--- /dev/null
+From The Skeptical Inquirer, Fall 1989, Vol. 14, No. 1, Pp. 35-44
+_______________________________________________________________________
+
+The Relativity of Wrong
+
+By Isaac Asimov
+
+I RECEIVED a letter 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, the writer 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, so I read on.)
+
+It seemed that in one of my innumerable essays, 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 proved to be wrong. It follows that the one thing we can say
+about our 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
+was under the impression I knew a great deal.
+
+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.
+
+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 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 the
+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 the 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 as 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 the 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
+that would lift the body's substance against gravity, and this 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. This "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 44/12755, or
+0.0034. This amounts to l/3 of 1 percent.
+
+To put it another way, on a flat surface, curvature is 0 per mile
+everywhere. On the earth's spherical surface, curvature is 0.000126
+per mile everywhere (or 8 inches per mile). On the earth's oblate
+spheroidal 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 a 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 I 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 pear-shaped, 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 pear-like 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 it with 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 cases other 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 the
+earth and life always existed as they do today. If that were so, it
+would make no difference whether the earth and life were billions of
+years old or thousands. Thousands were easier to grasp.
+
+But when careful observation showed that the earth and life were
+changing at a rate that was very tiny but not zero, then it became
+clear that the 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.
+
+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.
+
+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.
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