http://hermiene.net/essays-trans/relativity_of_wrong.html
Important
note for the readers: The sections in bold
red are the ones that seem to have been removed from the more
popular versions of this article, including the version published by the
Skeptical Inquirer.
The Relativity of Wrong
by Isaac
Asimov
I received
a letter from a reader the other day. It was handwritten in crabbed penmanship
so that it was very difficult to read. Nevertheless, I tried to make it out
just in case it might prove to be important.
In the
first sentence, he told me he was majoring in English Literature, but felt
he needed to teach me science. (I sighed a bit, for I knew very few English
Lit majors who are equipped to teach me science, but I am very aware of the
vast state of my ignorance and I am prepared to learn as much as I can from
anyone, however low on the social scale, so I read on.)
It seemed
that in one of my innumerable essays, here and elsewhere, I had expressed
a certain gladness at living in a century in which
we finally got the basis of the Universe straight.
I didn't
go into detail in the matter, but what I meant was that we now know the basic
rules governing the Universe, together with the
gravitational interrelationships of its gross components, as shown in the
theory of relativity worked out between 1905 and 1916. We also know the basic
rules governing the subatomic particles and their interrelationships, since
these are very neatly described by the quantum theory worked out between
1900 and 1930. What's more, we have found that the galaxies and clusters
of galaxies are the basic units of the physical Universe, as discovered between
1920 and 1930.
These are
all twentieth-century discoveries, you see.
The young
specialist in English Lit, having quoted me, went on to lecture me severely
on the fact that in every century people have thought they understood
the Universe at last, and in every century they were proven to be
wrong. It follows that the one thing we can say about out modern "knowledge"
is that it is wrong.
The young
man then quoted with approval what Socrates had said on learning that the
Delphic oracle had proclaimed him the wisest man in Greece. "If I am the
wisest man," said Socrates, "it is because I alone know that I know nothing."
The implication was that I was very foolish because I knew a great deal.
Alas, none of this was new to me. (There is very little
that is new to me; I wish my corresponders would
realize this.) This particular thesis was addressed to me a quarter of a century
ago by John Campbell, who specialized in irritating me. He also told me that
all theories are proven wrong in time.
My answer
to him was, "John, when people thought the Earth was flat, they were wrong.
When people thought the Earth was spherical, they were wrong. But if you
think that thinking the Earth is spherical is just as wrong as thinking
the Earth is flat, then your view is wronger
than both of them put together."
The basic
trouble, you see, is that people think that "right" and "wrong" are absolute;
that everything that isn't perfectly and completely right is totally and equally
wrong.
However,
I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to
an explanation of why I think so.
First,
let me dispose of Socrates because I am sick and tired of this pretense that
knowing you know nothing is a mark of wisdom.
No one
knows nothing. In a matter of days, babies
learn to recognize their mothers.
Socrates
would agree, of course, and explain that knowledge of trivia is not what
he means. He means that in the great abstractions over which human beings
debate, one should start without preconceived, unexamined notions, and that
he alone knew this. (What an enormously arrogant claim!)
In his
discussions of such matters as "What is justice?" or "What is virtue?" he
took the attitude that he knew nothing and had to be instructed by others.
(This is called "Socratic irony," for Socrates knew very well that he knew
a great deal more than the poor souls he was picking on.) By pretending ignorance,
Socrates lured others into propounding their views on such abstractions.
Socrates then, by a series of ignorant-sounding questions, forced the others
into such a mélange of self-contradictions that they would finally break
down and admit they didn't know what they were talking about.
It is the
mark of the marvelous toleration of the Athenians that they let this continue
for decades and that it wasn't till Socrates turned seventy that they broke
down and forced him to drink poison.
Now where
do we get the notion that "right" and "wrong" are absolutes? It seems to me
that this arises in the early grades, when children who know very little
are taught by teachers who know very little more.
Young children
learn spelling and arithmetic, for instance, and here we tumble into apparent
absolutes.
How do
you spell "sugar?" Answer: s-u-g-a-r. That is right. Anything else
is wrong.
How much
is 2 + 2? The answer is 4. That is right. Anything else is wrong.
Having
exact answers, and having absolute rights and wrongs, minimizes the necessity
of thinking, and that pleases both students and teachers. For that reason,
students and teachers alike prefer short-answer tests to essay tests; multiple-choice
over blank short-answer tests; and true-false tests over multiple-choice.
But short-answer
tests are, to my way of thinking, useless as a measure of the student's understanding
of a subject. They are merely a test of the efficiency of his ability to
memorize.
You can
see what I mean as soon as you admit that right and wrong are relative.
How do
you spell "sugar?" Suppose Alice spells it p-q-z-z-f and Genevieve spells
it s-h-u-g-e-r. Both are wrong, but is there any doubt that Alice is wronger than Genevieve? For that matter, I think it
is possible to argue that Genevieve's spelling is superior to the "right"
one.
Or suppose
you spell "sugar": s-u-c-r-o-s-e, or C12H22O11.
Strictly speaking, you are wrong each time, but you're displaying a certain knowledge of the subject beyond conventional
spelling.
Suppose
then the test question was: how many different ways can you spell "sugar?"
Justify each.
Naturally,
the student would have to do a lot of thinking and, in the end, exhibit how
much or how little he knows. The teacher would also have to do a lot of thinking
in the attempt to evaluate how much or how little the student knows. Both,
I imagine, would be outraged.
Again,
how much is 2 + 2? Suppose Joseph says: 2 + 2 = purple, while Maxwell says:
2 + 2 = 17. Both are wrong but isn't it fair to say that Joseph is wronger than Maxwell?
Suppose
you said: 2 + 2 = an integer. You'd be right, wouldn't you? Or suppose you
said: 2 + 2 = an even integer. You'd be righter. Or suppose you said: 2 +
2 = 3.999. Wouldn't you be nearly right?
If the
teacher wants 4 for an answer and won't distinguish between the various wrongs,
doesn't that set an unnecessary limit to understanding?
Suppose
the question is, how much is 9 + 5?, and you answer
2. Will you not be excoriated and held up to ridicule, and will you not be
told that 9 + 5 = 14?
If you
were then told that 9 hours had pass since midnight and it was therefore
9 o'clock, and were asked what time it would be in 5 more hours, and you
answered 14 o'clock on the grounds that 9 + 5 = 14, would you not be excoriated
again, and told that it would be 2 o'clock? Apparently,
in that case, 9 + 5 = 2 after all.
Or again
suppose, Richard says: 2 + 2 = 11, and before the teacher can send him home
with a note to his mother, he adds, "To the base 3, of course." He'd be right.
Here's
another example. The teacher asks: "Who is the fortieth President of the
United States?" and Barbara says, "There isn't any, teacher."
"Wrong!"
says the teacher, "Ronald Reagan is the fortieth President of the United States."
"Not at
all," says Barbara, "I have here a list of all the men who have served as
President of the United States under the Constitution, from George Washington
to Ronald Reagan, and there are only thirty-nine of them, so there is no fortieth
President."
"Ah," says
the teacher, "but Grover Cleveland served two nonconsecutive terms, one from
1885 to 1889, and the second from 1893 to 1897. He counts as both the twenty-second
and twenty-fourth President. That is why Ronald
Reagan is the thirty-ninth person to serve as President of the United States,
and is, at the same time, the fortieth President of the United States."
Isn't that ridiculous? Why should a person be counted
twice if his terms are nonconsecutive, and only once if he served two consecutive
terms? Pure convention! Yet Barbara is marked wrong—just as wrong as if she
had said that the fortieth President of the United States is Fidel Castro.
Therefore, when my friend the English Literature
expert tells me that in every century scientists think they have worked out
the Universe and are always wrong, what I want to know is how
wrong are they? Are they always wrong to the same
degree? Let's take an example.
In the
early days of civilization, the general feeling was that the Earth was flat.
This was
not because people were stupid, or because they were intent on believing
silly things. They felt it was flat on the basis of sound evidence. It was
not just a matter of "That's how it looks," because the Earth does
not look flat. It looks chaotically bumpy, with hills, valleys, ravines,
cliffs, and so on.
Of course,
there are plains where, over limited areas, the Earth's surface does
look fairly flat. One of those plains is in the Tigris-Euphrates area where
the first historical civilization (one with writing) developed, that of the
Sumerians.
Perhaps
it was the appearance of the plain that may have persuaded the clever Sumerians
to accept the generalization that the Earth was flat; that if you somehow
evened out all the elevations and depressions, you would be left with flatness.
Contributing to the notion may have been the fact that stretches of water
(ponds and lakes) looked pretty flat on quiet days.
Another
way of looking at it is to ask what is the "curvature"
of Earth's surface. Over a considerable length, how much does the
surface deviate (on the average) from perfect flatness. The flat-Earth theory
would make it seem that the surface doesn't deviate from flatness at all,
that its curvature is 0 to the mile.
Nowadays,
of course, we are taught that the flat-Earth theory is wrong; that
it is all wrong, terribly wrong, absolutely. But it isn't. The curvature
of the Earth is nearly 0 per mile, so that although the flat-Earth
theory is wrong, it happens to be nearly right. That's why the theory
lasted so long.
There were
reasons, to be sure, to find the flat-Earth theory unsatisfactory and, about
350 B.C., the Greek philosopher Aristotle summarized
them. First, certain stars disappeared beyond the Southern Hemisphere as
one traveled north, and beyond the Northern Hemisphere as one traveled south.
Second, the Earth's shadow on the Moon during a lunar eclipse was always
the arc of a circle. Third, here on Earth itself, ships disappeared beyond
the horizon hull-first in whatever direction they were traveling.
All three
observations could not be reasonably explained if the Earth's surface were
flat, but could be explained by assuming the Earth to be a sphere.
What's
more, Aristotle believed that all solid matter tended to move toward a common
center, and if solid matter did this, it would end up as a sphere. A given
volume of matter is, on the average, closer to a common center if it is a
sphere than if it is any other shape whatever.
About a
century after Aristotle, the Greek philosopher Eratosthenes noted that the
Sun cast a shadow of different lengths at different latitudes (all the shadows
would be the same length if the Earth's surface were flat). From the difference
in shadow length, he calculated the size of the earthly sphere and it turned
out to be 25,000 miles in circumference.
The curvature
of such a sphere is about 0.000126 per mile, a quantity very close to 0 per
mile as you can see, and one not easily measured by the techniques at the
disposal of the ancients. The tiny difference between
0 and 0.000126 accounts for the fact that it took so long to pass from the
flat Earth to the spherical Earth.
Mind you,
even a tiny difference, such at that between
0 and 0.000126, can be extremely important. That difference mounts up. The
Earth cannot be mapped over large areas with any accuracy at all if the difference
isn't taken into account and if the Earth isn't considered a sphere rather
than a flat surface. Long ocean voyages can't be undertaken with any reasonable
way of locating one's own position in the ocean unless the Earth is considered
spherical rather than flat.
Furthermore,
the flat Earth presupposes the possibility of an infinite Earth, or of the
existence of an "end" to the surface. The spherical Earth, however, postulates
an Earth that is both endless and yet finite,
and it is the latter postulate that is consistent with all later findings.
So although
the flat-Earth theory is only slightly wrong and is a credit to its inventors,
all things considered, it is wrong enough to be discarded in favor of the
spherical-Earth theory.
And yet
is the Earth a sphere?
No, it
is not a sphere; not in the strict mathematical sense. A sphere has
certain mathematical properties—for instance, all diameters (that is, all
straight lines that pass from one point on its surface, through the center,
to another point on its surface) have the same length.
That, however,
is not true of the Earth. Various diameters of the Earth differ in length.
What gave
people the notion the Earth wasn't a true sphere? To begin with, the Sun
and the Moon have outlines that are perfect circles within the limits of
measurement in the early days of the telescope. This is consistent with the
supposition that the Sun and Moon are perfectly spherical in shape.
However,
when Jupiter and Saturn were observed by the first telescopic observers,
it became quickly apparent that the outlines of those planets were not circles,
but distinct ellipses. That meant that Jupiter and Saturn were not true spheres.
Isaac Newton,
toward the end of the seventeenth century, showed that a massive body would
form a sphere under the pull of gravitational forces (exactly as Aristotle
had argued), but only if it were not rotating. If it were rotating, a centrifugal
effect would be set up which would lift the body's substance against gravity,
and the effect would be greater the closer to the equator you progressed.
The effect would also be greater the more rapidly a spherical object rotated
and Jupiter and Saturn rotated very rapidly indeed.
The Earth
rotated much more slowly than Jupiter or Saturn so the effect should be smaller,
but it should still be there. Actual measurements of the curvature of the
Earth were carried out in the eighteenth century and Newton was proved correct.
The Earth
has an equatorial bulge, in other words. It is flattened at the poles. It
is an "oblate spheroid" rather than a sphere. This means that the various
diameters of the earth differ in length. The longest diameters are any of
those that stretch from one point on the equator to an opposite point on
the equator. The "equatorial diameter" is 12,755 kilometers (7,927 miles).
The shortest diameter is from the North Pole to the South Pole and this "polar
diameter" is 12,711 kilometers (7,900 miles).
The difference
between the longest and shortest diameters is 44 kilometers (27 miles), and
that means that the "oblateness" of the Earth
(its departure from true sphericity) is 44/12,755,
or 0.0034. This amounts to 1/3 of 1 percent.
To put
it another way, on a flat surface, curvature is 0 per mile everywhere. On
Earth's spherical surface, curvature is 0.000126 per mile everywhere (or
8 inches per mile). On Earth's oblate spheroidical
surface, the curvature varies from 7.973 inches to the mile to 8.027 inches
to the mile.
The correction
in going from spherical to oblate spheroidal
is much smaller than going from flat to spherical. Therefore, although the
notion of the Earth as sphere is wrong, strictly speaking, it is not as
wrong as the notion of the Earth as flat.
Even the
oblate-spheroidal notion of the Earth is wrong,
strictly speaking. In 1958, when the satellite Vanguard 1 was put
into orbit about the Earth, it was able to measure the local gravitational
pull of the Earth—and therefore its shape—with unprecedented precision. It
turned out that the equatorial bulge south of the equator was slightly bulgier
than the bulge north of the equator, and that the South Pole sea level was
slightly nearer the center of the Earth than the North Pole sea level was.
There seemed
no other way of describing this than by saying the Earth was pearshaped and at once many people decided that the
Earth was nothing like a sphere but was shaped like a Bartlett pear dangling
in space. Actually, the pearlike deviation from
oblate-spheroid perfect was a matter of yards rather than miles and the adjustment
of curvature was in the millionths of an inch per mile.
In short,
my English Lit friend, living in a mental world of absolute rights and wrongs,
may be imagining that because all theories are wrong, the Earth may
be thought spherical now, but cubical next century, and a hollow icosahedron the next, and a doughnut shape the one
after.
What actually
happens is that once scientists get hold of a good concept they gradually
refine and extend if with a greater and greater subtlety as their instruments
of measurement improve. Theories are not so much wrong as incomplete.
This can
be pointed out in many other cases than just the shape of the Earth. Even
when a new theory seems to represent a revolution, it usually arises out
of small refinements. If something more than a small refinement were needed,
then the old theory would never have endured.
Copernicus
switched from an Earth-centered planetary system to a Sun-centered one. In
doing so, he switched from something that was obvious to something that was
apparently ridiculous. However, it was a matter of finding better ways of
calculating the motion of the planets in the sky and, eventually, the geocentric
theory was just left behind. It was precisely because the old theory gave
results that were fairly good by the measurement standards of the time that
kept it in being so long.
Again,
it is because the geological formations of the Earth change so slowly
and the living things upon it evolve so slowly that it seemed reasonable
at first to suppose that there was no change and that Earth and life
always existed as they do today. If that were so, it would make no difference
whether Earth and life were billions of years old or thousands. Thousands
were easier to grasp.
But when
careful observation showed that Earth and life were changing at a rate that
was very tiny but not zero, then it became
clear that Earth and life had to be very old. Modern geology came into being,
and so did the notion of biological evolution.
If the
rate of change were more rapid, geology and evolution would have reached
their modern state in ancient times. It is only because the difference between
the rate of change in a static Universe and the rate of change in an evolutionary
one is that between zero and very nearly zero that the creationists can continue
propagating their folly.
Again,
how about the two great theories of the twentieth century; relativity and
quantum mechanics?
Newton's
theories of motion and gravitation were very close to right, and they would
have been absolutely right if only the speed of light were infinite. However,
the speed of light is finite, and that had to be taken into account in Einstein's
relativistic equations, which were an extension and refinement of Newton's
equations.
You might
say that the difference between infinite and finite is itself infinite, so
why didn't Newton's equations fall to the ground at once? Let's put it another
way, and ask how long it takes light to travel over a distance of a meter.
If light
traveled at infinite speed, it would take light 0 seconds to travel a meter.
At the speed at which light actually travels, however, it takes it 0.0000000033
seconds. It is that difference between 0 and 0.0000000033 that Einstein corrected
for.
Conceptually,
the correction was as important as the correction of Earth's curvature from
0 to 8 inches per mile was. Speeding subatomic particles wouldn't behave
the way they do without the correction, nor would particle accelerators work
the way they do, nor nuclear bombs explode, nor the
stars shine. Nevertheless, it was a tiny correction and it is no wonder that
Newton, in his time, could not allow for it, since he was limited in his
observations to speeds and distances over which the correction was insignificant.
Again,
where the prequantum view of physics fell short
was that it didn't allow for the "graininess" of the Universe. All forms
of energy had been thought to be continuous and to be capable of division
into indefinitely smaller and smaller quantities.
This turned out to be not so. Energy comes in quanta,
the size of which is dependent upon something called Planck's constant. If
Planck's constant were equal to 0 erg-seconds, then energy would be continuous,
and there would be no grain to the Universe. Planck's constant, however,
is equal to 0.000000000000000000000000066 erg-seconds. That is indeed a tiny
deviation from zero, so tiny that ordinary questions of energy in everyday
life need not concern themselves with it. When, however, you deal with subatomic
particles, the graininess is sufficiently large, in comparison, to make it
impossible to deal with them without taking quantum considerations into account.
Since the
refinements in theory grow smaller and smaller, even quite ancient theories
must have been sufficiently right to allow advances to be made; advances
that were not wiped out by subsequent refinements.
The Greeks
introduced the notion of latitude and longitude, for instance, and made reasonable
maps of the Mediterranean basin even without taking sphericity
into account, and we still use latitude and longitude today.
The Sumerians
were probably the first to establish the principle that planetary movements
in the sky exhibit regularity and can be predicted, and they proceeded to
work out ways of doing so even though they assumed the Earth to be the center
of the Universe. Their measurements have been enormously refined but the
principle remains.
Newton's
theory of gravitation, while incomplete over vast distances and enormous
speeds, is perfectly suitable for the Solar System. Halley's Comet appears
punctually as Newton's theory of gravitation and laws of motion predict.
All of rocketry is based on Newton, and Voyager II reached Uranus
within a second of the predicted time. None of these things were outlawed
by relativity.
In the nineteenth century, before quantum theory was
dreamed of, the laws of thermodynamics were established, including the conservation
of energy as first law, and the inevitable increase of entropy as the second
law. Certain other conservation laws such as those of momentum, angular momentum,
and electric charge were also established. So were Maxwell's laws of electromagnetism.
All remained firmly entrenched even after quantum theory came in.
Naturally,
the theories we now have might be considered wrong in the simplistic sense
of my English Lit correspondent, but in a much truer and subtler sense, they
need only be considered incomplete.
For instance,
quantum theory has produced something called "quantum weirdness" which brings
into serious question the very nature of reality and which produces philosophical
conundrums that physicists simply can't seem to agree upon. It may be that
we have reached a point where the human brain can no longer grasp matters,
or it may be that quantum theory is incomplete and that once it is properly
extended, all the "weirdness" will disappear.
Again,
quantum theory and relativity seem to be independent of each other, so that
while quantum theory makes it seem possible that three of the four known
interactions can be combined into one mathematical system, gravitation—the
realm of relativity—as yet seems intransigent.
If quantum
theory and relativity can be combined, a true "unified field theory" may
become possible.
If all
this is done, however, it would be a still finer refinement that would affect
the edges of the known—the nature of the big bang and the creation of the
Universe, the properties at the center of black holes, some subtle points
about the evolution of galaxies and supernovas, and so on.
Virtually all that we know today, however, would remain
untouched and when I say I am glad that I live in a century when the Universe
is essentially understood, I think I am justified.