PARALLELS
100. General observations.—101. Cultural context.—102.
Universal elements.—103. Secondary parallelism in the
Indo-European languages.—104. Textile patterns and
processes.—105. Primary parallelism: the beginnings of
writing.—106. Time reckoning.—107. Scale and pitch of Pan’s
pipes.—108. Bronze.—109. Zero.—110. Exogamic institutions.—111.
Parallels and psychology.—112. Limitations on the parallelistic
principle.
100. GENERAL OBSERVATIONS
The principle of truly independent or convergent invention is more
difficult to establish by positive examples than imitative diffusion. It
has often been assumed as operative, more rarely proved; and even in the
latter cases has perhaps never been found to lead to complete identity.
In fact, the first observation to be made is that resemblance must not be
too close if independent development is to be the explanation. A complex
device used in two or more parts of the world suggests a connection
between them in very proportion to its complexity. A combination
of two or even three elements might conceivably have been repeated
independently. A combination of five or ten parts serving an identical
purpose in an identical manner must necessarily appeal as impossible of
having been hit upon more than once. One thinks almost under compulsion,
in such a case, of historical connection, of a transference of the idea
or machine from one people to the other.
If the resemblance includes any inessential or arbitrary parts, such as
an ornament, a proportion that so far as utility is concerned might be
considerably varied but is not, a randomly chosen number, or a name,
the possibility of independent development is wholly ruled out. Such
extrinsic features would not recur together once in a million times.
Their association forces a presumption of common origin, even though
it be difficult to account for the historical connection involved. The
significance of names in this situation has already been commented on.
There is nothing arbitrary about this limitation on the parallelistic
principle. We all apply similar checks in practical life. If in a
court of law several witnesses testify to the same facts in the same
language, without one of them adding or diminishing an item, if they
follow the identical order of events, if even details such as the
precise minute of an occurrence are stated without variation, judge and
jury will infallibly suspect that the several testimonies go back to a
single source of inspiration. Eyewitnesses will differ. They have seen
from different angles; have followed events with attention that varied
according to their participation and their previous habits and training;
have reacted with individually colored emotion. So with nations. Their
customs, interests, faculties are never wholly alike. Their independent
inventions and innovations, always springing out of a distinctive soil,
therefore necessarily take on a distinctive aspect even when they embody
the same idea. In the degree that the form as well as the substance of
culture traits coincide, does the probability of independent evolution
diminish in favor of some sort of connection.
101. CULTURAL CONTEXT
The presence or absence of other connections is also a factor of greatest
importance. In other words, no fact relating to human civilization may be
judged wholly without reference to its context or background. If there
are known connections, either in space or in time, between two nations,
the likelihood of their having separately evolved a common trait is much
less than as between two peoples in different continents or separated
by thousands of years. It is not known precisely how knowledge of the
true arch and of liver divination were carried from ancient western
Asia to the Etruscans of Italy. Yet the fact that Babylonia and Etruria
shared two such specific culture traits as these, greatly increases the
probability for each one having been borrowed from the Asiatic by the
European people. When the consideration is added that the ancients had
traditions of the Etruscans having come to Italy out of Asia Minor,
the likelihood of diffusion is strengthened to the point of practical
certainty.
Connection in space is a particularly cogent argument in favor of
diffusion, because of its powerful presumption of accompanying
communication. When several hundred Indian tribes without a break in
their ranks between Quebec and Argentina cultivate maize, it would be
absurd to dream of each of them having originated the domestication of
the plant for itself. To be sure, it is logically conceivable that maize
agriculture was independently developed by two or three of the most
advanced tribes of the hundreds and then became diffused until the two
or three areas of dispersion met and coalesced into one greater area.
Yet the principle that economy of explanation is the best would militate
even against this interpretation as compared with diffusion from a single
center, unless there were definite indications in favor of the multiple
origin explanation. Such indications might be radically distinct types
of the plant or of agricultural implements in several parts of the maize
area.
So, when the tribes on the Alaskan and Siberian sides of Behring Sea
relate similar Raven legends, the geographical proximity is so close
that it would be pedantic to let the fact that two continents are
involved stand in the way of an explanation by diffusion. Even where the
distribution of a trait penetrates much farther into both America and
Asia, as is true of the composite bow (§ 210), the continuity of area
leaves little doubt as to diffusion from a single center, especially
since it is reinforced by other traits showing the same intercontinental
distribution: the Magic Flight story, for instance. It is only when the
areas are discrete as well as remote, when other similarities between
them are few or absent, when their cultural backgrounds are radically
dissimilar, as in the case of the couvade, that parallelism begins to
knock at the door of interpretation with serious hope of admittance.
102. UNIVERSAL ELEMENTS
When a culture trait is very ancient and of practically world-wide
occurrence, it becomes difficult to estimate between diffusion and
independent invention. The fire-drill, flint chipping, the bow and arrow,
the doctrine of animism or belief in souls and spirits, sympathetic
magic, are in this class. The very universality of these elements tends
to obliterate tangible evidence as to their histories. A generation or
two ago it was generally taken for granted that such devices and beliefs
as these sprang more or less spontaneously out of the human mind as soon
as man had traversed a certain short distance of the evolutionary road
that led him away from the brutes. At present, anthropological opinion is
more cautious about such assumptions. It is perhaps spontaneous enough
for people in the habit of using tools to try to fashion them from
stone if other materials be lacking, and easy for a nation accustomed
to projectile weapons to invent the bow without ever having learned of
it. But this is far from proving what a people without these habits
might do. Intelligent as an ape is, and gifted with manual dexterity,
it rarely enters his mind to throw a stone as a missile and never to
split it into a knife or weapon. For all we know, it may have cost our
ancestors untold mental energy to bring themselves to the point of
fashioning their first stone implements; so much, indeed, that it is
possible all of them did without until one more gifted or fortunate group
made the difficult invention which was then imitated by the others. It is
temptingly but fatally easy to project our habits of mind into primitive
man—much easier to imagine ourselves in his position than to imagine
him, without reference to ourselves, as he was. Animal psychologists
have learned not to anthropomorphize, that is, endow the lower animals
with specifically human mind processes. Anthropologists have learned to
guard against the similar pitfall of interpreting low cultures by the
standards of our own, of assuming that because a thing seems “natural”
to us it must have seemed natural and therefore have been done by any
savage. It is clear that what did not happen was for every tribe or race
to originate for itself its fire-making, flint-chipping, bows, animism,
and magic. It is conceivable that each of these culture products traces
back to a single source in human history. There are authorities who have
held this very opinion; some expressedly, others by implication. It is
not necessary to go so far; in fact, wiser not to, because none of these
matters is yet susceptible of real proof. But it does seem profitable to
recognize the possibility of the truth of such views, and that the drift
of accumulating knowledge and experienced interpretation is in their
direction.
A simple consideration which has too often been neglected is that
diffusion and imitation undisputedly do take place in culture on a
vast scale. So far as independent developments occur, be that rarely
or frequently, they are therefore sure to be more or less intertwined
with disseminations. Even one particular device may be partly borrowed
and partly modified or further developed by original effort. Still more
intimate must be the combination of native and diffused elements in the
whole culture of any people. To wage an abstract battle as between two
opposite principles is sterile, when their manifestations are admittedly
frequent for one and at least certain for the other. It is clearly more
profitable to examine the associations and relations of diffusion and
convergence, the conditions under which they supplement each other.
Besides parallels springing up wholly independently, there are two ways
in which their relations to diffusion may be conceived. An original
single growth or wave of diffusion may differentiate into local or
temporal modifications, which even after separation continue to develop
along parallel lines or reconverge. Or, on the other hand, independent
starts in similar direction may become merged in, or assimilated by, a
subsequent diffusion.
103. SECONDARY PARALLELISM IN THE INDO-EUROPEAN LANGUAGES
Parallel growth secondary to a former unity and differentiation is
illustrated by the Indo-European languages. All the known ancient forms
of this speech family, Sanskrit, Avestan, Greek, Latin, Gothic, were
highly inflecting and compounding. Their tendency was synthetic (§ 51,
57).
Grammatical ideas such as voice, tense, number, case, were expressed by
elements affixed to the word stem and incapable of a separate existence.
For _they will have loved_ Latin says _ama-v-eru-nt_. The _-v-_ has the
force of _have_, the _-eru-_ of _will_, _-nt_ of _they_; but none of
these parts can be used alone, as their equivalents in English can be, or
as in French _ils auront aimé_. The two latter languages are analytical.
They break an idea into parts which they express by separate words that
change form but little. They retain only fragments of conjugations and
declensions. Sanskrit had eight noun cases, Latin six; English has only
two, the subjective-objective and the possessive, and French only one, or
rather no case-form at all.[15]
This development toward a more analytical form is not only traceable
in several non-Indo-European speech families, such as Chinese and
Malayo-Polynesian (§ 61), but has gone on in all the branches of
Indo-European. It is visible in the growth of English from Anglo-Saxon;
of French, Spanish, and Italian from Latin; of modern from ancient
Persian; of Hindi and Bengali from Sanskrit. True, some of these have
been in contact, like the Germanic and Latin languages, and might
therefore be imagined to have set one another an example, although there
is little evidence that languages seriously influence each other’s
forms. But many of the Indo-European idioms have not been in contact at
all for thousands of years. The Germanic and the Indo-Iranic branches,
for instance, must have separated at least four thousand years ago.
For the greater part of this period, accordingly, the related but no
longer communicating languages that have resulted in modern English and
Bengali, to take only one instance, have independently driven toward the
same goal of more and more analytical structure. It may well be that the
hidden germ of this impulse lay implanted in the common Indo-European
mother-tongue at the time of its differentiation five or more thousand
years ago. But the movement of its daughters has certainly been an
astoundingly parallel one.
104. TEXTILE PATTERNS AND PROCESSES
An analogous situation is provided by the similarity of diamond shaped
patterns woven in twilled baskets in parts of North and South America,
Asia and the East Indies, and Africa. This looks like parallelism and
is parallelism. But it is clearly a secondary result of the twilling
process, as this, in turn, flourishes most vigorously where woody
monocotyledonous plants—cane, bamboo, palms—are available to furnish
hard, durable, flat, pliable splints. The technique of the weave is such
that if materials of two colors are used, the characteristic patterns
evolve themselves almost of necessity. The twilling process may have
been invented independently in several of the regions addicted to it,
or have been devised only once in the world’s history. It is too simple
and too ancient a technique for modern knowledge to choose between the
alternatives with positiveness. Brazilian and East Indian patterns are
much more likely to have been each developed on the spot, as derivatives
from the more fundamental and possibly transmitted twilling process.
The coiling technique for making baskets looks from its distribution
in Africa and about the Mediterranean, in northeast Asia and northwest
America, in the southern extremity of South America, in Malaysia and
Australia, as if it had originated independently several times, and there
is partial confirmation in the fact that different varieties of coiling
are typical of most of the areas. If however further knowledge should
connect the now separate areas of coiling, the art would then have to be
regarded as probably due to diffusion from a single invention. In that
case, however, special varieties, such as half-hitch coiling in Tierra
del Fuego and Tasmania, and single-rod coiling in the East Indies and
California, would remain as instances of secondary parallelism affecting
particular aspects or parts of the generic process.
A blending of diffusion and parallelism is apparent also in other textile
processes. The fundamentals, as embodied in simple woven basketry, mats,
and wiers, were probably carried into America by the first immigrants.
Weaving from suspended warps and in an incomplete loom frame may possibly
have been similarly transmitted by diffusion or have been developed
locally. Thread spinning, however, the complete loom, and the heddle
were clearly devised in the middle region of America independently of
their invention in the Old World, as is evident from their absence in
the connecting areas of North America and Siberia (§ 187, 188). But the
treadle shed, the next step in the Eastern hemisphere, was never invented
in the Western, so that at this point the parallelism ends.
Again, diffusion and convergence both enter into the history of what is
known as resist dyeing, that is, the covering of portions of textile
patterns before immersion into the dye. Batik, when wax is used as the
protecting medium, is one form of resist dyeing. Another method is “to
tie little bunches of cloth with a cord either soaked in clay or wax
or spun from fiber which has no affinity for the colors and then dip
the tied web into the pot.” In the Old World, tie dyeing is of Asiatic,
probably of Indian origin, and was in use by the seventh century, perhaps
earlier. The Mohammedan conquests carried the art to Malaysia on the one
hand, to western Africa and Spain on the other, whence it was transmitted
to the Indians of Guatemala after their subjugation by the Spaniards—like
the double-headed eagle. The Peruvians, however, had long before hit upon
the same art, as attested by textile remains in pre-Columbian graves.
Here then, we have a wide and long enduring diffusion of the general
resist dyeing process, and a locally limited instance of independent
parallelism for one phase of it.
105. PRIMARY PARALLELISM: THE BEGINNINGS OF WRITING
Primary parallelism can be established fairly frequently, but usually
only with reference to a general principle, the applications of which
invariably retain evidence of their original separateness.
An illustration is furnished by the history of writing, as sketched in
the introductory paragraphs of the chapter on the Alphabet (§ 130-133).
Many nations have entered the simple stage of pictography. Only a few are
known to have gone on to the stage of rebus or transitional writing—mixed
pictograms or ideograms and phonograms. Of these, certainly two and
possibly as many as four, five, or six devised their own rebus systems:
the Egyptians, Sumerians, Chinese, Hittites, Cretans, and Mayas, in four
continents. But here the parallel ceases. The content of the systems,
the signs themselves and their sound values, are wholly different. The
similarity applies only to the principle of reading pictures or symbols
for their pictureless homonyms. The concrete application of this method
has nothing in common in the several parallel cases. Finally, complete
phonetic writing was invented but once, all alphabets, however diverse,
being historical descendants of the primitive Semitic alphabet, which
served as the sole source of a tremendous diffusion (§ 134-149).
It is worth noting, however, that the first or pictographic stage of
writing is by no means a thing that flows instinctively from all men.
There are peoples, like some of the Indians of Brazil and California,
deficient in the ability or habit, according as one may wish to term
it, of expressing themselves in linear representations. They do not
draw rude outlines to depict objects. Asked to do so, they profess
inability, though set an example, or make a pathetically crude attempt.
Their failure or refusal does not argue inherent lack of faculty, since
the children of the same races, when put to school, draw figures with
interest and often with success. The attitude of the adults is rather
that of a person who had never heard even a snatch of music of any kind
or seen an instrument, being taken to a concert and then asked to compose
a simple little song. He would look upon this task as transcendently
beyond his powers. There are no songless nations, but there are
pictureless ones. Consequently picture-writing is not the spontaneous
product which we, who as children are reared in an environment of
pictures, might imagine it to be. If pictography were due to a primary
parallelism, to a spontaneous outflow of the human mind, its absences
would be in need of explanation. If, on the other hand, it is the result
of a single diffusing development, this must have an antiquity of more
than fifteen thousand years, as attested by the Old Stone Age paintings,
and the failure of certain peoples to be affected is also in need of
explanation.
Another case of parallelism is the recurring tendency to write
syllabically instead of alphabetically. The Hindu inclination in this
direction is discussed below (§ 146). That the phonetic symbols of rebus
systems should be largely syllabic is small wonder, for they are pictures
of things named with whole words. But the Hindu script was derived
from a Semitic letter alphabet, and its essentially syllabic nature
thus represents a reversion. The Japanese in adding 47 purely phonetic
characters to the Chinese ideograms in order to express grammatical
elements, proper names, and the like in their speech, denoted a syllable
by each character. A third as many consonant and vowel signs would have
answered the same purpose. When Sequoya the Cherokee devised an alphabet
for his people in order to equate them with the whites, he incorporated
the forms of a number of the English letters, but the values of all his
signs were syllabic. The same holds of the West African Vei writing
invented in the nineteenth century by a native. He had had enough mission
schooling to be stimulated by the idea of writing, but “instinctively”
fell back on syllable signs even though this necessitated two hundred
different characters.
There is an evident psychological reason for the uniformity of these
endeavors: we image words, in fact produce them, in syllables, not in
sounds. Any one, in slow speech, tends to syllabify, whereas few wholly
illiterate people can be induced without patient training to utter
the separate consonants and vowels of a word, even for the purpose of
teaching a foreigner.
This case of parallelism rests, therefore, on a psychological fact
of apperception. But it was the “accidents” of culture, not innate
psychology, that determined the particular symbols, and their values,
chosen by the Hindus, Japanese, Cherokee, and Vei, with the result that
in these symbols there is no specific similarity.
106. TIME RECKONING
Still another case of primary parallelism is provided by the Maya-Aztec
system of time denotation by coupling two series of symbols in an
overlapping system of permutations, as described below (§ 197). This is
as if we denoted the successive days of the year 1 January, 2 February,
3 March, and so on, until, having come to 12 December we went on 13
January, 14 February, and so once more around until 31 July was reached,
when the next days would be 1 August and 2 September instead of February
1 and 2. Cumbersome and strange as this system appears, an exact parallel
to it in principle was devised by the Hellenistic philosophers when they
coupled the twenty-four hours of the day with the seven planets in a
168-hour cycle which gave the order and names to the days of the week (§
124). A third case occurs in China where ten “celestial stems” and twelve
“terrestrial branches” were permutated to form a sixty year chronological
cycle.[16] All three of these devices are based on the same mathematical
principle and serve the same end of time reckoning. But their content and
result is different. The Greeks combined 24 with 7, the Chinese 12 with
10, the Mayas 13 with 20 and 260 with 365; and the periods treated ranged
from hours to years.
These cases of primary parallelism allow the inference that there are
certain inherent tendencies of the human mind in certain directions,
such as operation in rebus reading, syllabic writing, reckoning by least
common multiples. Here, then, is a seeming approach for a definite
psychological interpretation of the history of civilization. Yet the
results of such a method of attack must not be overestimated. The
generic manner of culture in these several instances is indeed uniform
enough to permit the conclusion that it springs from a uniform impulse
or bent of the mind. But all the particular, concrete content of these
cultural manifestations is as diverse as their historical origins are
separate; which means that psychology may explain what is psychological
in the cases, but that a larger cultural constituent remains over before
which the generically valid principles of psychology are ineffective as
explanations. As in the case of the influence of physical environment it
might be said that psychological factors provide the limiting conditions
of cultural phenomena.
107. SCALE AND PITCH OF PAN’S PIPES
A startling parallelism has been demonstrated between the Pan’s pipes of
the Solomon islands in Melanesia and those of the northwest Brazilian
Indians. The odd pipes differ, each from the next, by the interval of a
fourth. The even pipes give notes half-way in pitch between the adjacent
odd ones, and thus form another “circle of fourths.” But the similarity
does not end here. The absolute pitch of the examined instruments from
Melanesia and Brazil is the same. Thus, the vibration rates in successive
pipes are 557 and 560.5; 651 and 651; 759 and 749; 880 and 879! This
is so close a coincidence as to seem at first sight beyond the bounds
of accidental convergence. The data have in fact been offered, and in
some quarters accepted, as evidence of a historical connection between
the western Pacific and South America. Yet the connection would have
had to be ancient, since no memory of it remains nor is it supported
by resemblances in race, speech, nor anything obvious in culture. The
instruments are perishable. Primitive people, working by rule of thumb,
would be unable to produce an instrument of given absolute pitch except
by matching it against another, and perhaps not then. Moreover, it is
not known that absolute pitch is of the least concern to them. It is
therefore incredible that this correspondence rests on any ancient
diffusion: there must be an error in the record somewhere, or the one
accident in a million has happened in the particular instruments examined.
The identity of scale or intervals however remains, and may be a true
case of parallelism. Only, as usual, it boils down to a rather simple
matter. The circles of fourths evidently originate in the practice,
in both regions, of overblowing the pipes. This produces over-tones;
of which the second, the “third partial tone,” is the fifth above the
octave of the fundamental, so that successive notes in either the odd
or even series of pipes, would, on the octave being disallowed, differ
by fourths. The basis of the resemblance, then, is a physical law of
sound. The cultural similarity shrinks to the facts of pipes in series,
the use of overblown tones, and the intercalating odd-even series. Even
these resemblances are striking, and more specific than many cited cases
of parallelism. In fact, were they supported by enough resemblances in
other aspects of culture, they would go far to compel belief in actual
connections between Melanesia and Brazil.
108. BRONZE
A striking case of independent development is offered by the history of
bronze. Bronze is copper alloyed with five to twenty per cent of tin.
The metals form a compound with properties different from those of the
two constituents. Tin is a soft metal, yet bronze is harder than copper,
and therefore superior for tools. Also, it melts at a lower temperature
and expands in solidifying from the molten condition, and thus is better
material for castings.
In the eastern hemisphere bronze was discovered early and used widely.
For nearly two thousand years it was the metal par excellence of the more
advanced nations. A Bronze Age, beginning about 4,000 B.C., more or less
simultaneously with the first phonetic writing, is recognized as one of
the great divisions of cultural time (§ 66, 225).
In the western hemisphere bronze was apparently invented later than in
the eastern and spread less extensively. It was discovered in or near
the Bolivian highland, which is rich in tin (§ 196). From there its use
diffused to the Peruvian highland, then to the coast, then north to about
Ecuador, and finally, perhaps by maritime contacts, to Mexico, where
local deposits of tin were probably made use of after their value was
realized.
Theoretically, it might be queried whether knowledge of bronze had
possibly been carried to the Andes from the eastern hemisphere by
some now forgotten migration or culture transmission. Against such a
supposition there stands out first of all the isolated and restricted
distribution of the South American bronze art. It is ten thousand miles
by land from the metal-working nations of Asia to the middle Andes. A
people or culture wave that had traveled so far could not but have left
traces of its course by the way. The utilitarian superiority of bronze
over stone tools is so great that no people that had once learned the art
would be likely to give it up. Even if here and there a group of tribes
had retrograded, it cannot be imagined that all the nations between China
and Peru could have slipped back so decisively. Certainly peoples like
the Mayas and Chibchas, expert metallurgists, would never have abandoned
bronze-making.
The theory of a Chinese junk swept out of its course and washed on a
South American shore might be invoked. But the original South American
bronze culture occupies an inland mountain area. Further, while Asiatic
ships have repeatedly been wrecked on the Pacific coast of North America
and probably at times also on that of South America, there is everything
to indicate that the civilizational effects of such accidents were
practically nil. The highest cultures of Mexico and South America
were evolved in interior mountain valleys or plateaus. Not one of the
great accomplishments of the American race—architecture, sculpture,
mathematics, metallurgy—shows any specific localization on the shore of
the Pacific.
Further, it is hard to understand how the arrival of a handful of
helpless strangers could initiate an enduring culture growth. It is easy
enough for us, looking backward through the vista of history, to fancy
the lonely Indians standing on the shore to welcome the strangers from
the west, and then going with docility to school to learn their superior
accomplishments. Actually, however, people normally do not feel or act in
this way. Nations are instinctively imbued with a feeling of superiority.
They look down upon the foreigner. Even where they admit his skill in
this matter or that, they envy rather than admire him. Thus, there is
historic record of Oriental and European vessels being wrecked on the
Pacific coast of North America, during the last century and a half, among
tribes that were still almost wholly aboriginal. In no case did the
natives make any attempt to absorb the higher culture of the strangers.
Generally these were enslaved or killed, their property rifled; sometimes
the wreck was set on fire. The greed for immediate gain of the treasures
in sight proved stronger than any dim impulses toward self-improvement by
learning.
As one conservative author has put it, occasional visits of Asiatics or
Pacific islanders to the shores of America would be, from the point of
view of the growth of the vast mass of culture in that continent, “mere
incidents.” From the review given below, in Chapter XIII, it is clear
that the main determinants of American culture accumulation, after the
first primitive start, were internal; and the case seems as clear for
metal working as for any phase.
109. ZERO
One of the milestones of civilization is the number symbol zero. This
renders possible the unambiguous designation of numbers of any size
with a small stock of figures. It is the zero that enables the symbol 1
to have the varying values of one, ten, hundred, or thousand. In our
arithmetical notation, the symbol itself and its position both count:
1,234 and 4,321 have different values although they contain the identical
symbols. Such a system is impossible without a sign for nothingness: 123
and 1,023 would be indistinguishable. Our zero, along with the other nine
digits, appears to be an invention of the Hindus approximately twelve or
fifteen hundred years ago. We call the notation “Arabic” because it was
transmitted from India to Europe by the Arabs.
[Illustration: FIG. 28. Maya symbols for zero: _a_, monumental; _b_, _c_,
cursive. (From Bowditch.)]
Without a zero sign and position values, two methods are open for the
representation of higher numerical values. More and more signs can be
added for the high values. This was done by the Greeks and Romans. MV
means 1,005, and only that. This is simple enough; but 1,888 requires
so cumbersome a denotation as MDCCCLXXXVIII—thirteen figures of six
different kinds. A simple system of multiplying numbers expressed like
this one is impossible. The unwieldiness is due to the fact that the
Romans, not having hit upon the device of representing nothingness,
employed the separate signs I, X, C, M for the quantities which we
represent by the single symbol 1 with from no to three zeroes added.
The other method is that followed by the Chinese. Besides signs
corresponding to our digits from 1 to 9, they developed symbols
corresponding to “ten times,” “hundred times,” and so on. This was much
as if we should use the asterisk, *, to denote tens, the dagger, †,
for hundreds, the paragraph, ¶, for thousands. We could then represent
1,888 by 1 ¶ 8 † 8 * 8, and 1,005 by 1 ¶ 5, without any risk of being
misunderstood. But the writing of the numbers would in most cases require
more figures, and mathematical operations would be more awkward.
The only nation besides the Hindus to invent a zero sign and the
representation of number values by position of the basic symbols, were
the Mayas of Yucatan. Some forms of their zero are shown in Figure 28.
This Maya development constitutes an indubitable parallel with the
Hindu one. So far as the involved logical principle is concerned, the
two inventions are identical. But again the concrete expressions of the
principle are dissimilar. The Maya zero does not in the least have the
form of our or the Hindus’ zero. Also, the Maya notation was vigesimal
where ours is decimal. They worked with twenty fundamental digits instead
of ten. Their “100” therefore stood for 400, their “1,000” for 8,000.[17]
Accordingly, when they wrote, in their corresponding digits, 1,234, the
value was not 1,234 but 8,864. Obviously there can be no question of a
common origin for such a system and ours. They share an idea or a method,
nothing more. As a matter of fact, these two notational systems, like
all others, were preceded by numeral word counts. Our decimal word count
is based on operations with the fingers, that of the Maya on operations
with the fingers and toes. Twenty became their first higher unit because
twenty finished a person.
It is interesting that of the two inventions of zero, the Maya one was
the earlier. The arithmetical and calendrical system of which it formed
part was developed and in use by the time of the birth of Christ. It may
be older; it certainly required time to develop. The Hindus may have
possessed the prototypes of our numerals as early as the second century
after Christ, but as yet without the zero, which was added during the
sixth or according to some authorities not until the ninth century. This
priority of the Maya must weaken the arguments sometimes advanced that
the ancient Americans derived their religion, zodiac, art, or writing
from Asia. If the zero was their own product, why not the remainder of
their progress also? The only recourse left the naïve migrationist would
be to turn the tables and explain Egyptian and Babylonian civilization as
due to a Maya invasion from Yucatan.
110. EXOGAMIC INSTITUTIONS
In many parts of the world nations live under institutions by which
they are divided into hereditary social units that are exogamous to one
another. That is, all persons born in a unit must take spouses born in
some other unit, fellow members of one’s unit being regarded as kinsmen.
The units are generally described as clans, gentes, or sibs; or, where
there are only two, as moieties. In many cases the sibs or moieties are
totemic; named after, or in some way associated with, an animal, plant,
or other distinctive object that serves as a badge or symbol of the
group. Often the association finds expression in magic or myth. Since
under this system one is born into his social unit, cannot change it,
and can belong to one only, it follows that descent is unilateral. It
is impossible for a man to be a member of both his father’s and his
mother’s sib or totem; custom has established everywhere a rigid choice
between them. Some tribes follow descent from the mother or matrilinear
reckoning, others are patrilinear.[18]
Institutions of this type have a wide and irregular distribution. They
are frequent in Australia, New Guinea, and Melanesia; found in parts
of the East Indies and southeastern Asia; quite rare or stunted in the
remainder of Asia and Polynesia; fairly common in Africa, though they
occur in scattered areas; characteristic again of a large part of North
America, but confined to a few districts of South America. At a rough
guess, it might be said that about as many savage peoples, the world
over, possess totemic-exogamous clans or moieties as lack them. The
patchiness on the map of exogamic institutions argues against their being
all the result of a wave of culture transmission emanating from a single
source. Had such a diffusion occurred, it should have left its marks
among the numerous intervening tribes that are sibless. Further, both
in the eastern and western hemispheres, the most primitive and backward
tribes are, with fair regularity, sibless and non-totemic. If therefore
a hypothetical totem-sib movement had encircled the planet, it could not
have been at an extremely ancient date, else the primitive tribes would
have been affected by it; and since records go back five thousand years
in parts of the Mediterranean area, the movement, if relatively late,
should have left some echo in history, which it has not.
[Illustration: FIG. 29. Distribution of types of exogamic institutions
in Australia: _2M_, two classes, matrilinear; _4M_, four classes,
matrilinear; _4P_, four classes, patrilinear; _8P_, eight classes,
patrilinear; black areas, no classes, patrilinear exogamic totems; _X_,
totems independent of classes; _Y_, totems replace sub-classes; _Z_, no
organization; _?_, uninhabited or unknown. (After Thomas and Graebner.)]
It is therefore probable that totem-sib institutions did not all emanate
from one origin, but developed independently several times. The question
then becomes, how often, and where?
The evidence for America has been reviewed in another connection (§ 185).
It can be summarized in the statement that at least two of the three
sib areas[19] of North America, and probably the two principal ones of
South America, seem to have resulted from a single culture growth which
perhaps centered at one time, although subsequently superseded, in the
middle sector of the double continent. This movement may have had first
a patrilinear and then a matrilinear phase, though at no great interval
of time. The third North American area may have got its patrilinear sib
institutions from the same source but probably developed its matrilinear
ones locally as a subsequent growth. If so, this would be an instance of
convergence on the same continent—a rather rare phenomenon.
For Australia, New Guinea, and Melanesia, the geographical proximity is
so close as to suggest a single origin for the whole area. Patrilinear
and matrilinear descent are both found in Australia as well as Melanesia.
This fact has been interpreted as the result of an earlier patrilineal
and a later matrilineal phase of diffusion. It is interesting that this
conclusion parallels the tentative one independently arrived at for
America, although in both hemispheres further analysis and distributional
study must precede a positive verdict.
In the principal other sib area, Africa, the reckoning is so prevailingly
patrilineal, that the few cases of matrilineate can scarcely be looked
upon as anything but secondary local modifications. As to whether the
totemism and exogamy of Africa can be genetically connected with those
of Australia-Melanesia, it is difficult to decide. The more conservative
attitude would be to regard them as separate growths, although so many
cultural similarities have been noted between western Africa and the
area that stretches from Indo-China to Melanesia, as to have raised
suspicions of an actual connection (§ 270). Yet even if these indications
were to be confirmed, thus sweeping most or all the Old World sib
institutions into a single civilizational movement, the distinctness of
this from the parallel development of the New World would remain.
It is significant that in the three successive continents of America,
Oceania, and Africa the patrilinear and matrilinear phases of the sib
type of society exist side by side, and that the same duality even
holds for each of the separate areas in America. That is, the Northwest
American sib area includes matrilinear as well as patrilinear tribes; the
Southwest area includes both; and so on.
A similar tendency toward geographical association is found in other
phases of social structure: the clan and moiety, and again totemism and
exogamy.
The clan or multiple form of sib organization is logically distinct from
the moiety or dual form. Under the plural system, a person, being of
clan A, may marry at will into clans B, C, D, E, F. Three of his four
grandparents would normally be of other clans than his own, but of which
they were members, would vary in each individual case. In a patrilineal
society, one member of clan A would have his maternal uncles of clan B;
the next, of clan C; a third, perhaps of clan F; according to the choices
which their fathers had made of wives.
Under the dual system, however, a member of moiety A may just as well be
regarded as having a wife of moiety B prescribed or predestined for him
as being forbidden an A wife. Two of his grandparents, say his father’s
father and his mother’s mother, are inevitably of his own moiety, the two
others of the opposite one. Every possible kinsman—his maternal uncle,
his cross cousin, his father-in-law, his wife’s brother-in-law, his
daughter’s son—has his moiety affiliation foreordained. Where descent is
paternal, for instance, everybody knows that his future mother-in-law
must be of his own moiety. Evidently the effect of this dual system on
the relations between kinsfolk, on social usages, on the individual’s
attitude of mind toward other individuals, should normally tend to be
profoundly different from the influence of a multiple clan system. On
theoretical grounds it might seem likely that the dual and multiple
schemes had nothing to do with each other, that they sprang from
distinct psychological impulses.
Yet such a belief would be ungrounded, as the facts of distribution
promptly make clear. In every multiple sib area of any moment, moieties
also occur, and vice versa. In the California-Southwest region, for
instance, tribes like the Miwok are divided into moieties only, the
Mohave and Hopi into clans only, the Tewa and Cahuilla into moieties
subdivided into clans. So in the Eastern, the Plains, and the Northwest
areas of North America, clan tribes and moiety tribes live side by
side; whereas as soon as these regions are left behind, there are vast
districts—much of Mexico, Texas, the Great Basin and Plateau, northern
Canada and the Arctic coast—whose inhabitants get along without either
clans or moieties. So again in Melanesia and in Australia (Fig. 29), the
two types of organization exist side by side, while most of Polynesia,
Asia, and Europe are void of both. Only Africa shows some development of
multiple clan institutions but no moieties. In short, as soon as areas
of some size are considered, they prove in the main to be of two kinds.
Either they contain both clan tribes and moiety tribes, or they contain
neither. That is, the clan institution and the moiety institution are
correlated or associated in geography, as patrilinear and matrilinear
descent are correlated, which indicates a community of origin for them.
A similar relation exists between exogamic units, be they moieties or
clans, and totemism. The first constitutes a scheme of society, a method
of organization; the second, a system of symbolism. Sibs are social
facts, totems a naming device with magico-religious implications. There
is no positive reason why they should be associated. They are not always
associated. There are American tribes like the Navaho and Gros Ventre
that live under unilateral and exogamic institutions without totems.
Placenames or nicknames distinguish the groups. In Australia, the Arunta
possess unilaterally reckoning exogamic groups as well as totems, but
the two are dissociated; a person takes his group by descent, his totem
wholly irrespective of this according to place of birth or conception.
In Africa there are no less than six tribes or series of tribes in which
exogamy and totemism are thus dissociated; a person takes his totem
from his father, his exogamic unit from his mother, so that the two
ordinarily do not coincide for parent and child. Exogamy and totemism,
then, are theoretically separate factors.
Yet since they are distinct, it is remarkable that in probably seven
or eight tenths of all cases they coincide, and that in each of the
continents or areas containing them they are found associated. If exogamy
and totemism had grown out of separate roots, one could expect at least
one considerable area somewhere in which one of them appeared without the
other. But there is no such area. Wherever social exogamy appears among a
larger group of nations, social totemism also crops out; and vice versa.
It must then be concluded that exogamy and totemism, matrilineate and
patrilineate, multiple and dual sibs, all show a strong tendency toward
association with one another. In other words, their correlation is
positive and strong. Even where they seem mutually exclusive in their
very nature, like matrilinear and patrilinear reckoning, ways have been
found by unconscious human ingenuity to make them coexist among one
people, as when one reckoning is attached to the exogamy, the other to
the totemism; and still more often they occur among adjacent tribes.
111. PARALLELS AND PSYCHOLOGY
Such associations as these are common enough in the history of
civilization. A number are touched upon elsewhere in this volume under
the name of culture trait associations or complexes (§ 97, 149).
But usually such a complex or nexus consists of culture elements
that have no necessary connection: Christianity and trousers, for
instance. It is accident that first throws them together; association
ties them one to the other; once the cluster is established by usage,
its coherence tends to persist. But there is something arbitrary
about this cohesion, generally. There is no inherent reason why a
hundred American tribes that grow maize should also grow beans and
squashes and nothing else; but they do limit themselves to the three.
The distinctive feature of the sib-complex is that it has an almost
reasonable quality. Its elements, however separate or even opposite
logically, do have a certain psychological affinity to one another.
Also, the arbitrary maize-beans-squash complex and other complexes
are generally not duplicated. But the intricate and psychologically
founded totemism-exogamy-descent complex looks as if it might have been
triplicated or quadruplicated. This parallelism, if the facts prove to
substantiate it, is parallelism raised to a higher power than any yet
considered. Heretofore the discussion has been of the parallelism of
single culture traits. Here it is a case of parallelism of a complex of
culture traits. Such complex convergence might suggest something peculiar
to or inherent in the human mind, leading it, once it is stimulated to
commence the development of one of the factors of the complex, to follow
with the production of the other factors.[20]
Similar instances would be the tendency of agriculture to be followed by
town life, if it could be demonstrated, though this seems doubtful; of
settled living to be accompanied by migration legends; of religions with
personal founders to become propagandizing and international but in time
to die out among the nations in which they were originated.
In regard to all such cases it may be said first of all that an
exhaustive analysis is necessary to ascertain whether the seeming
association or correlation is borne out by the facts. Second, the
possibility of diffusion must be eliminated. If Melanesian and African
totem-exogamy are both products of one culture growth, they cannot
be counted as two examples of the same association. If they should
ultimately both prove to be linked with the American system by a wave
of migration or culture contact, as has, indeed been maintained in
two separate hypotheses recently advanced, parallelism is of course
disproved altogether. But such views are as yet undemonstrated and seem
extreme; and if, after continued search of the evidence, two or more
such associations or complex parallels as the exogamic-totemic scheme
of society stand as independent growths, it is evident that they will
be something in the nature of cultural manifestations of psychological
forces. In short, we should then be beginning to grasp specific
psychological determinants for the phenomena or events of civilization.
But as yet such a causal explanation of the data of anthropology by the
mechanism of psychology has not been achieved.
112. LIMITATIONS ON THE PRINCIPLE
From the evidences reviewed in this and the last chapter, the conclusion
is confirmed which social philosophers had long since reached, that
imitation is the normal process by which men live, and that invention is
rare, a thing which societies and individuals oppose with more resistance
than they are ever aware of, and which probably occurs only as the
result of the pressure of special circumstances, although these are as
yet little understood. Not only are a hundred instances of diffusion
historically traceable for every one of parallelism, but the latter is
regularly limited in scope. Something tends to make us see phenomena
more parallel than they actually are. They merely spring from the same
impulse, they inhere in the properties of objects or nature, they bear
resemblance at one point only—and differ at all other points. Yet they
tend to impress us, in some mysterious way, as almost identical. The
history of civilization has no more produced two like cultures, or two
separately developed identical culture traits, than has the evolution
of organic life ever duplicated a species by convergently modifying
two distinct forms. A whale may look fishlike, he is a mammal. The
Hindu and the Maya zero are logically the same; actually they have in
common nothing but their abstract value: their shapes, their place in
their systems, are different. The most frequent process of culture
history therefore is one of tradition or diffusion in time and space,
corresponding roughly to hereditary transmission in the field of organic
life. Inventions may be thought of as similar to organic mutations, those
“spontaneous” variations that from time to time arise and establish
themselves. The particular causes of both inventions and mutations remain
as good as unknown. Now and then a mutant or an invention heads in the
same direction as another previously arisen one. But, since they spring
from different antecedents, such convergences never attain identity. They
remain on the level of analogous resemblance. Substantial identity, a
part for part correspondence, is invariably a sign of common origin, in
cultural as well as organic history.