recognized. Of course, in the new paradigm, the fact in question is
no longer an anomaly.
The terms "fact-in-itself" and "reasoned fact" used by Gemma Frisuis were
actually taken from Aristotle's system of logic, the Posterior Analytics,
where Aristotle distinguishes between the to oti (fact-in-itself) and the di
oti (reasoned fact) . The assumptions that the coincidence of retrograde
motion and opposition of planets is an accident or that the fit of the
continents is an accident might be regarded as "explanations" of these
observed facts. But these assumptions are not reasoned explanations--they do
not have the logical force of the explanations easily provided by the
sun-centered astronomical system or the principle of natural selection. And
the anomaly in the old framework is not recognized as an anomaly until the
reasoned explanation of the new. The term "retrorecognition" actually stands
for recognition after a reasoned explanation.
We have described a special class of scientific anomalies. In fact, there is a
continuum of kinds of scientific anomalies, ranging from those that initially
draw no concern whatever, like the perigee-opposition problem, to those that
are soon recognized as serious and perhaps fatal to the existing model, such
as Ernest Rutherford's discovery that alpha particles shot at atoms sometimes
scatter backwards, thus demolishing the "plum pudding" atomic model in which
the positive and negative charges are distributed diffusely throughout the
Even within the class of anomalies discussed here, the situations are not
identical. No explanation at all was initially proposed for the
perigee-opposition problem or for the equality of intertial and gravitational
mass. For the continental-fit problem, between 1800 and 1960 some scientists
proposed various theories of continental drift, but in the absence of a
mechanism the proposals were not taken seriously. Not surprisingly, scientists
strongly prefer explanations that are mechanistic, logical, and calculable.
The flatness problem is perhaps the most complicated of the examples we have
considered. Unlike the other examples, the new paradigm, the inflationary
universe model, is by no means universally accepted among practicing
cosmologists, nor is the legitimacy of the flatness problem. However, since
the inflationary universe model was proposed, many more cosmologists recognize
the peculiarity of the observational facts.
There are several factors at work in the retrorecognition phenomenon, their
relative importance varying with the specific example and the particular group
of scientists reacting to that example: (i) the intellectual difficulty of
recognizing anomalies initially, (ii) the tendency to ignore a problem when
one has no idea how to solve it, and (iii) the conservatism of science. By
definition, many retrorecognition anomalies go unnoticed initially, are not
seen as requiring explanation, and are not appreciated as anomalous. Thus, it
is hard to document them.
In the case of the flatness problem, for example, some scientists (exemplified
by the comments of Misner) did not regard the problem as serious because they
had no good ideas about how to solve it. By contrast, the perigee-opposition
problem was not recognized as a problem to begin with.
Science is a conservative activity, and scientists are reluctant to change
their explanatory frameworks. As discussed by sociologist Bernard Barber,
there are a variety of social and cultural factors that lead to conservatism
in science, including commitment to particular physical concepts, commitment
to particular methodological conceptions, professional standing, and
investment in particular scientific organizations . Although such
conservatism may seem inflexible and ultimately destructive, it has the
short-term asset of allowing each current conceptual framework to be
articulated so clearly that it is well understood and can serve as an
organizing principle for the multitude of facts that scientists observe.
Furthermore, it may be intellectually difficult to recognize the importance of
each of these multitude of facts and to spot the one peculiar fact that
heralds a fundamental flaw with the current theory.
Scientists may also be reluctant to change paradigms for the purely
psychological reasons that the familiar is often more comfortable than the
unfamiliar and the inconsistencies in belief are uncomfortable. In his Theory
of Cognitive Dissonance, psychologist Leon Festinger says that "the existence
of dissonance [inconsistency], being psychologically uncomfortable, will
motivate the person to try to reduce the dissonance and achieve consonance
[consistency]. When dissonance is present, in addition to reducing it, the
person will actively avoid situations and information which would likely
increase the dissonance" (18, p. 3).
We suggest that the phenomenon discussed here--the recognition of some
anomalies only after they are given reasoned explanations by a new conceptual
framework--is in some cases an extreme example of the conservatism of science.
At times, scientists may be so resistant to replacing their current paradigm
that they cannot acknowledge certain facts as anomalous. To be sure, such
facts are observed and recorded. The ancient Greeks duly noted that the
superior planets were in retrograde motion and brightest at opposition;
naturalists cataloged the many varied characteristics of animals and plants;
astronomers in this century carefully measured the close balance between
expansion energy and gravitational energy of the cosmos; geographers noted the
remarkable fit of the continents; physicists measured the equal rates of
acceleration of falling bodies. But these anomalous facts, and others like
them, were not initially recognized as anomalies. If unexplained facts can be
glossed over or reduced in importance or simply accepted as givens, the
possible inadequacy of the current theory does not have to be confronted.
Then, when a new theory gives a compelling explanation of the previously
unexplained facts, it is "safe" to recognize them for what they are.
REFERENCES AND NOTES
 T.S. Kuhn, The Structure of Scientific Revolutions (Univ. of Chicago
Press, Chicago, ed. 2, 1970).
 For a discussion of the standard Big Bang model, see S. Weinberg, The
First Three Minutes (Basic Books, New York, 1977). For a review of new ideas
in cosmology, including recent observational results, discussions of [omega],
the flatness problem, and the inflationary universe model, see A. Lightman,
Ancient Light (Harvard Univ. Press, Cambridge, MA, 1991).
 R. H. Dicke, Gravitation and the Universe: The Jayne Lectures for 1969
(American Philosophical Society, Philadelphia, 1970), p. 62.
 A. Lightman and R. Brawer, Origins: The Lives and Worlds of Modern
Cosmologists (Harvard Univ. Press, Cambridge, MA, 1990).
 A. Guth, Phys. Rev. D 23, 347 (1981).
 Reiner Gemma Frisius, in Johannes Stadius, Ephemerides Novae et Auctae
(Cologne, 1560), si. b3-b3v; trans. by O. Gingerich and R. S. Westman, The
Wittich Connection: Conflict and Priority in Late Sixteenth-Century Cosmology,
Trans. Am. Philos. Soc. 78, part 7, 42 (1988).
 Francis Bacon is often cited as having pointed out the unusually good fit
of the continents, in a passage in The New Organon (1620), but a close
examination of the passage suggests that Bacon was probably referring only to
the similarity of shapes of two western coasts, rather than to the fit of an
east coast with a west coast.
 For a comprehensive history of the theory of continental drift, see U. B.
Marvin, Continental Drift (Smithsonian Institution Press, Washington, DC,
1973). For a discussion of Wegener, see N. Oreskes, Hist. Stud. Phys. Biol.
Sci. 18, 311 (1988).
 J. Ray, The Wisdom of God Manifested in the Works of the Creation (1704)
(Samuel Smith, London, 1704).
 J. J. Rousseau, Profession of Faith of a Savoyard Vicar (1765), trans. in
Harvard Classics, C. W. Eliot, Ed. (P. F. Collier and Son, New York, 1910),
 C. Darwin, The Origin of Species (1859) (Collier Books, New York, 1962).
 Galileo, De Motu (1592), trans. in Galileo on Motion and on Mechanics by
I. E. Drabkin and S. Drake (Univ. of Wisconsin Press, Madison, 1960).
 I. Newton, System of the World, F. Cajori, Ed. (Univ. of California
Press, Berkeley, 1934), sect. 19.
 R. V. Eotvos, Math. Naturw. Ber. Ungarn 8, 65 (1889).
 A. Einstein, Ann. Phys. 35, 898 (1911), trans. in The Principle of
Relativity by H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl (Dover,
New York, 1952).
 Aristotle, Posterior Analytics, 1.13. In the Middle Ages the
fact-in-itself was called a quia and the reasoned fact was called a propter
 B. Barber, Science 134, 596 (1961).
 L. Festinger, A Theory of Cognitive Dissonance (Stanford Univ. Press,
Stanford, CA, 1957), p. 3.
 For helpful discussion and comments we thank R. Brawer, S. Brush, P.
Galison, S. J. Gould, G. Holton, H. Margolis, U. Marvin, A. Pickering, H.
Ritvo, and F. Sulloway.
A. Lightman is in the Program in Writing and Humanistic Studies and in the
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA
02139. O. gingerich is at the Harvard-Smithsonian Center for Astrophysics, 60
Garden Street, Cambridge, MA 02138.
[I am sending forth these memes, not because I agree wholeheartedly with
all of them, but to impregnate females of both sexes. Ponder them and
spread them. Meme 037 is "Frank's Continued Abandonment of Reality, sent
2004 Beethoven's Birthday. I forgot to call it a meme.]
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