I s a a c A s i m o v
The Relativity of Wrong
received a letter the other day. It was handwrit-ten in crabbed penmanship so that it was very diffi-cult to read. Nevertheless, I tried to make it out just in ca it might prove to be important. In the first ntence, the writer told me he was majoring in En g lish literature, but felt he needed to teach me science. (I sighed a bit, for I knew very few En g lish 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 emed that in one of my innumerable essays, I had expresd a certain gladness at living in a century in which we finally got the basis of the univer straight.I didn’t go into detail in the matter, but what I meant was that we now know the basic rules governing the univer, together with the gravitational inter-relationships 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 the 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 univer, as discovered between 1920 and 1930.1The are all twentieth- c entury discoveries, you e.The young specialist in En g lish Lit, having quoted me,
went on to lecture
me verely on the fact that in every century people have thought they under-stood the univer at last, and in every century they w ere 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 wist man in Greece.2 “If I am the wist man,” said Socrates, “it is becau I alone know that I know nothing.” The implication was that I was very foolish becau I was under the impression I knew a great deal.大腿肌肉萎缩
My answer to him was, “John, when people thought the earth was flat, they w ere wrong. When people thought the earth was spherical, they w ere 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.”1. A lbert Einstein (1879–1955) announced the special theory of relativity in 1905 and developed the general theory of relativity over the next de c ade; physicist Maxwell Planck (1858–1947) and others developed quantum theory; astronomer Edwin Hubble (1889–1953) demonstrated the existence of external galaxies in 1924.
2. S ocrates (c. 470–), ancient Greek phi l os o p her; Delphic oracle or Pythia, priestess
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of the Temple of Apollo on Mount Parnassus.I Published in the Skeptical Inquirer (1989), the journal of the Committee for Scientific Investigation of Claims of the Paranormal (CSICOP), now the Committee for Skeptical Inquiry.
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The basic trouble, you e, 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 ems 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 En g lish literature expert tells me that in every cen-tury scientists think they have worked out the univer 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 becau people w ere stupid, or becau they w ere 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,” becau the earth does not look flat. It looks chaotically bumpy, with hills, valleys, ravines, cliffs, and so on.
Of cour there are plains where, over limited areas, the earth’s surface does look fairly flat. One of tho plains is in the Tigris- E uphrates 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 Sume-rians 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- e arth theory would make it em that the surface d oesn’t deviate from flatness at all, that its curvature is 0 to the mile.
Nowadays, of cour, we are taught that the flat- e arth 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- e arth theory is wrong, it happens to be nearly right. That’s why the theory lasted so long.
There w ere reasons, to be sure, to find the flat- e arth theory unsatisfactory and, about 350 B.C., th
e Greek phi l os o p her Aristotle summarized them. First, certain stars disappeared beyond the Southern Hemi s phere as one traveled north, and beyond the Northern Hemi s phere as one traveled south. Second, the earth’s shadow on the moon during a lunar eclip was always the arc of a circle. Third, h ere on the earth itlf, ships disappeared beyond the horizon hull- fi rst in what e ver direction they w ere traveling.
All three obrvations could not be reasonably explained if the earth’s sur-face w ere 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, clor to a common center if it is a sphere than if it is any other shape what e ver.
About a century after Aristotle, the Greek phi l os o p her Eratosthenes noted that the sun cast a shadow of different lengths at different latitudes (all the 10 15
shadows would be the same length if the earth’s surface w ere 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 clo to 0
怎么报保险per mile, as you can e, and one not easily mea s ured 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 sur-face. Long ocean voyages c an’t be undertaken with any reasonable way of locat-ing one’s own position in the ocean unless the earth is considered spherical rather than flat.Furthermore, the flat earth presuppos 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 pos-tulate that is consistent with all later findings.So, although the flat- e arth 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- e arth theory.And yet is the earth a sphere?No, it is not a sphere; not in the strict mathematical n. A sphere has certain mathematical properties— f or 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 dif-
fer in length.
What gave people the notion the earth w asn’t a true sphere? To begin with, the sun and the moon have outlines that are perfect circles within the limits of mea s ure m ent in the early days of the telescope. This is consistent with the sup-position that the sun and the moon are perfectly spherical in shape.
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However, when Jupiter and Saturn w ere obrved by the first telescopic obrvers, it became quickly apparent that the outlines of tho planets w ere not circles, but distinct ellips. That meant that Jupiter and Saturn w ere not true spheres.
Isaac Newton,3 toward the end of the venteenth 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 w ere not rotating. If it w ere rotating, a centrifugal effect would be t up that would lift the body’s substance against gravity, and this effect would be greater the clor to the equator you progresd. The effect would also be greater the more rapidly a spherical object rotated, and Jupiter and Saturn rotated very rapidly indeed.
3. E n g lish mathematician and physicist (1642–1727).
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The earth rotated much more slowly than Jupiter or Saturn so the effect should be smaller, but it should still be there. Actual mea s ure m ents of the cur-vature of the earth w ere carried out in the eigh t eenth century and Newton was proved correct.
微信网名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 vari-ous diameters of the earth differ in length. The longest diameters are any of tho 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 diam-eter” is 12,711 kilometers (7,900 miles).
The difference between the longest and shortest diameters is 44 kilome-ters (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 1/3 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 sph
eroidal surface, the curvature var-ies from 7.973 inches to the mile to 8.027 inches to the mile.
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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- s pheroidal 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 mea s ure the local gravitational pull of the earth— a nd therefore its shape— w ith unpre c e d ented 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 a level was slightly nearer the center of the earth than the North Pole a level was.
There emed no other way of describing this than by saying the earth was pear- s haped, 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- s pheroid 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 En g lish Lit friend, living in a mental world of absolute rights and wrongs, may be imagin
ing that becau all theories are wrong, the earth may be thought spherical now, but cubical next century, and a hollow icosahe-dron 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 mea s ure m ent improve. Theories are not so much wrong as incomplete.
This can be pointed out in many cas other than just the shape of the earth. Even when a new theory ems to reprent a revolution, it usually aris out of small refinements. If something more than a small refinement w ere needed, then the old theory would never have endured.30 35
Copernicus 4 switched from an earth- c entered 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 precily becau the old the-ory gave results that w ere fairly good by the mea s ure m ent standards of the time that kept it in being so long.Again, it is becau the geological formations of the earth change so slowly and the living things upon it evolve so slowly that it emed reasonable at first to suppo that there was no chang
e and that the earth and life always existed as they do today. If that w ere so, it would make no difference whether the earth and life w ere billions of years old or thousands. Thousands w ere easier to grasp.But when careful obrvation showed that the earth and life w ere chang-ing 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 w ere more rapid, geology and evolution would have reached their modern state in ancient times. It is only becau the difference between the rate of change in a static univer 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 w ere not wiped out by subquent 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 u latitude and longitude today.The Sumerians w ere probably the first to establish the principle that plan-
斗鱼养殖etary 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 univer. Their mea s ure m ents have been enormously refined but the principle remains.
Naturally, the theories we now have might be considered wrong in the sim-plistic n of my En g lish Lit correspondent, but in a much truer and subtler n, they need only be considered incomplete.
4. N icolaus Copernicus (1473–1543), Polish astronomer.
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45mla citation
Asimov, Isaac. “The Relativity of Wrong.” 1989. The Norton Reader: An Anthology of Nonfiction . Ed. Melissa A. Goldthwaite et al. 14th ed. New York: Norton,
2016. 824–28. Print.
Q u e s t i o n s
1. I saac Asimov frames his essay as a respon to a letter from a “young special-ist in En g lish Lit” (paragraph 5) whom he calls “wronger” (paragraph 6) than tho
