Anaxagoras and the solar eclipse of 478 BC.
The sun exceeds the Peloponnesus in size. (Hippol Haer 1 8 8)
Anaxagoras [says that the moon] is as large as the Peloponnesus. (Plu De fac orb lun 932a)
Anaxagoras [says the sun is] many times the size of the Peloponnesus. (Aetius 2 21 3) (1)
Anaxagoras of Clazomenae (ca. 500-428 BC) was perhaps the most famous scientist-philosopher of his time. Although he spent some thirty years in Athens and enjoyed the patronage of the city's leading citizen, Pericles, there is much we do not know about the philosopher and his theory. His estimate of the sun's and moon's sizes is unique in its specificity and its geographical reference and consequently puzzling. Two scholars working independently have hypothesized that the estimate is based on an actual solar eclipse. (2) This hypothesis does not seem to have gained much attention, and the specific proposals run into historical problems; but it raises interesting questions that may illuminate Anaxagoras' scientific activity. We wish to show that this hypothesis can be supported by astronomical evidence which reveals some interesting information about the researcher, his methods, and his contributions to astronomy.
1 The Theory
Ancient sources tell us that Anaxagoras held an essentially correct theory of eclipses, both solar and lunar. (3) What is less clear is whether he was the first philosopher to propose the correct theory. Some sources give him credit as the discoverer of the true explanation of eclipses; others credit Thales, more than a century earlier. (4) Anaxagoras' slightly younger contemporary Empedocles (of Acragas, in Sicily) held virtually the same view, and since it is controversial which philosopher published his work first, it is possible that Empedocles was the discoverer. (5) Astronomical phenomena will have something to contribute to these questions. We shall speak about questions of historical priority in the third section. For now, suffice it to say that there are serious doubts about Thales' ability either to predict or to explain an eclipse, and no sign that anyone after him had a correct understanding of eclipses until the generation of Anaxagoras and Empedocles. Whatever Thales' insights may have been, explanations of eclipses were not founded on a scientific basis until the time of Anaxagoras.
Like most theorists before him, Anaxagoras saw the earth as a flat body lying at the center of a cosmos, with the sun, moon, and stars circling it. (6) Unlike his predecessors, he viewed the heavenly bodies as being massy and held aloft by a strong vortex motion of the upper heavens, and perhaps fiery as a result of friction. In his theory the heavenly bodies were roughly spherical in shape. The earth was a thin disk, held in place by air pressure. (7) The sun generated its own light, but the moon shone by reflecting the light of the sun. (8) Thus when the earth was interposed between the sun and the moon, it would block the sun's light and cause it to be darkened, producing a lunar eclipse. If the moon crossed directly between the earth and the sun, it would obscure the sun and cause a solar eclipse. All of this is very elementary astronomy today, but in its time the theory marked a sudden advance to the first scientifically correct explanation of eclipses in the history of the world, so far as we know. (9)
It followed from the theory that the moon would cast a shadow on the flat earth for the duration of a solar eclipse. Assuming that the sun was far distant from the earth and the moon relatively close, the sun's rays would approximate parallel lines and projecting a shadow roughly the size of the moon towards the earth. If the moon were smaller than the earth, its shadow would cover only a portion of the earth's surface. The shadow would be elongated if it struck the earth at an oblique angle, but in any case its size would be a function of the moon's size. Thus the shadow of a solar eclipse has significance for astronomical measurements on this theory.
While we have no quotations from Anaxagoras that indicate his awareness of these implications of his theory, we do get a recognition of them from his contemporary Empedocles, whose philosophic poem On Nature contains the following lines, speaking of the moon: (10)
... it did away with (11) its [the sun's] rays to the earth from above, and it obscured the earth as much as the width of the bright-eyed moon. (31B42 DK)
The moon blocks the sun's light in proportion to the width of the moon. Thus someone in the early fifth century BC made the connection between a solar eclipse and a measurable shadow.
2 Historical Eclipses
More than thirty years ago two attempts were made to identify the eclipse that Anaxagoras used to make his calculation of the sun's size. The first was by M. L. West: 'In 557 BC the track of a total eclipse crossed the Peloponnesus from west to east. Discovering the memories of this, Anaxagoras might have argued (falsely) "the moon's shadow must be the same size as the moon" (so Emp[edocles] B42), "therefore the moon is as big as the Peloponnese, therefore the sun, which looks the same size but is much further away, must be that much bigger than the Peloponnese"' (West 1971: 233n 1). The eclipse of 557 covered the appropriate area. (12) There is, however, a practical problem for West's account: the event occurred some seventy-five years before Anaxagoras' majority. How could he recover memories of it? At the time there were no public records kept of such occurrences, no scientific research institutes, no archives, no databases, no scientific journals or daily newspapers in a culture in which modes of communication were predominantly oral. Furthermore, since each city had its own way of computing years, there was no easy way to synchronize, say, an observation in Argos with an observation in Elis, much less to compare them with an observation in Thebes, outside the umbra of the eclipse. (13) West does talk of memories, not records, but whose memories? Members of the generation that witnessed the eclipse were all dead, except for those too young to remember it. In Babylon, indeed, priests kept meticulous records of unusual phenomena, and had been recording eclipses since the seventh century BC. (14) But they limited their observations to the skies of Babylonia and were not, so far as we know, in contact with Greek researchers in this time. (15) The Babylonians' interest, in any case, was in astrology for the sake of anticipating omens, especially those concerning the fate of their ruler. (16) Such data as were available in the early fifth century were in archives far removed from Greece, in a foreign language using the cuneiform writing system. In the absence of scientific records it is difficult to give credence to West's proposed eclipse.
David Sider (1973: 129) has argued, 'The only possible subject of Anaxagoras' investigation is the eclipse of April 30, 463 B.C, which passed through Greece in an east-west direction.' (17) He suggested that Anaxagoras collected information at a panhellenic festival and on that basis estimated the size of the shadow. Sider's proposed eclipse is in many ways the most obvious one, for it occurred when Anaxagoras was about thirty-seven years old, at the height of his intellectual powers, probably present in Athens with access to local information and in an ideal position to make inquiries abroad; for at the time Athens was the dominant power of the region, the capital and emporium of the Greek world. Yet here too there is a problem. For the total eclipse was not visible in Athens, nor anywhere in the Peloponnesus. Of course Anaxagoras' interest in celestial phenomena might easily lead him to pursue the question of the extent of the eclipse and to find that a total eclipse was visible in central Greece. But why should he then project the size of the eclipse onto the Peloponnesus? The act presupposes at least that there was an accurate map of Greece to scale, with which one could, using a compass or straightedge, transfer the shadowed area from the north to the south. We know that there were maps from the time of Anaximander (sixth century BC) on. But writing in the later fifth century the historian Herodotus found them laughably schematic. (18) Maps to scale would be out of the question, especially since the Greeks had no reliable way of measuring overland distances, and no straight roads on the mountainous terrain. Hence, to transfer observations from the north to the south would introduce an unnecessary error into the calculation. In any case, what is the motivation for transferring the measurement in the first place? To some sailors the Peloponnesus might be better known. But those same sailors had sailed up the coasts of Thessaly and Macedonia. Why not say the sun is larger than Thessaly, where the total eclipse was actually observed?
Let us briefly review the two eclipses Anaxagoras could have experienced in his maturity. On April 30th, 463 BC, as Sider notes, a total eclipse was visible in parts of Greece. The umbra of the moon crossed from the western Atlantic Ocean to the northwestern coast of Morocco, the northern edge of modern Algeria, the southeastern Mediterranean brushing the southern tip of Sardinia and the northwest tip of Sicily, across the Tyrrhenian Sea, across Lucania and ancient Calabria in southern Italy, the Straits of Otranto, over Epirus, Thessaly and Chalcidice, the northern Aegean, and headed eastward across northern Anatolia. At the time Anaxagoras was about thirty-seven, Empedocles perhaps thirty-two years old. The poet Pindar may have sung of this eclipse, though it was not visible in his native Boeotia. (19)
There had been another eclipse fifteen years earlier. On February 17th, 478 BC, as the moon was 394,015 kilometers from earth (about halfway between its average distance and its apogee), it passed between the earth and the sun (0.9974 AU distant), producing an annular eclipse. The shadow of the eclipse moved eastward over the Atlantic Ocean, covered the western coast of Morocco, continued east over the desert south of Carthage, then turned northeastward over the central Mediterranean, staying south of Sicily, crossed the Ionian Sea, covered the whole breadth of the Peloponnesus except for the extreme northwest, traversed the Attic peninsula, headed northeast over the Aegean, covered northern Ionia and Mysia, brushed the Hellespont, darkened the Bosporus, crossed portions of western Black Sea, and then continued northeast across southern Russia. At the time of the eclipse of 478 Anaxagoras was approximately twenty-two years old, Empedocles perhaps seventeen. (20)
Of these two solar eclipses, the only ones noticeable in Greek lands during Anaxagoras' maturity, only the earlier one could provide an immediate basis for Anaxagoras' measurement of the sun's size. In it, the antumbra cast by the moon covered almost the whole of the Peloponnesus but none of the cities of the northern Aegean coast. (21) The eclipse of 463 was total in Larissa, but only partial in Athens and the Peloponnesus. It would be appropriate and wholly natural for Anaxagoras to say of the eclipse of 478-but not that of 463-that it showed the moon was as large as the Peloponnesus. (22)
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It is striking, indeed, how well the 478 eclipse fits with Anaxagoras' estimate. There is no a priori guarantee that the data to support the estimate should be available within a lifetime of observations. (23) Yet there is an eclipse that precisely confirms the estimate, based on the assumptions noted in the previous section, that could have been observed by the theorist. The one other eclipse that might satisfy the conditions set by Anaxagoras' estimate, namely that of 557 BC, would have been practically impossible to investigate. Some scholars seem to dismiss the eclipse of 478 because it was not total and allegedly might have been missed. (24) Yet this eclipse was 95% complete and surely would have been an impressive sight to all who witnessed it. The sun was flanked on the east by Mercury, and on the west by Saturn, then farther out by Mars, then Venus. As the sky drew dark shortly before midday watchers would have seen at least Venus and perhaps all four planets shine forth. (25) The decisive event that seems to make sense of the estimate is the eclipse of 478 BC, which we believe should be recognized as the eclipse Anaxagoras studied to calculate the sun's size.
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If the eclipse of 478 provided the data for Anaxagoras' estimate of the size of the sun, we can learn something about both Anaxagoras' life and his contributions to science. In this setting we shall speak only summarily about the former topic. As we mentioned at the outset, he spent thirty years in Athens; yet it is controversial when Anaxagoras spent those thirty years: roughly 480-450, or 460-430? There is some historical evidence on each side. (26) The fact of the eclipse counts strongly for the former dates. The eclipse was visible in Anaxagoras' native Clazomenae on the central Aegean coast of Asia Minor. But a war was under way between the Greek cities of the mainland and the Persian Empire, which controlled Clazomenae and the Ionian coast of Asia Minor. Communications with the mainland would have been sporadic at best and non-existent at worst. Consequently it would have been practically impossible to find out how widely visible the eclipse was in mainland Greece. Again the question arises as to why Anaxagoras would want to estimate the size of the moon by reference to distant site when he could very well use local geography, for instance Ionia. If, however, Anaxagoras was in Athens, he could have both witnessed the annular eclipse and found out who else had seen the eclipse simply by hanging out in Athens' port the Piraeus and talking with seamen, merchants and travelers. This finding suggests a precocious thinker, something of a Wunderkind. Yet it strikingly confirms the one ancient claim that has him starting his career in Athens in 480, and so has at least one piece of biographical information in its favor. (27)
In fact, Anaxagoras seems to have used data from the eclipse of 478 to establish and refine his theory. And here we come to implications of more than biographical importance, implications of scientific methodology. What was Anaxagoras doing in collecting data on the visibility of the eclipse? To get an accurate report in an age with few written records, and no periodicals or journals, he must have collected information soon after the event. For memories are fleeting, and in particular memories of what one did not see at a given time. But Anaxagoras would have collected data on the geographical extent of the eclipse only if he thought there were some reason to do so. Now data concerning the extent of the eclipse would have been relevant only on the basis of a certain kind of theory. Let us turn briefly to earlier theories of eclipses to see what their implications were for visibility.
Thales became famous for allegedly predicting an eclipse. (28) But if he did so, or more vaguely announced that an eclipse was possible in the following year, he could have done so only on the basis of Babylonian records in which repeating cycles of eclipses could be discerned. (29) This method provided no causal explanations of the phenomena, and no actual astronomical theories are recorded for Thales. (30) His student Anaximander did have an elaborate theory of the heavens, including a theory of eclipses. According to him, the moon and the sun were rings of fire extending over the whole orbit of the bodies, enclosed by opaque air. At one place in the ring was a hole through which the fire was visible. Rotation of the ring caused the hole to move. When the hole was blocked up an eclipse occurred. (31) The theory is remarkable for its ingenuity, but it shows no understanding of the physical nature of the sun and moon, the moon's dependence on the sun for its light, or finally the causes of eclipses. If his teacher Thales had understood eclipses, it is puzzling that he failed to pass on his knowledge to his student, including a knowledge of how the moon gets its light from the sun--a fact that is empirically verifiable by following the phases of the moon in relation to its angular distance from the sun.
Anaximander's student Anaximenes viewed the heavenly bodies, or at least the sun and moon, as thin flat disks floating on the air like leaves. (32) These bodies did not move under the earth but circled around it and seemed to set when they were obscured by high mountains to the north. (33) Although no theory of eclipses is recorded in Anaximenes' name, one anonymous theory has been plausibly attributed to him. According to this theory, an eclipse results from a cloud covering the moon or sun.(34)
Xenophanes seems to have believed that the earth was an infinite plane rather than a finite disk. (35) There were multiple suns (apparently caused by similar conditions) visible in different regions of the earth. (36) A solar eclipse occurred when the sun was 'treading on nothing' over an uninhabited section of the earth; probably he believed the sun went dark when moisture in the air, which fueled its fires, was not available. (37)
Heraclitus pictured the sun and moon as solid bowls full of fire. When the moon turned its convex side towards the earth, the moon was darkened. An eclipse of the sun or moon occurred when there was a sudden revolution of the bowl. (38)
On none of these theories is there any reason to measure the size of the area affected by an eclipse. On the theories of Anaximander and Heraclitus an eclipse should be visible from any place on the (flat) earth. On the theory of Xenophanes, it should be visible in any zone of the earth where a given sun is visible. On the theory of Anaximenes, a shadow would be cast by a cloud covering the heavenly body. But since the cloud would likely be irregular in shape and of only temporary duration, to measure the shadow would only tells us something about an ephemeral meteorological event; it would be of dubious value for estimating the size of the sun and of no value whatsoever for estimating the size of the moon.
Why then would Anaxagoras be inspired to ask the right questions and collect data on the region in which the eclipse was visible? There was one important advance made in astronomical theory before Anaxagoras. Some time between 500 and 480 BC, Parmenides of Elea developed a cosmology in which he recognized the sun as the cause of the moon's light. Two fragments from his philosophical poem verify that he did make this observation, and thereby gave the correct explanation of the moon's phases. (39) By simply observing how the phases of the moon correlated with its position relative to the sun during the course of a month, any observer could confirm Parmenides' hypothesis about the cause of the moon's light. From his discovery Anaxagoras could infer a number of further results, many of which seem trivially obvious today, but which were violated by some or all earlier theories. One of the these was that the sun and moon continued in existence when they were not visible. Another was that the moon was solid and roughly spherical in shape (this was needed to account for the shape of the moon's shadow in its phases). (40) Another was that the sun's distance from the earth was greater than the moon's (otherwise the moon would never be completely obscured at the time of the new moon).
If the moon was a solid body in an orbit lower than the sun's, and orbiting in a similar plane (as was already recognized), it could in principle intervene between the earth and the sun and obscure the sun. Similarly, the earth could intervene between the sun and the moon, causing the moon to fall into the earth's shadow and hence be obscured. If events of this sort occurred, they would happen because of contingent facts about the alignment of the sun, moon, and earth on certain occasions. In other words, nothing about Parmenides' theory of the moon's light entails that screenings were inevitable. (41) On the other hand, if they did occur, they would appear to observers on the earth as eclipses, that is: phenomena in which the sun or moon would lose its radiance. Hence, Parmenides' theory would provide a possible mechanism for explaining eclipses-without any further conditions being met than geometrical alignment. Incidentally, it would be more natural to apply Parmenides' insight to the lunar eclipse than to the solar, since the moon shines by borrowed light; if it loses its light, something must be interfering with the sun's rays. Since the earth is, by Anaxagoras's assumptions, considerably larger than the moon and lies between the sun and moon at the time of the full moon, it provides a potential obstacle at just the right time of month. As for a solar eclipse, since the sun generates its own light, it could be darkened either by the sun's burning out (as in Xenophanes' theory) or by an occultation. And any dark body of roughly the right size could produce an occultation. The new moon would, however, provide a dark body approximately the right size and location for an occultation. By observing an actual solar eclipse, Anaxagoras could see a circular shadow draw across the sun (or its reflection) in what would look like an occultation rather than an extinguishing of light.
The condition of alignment would require that a solar eclipse could occur only during a new moon, when the two bodies were in conjunction; and a lunar eclipse could occur only at a full moon, when the two bodies were in opposition. If the condition were met for a solar eclipse, assuming the sun was distant enough that its rays were almost parallel, the area in which the eclipse was visible would be limited to the area shadowed by the moon, and the moon's size would be roughly the same as that of its shadow on earth. (42) If the sun were significantly farther from the earth than the moon, it could be significantly larger than the moon. (43)
Thus, while Parmenides' theory of lunar light does not entail that eclipses should be caused by blocking of solar light, it does allow for the possibility, as a further extension and elaboration of the original theory. We know with reasonable certainty that both Anaxagoras and Empedocles were impressed by Parmenides' poem, principles of which they both adopted in their own theories. (44) Moreover, Empedocles echoed Parmenides' language in talking about the moon in particular. (45) And both Anaxagoras and Empedocles propounded the correct explanations of eclipses. Thus they seem to have made the leap from the correct account of the moon's light to a possible application in the problem of eclipses.
When did they do so? To confirm the hypothesis that solar eclipses are occultations, Anaxagoras would need to test it in an actual eclipse. The occultation hypothesis would entail that the area in which a solar eclipse was visible was a shadow, an umbra, of the moon. Earlier theories, as we have seen, had no such entailments and would not call for a geographical survey of the region affected. Thus the very fact that Anaxagoras must have collected geographical data suggests that he already had arrived at the hypothesis before the eclipse of 478. What he did was to test his hypothesis, and, with the limited means at his disposal, to confirm it to the best of his ability.
He would have found that the eclipse occurred during the new moon, as predicted by the theory; and that it was visible over a limited region, as predicted by the theory with suitable assumptions. He would further have been able to observe visually that the cause of the eclipse was at least an opaque circular body, as it stood silhouetted by the sun during the annular eclipse. This observation was consistent with the hypothesis of a spherical solid body, the moon, being the cause. And in the event, Anaxagoras would have seen that the sun was larger than the moon, for its periphery was visible outside the dark disk of the moon in the annular eclipse; hence it would be appropriate to infer that the moon was about the size of the geographical region shadowed and the sun was larger than that region. In all of this, Anaxagoras would have found preliminary confirmation of his theory that eclipses are screenings, caused by the blocking of the sun's light by a heavenly body. He made measurements of the sun's size based on geographical data. And he was in a position to propound, for the first time, the correct theory of eclipses, derived from Parmenides' theory of lunar light and confirmed by empirical data.
That Empedocles could have anticipated Anaxagoras or have discovered the cause of eclipses at the same time seems doubtful. In the first place, he was probably not yet of age when Anaxagoras made his discovery, being only seventeen years of age or younger. Second, he was not in a position to see more than a partial eclipse at Acragas on Sicily in 478, when the umbra passed south of Sicily. Third, there is no record that he collected data on the eclipse which would suggest he appreciated its significance. Indeed, his own view of the sun is that it is larger than the earth--a correct estimate, but not, so far as we know, based on empirical data. (46) In the eclipse of 463, the umbra passed north of Sicily, so that again geography probably kept Empedocles from experiencing a full eclipse. That he could have made the same theoretical connections as Anaxagoras is quite possible, but it is doubtful he could have done so early enough to precede Anaxagoras in his discovery, or actually have tested his hypothesis in any immediate way.
Accordingly, while Empedocles could have arrived at a correct account of eclipses independently of Anaxagoras, the evidence points to the priority of Anaxagoras in proposing and testing the theory. This finding confirms the opinion of some scholars, ancient and modern, that Anaxagoras was the one who discovered the cause of eclipses. (47) On the reconstruction presented here, he saw the potential application of the correct theory of lunar light for the problem of eclipses; he predicted conditions that a solar eclipse would create; and he collected data which tended to confirm his explanation. On the basis of his results he propounded a general theory of eclipses as occultations of solar light. His theory may indeed have been more general than the one we use today, for he may have allowed for bodies other than the sun and the moon to create occultations. (48) He posited the existence of invisible massive bodies below the moon--in modern terms, asteroids--which may have been capable of causing eclipses. The presence of asteroids was probably necessary to account for lunar eclipses which occurred low in the sky, and hence when, on Anaxagoras' theory, the flat earth was not interposed between the sun and the moon. (49)
A number of objections have been raised to this account. We shall briefly present them and reply to them, at the risk of repeating ourselves on some points.
(1) A good deal of the doxographical information concerning Anaxagoras's astronomy comes from Hippolytus. But Osborne (1987) has argued that a full understanding of Hippolytus' testimony should take into account his reactions to and applications of his material. In general, it is not clear how considerations of context could change the content of the doxographical reports in Hippolytus. Indeed, Osborne states that 'it looks as though chapters 6-9 [Anaxagoras is dealt with in ch. 8] are an almost verbatim copy of a brief systematic report' (196). We tend to agree with those who point out that Hippolytus is heavily dependent on his sources. (50) In any case, where we can check Hippolytus against other doxographical sources, we find a high degree of correlation. Thus Hippolytus seems to transmit source material reliably, and this is all we need for our explication.
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(2) Anaxagoras offered nothing new that Thales had not already established. As we have indicated, Thales' alleged prediction is based on no known theory (although it may be based on empirically derived patterns of repetition). To be sure, later scholars, including Eudemus and Aristarchus, attributed the correct theory of eclipses to Thales. But that seems to have been pure reconstruction on their part. Certainly earlier generations of researchers (including Aristotle) had no information to justify the reconstruction, other than the alleged prediction itself. The fact that Thales' immediate successors had no clue about the true physical nature of the sun and moon should make us suspect that their master did not either.
(3) The attribution of the correct theory of eclipses to Anaxagoras is anachronistic. On the contrary, all ancient sources agree that Anaxagoras and Empedocles had the right theory. And the following generation of thinkers recognized it as the right theory (in contrast to Thales' alleged discovery). We have described Anaxagoras' reasoning in terms of hypotheses and confirmations in what may be an anachronistic use of scientific terminology (although the term hypothesis in some scientifi c sense is well attested in the fifth century). (51) What little information we have about scientific reasoning in the fifth century indicates that it could be sophisticated. (52) In any case, all that is needed are some fairly basic principles of informal logic to account for his discovery. Further, Anaxagoras would need to know that the moon gets its light from the sun (supplied by Parmenides) and believe that the moon casts a shadow on the earth roughly equal in size to the moon (an incorrect belief, but plausible, and one attested by Empedocles B42, quoted above). So there is nothing anachronistic about Anaxagoras' discovery, in contrast to Thales' alleged discovery.
(4) No ancient source connects the sizes of the sun and moon in Anaxagoras with the theory of eclipses. True, but not decisive. The fate of ancient theories was to be chopped up into handbooks of opinions (derived from the great collection of Theophrastus), in which the doctrine of one ancient source on a narrow topic, for instance the size of the sun, was set next to the doctrine of another ancient source. (53) The doctrines were often arranged to bring out contrasting viewpoints to prepare dialectical choices. (54) Thus doctrines were taken out of context for purely dialectical reasons. It appears that at some point when researchers became interested in biography, scattered doctrines were reassembled by figure rather than topic. (55) But by this time original texts were rare and difficult to consult, so that the doctrines remained a collection of disiecta membra without context. Thus many systematic connections between doctrines were inevitably lost. The fact, then, that our ancient testimonies do not connect the size of the sun and moon with the theory of eclipses does not tell against the possibility of an original connection.
(5) Anaxagoras's choice of a geographical reference point may have been arbitrary. Indeed, it is possible. Perhaps Anaxagoras chose the Peloponnesus simply because it was a large roughly circular land mass. Then the fact that it fell under the shadow of a contemporary eclipse was a lucky coincidence. We cannot rule this out. On the other hand, this move effectively gives no explanation for the choice of a referent. The present hypothesis, on the other hand, is the only one we know of that offers anything like a genuine and historically viable explanation of the coincidence. The choice, then, is between this explanation and no explanation at all. If, as we have tried to show, the hypothesis offered here fits with the known theories and assumptions of Anaxagoras and his contemporary Empedocles and draws on an important astronomical event of the time, it deserves careful consideration.
Whether Anaxagoras used a measurement of the moon's shadow as evidence for the size of the moon or not, he and his contemporary Empedocles did hit on the correct account of eclipses, both solar and lunar, for the first time and for the right reasons. Of the two philosophers, only Anaxagoras was in a position (temporally and geographically) to test whatever theory he had against his own observations of an eclipse (whether in Athens or in Clazomenae). Anaxagoras' discovery was one of the most important of early astronomy and demonstrates that the philosopher used scientific reasoning effectively. If he used the shadow of the eclipse of 478 to estimate the size of the sun and moon, and to confirm his conjecture about the nature of solar eclipses, he used empirical data in an elegant and powerful way, even though in the end his incorrect assumptions led to erroneous results. If not, he was incredibly lucky in providing an estimate that just happened to coincide with the empirical evidence available from the eclipse. In any case just to come to the right theory of eclipses, he must have used some empirical information together with scientific theory effectively enough to establish himself as a genuine scientist--perhaps the first empirical astronomer. (56)
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(1) All translations by DWG.
(2) West (1971), 233n1; Sider (1973)
(3) Hippolytus Haer 1 8 9-10 = Diels (1951) (hereafter: DK) 59A42
(4) This was the view of Eudemus (DL 1 23 = DK 11A1, Dercyllides from Theo Sm 198 14-18 = 11A17) and Aristarchus of Samos (POxy Vol. 53, no 3710, col ii, lines 36-43).
(5) DK 31B42 (which will be quoted below) seems to give the correct account of a solar eclipse. On the chronology of Anaxagoras and Empedocles the earliest source is Aristotle Metaph 984a11-13: 'Anaxagoras of Clazomenae, being prior to [Empedocles] in age, but posterior in works, says the principles are infinite.' Unfortunately what Aristotle means by 'posterior' is disputed: later it time,inferior in quality, or more up-to-date in quality?
(6) The only early theorists who did not hold such a view were Thales (so far as we know from scanty evidence), who compared the earth to a raft floating on a vast (infinitely extended?) sea (Aristotle Cael 294a28-33 = 11A14); and Xenophanes(21B28, 21A41, with Mourelatos [2002a]). Even the mythographer Hesiod sees the earth as a disk surrounded by a firmament above and below: Th 116-28, 721-6.
(7) DL 2 8-9 = 59A1; Hippol Haer 1 8 3-6 = 59A42
(8) Hippol Haer 1 8 8; 59B18. Anaxagoras may have attributed to the moon a secondary light resulting from the sun's residual action: Plato Cra 409b = 59A76, O'Brien (1968a), 125-7.
(9) The only claim for someone other than the Greeks having this knowledge is for the Egyptians, in Beatty (1997-98), which seems based on a very generous reading of mythological material. The Babylonians were the best observers of the heavenly bodies, and aware of correlations of eclipses with phases of the moon, but show no interest of causal analysis in their astrology: Neugebauer (1975), 1:550.
(10) Plu De fac orb lun 929c-e
(11) Reading upeskefas<s>e; see Mesturini (1987-88: 176). Cf. Lucr 5 753-5.
(12) See http://sunearth.gsfc.nasa.gov/eclipse/SEhistory/SEplot/SE-0556May19T.gif, a map provided by NASA researchers.
(13) See Bickerman (1980).
(14) Hunger and Pingree (1999), 118-22
(15) Lloyd (1979), 176-7; Graham (2002), 371n55
(16) Hunger and Pingree (1999), 1-70
(17) Sic: in solar eclipses the moon's shadow travels west to east.
(18) DL 2 2 = 12A1; Agathem 1 1, Str 1 1 11= 12A6; Hdt 4 36
(19) Pi Pae 1-20, fr. 142 Schroeder; Stephenson (1997), 344-6
(20) See Figure 1 for map. This map is based on calculations in Table 1, prepared by EH.
(21) An annular eclipse casts an antumbra rather than an umbra; see Figure 3. Anaxagoras and his generation presumably had no knowledge of this phenomenon and would have treated the antumbra as an umbra.
(22) Thus Panchenko (1999), 37n47, but without argument.
(23) At any given point on the earth's surface the average frequency of a total eclipse is less than once in three hundred years.
(24) Sider (1973), 129n10; Stephenson (1997), 345-6, claims that since the eclipse covered only 0.89 of the sun's diameter 'it might well have passed unnoticed.' Yet he attributes to a non-astronomer, Thucydides, the ability to discern a 'small' eclipse of 0.72 in 424 BC (347).
(25) See Figure 4.
(26) For the former date, Taylor (1917); O'Brien (1968b); Woodbury (1981); for the latter (the more traditional) view, Mansfeld (1979-80); cf. Sider (2005), 6, who gives the dates 464-434.
(27) DL 2 7 = 59A1 says two apparently contradictory things: that Anaxagoras was twenty years old at the time of Xerxes' invasion (= 480 BC), and that he started philosophizing in Athens at twenty in the year of (the eponymous archon) Callias (= 456). The two statements can be reconciled by emending 'Callias' to 'Calliades', archon for 480.
(28) Hdt 1 74; Plin HN 2 53 = 11A5. The eclipse associated with his name is most likely that of 585 BC: Stephenson and Fatoohi (1997). Thales became renowned shortly after: DL 1 22 = A1.
(29) Thus Blanche (1968) argues that Thales used the Saros cycle to predict an eclipse eighteen years after the eclipse of 603 (visible in Egypt, but not in Greece). Hartner (1969) defends his use of the Exeligmos, equal to three Saros cycles (and more accurate for predictions). Aaboe (1972) points to the possibility of correlating solar eclipses with lunar eclipses (with the latter being much easier to predict). All of this is highly conjectural, and recent studies cast doubt on the development of reliable predictions in Babylonian astronomy: 'no clear evolution from early to late texts which would show "theory" emerged from "observation" can be demonstrated' (Rochberg-Halton , 120).
(30) See Graham (2002), 352-8; for recent defenses of Thales, see Panchenko (1994), (1996); O'Grady (2002), 142; for a classic skeptical account see Dicks (1959); for a recent rejection, Stephenson (1997), 342-4. Aaboe (see previous note), 106, 116, infers (but does not argue) that a method of predicting the possibility of solar eclipses in relation to lunar eclipses presupposes a knowledge of the mechanisms of eclipses. But a mere correlation of observations would do for the prediction.
(31) Hippol Haer 1 6 5 = 12A11; Aetius 2 20 1, 2 21 1, 2 24 2 = A21 (on the sun); Aetius 2 25 1, 2 29 1 = A22
(32) Hippol Haer 1 7 4 = 13A7; Aetius 2 22 1 = B2a
(33) Hippol ibid, 6; Arist Meteor 354a28-32, Aetius 2 16 6 = A14
(34) Aetius 2 24 5 with Bicknell (1969: 62-5)
(35) See Mourelatos (2002a).
(36) Hippol Haer 1 14 3 = 21A33
(37) Aetius 2 24 9 with Bicknell (1967b)
(38) DL 9 10 = 22A1; Aetius 2 28 6, 2 24 3 = 22A12
(39) 28B14-15 with Wohrle (1995), Graham (2002), 363-78. Evans (1998), 45-6, questions whether Parmenides understood the cause of the moon's illumination; but the most plausible understanding of allotrion phos in B14 is 'with borrowed light', a point picked up by Empedocles in 31B45, where he echoes Parmenides' language: the moon 'spins around the earth, a circular borrowed light [allotrion phos],' clearly embedded in the correct theory (B42-43, B48). Empedocles had access to Parmenides' complete poem and seems to see himself as just reiterating his predecessor's theory on the source of the moon's light. There is no direct evidence as to how Parmenides arrived at his important insight, but he may have drawn on the cloud theory of Xenophanes, as Mourelatos (2002b) suggests.
(40) Recognized by Arist Cael 291b18-21.
(41) The fact that Parmenides does not present the correct theory of eclipses is a stumblingblock for O'Brien (1968a), 12; it need not be: Graham (2002), 365.
(42) Sider (2005), 86-9, connects Anaxagoras' statements of the sizes of the heavenly bodies with a theory of perspective (see Vitr 7 preface 11 = DK 59A39). This could account for some of his statements, e.g. B3, but it does not explain how he used the Peloponnesus as a point of comparison.
(43) As the testimony of Aetius cited at the beginning says. Yet Aetius is a late and derivative source, and the reports of Diogenes Laertius and Hippolytus, which merely make the sun larger than the Peloponnesus, may be more reliable. Sider (1973); Sider (2005), 10, 18-19, 86-8, stresses Anaxagoras's contributions to perspective, which he would have applied to astronomy.
(44) 59B17; 31B8-9, 11-12 et passim.
(45) 31B45, 47
(46) Aetius 2 21 2 = 31A56; this report is part of an account of the sun which seems to us to be confused (cf. Wright 1981: 201-2), but the confusion does not concern the size of the sun.
(47) Hippol Haer 1 8 10 = 59A42; Plu Nic 23 2-3 =A18; probably the more prevalent view, supported by Eudemus, the main researcher into astronomical explanations, was that Thales discovered the causes; see n. 4 above. Boll (1909), 2343, already supports this view, as well as Heath (1913), 78-80. Dicks (1970), 58-9, seems to accept Hippolytus' report with little recognition of the historical novelty of the explanation. See also Thoren (1971).
(48) Hippol Haer 1 8 6 and 9 = 59A42.
(49) Boll (1909), 2343-4. See Bicknell (1967a), 16-18, and Tigner (1979), 331-2, for other phenomena they might account for. See Figure 2 for reconstruction. One treatment of Anaxagoras' earth by Aristotle (Meteor 365a19-25) might suggest that Anaxagoras had a spherical earth (see Dicks 1970: 58); but there is much evidence for a flat earth, including Hippol 1 8 3, DL 2 8, by implication Pl Phd 99b-c; and see Panchenko (1997) with Arist Cael 293b33-4a4, Mart Cap 6 590, 592.
(50) See especially Mueller (1989); Mourelatos (1990). For a historical treatment of Hippolytus, see Mansfeld (1992), who points out that Hippolytus does order his sources for the sake of his later discussion (18-19).
(51) Hp. VM 1, 15; Lloyd (1979), 111-15; on Plato's usages, Robinson (1953), 93-179, 223-80.
(52) See, e.g., Graham (2003), dealing with Herodotus' analyses of positions in natural philosophy.
(53) The original comprehensive study is Diels (1879), 1-263, now supplemented and corrected by Mansfeld and Runia (1997). The original work in this genre is Theophrastus' Phusikon doxai ('Doctrines of the Natural Philosophers', according to Diels) or Phusikai doxai ('Doctrines on Nature', according to Mansfeld), in sixteen books (DL 5 48).
(54) Mansfeld (1999), 28-31
(55) Mansfeld (1999) 36
(56) Calculations for this study were determined from StarryNight Pro software, version 6.0 (2006), by EH, which factors in [??]T. Early calculations of eclipses are unreliable owing to the failure to compensate for '[??]T', the gradual slowing of the earth's rotation and the gradual expansion of the moon's orbit; see Stephenson (1997). One of the authors, DWG, became interested in this question as a result of discussions he had with Dmitri Panchenko at a conference in Lille, France, in 2000; Panchenko holds the view that Anaxagoras used the eclipse of 478 to make his calculation of the moon's size (see n. 22 above); but he also believes that Thales had already understood the nature of eclipses (see n. 30), which makes Anaxagoras' investigations seem less innovative than we think they were. In any case, we are deeply indebted to his researches and insights in this area. Needless to say, if the argument in this paper is correct, it vindicates the general approach of M. L. West and David Sider. We are grateful to David Sider, Patricia Curd, and Stephen A. White for comments on a draft of this paper.
Table 1 Planets Potentially Visible During 478 B.C. Eclipse RA Dec Distance Mag Sun/Moon 21 h 41.9m -13d 59.5" -- -- Venus 0h 7.2m 5d 55.4" 41.4 degrees E -4.46 Mars 23h 47.4m -1 d 41.5" 33.7 degrees E 1.44 Saturn 22h 44.2m -10d 29.3" 29.0 degrees E 0.57 Mercury 20h 22.5m -21 d 47.9" 21.3 degrees W -0.18 Path of February 17th, 478 B.C. Eclipse Time Center Long E. Lat. N Lat S. UT 10 35:00:00 31:50:00 10:22 11 35:10:00 32:10:00 10:23 12 35:15:00 32:20:00 10:25 13 35:30:00 32:30:00 10:28 14 35:45:00 32:45:00 10:30 15 36:00:00 32:55:00 10:33 16 36:15:00 33:05:00 10:35 17 36:30:00 33:20:00 10:39 18 36:45:00 33:40:00 10:41 19 37:15:00 34:15:00 10:45 20 37:30:00 34:35:00 10:48 21 37:55:00 35:00:00 10:51 22 38:15:00 35:25:00 10:53 23 38:40:00 35:55:00 10:56 24 39:00:00 36:20:00 10:59 25 39:35:00 36:45:00 11:02 26 40:00:00 37:20:00 11:04 27 40:40:00 37:50:00 11:08 28 41:20:00 38:20:00 11:10 29 41:50:00 38:55:00 11:14 30 42:10:00 39:20:00 11:16 Path of April 30, 463 B.C. Eclipse Time Center Long E. Lat. N Lat S. UT 10 38:50:00 37:10:00 13:31 11 39:15:00 37:40:00 13:33 12 39:25:00 37:50:00 13:36 13 39:40:00 37:55:00 13:38 14 39:50:00 38:00:00 13:40 15 39:55:00 38:10:00 13:41 16 40:05:00 38:15:00 13:43 17 40:05:00 38:30:00 13:45 18 40:15:00 38:40:00 13:47 19 40:20:00 38:45:00 13:49 20 40:35:00 38:55:00 13:50 21 40:30:00 38:55:00 13:53 22 40:40:00 39:00:00 13:54 23 40:45:00 39:05:00 13:56 24 40:50:00 39:05:00 13:58 25 40:50:00 39:10:00 13:59 26 40:55:00 39:15:00 14:00 27 41:00:00 39:20:00 14:01 28 41:00:00 39:25:00 14:03 29 41:00:00 39:25:00 14:04 30 40:55:00 39:25:00 14:06
Daniel W. Graham
Department of Philosophy
Brigham Young University
Provo, UT 84602 Provo,
Department of Physics and Astronomy
Brigham Young University
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|Author:||Graham, Daniel W.; Hintz, Eric|
|Date:||Dec 1, 2007|
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