The following excerpt was published in Broca's
Brain (1979).
by Carl Sagan
"Nothing is rich but the inexhaustible wealth
of nature. She shows us only
surfaces, but she is a million fathoms deep."
ó Ralph Waldo Emerson
Science is a way of thinking much more than
it is a body of knowledge. Its goal is to
find out how the world works, to seek what
regularities there may be, to penetrate the
connections of thingsófrom subnuclear particles,
which may be the constituents of all matter,
to living organisms, the human social community,
and thence to the cosmos as a whole. Our intuition
is by no means an infallible guide. Our perceptions
may be distorted by training and prejudice
or merely because of the limitations of our
sense organs, which, of course, perceive directly
but a small fraction of the phenomena of the
world. Even so straightforward a question
as whether in the absence of friction a pound
of lead falls faster than a gram of fluff
was answered incorrectly by Aristotle and
almost everyone else before the time of Galileo.
Science is based on experiment, on a willingness
to challenge old dogma, on an openness to
see the universe as it really is. Accordingly,
science sometimes requires courageóat the
very least the courage to question the conventional
wisdom.
Beyond this the main trick of science is to
really think of something: the shape of clouds
and their occasional sharp bottom edges at
the same altitude everywhere in the sky; the
formation of the dewdrop on a leaf; the origin
of a name or a wordóShakespeare, say, or
"philanthropic"; the reason for human social
customsóthe incest taboo, for example; how
it is that a lens in sunlight can make paper
burn; how a "walking stick" got to look so
much like a twig; why the Moon seems to follow
us as we walk; what prevents us from digging
a hole down to the center of the Earth; what
the definition is of "down" on a spherical
Earth; how it is possible for the body to
convert yesterday's lunch into today's muscle
and sinew; or how far is upódoes the universe
go on forever, or if it does not, is there
any meaning to the question of what lies on
the other side? Some of these questions are
pretty easy. Others, especially the last,
are mysteries to which no one even today knows
the answer. They are natural questions to
ask. Every culture has posed such questions
in one way or another. Almost always the proposed
answers are in the nature of "Just So Stories,"
attempted explanations divorced from experiment,
or even from careful comparative observations.
But the scientific cast of mind examines the
world critically as if many alternative worlds
might exist, as if other things might be here
which are not. Then we are forced to ask why
what we see is present and not something else.
Why are the Sun and the Moon and the planets
spheres? Why not pyramids, or cubes, or dodecahedra?
Why not irregular, jumbly shapes? Why so symmetrical
worlds? If you spend any time spinning hypotheses,
checking to see whether they make sense, whether
they conform to what else we know, thinking
of tests you can pose to substantiate or deflate
your hypotheses, you will find yourself doing
science. And as you come to practice this
habit of thought more and more you will get
better and better at it. To penetrate into
the heart of the thingóeven a little thing,
a blade of grass, as Walt Whitman saidóis
to experience a kind of exhilaration that,
it may be, only human beings of all the beings
on this planet can feel. We are an intelligent
species and the use of our intelligence quite
properly gives us pleasure. In this respect
the brain is like a muscle. When we think
well, we feel good. Understanding is a kind
of ecstasy.
But to what extent can we really know the
universe around us? Sometimes this question
is posed by people who hope the answer will
be in the negative, who are fearful of a universe
in which everything might one day be known.
And sometimes we hear pronouncements from
scientists who confidently state that everything
worth knowing will soon be knownóor even
is already knownóand who paint pictures of
a Dionysian or Polynesian age in which the
zest for intellectual discovery has withered,
to be replaced by a kind of subdued languor,
the lotus eaters drinking fermented coconut
milk or some other mild hallucinogen. In addition
to maligning both the Polynesians, who were
intrepid explorers (and whose brief respite
in paradise is now sadly ending), as well
as the inducements to intellectual discovery
provided by some hallucinogens, this contention
turns out to be trivially mistaken.
Carl Sagan (1934-1996)
Let us approach a much more modest question:
not whether we can know the universe or the
Milky Way Galaxy or a star or a world. Can
we know, ultimately and in detail, a grain
of salt? Consider one microgram of table salt,
a speck just barely large enough for someone
with keen eyesight to make out without a microscope.
In that grain of salt there are about 1016
sodium and chlorine atoms. That is a 1 followed
by 16 zeros, 10 million billion atoms. If
we wish to know a grain of salt we must know
at least the three-dimensional positions of
each of these atoms. (In fact, there is much
more to be knownófor example, the nature
of the forces between the atomsóbut we are
making only a modest calculation.) Now, is
this number more or less than a number of
things which the brain can know?
How much can the brain know? There are perhaps
1011 neurons in the brain, the circuit elements
and switches that are responsible in their
electrical and chemical activity for the functioning
of our minds. A typical brain neuron has perhaps
a thousand little wires, called dendrites,
which connect it with its fellows. If, as
seems likely, every bit of information in
the brain corresponds to one of these connections,
the total number of things knowable by the
brain is no more than 1014, one hundred trillion.
But this number is only one percent of the
number of atoms in our speck of salt.
So in this sense the universe is intractable,
astonishingly immune to any human attempt
at full knowledge. We cannot on this level
understand a grain of salt, much less the
universe.
But let us look a little more deeply at our
microgram of salt. Salt happens to be a crystal
in which, except for defects in the structure
of the crystal lattice, the position of every
sodium and chlorine atom is predetermined.
If we could shrink ourselves into this crystalline
world, we would see rank upon rank of atoms
in an ordered array, a regularly alternating
structureósodium, chlorine, sodium, chlorine,
specifying the sheet of atoms we are standing
on and all the sheets above us and below us.
An absolutely pure crystal of salt could have
the position of every atom specified by something
like 10 bits of information. This would not
strain the information-carrying capacity of
the brain.
If the universe had natural laws that governed
its behavior to the same degree of regularity
that determines a crystal of salt, then, of
course, the universe would be knowable. Even
if there were many such laws, each of considerable
complexity, human beings might have the capability
to understand them all. Even if such knowledge
exceeded the information-carrying capacity
of the brain, we might store the additional
information outside our bodiesóin books,
for example, or in computer memoriesóand
still, in some sense, know the universe.
Human beings are, understandably, highly motivated
to find regularities, natural laws. The search
for rules, the only possible way to understand
such a vast and complex universe, is called
science. The universe forces those who live
in it to understand it. Those creatures who
find everyday experience a muddled jumble
of events with no predictability, no regularity,
are in grave peril. The universe belongs to
those who, at least to some degree, have figured
it out.
It is an astonishing fact there are laws of
nature, rules that summarize convenientlyónot
just qualitatively but quantitativelyóhow
the world works. We might imagine a universe
in which there are no such laws, in which
the 1080 elementary particles that make up
a universe like our own behave with utter
and uncompromising abandon. To understand
such a universe we would need a brain at least
as massive as the universe. It seems unlikely
that such a universe could have life and intelligence,
because beings and brains require some degree
of internal stability and order. But even
if in a much more random universe there were
such beings with an intelligence much greater
than our own, there could not be much knowledge,
passion or joy.
Fortunately for us, we live in a universe
that has at least important parts that are
knowable. Our common-sense experience and
our evolutionary history have prepared us
to understand something of the workaday world.
When we go into other realms, however, common
sense and ordinary intuition turn out to be
highly unreliable guides. It is stunning that
as we go close to the speed of light our mass
increases indefinitely, we shrink towards
zero thickness in the direction of motion,
and time for us comes as near to stopping
as we would like. Many people think that this
is silly, and every week or two I get a letter
from someone who complains to me about it.
But it is a virtually certain consequence
not just of experiment but also of Albert
Einstein's brilliant analysis of space and
time called the Special Theory of Relativity.
It does not matter that these effects seem
unreasonable to us. We are not in the habit
of traveling close to the speed of light.
The testimony of our common sense is suspect
at high velocities.
Or consider an isolated molecule composed
of two atoms shaped something like a dumbbellóa
molecule of salt, it might be. Such a molecule
rotates about an axis through the line connecting
the two atoms. But in the world of quantum
mechanics, the realm of the very small, not
all orientations of our dumbbell molecule
are possible. It might be that the molecule
could be oriented in a horizontal position,
say, or in a vertical position, but not at
many angles in between. Some rotational positions
are forbidden. Forbidden by what? By the laws
of nature. The universe is built in such a
way as to limit, or quantise, rotation. We
do not experience this directly in everyday
life; we would find it startling as well as
awkward in sitting-up exercises, to find arms
out stretched from the sides or pointed up
to the skies permitted but many intermediate
positions forbidden. We do not live in the
world of the small, on the scale of 10-13
centimeters, in the realm where there are
twelve zeros between the decimal place and
the one. Our common-sense intuitions do not
count. What does count is experimentóin this
case observations from the far infrared spectra
of molecules. They show molecular rotation
to be quantized.
The idea that the world places restrictions
on what humans might do is frustrating. Why
shouldn't we be able to have intermediate
rotational positions? Why can't we travel
faster than the speed of light? But so far
as we can tell, this is the way the universe
is constructed. Such prohibitions not only
press us toward a little humility; they also
make the world more knowable. Every restriction
corresponds to a law of nature, a regulation
of the universe. The more restrictions there
are on what matter and energy can do, the
more knowledge human beings can attain. Whether
in some sense the universe is ultimately knowable
depends not only on how many natural laws
there are that encompass widely divergent
phenomena, but also on whether we have the
openness and the intellectual capacity to
understand such laws. Our formulations of
the regularities of nature are surely dependent
on how the brain is built, but also, and to
a significant degree, on how the universe
is built.
For myself, I like a universe that includes
much that is unknown and, at the same time,
much that is knowable. A universe in which
everything is known would be static and dull,
as boring as the heaven of some weak-minded
theologians. A universe that is unknowable
is no fit place for a thinking being. The
ideal universe for us is one very much like
the universe we inhabit. And I would guess
that this is not really much of a coincidence.
( Carl Sagan, "Can We Know the Universe?:
Reflections on a Grain of Salt;" from Broca's
Brain: Reflections on the Romance of Science,
New York: Random House, 1979, pp. 13-18. )
