In the fabric of knowledge we call science, there was a rent here,
a hole. It was filled by young enthusiasts not burdened by wise old men.
This gap made me wonder about the space of science.
Scientific knowledge is a parallel distributed system. It has no center,
no one in control. A million heads and dispersed books hold parts of it.
It too is a web, a coevolutionary system of fact and theory interacting
and influencing other facts and theories. But the study of science as a
network of agents searching in parallel over a rugged landscape of
mysteries is a field larger than any I've tackled here. To deal fairly
with the mechanics of science alone would require a larger book than
I've written so far. I can only hint at such a system in these closing
Knowledge, truth, and information flow in networks and swarm systems. I
have always been interested in the texture of scientific knowledge
because it appears to be lumpy and uneven. Much of what we collectively
know derives from a few small areas, yet between them lie vast deserts
of ignorance. I can interpret that observation now as the effect of
positive feedback and attractors. A little bit of knowledge illuminates
much around it, and that new illumination feeds on itself, so one corner
explodes. The reverse also holds true: ignorance breeds ignorance. Areas
where nothing is known, everyone avoids, so nothing is discovered. The
result is an uneven landscape of empty know-nothing interrupted by hills
of self-organized knowledge.
Of this culturally produced space, I am most fascinated by the
deserts -- by the holes. What can we know about what we don't know? The
greatest promise looming in evolution theory is unraveling the mystery
of why organisms don't change, because stasis is more common than change
yet harder to explain. What can we know about no-change in a system of
change? What do the holes of change tell us about the whole of change?
And so, it is the holes in the space of wholes that I'd like to explore
This very book is full of holes as well as wholes. What I don't know
far exceeds what I know, but unfortunately, it is far easier to write
about what I know than about what I don't know. By the nature of
ignorance, I am, of course, not aware of all the places and gaps where
my own knowledge fails. Recognizing one's own ignorance is quite a
trick. That goes for science, too. Mapping the holes of ignorance is
perhaps science's next advance.
Scientists today believe science is revolutionary. They explain how
science works via a model of ongoing minirevolutions. According to this
perspective, researchers build a theory to explain facts (for example,
rainbows occur because light is a wave). The theory itself will suggest
places to look for new facts (can you bend a wave?). It's the law of
increasing returns again. As new facts are uncovered they are
incorporated into the theory, buttressing its strength and reliability.
Occasionally, scientists uncover new facts that aren't readily explained
by the theory (light sometimes acts like a particle). These are called
anomalies. Anomalies are set aside at first, while new facts that concur
with the reigning theory continue to stream in. At some point, the
accumulating anomalies prove too great, too troublesome, or too numerous
to ignore. Inevitably then, some young turk proposes a revolutionary
different model that explains the anomalies (such as, light is both wave
and particle). The old is gone; the new quickly reigns.
In the terminology of science historian Thomas Kuhn, the reigning
theory forms a self-reinforcing mindset called a paradigm that dictates
what is fact and what is mere noise. From within the paradigm, anomalies
are trivia, curiosities, illusions, or bad data. Research proposals
endorsing the paradigm win grants, lab space, and degrees. Proposals
operating outside the paradigm -- those dabbling in distracting trivia -- get
nothing. The famous scientist who made his great revolutionary discovery
while denied funds or credibility is so common it's become cliché; I've
trotted out several of those cliché stories in this book. One example is
the ignored work of scientists dabbling in ideas that contradict
Real discovery in science, according to Kuhn in his seminal The
Structure of Scientific Revolutions, only "commences with the awareness
of anomaly." Progress is an acknowledgment of the opposition. A series
of established paradigms are overthrown by downtrodden and oppressed
anomalies (and their finders) as they rebel and usurp the throne by
their countertruth. The new ideas reign, at least for a while, until
they too become ossified and insensitive to the squawks of new
anomalies, and are eventually overthrown themselves.
Kuhn's model of paradigm shift in science is so convincing that it has
become a paradigm itself -- the paradigms of paradigms. We now see
paradigms and paradigm overthrows everywhere, inside of science and out.
Paradigm shifts are our paradigm. The fact that things don't really work
that way is, well, an anomaly.
Alan Lightman and Owen Gingerich, writing in a 1991 Science article,
"When Do Anomalies Begin?," claim that contrary to the reigning Kuhnian
model of science, "certain scientific anomalies are recognized 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." In other words, the real
anomalies that eventually overthrow a reigning paradigm are at first not
even perceived as anomalies. They are invisible.
A few brief examples of "retrorecognition," based on Lightman's and
The fact that the shape of South America and Africa fit together
like a lock and key did not bother any pre-1960s geologists. There was
nothing troubling to them or their theories of continent formation in
this observation, or in the observed ridges down the center of the
oceans. Although the remarkable fit had been noticed since the Atlantic
Ocean was first mapped, it was a fact that did not even need an
explanation. Only later was the fit retrorecognized as something to
Newton precisely measured the inertial mass of a great many objects
(what it took to get them moving, as in getting a pendulum started) and
their gravitational mass (how fast they fell to the Earth), to determine
that the two forces were equal, if not equivalent, and could be canceled
out when doing physics. For hundreds of years this relationship was not
questioned. Einstein, however, was struck that "the law has not found
any place in the foundations of our edifice of the physical universe."
Unlike others, he was perplexed by this observation which he
successfully explained in his revolutionary general theory of
For decades, the almost exact balance between the universe's kinetic
and gravitational energies -- a pair of forces that kept the expanding
universe balanced between blowing up or collapsing -- was noted in passing
by astronomers. But it was never a "problem" until the revolutionary
"inflationary universe" model came along in 1981 and made this fact a
troubling paradox. The observation of the balance did not begin to be an
anomaly until after the paradigm shift, when in retrospect, it was seen
as a troublemaker.
The common theme in each example is that anomalies begin as observed
facts that don't require any explanation at all. They are not
troublesome facts; they just are. Rather than the cause of a paradigm
shift, anomalies are the result of the shift.
In a letter to Science, David P. Barash tells of his own experience with
nonanomalies. He wrote a textbook of sociobiology in 1982, where he
stated that "evolutionary biologists, beginning with Darwin, have been
troubled by the fact that animals often do things that appear to benefit
others, often at great cost to themselves." Sociobiology was launched by
the 1964 publication of William Hamilton's inclusive fitness theory,
which provided a workable, though controversial, way to interpret animal
altruism. Barash writes, "However, stimulated by the Lightman-Gingerich
thesis, I have reviewed numerous pre-1964 textbooks of animal behavior
and evolutionary biology and have discovered that, in fact -- and contrary
to my own above-cited assertion -- before Hamilton's insight, evolutionary
biologists were not very much troubled by the occurrence of apparently
altruistic behavior among animals (at least they did not devote much
theoretical or empirical attention to the phenomenon)." He ends his
letter by suggesting, half in jest, that biologists "teach a course in
what we don't know about, say, animal behavior."