_Homer’s perceptions and use of Number._
While the faculties of Homer were in many respects both intense and
refined in their action, beyond all ordinary, perhaps we might say
beyond all modern, examples, there were other points in which they
bear the marks of having been less developed than is now common even
among the mass of many civilized nations. In the power of abstraction
and distinct introspective contemplation, it is not improbable that he
was inferior to the generality of educated men in the present day. In
some other lower faculties, he is probably excelled by the majority
of the population of this country, nay even by many of the children
in its schools. I venture to specify, as examples of the last-named
proposition, the faculties of number, and of colour. It may be true of
one or both of these, that a certain indistinctness in the perception
of them is incidental everywhere to the early stages of society. But
yet it is surprising to find it where, as with Homer, it accompanies a
remarkable quickness and maturity not only of great mental powers, but
of certain other perceptions more akin to number and colour, such as
those of motion, of sound, and of form. But let us proceed to examine,
in the first place, the former of these two subjects.
It may be observed at the outset, that probably none of us are aware
to how great an extent our aptitudes with respect to these matters are
traditionary, and dependent therefore not upon ourselves, but upon
the acquisitions made by the human race before our birth, and upon
the degree in which those acquisitions have circulated, and have been
as it were filtered through and through the community, so as to take
their place among the elementary ideas, impressions, and habits of
the population. For such parts of human knowledge, as have attained
to this position, are usually gained by each successive generation
through the medium of that insensible training, which begins from the
very earliest infancy, and which precedes by a great interval all the
systematic, and even all the conscious, processes of education. Nor am
I for one prepared by any means to deny that there may be an actual
‘traducianism’ in the case: on the contrary, in full consistency with
the teaching of experience, we may believe that the acquired aptitudes
of one generation may become, in a greater or a less degree, the
inherited and inborn aptitudes of another.
We must, therefore, reckon upon finding a set of marked differences in
the relative degrees of advancement among different human faculties in
different stages of society, which shall be simply referable to the
source now pointed out, and distinct altogether from such variations
as are referable to other causes. It is not difficult to admit this to
be true in general: but the question, whether in the case before us
it applies to number and colour, can of course only be decided by an
examination of the Homeric text.
Yet, before we enter upon this examination, let us endeavour to throw
some further light upon the general aspect of the proposition, which
has just been laid down.
Of all visible things, colour is to our English eye the most striking.
Of all ideas, as conceived by the English mind, number appears to be
the most rigidly definite, so that we adopt it as a standard for
reducing all other things to definiteness; as when we say that this
field or this house is five, ten, or twenty times as large as that.
Our merchants, and even our schoolchildren, are good calculators. So
that there is a sense of something strikingly paradoxical, to us in
particular, when we speak of Homer as having had only indeterminate
ideas of these subjects.
~_Conceptions of Number not always definite._~
There are however two practical instances, which may be cited to
illustrate the position, that number is not a thing to be as matter
of course definitely conceived in the mind. One of these is the case
of very young children. To them the very lowest numbers are soon
intelligible, but all beyond the lowest are not so, and only present
a vague sense of multitude, that cannot be severed into its component
parts. The distinctive mark of a clear arithmetical conception is, that
the mind at one and the same time embraces the two ideas, first of the
aggregate, secondly of each one of the units which make it up. This
double operation of the brain becomes more arduous, as we ascend higher
in the scale. I have heard a child, put to count beads or something of
the sort, reckon them thus: ‘One, two, three, four, a hundred.’ The
first words express his ideas, the last one his despair. Up to four,
his mind could contain the joint ideas of unity and of severalty, but
not beyond; so he then passed to an expression wholly general, and
meant to express a sense like that of the word multitude.
But though the transition from number definitely conceived to number
without bounds is like launching into a sea, yet the conception of
multitude itself is in one sense susceptible of degree. We may have
the idea of a limited, or of an unbounded, multitude. The essential
distinction of the first is, that it might possibly be counted;
the notion of the second is, that it is wholly beyond the power of
numeration to overtake. Probably even the child, to whom the word
‘hundred’ expressed an indefinite idea, would have been faintly
sensible of a difference in degree between ‘hundred’ and ‘million,’
and would have known that the latter expressed something larger
than the former. The circumscribing outline of the idea apprehended
is loose, but still there is such an outline. The clearness of the
double conception is indeed effaced; the whole only, and not the whole
together with each part, is contemplated by the mind; but still there
is a certain clouded sense of a real difference in magnitude, as
between one such whole and another.
And this leads me to the second of the two illustrations, to which
reference has been made. That loss of definiteness in the conception of
number, which the child in our day suffers before he has counted over
his fingers, the grown man suffers also, though at a point commonly
much higher in the scale. What point that may be, depends very much
upon the particular habits and aptitudes of the individual. A student
in a library of a thousand volumes, an officer before his regiment of a
thousand men upon parade, may have a pretty clear idea of the units as
well as of the totals; but when we come to a thousand times a thousand,
or a thousand times a million, all view of the units, for most men,
probably for every man, is lost: the million for the grown man is in
a great degree like the hundred for the child. The numerical term has
now become essentially a symbol; not only as every word is by its
essence a symbol in reference to the idea it immediately denotes; but,
in a further sense, it is a symbol of a symbol, for that idea which
it denotes, is itself symbolical: it is a conventional representation
of a certain vast number of units, far too great to be individually
contemplated and apprehended. As we rise higher still from millions,
say for example, into the class of billions, the vagueness increases.
The million is now become a sort of new unit, and the relation of two
millions to one million, is thus pretty clearly apprehended as being
double; but this too becomes obscured as we mount, and even (for
example) the relation of quantity between ten billions of wheat-corns,
and an hundred billions of the same, is far less determinately conveyed
to the mind, than the relation between ten wheat-corns and one. At this
high level, the nouns of number approximate to the indefinite character
of the class of algebraic symbols called known quantities.
In proportion as our conception of numbers is definite, the idea of
them, instead of being suited for an address to the imagination,
remains unsuited for poetic handling, and thrives within the sphere
of the understanding only. But when we pass beyond the scale of
determinate into that of practically indeterminate amounts, then the
use of numbers becomes highly poetical. I would quote, as a very noble
example of this use of number, a verse in the Revelations of St. John.
‘And I beheld, and I heard the voice of many angels round about the
throne, and the beasts and the elders: and the number of them was ten
thousand times ten thousand, and thousands of thousands[790].’ As a
proof of the power of this fine passage, I would observe, that the
descent from ten thousand times ten thousand to thousands of thousands,
though it is in fact numerically very great, has none of the chilling
effect of anticlimax, because these numbers are not arithmetically
conceived, and the last member of the sentence is simply, so to speak,
the trail of light which the former draws behind it.
[790] Rev. v. 11.
Now we must keep clearly before our minds the idea, that this poetical
and figurative use of number among the Greeks at least preceded what
I may call its calculative use. We shall find in Homer nothing that
can strictly be called calculation. He repeatedly gives us what may
be termed the factors of a sum in multiplication; but he never even
partially combines them, even as they are combined for example in
Cowper’s ballad,
John Gilpin’s spouse said to her dear,
Though wedded we have been
These _twice ten_ tedious years, yet we
No holiday have seen.
Reference has been made to the convenience which we find in using
number as a measure of quantity, and as a means of comparing things
of every species in their own kind. But we never meet with this use
of it in Homer. He has not even the words necessary to enable him to
say, ‘This house is five times as large as that.’ If he had the idea
to express, he would say, Five houses, each as large as that, would
hardly be equal to this. The word τρὶς may be called an adverb of
multiplication; but it is never used for these comparisons. Indeed,
Damm observes, that in a large majority of instances it signifies an
indefinite number, not a precise one. Τετράκις is found only once, and
in a sense wholly indeterminate: the passage is[791] τρισμάκαρες Δαναοὶ
καὶ τετράκις. Πεντάκις does not even exist. Ajax lifts a stone, not
‘twice as large as a mortal of to-day could raise’, but so large that
it would require two such mortals to raise it. All Homer’s numerical
expressions are in the most elementary forms; such forms, as are
without composition, and refuse all further analysis.
[791] Od. v. 306.
~_Greek estimate of the discovery of Number._~
His use of number appears to have been confined to simple addition: and
it is probable that all the higher numbers which we find in the poems,
were figurative and most vaguely conceived. If we are able to make
good the proof of these propositions from the Homeric text, we shall
then be well able to understand the manner in which Numeration, or
the science of number, is spoken of by the Greeks of the historic age
as a marvellous invention. It appears in Æschylus, as among the very
greatest of the discoveries of Prometheus[792]:
[792] Æsch. Prom. V. 468. see also Soph. Naupl. Fragm. v.
καὶ μὴν ἀριθμὸν, ἔξοχον σοφισμάτων,
ἐξεῦρον αὐτοῖς·
he goes on to add,
γραμμάτων τε συνθέσεις.
So that the use of numbers by rule was to the Greek mind as much a
discovery as the letters of the alphabet, and is even described here
as a greater one: much as in later times men have viewed the use of
logarithms, or of the method of fluxions or the calculus. In full
conformity with this are the superlative terms, in which Plato speaks
of number. Number, in fact, seems to be exhibited in great part of the
Greek philosophy, as if it had actually been the guide of the human
mind in its progress towards realizing all the great and cardinal ideas
of order, measure, proportion, and relation.
Up to what point human intelligence, in the time of Homer, was able to
push the process of simple addition, we do not precisely know. It is
not, however, hastily to be assumed that, in any one of his faculties,
Homer was behind his age; and it is safer to believe that the poems,
even in these points, represent it advantageously. Now, in one place
at least, we have a primitive account of a process of addition. The
passage is in the Fourth Odyssey, where Menelaus relates, how Proteus
counted upon his fingers the number of his seals[793]. That it was
a certain particular number is obvious, because when four of them
had been killed by Eidothee, their skins were put upon Menelaus and
his three comrades, and the four Greeks were then counted into the
herd, so that the word ἀριθμὸς here evidently means a definite total.
This addition by Proteus, however, was not addition in the proper
arithmetical sense, and would be more properly called enumeration: it
was probably effected simply by adding each unit singly, in succession,
to the others, with the aid of the fingers, (proved through the word
πεμπάσσεται,) but not by the aid of any scale or combination of units,
either decimal or quinal. In the word δεκὰς we have, indeed, the first
step towards a decimal scale; but we have not even that in the case
of the number five, there being no πεντὰς or πεμπτάς. The meaning of
πεμπάσσεται evidently is, not that he arranged the numeration in fives,
but that, by means of the fingers of one hand, employed upon those of
the other, he assisted the process of simple enumeration.
[793] Od. iv. 412, 451.
~_Highest numerals of the poems._~
Homer’s highest numeral is μύριοι. He describes the Myrmidons as being
μύριοι[794], though, if we assume a mean strength of about eighty-five
for their crews, the force would but little have exceeded four
thousand: and at the _maximum_ of one hundred and twenty for each ship,
it would only come to six thousand. Again, Homer uses the expression
μύρια ᾔδη, to denote a person of instructed and accomplished mind[795].
[794] Il. xxiii. 29.
[795] Od. ii. 16.
Next to the μύρια, the highest numerals employed in the poems are
those contained in the passage where the Poet says that the howl of
Mars, on being wounded by Diomed, was as loud as the shout of an army
of nine thousand or ten thousand men[796]:
[796] Il. v. 860.
ὅσσον τ’ ἐννεάχιλοι ἐπίαχον ἢ δεκάχιλοι
ἀνέρες ἐν πολέμῳ.
But it is clear that the expressions are purely poetical and
figurative. For he never comes near the use of such high numbers
elsewhere; and yet it obviously lay in his path to use these, and
higher numbers still, when he was describing the strength of the Greek
and Trojan armies.
The highest Homeric number, after those which have been named, is
found in the three thousand horses of Erichthonius. This we must also
consider poetical, because it is so far beyond the ordinary range
of the poems, and in some degree likewise because of the obvious
unlikelihood of his having possessed that particular number of
mares[797].
[797] Il. xxi. 251.
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
herds[798]. 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.
[798] Il. vii. 571. viii. 562. xi. 244.
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 Ithaca[799];
[799] Od. xiv. 20.
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 words[800],
[800] Od. xiv. 93.
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 elsewhere[801] 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.
[801] Agorè, p. 82.
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 Troy[802], 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
four[803]. 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.
[802] Il. ii. 450.
[803] Il. xxiii. 703, 5.
~_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
gilt[804];
[804] Il. vi. 236.
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 11⅑:1.
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
occasion[805]: 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 Priam[806],
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.
[805] Il. xxi. 79.
[806] Il. xxi. 42.
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 cupbearer[807].’ 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.
[807] Il. ii. 123-8.
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 men[808]. 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 fifty[809]. 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 stewards[810] and the
minor officers[811]; for the number mentioned by Alcinous[812] 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
respectively[813].
[808] Il. ii. 362-8.
[809] Il. ii. 509, 719.
[810] Il. xix. 44.
[811] Il. ii. 362, 5.
[812] Od. viii. 35.
[813] Sup. Agorè, p. 135.
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 chiefs[814];
[814] Il. ii. 577.
ἅμα τῷγε πολὺ πλεῖστοι καὶ ἄριστοι
λαοὶ 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 bivouac[815];
[815] Il. viii. 562.
χίλι’ ἄρ’ ἐν πεδίῳ πυρὰ καίετο· πὰρ δὲ ἑκάστῳ
εἵατο 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 together[816].
[816] Od. xiv. 13-20.
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 κορώνη
ἀνδρῶν 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
arithmetic[817].
[817] I subjoin the rest of this curious fragment;
ἔλαφος δέ τε τετρακόρωνος·
τρεῖς δ’ ἐλάφους ὁ κόραξ γηράσκεται· αὐτὰρ ὁ φοίνιξ
ἐννέα τοὺς κόρακας· δέκαδ’ ἡμεῖς τοὺς φοίνικας
νύμφαι ἐϋπλόκαμοι, κοῦραι Διὸς αἰγιόχοιο.
It is noticed by Pliny, (Nat. Hist. vii. 48.) who terms it fabulous;
but it is with more propriety, I think, to be called poetical.
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 Catalogue[818], Crete is called ἑκατόμπολις; and that in
the Nineteenth Odyssey[819] we are told of it,
[818] Il. ii. 649.
[819] Od. xix. 173.
ἐν δ’ ἄνθρωποι
πολλοὶ, 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 Achilles[820], I may get to Phthia on the
third day: and again, we hear of the distance that a ship can perform
within the day[821]. 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 year[822]: without doubt drawing his
idea from those birds which periodically migrate.
[820] Il. ix. 362.
[821] ὅσσον τε πανημερίη νηῦς ἤνυσε, Od. iv. 356.
[822] Od. iii. 322. With this compare the Tempest, Act ii. Sc. 1;
where, be it observed, Shakespeare is treating his subject as one of
Dreamland.
_Ant._ Who’s the next heir of Naples?
_Seb._ Claribel.
_Ant._ She that is queen of Tunis: she, that dwells
Ten leagues beyond man’s life; she that from Naples
Can have no note, unless the sun were post,
(The man i’ th’ moon ’s too slow,) till new-born chins
Be rough and razorable.
~_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
conception[823].
[823] Od. xi. 248.
~_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 Book[824], which describes the age of
Nestor;
[824] Il. i. 250-2.
τῷ δ’ ἤδη δύο μὲν γενεαὶ μερόπων ἀνθρώπων
ἐφθίαθ’, οἵ οἱ πρόσθεν ἅμα τράφεν ἠδ’ ἐγένοντο
ἐν Πύλῳ ἠγαθέῃ, μετὰ δὲ τριτάτοισιν ἄνασσεν.
I take the word γενεὴ to mean here, ‘the term of thirty years,’ but
with the necessary qualification of ‘_or_ thereabouts;’ and for the
following reasons:
Nestor is represented in the Iliad as the oldest of the Greek
chieftains of the first order. Yet Ulysses[825] was elderly, ὠμογέρων.
Idomeneus, again, was older than Ulysses, as is plain from the
more marked manner in which his advance in years is described. He
is μεσαιπόλιος[826], and not fully ablebodied, as appears from his
somewhat limited share in military operations; but Nestor is evidently
older than Idomeneus, as he always addresses the whole body with the
authority that belongs to the most extended experience, and as he
never takes an active part, either in battle or in the games. We must,
accordingly, suppose Nestor to be represented as at this time an old
man of seventy, or from that to seventy-five.
[825] Il. xxiii. 791.
[826] Il. xiii. 361.
Now the passage implies that he was in the third γενεὴ, and in the
midst, i. e. not at either extremity, of it: the words are μετὰ
τριτάτοισιν. No lower number than thirty years will place Nestor fairly
among, or in the midst of, the third generation from his birth. If, for
example, we take five and twenty years as the term, he would have been
not so much among the third as on the eve of arriving within the fourth
generation. But neither can we assign to γενεὴ any meaning, which shall
make it sensibly exceed thirty years. For as we may say with confidence
that the Nestor of the Iliad is over seventy, so, on the other hand,
we may fairly compute that he is under eighty; inasmuch as, though
he takes no part in exertions actually athletic, he spares himself
nothing else. He is found by Agamemnon, when the commander in chief
goes his rounds, on the field and at the head of his division: he is
wakeful for the night council, and he goes about awaking others[827].
Retaining so large a share of bodily activity, he is still not
represented as possessed of strength in such a degree as to border upon
the marvellous; he is simply, in regard to corporal qualities, what
would now be called a remarkably fine old gentleman. But if instead of
thirty we were to take forty years, then, in order to have well entered
into the third term he must have been already much beyond eighty,
indeed, probably beyond ninety, in the Iliad, and above an hundred in
the Odyssey; an age, which, as he retains in that poem all his mental
powers, we may be quite sure Homer did not mean to assign to him. If,
then, γενεὴ meant any term of years, it must, in all likelihood, have
been somewhere about thirty years.
[827] Il. x. 157.
Homer has been careful, in the case of Nestor, to mark, by an
appropriate change of expressions, the difference between his age in
the two poems respectively. In the Iliad he is exercising the kingly
office _among_ the third generation since his birth. In the Odyssey he
is said to have exhausted the three terms[828];
[828] Od. iii. 245. The meaning may be that he had _reigned_ for above
two generations: but in the Iliad no more is implied than that he had
_lived_ well into a third.
τρὶς γὰρ δή μίν φασιν ἀνάξασθαι γενε’ ἀνδρῶν.
That lucidity and accuracy in Homer’s expressions, to which we are so
often beholden, may stand us yet further in good stead. Two γενεαὶ
had passed, not of men at large, but of _the_ men οἵ οἱ πρόσθεν ἅμα
τράφεν ἠδ’ ἐγένοντο, of those who were bred and born with him, of his
contemporaries. Now this proves that by γενεὴ Homer does not mean the
full duration of human life, but that average interval between the
successions of men, which general experience places at about thirty
years. For if Homer had meant by γενεὴ the whole time required for
the dying out of a generation, Nestor could not have outlived two
generations of contemporaries. In this sense, his contemporaries were
manifestly not two generations, but one, or little more. But if the
Poet meant the usual interval at which child succeeds to, or rather
follows upon, father, the expression is clear; for the meaning is, that
he had seen two of these terms of years, or successions, pass over
those who were born at the same time with himself. And in fact this
sense of the term γενεὴ is much closer to its etymology than any other.
We may, then, on the whole, pretty safely assume it to be a term of
years, having the number thirty, so to speak, for its pivot. And thus
the three decades of the war become yet more inadmissible as historical
expressions, because they are under the strongest suspicion of being
poetically employed in order to make up the γενεὴ, so far at least as
they and it can be considered to approximate to an actual number at all.
In full conformity with this reasoning, it has been shown by Mure,
that the events of the third decade, with their times, instead of ten
years only, make up eight years and seven months[829]: and he proceeds
in the same direction with the foregoing argument so far, at least, as
to observe, that the decades and their arrangement are conceived ‘in a
mixed spirit of hyperbole and method,’ which commonly marks the genius
of heroic romance[830].
[829] Lit. Greece, i. 460. ii. 139.
[830] Ibid. ii. 138.
That, however, which enables me with great confidence at once to urge
Homer’s historical authority, and yet to decline recognising him as a
chronologist at all, is the fact, that he nowhere founds his history at
all in chronology, or in the numbering of events by years, more than
he numbers distances by miles, but that he arranges the succession
of occurrences by the γενεαὶ or succession of human generations. On
these generations we must look as the real time-keeping organism of his
works: and the time with its elastic periods, although indeterminate in
its details, is kept by him most accurately and effectually as a whole;
so that his generations, which are dispersedly recorded in various
parts of the poems, always tally when they meet. This is not the place
for the proof of the assertion: I only refer to it, because it may help
to dispel the illusion apt to possess the mind with respect to Homer’s
decades. We, with our definite numerical ideas, may naturally consider
that if an author of our own day had said a war lasted in preparation,
action, and return, each ten years, and if it was afterwards found
perhaps to have lasted (say) only for ten years altogether or little
more, such an author would have proved himself unworthy of belief: he
would have broken faith with us. But Homer does not break faith with
us in using numbers poetically; they belong to his pictorial and not
to his historical apparatus, and in connection with this pictorial
apparatus it is that he constantly employs them. I doubt if there is
any exception to be made to the broad assertion, that, unless in the
single case of the war, with the preceding and following decades,
Homer never applies number to narrative. And yet the poems are full of
independent narratives. Of all these, very few indeed are left unfixed
in date; and in every case the date, when found, is found, of course
with a certain margin, by means of the order of generations.
~_Difficulties of the literal interpretation._~
Now this view of Homer’s mode of chronology will serve, I think, to
explain some difficulties that have heretofore led to much of needless
perplexity. If I am right, it will follow that we must not adopt
these decades as a guide to determine arithmetically the order of
events, because Homer has never conceived them arithmetically, but
has conceived them rather as we conceive millions or billions. Hence
they are more justly to be viewed as a drapery thrown loosely over
his action, than as a rigid framework into which it must at all costs
be made to fit. Let us apply this to various cases; and among them
to those of Telemachus and Neoptolemus respectively. Ulysses left
Telemachus a mere child, νέον γεγαῶτ’ ἐνὶ οἴκῳ[831]. He comes back and
finds him not a full man, for if he had been a full man, he would have
been guilty of a rooted cowardice beyond excuse, which there is no sign
that Homer meant to impute to him; but yet he was approaching manhood.
Still he is contemptuously called νέος παῖς[832] by Antinous. Upon the
whole, the case of Telemachus would perhaps, according to the analogy
of the poems, best fall in with an absence of not more than fifteen
years, though it does not absolutely exclude nineteen. Here there may
be a slight, yet there is not a glaring, discrepancy. But in another
case, that of the number of the days for which Telemachus was absent,
Mure has shown how little Homer cares to follow the lapse of time, in
a case where it does not essentially touch the general order of the
poem, with the precision that he observes in everything that he treats
historically[833]. I cannot treat this as a difficulty with respect to
the question of authorship, or admit it to be one: it is his childlike
and indeterminate but poetical habit of handling numbers for effect,
just as a painter handles colour. On the other hand, in the case of
Argus, on whom dark death laid hold[834],
[831] Od. xii. 112, 144.
[832] Od. iv. 665.
[833] Mure, Hist. Lit. Greece, vol. i. p. 437.
[834] Od. xvii. 327.
αὐτίκ’ ἰδόντ’ Ὀδυσῆα ἐεικοστῷ ἐνιαυτῷ,
he precisely coincides with his own decades. Yet I believe he does
this not from any sense of the necessity of such coincidence, but
because in that incomparable passage he had the extreme old age of a
dog to represent, and to this the expression of the twentieth year
was suited. When, however, we come to the case of Neoptolemus, we
find this to be one extremely difficult of adjustment for any critic,
who would insist upon a merely numerical precision in Homer. We must
indeed dismiss from our minds the tales about the concealment of a
beardless Achilles at Scyros, under a female disguise; from which he
was extracted by the art of Ulysses. Of these stories Homer knows
nothing; though it seems probable that the grace and beauty of the
great warrior, as he stands in Homer, may have been connected with,
or may have suggested, them. But what the Poet does represent is,
that Achilles went to Troy when without experience in war, that he
was put under a certain tutelage of Phœnix his original teacher, and
now one of his lieutenants, that Patroclus as his senior was desired
by Peleus to give him good advice, and that he is called νήπιος[835].
Yet his son Neoptolemus succeeds him in command before the close of
the war, and attains to very high distinction. It is yet more needful
to be observed, that his distinction is in council, as well as in
the field[836]. The age of Achilles is, indeed, presumably somewhat
raised by the fact, that Phœnix seems to represent himself as a good
deal younger than Peleus, who, he says, treated him as a father might
have done[837]. And again, Achilles is never represented as a young
man in the Iliad, while Diomed is so represented. Still there is a
decided incompatibility in the statements as to Achilles and his son,
if we suppose that Homer carried in his mind the effect of his three
decades, as determining precisely the growth of Neoptolemus in years
and strength; for Neoptolemus is more advanced at the end of the war,
than his illustrious father had been at its beginning. Mure has been
at the pains[838] to arrange all these matters which depend on the
decades chronologically, without, I think, removing the impression that
mere chronology is considerably strained by them, and that if strictly
judged, the narrative is, to all appearance, chargeable with some few
years of maladjustment. It seems to me more near the truth to consider
the three decades, together making up a γενεὴ, as a distribution of
time which the Poet adopted for its symmetry and grandeur, since it
represented the war as absorbing an age or generation of men: but not
to hold him bound to adjust the relations of all the events he narrates
with reference to a minute regularity of progression, which he seems
not to have taken into account, and which his hearers were probably
quite incapable of appreciating. If we wish to test his historical
credit, we may try him by his own scheme of chronology, namely, his
genealogies. His legends embrace some seven generations. The same
characters are produced and reproduced in many of them; but they are
nowhere presented in such a way as to be inconsistent with their order
of succession according to the ordinary laws of human nature.
[835] Il. ix. 438. and xi. 783.
[836] Od. xi. 510-12.
[837] Il. ix. 481.
[838] Lit. Greece, ii. 141.
~_Uses of the proposed interpretation._~
The application of these considerations to the poems will assist in
explaining difficulties, which it has been thought worth while by
learned men to raise.
For instance; while we take the three decades of years historically,
we are perplexed by such questions as, How it came about that the
Greeks[839] never had been mustered till nine years had passed.
Secondly, how it was that the Trojans had never until then seen them
in such force[840]; whereas we know that multitudes of the Greek army
had died[841]; and there is no sign that any such communication with
their native country took place during the course of the war, as might
have sufficed to replenish their ranks. Thirdly, why the Trojans had
remained so closely shut within the walls, and yet at the same time
the Greeks had so seldom come near them, that Priam should not have
learnt to know Agamemnon and his compeers by sight during so long a
period; and this although Achilles may probably have been absent, for
considerable intervals, on his predatory expeditions. Fourthly, how it
came about that the great number of allies speaking various tongues,
who had gathered round Priam to assist him, should, like the Greek
army, not have been marshalled at an earlier time.
[839] Il. ii. 360.
[840] Il. ii. 799.
[841] Il. i. 52. ii. 302.
But if we suppose the term of ten years to be in the main a figurative
expression for conveying the idea of effort lengthened in duration, as
well as extraordinary in intensity, difficulties like these, which at
the worst are perhaps not very serious, either wholly vanish, or are
reduced to insignificant proportions. We are then at liberty to suppose
that, without at all departing from the general truth of history, Homer
felt himself authorized to compress, to expand, or to group the events
of the war, in such a manner as he thought best for the concentration
of interest, and for the production of adequate poetical and national
effect.