Studies on Homer and the Homeric Age, Vol. 3 of 3

Only thrice, besides the instances already quoted, does Homer use the fourth power of numbers; it is in the case of the single thousand. A thousand measures of wine were sent by Euneos as a present to Agamemnon and Menelaus. A thousand watch-fires were kindled by the Trojans on the plain. Iphidamas, having given an hundred oxen in order to obtain his wife, then promised a thousand goats and sheep out of his countless herds798. In all these three cases, it is more than doubtful whether the word thousand is not roughly and loosely used as a round number. The combination of the thousand sheep and goats with the hundred oxen, immediately awakens the recollection that even the Homeric hecatomb, though meaning etymologically an hundred oxen, practically meant nothing of the kind, but only what we should call a lot or batch of oxen. Again, it is so obviously improbable that the Trojans should in an hurried bivouac have lighted just a thousand fires, and placed just fifty men by each, that we may take this passage as plainly figurative, and as conveying no more than a very rude approximation, of such a kind as would be inadmissible where the practice of calculation is familiar. It is then most likely, that in the remaining one of the three passages, the Poet means only to convey that a large and liberal present of wine was sent by Euneus, as the consideration for his being allowed to trade with the army. There is certainly more of approximation to a definite use of the single thousand, than of the three, the nine, or the ten: but this difference in definiteness is in reality a main point in the evidence. Most of all does this become palpable, when we consider how strange is in itself the omission to state the numbers of the combatants on either side of this great struggle: an omission so strange, of what would be to ourselves a fact of such elementary and primary interest, that we can hardly account for it otherwise than by the admission, that to the Greeks of the Homeric age the totals of the armies, even if the Poet himself could have reckoned them, would have been unintelligible.

Among all the numbers found in Homer, the highest which he appears to use with a clearly determinate meaning, is that of the three hundred and sixty fat hogs under the care of Eumæus in Ithaca799;

οἱ δὲ τριηκόσιοί τε καὶ ἑξήκοντα πέλοντο.

The reason for considering this number as having a pretty definite sense in the Poet’s mind (quite a different matter, let it be borne in mind, from the question whether the circumstance is meant to be taken as historical) is, that it stands in evident association with the number of days, as it was probably then reckoned, in the year. It seems plain that he meant to describe the whole circle of the year, where he says, that for each of the days and nights which Jupiter has given, or, in his own words800,

ὅσσαι γὰρ νύκτες τε καὶ ἡμέραι ἐκ Διός εἰσιν,

the greedy Suitors are not contented with the slaughter of one animal, or even of two. Eumæus then gives an account of the wealth of Ulysses in live stock, both within the isle and on the mainland, from whence the animals were supplied: and adds, that from the Ithacan store a goatherd took down daily a fat goat, while he himself as often sent down a fat hog. I have dwelt thus particularly on the detail of this case, because it may fairly be inferred from the correspondence between the number of the hogs and the days of the year, that for once, at all events, the Poet intended to speak, though somewhat at random, yet in a degree arithmetically, and that of so high a number as 360.

There are other cases of lower numbers in different parts of the poems, where it may be argued, with varying measures of probability, that Homer had a similar intention.

The ἑκατομβὴ and numerals of value.

The word ἑκατομβὴ, without doubt, affords a striking proof of vagueness in the ideas of the heroic age with respect to number: and this vagueness extends, yet apparently in varying degrees, to the adjective ἑκατομβοῖος. I have elsewhere801 referred to adjectives of this formation as indicative of the fact, that for those generations of mankind oxen may be said to have constituted a measure of value; and this fact certainly involves an aim at numerical exactitude. It seems, indeed, on general grounds far from improbable, that the business of exchange may have been the original guide of our race into the art, and thus into the science, of arithmetic.

In the description of the Shield of Minerva, which had an hundred golden drops or tassels, we are told that each of them was ἑκατομβοῖος, or worth an hundred oxen. This use of the word must be regarded as strongly charged with figure. Minerva was arming to mingle among men upon the plain of Troy802, and it is not likely, therefore, that the Poet would represent her in dimensions utterly inordinate. He judiciously reserves this license of exaggeration without bounds for scenes where he is beyond the sphere of relations properly human, as for example, the Theomachy and the Under-world. Now we may venture to take the Homeric value of an ox before Troy at half an ounce of gold. In the prizes of the wrestling match, where a tripod was worth twelve oxen, a highly skilled woman (πολλὰ δ’ ἐπίστατο ἔργα) was worth four803. Two ounces of gold would be a low price for such a person in almost any age. According to this computation, each drop on the Ægis of Minerva would weigh fifty ounces: the whole would weigh above 300 lbs. avoirdupois, and if we were to assume the purely ornamental fringe in a work of this kind to weigh one tenth part of the whole, the Ægis itself would weigh nearly a ton and a half. Primâ facie, this is susceptible of explanation in either of two ways: the one, that the numbers are used poetically and not arithmetically; the other, that of sheer intentional exaggeration in bulk. The rules of the Poet, as they are elsewhere applied, oblige us to reject the latter solution, and consequently throw us back upon the former.

The numerals of value.

Again, we are told that, when Diomed obtained the exchange of arms from Glaucus, he gave a suit of copper, and obtained in return a suit of gilt804;

χρύσεα χαλκείων, ἑκατόμβοι’ ἐννεαβοίων.

Here there seems to be a mixture of the metaphorical and the arithmetical use. For, on the one hand, it is singular that he should have chosen numbers which require the aid of a fraction to express their relation to one another. He could certainly not have meant to say that the values of the two suits were precisely as 100:9, or as 11 :1. And yet, on the one hand, he could scarcely use the term ἐννεαβοῖα, except with reference to the known and usual value of a suit of armour, while the ἑκατομβοῖα, from its use in other places, must be suspected of having no more than a merely indeterminate force.

With this fractional relation of 100:9, may be compared the arrangement at the feast in Pylos, where each division of five hundred persons was supplied with nine oxen. These numbers, however, are probably less vague than in some other cases: for the provision stated, though large, is not beyond what a rude plenty might suggest on a great public occasion.

Again, Lycaon, when captured for the second time by Achilles, reminds that hero of what he had fetched or been worth to him on the former occasion805: ἑκατόμβοιον δέ τοι ἦλφον. Here we have a decisive proof of the figurative use of number. Had the young prince been ransomed by Priam, a great price, no doubt, would have been given. But Achilles sold him into Lemnos, ἄνευθεν ἄγων πατρός τε φίλων τε: and to the Lemnians he could hardly have value but as a labourer, although indeed it chanced that he was afterwards redeemed, by a ξεῖνος of Priam806, at a high price. We cannot, then, suppose that he had brought any such return as would be represented by a full hundred of oxen.

The evidence thus far, I think, tends powerfully to support the hypothesis, that there is an amount of vagueness in Homer’s general use of numbers, unless indeed as to very low ones, which cannot be explained otherwise than as metaphorical or purely poetical: and that his mind never had before it any of those processes, simple as they are to all who are familiar with them, of multiplication, subtraction, or division.

I admit it to be possible, that his manner of treating number may have been owing to his determination to be intelligible, and to the state of the faculties of his hearers, as much as, or even more than, his own. But to me the supposition of the infant condition even of his faculties with respect to number, though at first sight startling, approves itself on reflection as one thoroughly in conformity with analogy and nature. Indeed the experience of life may convince us that to this hour we should be mistaken, if we supposed arithmetical conceptions to be uniform in different minds; that the relations of number are faintly and imperfectly apprehended, except by either practised or else peculiarly gifted persons; and that, in short, there is nothing more mysterious than arithmetic to those who do not understand it. As one illustration of this opinion, I will cite the difficulty which most educated persons, when studying history, certainly feel in mastering its chronology; while to those who are apt at figures it is not only acquired with ease, but it even serves as the nexus and support of the whole chain of events.

There were several occasions, upon which it would have been most natural and appropriate for Homer to use the faculty of multiplication; yet on no one of these has he used it. He constantly supplies us with the materials of a sum, but never once performs the process.

Silence as to the numbers of the armies.

The first example in the Iliad is supplied by that passage of the unhappy speech of Agamemnon to the Assembly in the Second Book, which causes the fever-fit of home-sickness. He compares the strength of the Greek army with that of the Trojans; and he only effects the purpose by this feeble but elaborate contrivance. ‘Should the Greeks and Trojans agree to be numbered respectively, and should the Trojans properly so called be placed one by one, but the Greeks in tens, and every Trojan made cupbearer to a Greek ten, many of our tens would be without a cupbearer807.’ In the first place, the fact that he calls this ascertaining of comparative force numbering ἀριθμηθημέναι is remarkable; for it would not have shown the numbers of either army; nor even the difference, by which the Greeks exceeded a tenfold ratio to the Trojans; but simply, by leaving an unexhausted residue, the fact that they were more, whether by much or by little, than ten times as many as the besieged. Secondly, it seems plain that, if Homer had known what was meant by multiplication, he would have used the process in this instance, in lieu of the elaborate (yet poetical) circumlocution which he has adopted; and would have said the Greeks were ten times, or fifteen times, or twenty times, as many as the inhabitants of Troy.

After this, Ulysses reminds the Assembly of the apparition of the dragon they had seen at Aulis. The phrase χθιζά τε καὶ πρώιζα, which he employs, may grammatically either belong to the epoch of the gathering at Aulis, or to the time of the plague, which had carried off a part of the force a fortnight or three weeks before. In whichever connection of the two we place it, it affords an instance of extreme indefiniteness in the use of two adverbs which are at once expressive of time and of number; for on one supposition he must use them to express whole years, and on the other they must mean near a fortnight, and therefore a certain number of days.

The next case is remarkable. It is that of the Catalogue.

The resolution, which introduces it, was not a resolution to number the host; but simply to make a careful division and distribution of the men under their leaders, with a view to a more effective responsibility, both of officers and men808. But when the Poet comes to enumerate the divisions, it is evidently a great object with him to make known the relative forces, and thus the relative prominence and power, of the different States of Greece. Yet nothing can be more imperfect than the manner in which the enumerating portion of his task is executed. In the first place, we trace again the old habit of the loose and figurative use of numbers. For Homer could hardly mean us to take literally all the numbers of ships, which he has stated in the Catalogue: since, in every case where they come up to or exceed twenty, they run in complete decades without odd numbers; subject to the single exception of the twenty-two ships of Gouneus. Podalirius and Machaon have thirty, the Phocians forty, Achilles fifty, Menelaus sixty, Diomed eighty, Nestor ninety, Agamemnon an hundred: the only full multiple of ten omitted being the utterly intractable ἑβδομήκοντα. But again, he gives us no effectual clue to the numbers of the crews. Each of the fifty ships of the Bœotians had one hundred and twenty men, and each of the seven ships of Philoctetes had fifty809. Thus he supplies us with the two factors of the sum, which would find the number of men, in each of these two cases; but in neither case does he perform the sum; and such is the uniform practice throughout the poems. For the Greek force generally, he has not even given us the factors. It has indeed been conjectured, that fifty may have been the smallest ship’s company, and one hundred and twenty the largest: but this is mere conjecture; and even if it be well founded, still we do not know whether the generality of the ships were about the mean, or nearer one or the other of the extremes. Again, it would appear probable from the Odyssey, that these numbers, of fifty and one hundred and twenty, are exclusive at least of pilots and commanders, if not also of the stewards810 and the minor officers811; for the number mentioned by Alcinous812 is fifty-two; and although he says that all were to sit down to row, the texts when compared cannot but suggest, that the number fifty was an usual complement of oars, and that the two were the captain and pilot respectively813.

Plainly, there must have been very great inequalities in the crews of the Greek armament; or Homer could not have said, after giving Agamemnon an hundred ships, that he had by far the largest force of all the chiefs814;

ἅμα τῷγε πολὺ πλεῖστοι καὶ ἄριστοιλαοὶ ἕποντ’.

For Diomed and Idomeneus have each eighty ships, and Nestor has ninety, so that their numbers would come very near Agamemnon’s, unless their ships were smaller. But to sum up this discussion. It is evident that, if only we suppose the Greeks of Homer’s time to have had a definite and well developed sense of number, the mention by Homer of the amount of force in the Trojan expedition would have been a fact of the highest national interest and importance. Yet he has left us nothing, which can be said even definitely to approximate to a record of it, though the enumeration of the Catalogue appears almost to force the subject upon him. The fair inferences seem to be, that he did not understand the calculative use of numbers at all, or beyond some very limited range; and that, even within that range, he for the most part employed them poetically and ornamentally; they were decorative and effective, like epithets to his song, but they were not statistical; as expressions of force they were no more than (as it were) tentative, and that but very rudely.

I am further confirmed in the belief of Homer’s indeterminate conception of number, from the strange result to which the contrary opinion would lead. He tells us of the Trojan bivouac815;

χίλι’ ἄρ’ ἐν πεδίῳ πυρὰ καίετο· πὰρ δὲ ἑκάστῳεἵατο πεντήκοντα.

In this case he has given us again the factors of a sum in multiplication, though not the product. Did he mean them to be taken literally? If he did, then it is indeed strange that, although he says nothing whatever on the subject of number in the Trojan Catalogue, yet he has here supplied us with all the particulars necessary for estimating the Trojan force, while as to the Greek army, we remain unable to say whether it amounted to fifty thousand, or to half, or to twice or thrice that number. But it is quite plain from the total absence of specified numbers in the Trojan Catalogue, that he had no desire, as indeed he had no occasion, to give an accurate account of the Trojan force. On the other hand it appears, from the details of the Greek Catalogue, that he did wish to describe the amount of the force on that side, as far as he could conceive or convey it. If all this be so, then nothing can show more clearly than the thousand Trojan watch-fires, with their fifty men at each, Homer’s figurative manner of employing numerical aggregations. If however we admit the figurative use, we at once find everything harmonious. He describes the Trojans by the method of bold enhancement, at a juncture of the poem where it is his purpose to make them terrible to the Greek imagination.

The instance of Proteus in the Odyssey has already been referred to: but one more marked is afforded by the description that Eumæus gives of the herds and flocks of Ulysses. This, again, is one of the instances where the spirit and gist of the passage almost required that a total should be stated. For the object is to give a telling account. The wealth of this prince, says the Poet, was boundless; none of the heroes, whether of Ithaca or of the fertile continent, had so much; no, nor had any twenty of them. Then he mentions how many herds of cattle, goats, and swine, and flocks of sheep there were, but gives no numbers of any of the herds, nor any total: though, shortly before, the poem had mentioned the three hundred and sixty fat hogs under the care of Eumæus, and had also given us the sows in the usual manner, stating that there were twelve sties with fifty in each; but not specifying anywhere the total of six hundred which these figures yield when multiplied together816.

Again, then the result of all these passages, as well as of more which might be quoted, is, I think, to show that Homer’s conceptions of number, and his use of number, especially when beyond a very low limit, were so indeterminate, that they may not improperly be called figurative.

Hesiod’s age of the Nymphs.

In support and in illustration of this belief with respect to Homer, I would once more refer to the curious fragment ascribed to Hesiod respecting the age of the Nymphs with beauteous locks, which begins,

ἐννέα τοι ζώει γενεὰς λακέρυζα κορώνηἀνδρῶν ἡβώντων.

In the Etymol. Magn. 13. 36, the reading is γερώντων; and Ausonius, following this authority in his Eighteenth Idyll, makes the γενεὴ no less than 96 years. But the sense of γενεὴ is fixed by Homer’s account of Nestor, and otherwise, in such a way as greatly to favour the reading ἡβώντων. The word therefore means the term between birth and the prime of life, which may well be taken at thirty years. Then comes a table as follows.

The age of the daw = 9 ages of men.

The age of the stag = 4 of daws = 36 of men.

The age of the crow = 3 of stags = twelve of daws = 108 of men.

The age of the palm = 9 of crows = 27 of stags = 108 of daws = 972 of men.

The age of the Nymph = 10 of palms = 90 of crows = 270 of stags = 1080 of daws = 9720 of men.

And if the γενεὴ be 30 years, the age of the Nymphs = 30 × 9720 = 291,600 years. But the point most remarkable for us is, that while Hesiod, if Hesiod it be, supplies us with the whole of the first factors after the γενεὴ, for this long sum, he does not actually perform one single multiplication; nor does he even define the γενεὴ, which is the first and most vital element of all.

He has thus given us at once a very pretty poetical invention for expressing approximately the age of Nymphs, who are Jove-born indeed, yet are not immortal, and a remarkable proof of the indefiniteness of numerical conceptions, and of total unacquaintance with the rules of arithmetic817.

One consequence of the proposition I have advanced with respect to Homer is, to destroy altogether a supposed discrepancy between the Iliad and the Odyssey, which has often been paraded as a reason, among others, for assigning them to different authors. It is truly alleged that, in the Catalogue818, Crete is called ἑκατόμπολις; and that in the Nineteenth Odyssey819 we are told of it,

ἐν δ’ ἄνθρωποιπολλοὶ, ἀπειρέσιοι, καὶ ἐννήκοντα πόληες.

Each of these words appears to be interpreted as strictly, as it would be if caught by an auditor in the accounts of some delinquent Joint-Stock Company; and thus, forsooth, a diversity of authors for the two poems is to be made good. Now it is not a little odd, if both these poets looked at the subject with the eye of statisticians, that while each found a different number of cities in Crete, yet each found an even, and more or less a round number. But why is ἑκατόμπολις to be more strictly interpreted than ἑκατομβή? And again, if we are to construe ἐννήκοντα statistically, what are we to do with the very word that precedes it, namely, ἀπειρέσιοι? The simple fact of the juxtaposition of that word with the ἐννήκοντα πόληες should surely have sufficed to show, that the whole manner of speech was (what we now call) poetical. So regarding it, I venture even to say that the effect of a comparison with the epithet in the Catalogue is to establish, not a discrepancy in point of fact, but rather a similarity in the measure of figurative conception and expression: so that in consequence, as far as it is worth any thing, it rather tends to prove the identity, than the diversity, of authorship between the two poems.

A second consequence, which must be drawn from the foregoing conclusions, is this; that we shall do wrong to search the poems of Homer for any scheme of chronology. The minute enumerations of the Mosaic books have perhaps given the tone to our ordinary historical inquiries: but, at least with respect to Homer, it must appear an erroneous course to use his numerical statements as literal, when they are applied to time, after we have had so much evidence of their generally ornamental and figurative character.

When Homer has occasion to define distance, he does not attempt to do it by a fixed measure, but by reference always to human or other action: it is as far as a man can throw a spear, (δουρὸς ἐρώη); or as far as a man’s cry can be heard (ὅσον τε γέγωνε βόησας); or as far, when we come to larger spaces, as we can sail within a certain time; if I make a good passage, says Achilles820, I may get to Phthia on the third day: and again, we hear of the distance that a ship can perform within the day821. The horses of the gods in Homer clear, at each bound, a space as large as the eye can cover along the surface of the sea. As he comes to speak of points more remote and less known, he becomes greatly more vague, and says of Egypt, that even the birds do not get back from it within the year822: without doubt drawing his idea from those birds which periodically migrate.

No scheme of Chronology in Homer.

As with spaces, so with times. The year indeed by its revolution forms itself into a natural whole, and is thus in a manner self-defined. So the waxing and waning moon defines the month. But even with these well marked terms Homer deals loosely; for the birth of infants is promised to take place after the revolution of a year from the time of conception823.

Case of the three decades of years.

I do not remember that he ever mentions a very high number of days or of years, but his use of both days and years, when it does not embrace terms defined by custom, has the marks of being highly poetical. Take for instance the principal and almost only statements of the poem, that can claim to be called chronological. They are those which represent the period of the siege as a decade of years, preceded by a decade of preparation, and followed by a third decade for the vicissitudes of the Return. Here are three terms of years, all found in a Poet, who does not elsewhere deal in terms of years at all. Of history, or what purports to be such, Homer has given us a great deal, and he has placed it in the exactest and clearest order. But in no one instance, out of all his prior history, does he found himself on any numerical definitions of time. Moreover, these three terms of years are all exactly equal, which heightens the unlikelihood of their being historical. Lastly, the three terms are just of the number of years required to make up what was, according to all appearances, the Homeric term of a γενεὴ, or generation of men.

The passage, on which the proof of this last assertion must principally be founded, is that in the First Book824, which describes the age of Nestor;