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Computers Math. Applic. Vol. 17, No. 4-6, pp. 697-708, 1989
0097-4943/89 $3.00+0.00 Printed in Great Britain. All rights
reserved Copyright 1989 Pergamon Press pie
UNCERTAINTY PRINCIPLE AND SYMMETRY IN METAPHORS
L. BENCZE Department of Modern Hungarian, E6tv6s Lor~nd
University, P.O. Box 105, Budapest, H-1364, Hungary
Abstract--Analogies taken from the humanities are common
epistemological means in teaching and explaining phenomena in
sciences. This paper, however, follows a more or less opposite
approach by taking formal and functional analogies from the
sciences (uncertainty principle and symmetry) in order to
illustrate the phenomenon of metaphor in language in an attempt to
get closer to its nature, behavior and function.
Interdisciplinarity characterizes current trends in sciences and
humanities. This is not just a matter of fashion. Aristotle was
still able to command all the sciences, and like a shepherd he
could gather them as one flock into one sheepfold--philosophy. With
Christianity and from the early Middle Ages onwards, scientific
knowledge disintegrated into different branches of science and
humanities in an accelerating way. This process has achieved an
immensely high degree of specialization in the twentieth century.
This trend has been accompanied by a stronger and stronger need for
integration within each science as well as among all sciences [1,
pp. 381-413]. This began as early as the twelfth century with the
foundation of universities and was expressed in the name itself as
the etymology shows [unus (--one)+ verto (--to turn): universus
(--turned into one, combined into a whole)].
One of the unifying principles of an integrated system of
knowledge of man and his world seems to be the concept of symmetry
[2].
For more than 20 years I have walked under Norman and Gothic
vaults and arches, which day after day imposed the ideas of
reflectional, rotational and translational symmetries on my mind
(Figs 1 and 2) [3]. Tension and dynamism in my wife's designs and
tapestries (and perhaps in our marriage) may be the manifestation
of a sophisticated balance of dominating reflectional,
translational and color symmetries and of their absence as well
(Figs 3 and 4) [4, 5]. Translational symmetry was probably
responsible for the boredom of musical training in my childhood as
well as for the nice melodies I cannot forget [6]. For almost 30
years I have been studying and teaching problems of rhythm, rhyme
[7] and metaphor in literature and language and have tried to find
the reason for their aesthetic functions. Yet, it was only recently
that some works reminded me that a common core and connecting
principle of all the above may be symmetry [2, 8-10].
In relation to human life the phenomenon of symmetry can be
compared to health. If one is healthy he is not interested in it,
does not take care of it and does not feel it. The presence of
health is something unnoticed in life and the absence of it, i.e.
illness, is something which is noticed and which directs all our
attention, aims and wishes to health. Symmetry in nature and art
surrounds us permanently, more or less unconscious in us and
unnoticed by us, while the lack of it calls our attention to its
repletive omnipresence. Such is the linearity of time in human
life, this unidirectional and irreversible passing and lethal
asymmetry of the two endpoints in our lives--birth and death. This
personal and irreversible process of the individual pushes the
human mind towards the idea of a bilateral reflectional symmetry,
i.e. to the hope and belief of another life to come with its
antisymmetrical items of reward and punishment. According to this
there was a paradise (lost) at the beginning of time and there will
be a paradise (regained) at the end of time and the axis of
reflection is a Messiah in the middle of time. His person is again
a symmetry in itself, the incarnation of divinity (Deus ~homo) and
the deification of man (homo-,Deus) [11].
If a linguist approaches these phenomena of symmetry exclusively
from a linguistic point of view and deals with the meanings of
expressions he says they are metaphors. A metaphor comprehends a
"real life", of which the traditional name is literal sense, and an
"uncertain life to come", called f igurative sense [12, p. 3; 13,
p. 552; 14].
697
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698 L. BENCZE
Fig. 1. The nave of St Martin's Basilica at the Archabbey of
Pannonhalma, Hungary. (Photo: A. Alapfy.)
Skipping a vast number of definit ions for metaphor [15, pp.
300-331; 16, 17], I quote here a few examples beginning with
Aristotle:
"Metaphor is the transference of a strange name",
in Bywater's translat ion,
"Metaphor consists in giving the thing a name that belongs to
something else" [18, 19];
and another one from I. A. Richards, a great twentieth century
scholar of metaphor research:
"In the simplest formulation when we use a metaphor we have two
thoughts of different things active together and supported by a
single word, or phrase, whose meaning is a resultant of their
interaction" [20, p. 93];
and two from two encyclopedias:
"Metaphor. A condensed verbal relation in which an idea, image,
or symbol may, by the presence of one or more other ideas, images,
or symbols, be enhanced in vividness, complexity or breadth of
imph.'cation" [21]; "By common definition and by etymology a
metaphor is a transfer of meaning both in intension and extension"
[22].
Consequently, the term metaphor in its etymological and wider
sense means every transference in language, i.e. tropes (Cicero:
verborum immutat io- - -changing of words) [13, pp. 552, 553,556]
while tradit ional ly its meaning has also been restricted to
transference based on similitude, e.g. "he
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Symmetry in metaphors 699
Fig. 2. The splendid vaulting of St Benedict's Chapel at the
Archabbey of Pannonhalma, Hungary. (Photo: A. Alapfy.)
is a lion", which means he is as brave, as strong etc. as a lion
(Cicero: verbum translatum-- transference of words) [13, pp. 552,
553, 556].
One of the most common and ridiculous superstitions of the
Western civilization has been that metaphors (or tropes in general)
are to adorn style [20, p. 90; 23, p. 359]. It is a tradition which
may be traced back to a superficial reading of Quintilian and a
fatal misunderstanding as a consequence of it: " . . . there are
some (i.e. tropes) which are intended solely to the purpose of
embellishment" (eruntque quidam tantum ad speciem accomodati) [24,
p. VII. VI. 5] (present author's italics). Several times he makes
clear distinctions between tropes, which are to express meaning(!)
and those which are to ornament speech: " . . . some are for the
sake of meaning, others for the sake of decoration" ( . . . quosdam
gratia significationis, quosdam decoris assumi) [24, p. VIII. VI.
2]; " . . . tropes employed to express our meaning involve ornament
as well, though
Fig. 3. Struggle for Light; tapestry, wool, 150x 150 cm. Fig. 4.
The Seventh Door; tapestry, wool, 122 172 cm. Designed and woven by
S. t)rsi, 1978. Designed and woven by S. Orsi, 1985.
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700 L. BENCZE
the converse is not the case" ( . . . qui significandi gratia
adhibentur esse et ornatum, sed non idem accidet contra); " . . .
to make our meaning clearer.. , or to produce decorative effect. .
." (quia significantius est aut quia decentius) [24, p. VIII. VI.
6].
Though Quintilian was interested in the type which decorates
speech, he was still aware of the other type as well, In doing so
he relied on Aristotle, for whom the information-giving nature of
metaphor was of vital importance [25]:
"We will begin by remarking that we all naturally find it
agreeable to get hold of new ideas easily: words express ideas, and
therefore those words are the most agreeable that enable us to get
hold of new ideas. Now strange words simply puzzle us; ordinary
words convey only what we know already; it is from metaphor that we
can best get hold of something fresh." [26]
In any case metaphor has been a "disturbing enigma" for scholars
[12, p. 13] since Aristotle. There are at least three reasons for
this:
(1) nature of metaphor; (2) birth and behavior of metaphorical
relations in speech/text; (3) effect, function and relation of
metaphor concerning human personality (think-
ing, emotions, instincts etc.).
According to different approaches of various disciplines to
metaphor, theories have been labeled as comparison (Quintilian),
analogy (Aristotle), interaction (Black, Richards), improper usage
(Locke, Wittgenstein), opposition, logical absurdity (Beardsley),
matter of emotion (Carnap), intuition (Wheelwright), substitution,
similarity, juxtaposition, identity, tension, collision, fusion,
deviance, anomaly, mistake etc. [12, p. 3; 15, pp. 300-331; 22,
27]
This simple list of the technical terms of theories refers to
the essence of metaphor: "the literal meaning does not disappear"
[12, p. 13] but goes hand in hand with the figurative meaning in
every moment (cf. comparison of two, interaction between two,
tension between two etc.). The result is a tension in our mind, an
oscillation [15, p. 313]. Is it a matter of empirical falsity or
semantic anomaly [34], of relation of denotata and/or of
significata [29, p. 50], of intension and/or of extension [22]?
When one says "Peter is a lion", he sets up a contradiction
according to the rules of traditional logic, as he transgresses
logical categories: "Peter is a man", "A lion is a lower animal",
consequently "A man is a lower animal"! Yet we have no problem in
understanding the sentence "Peter is a lion". Suddenly we recognize
common features in Peter and in the lion (tertium comparationis)
[19, pp. 90-92; 30, pp. 27; 38; 153]; (ground) [20, p. 93; 28, 35,
pp. 25-47, 33]. We do not care about all the potential features of
the two meanings, but simply make some of the virtual features
actual (brave, strong etc.) [35, p. 44]. At this stage another
problem arises: which features are actualized? Brave, strong or
some others or both? Do we delete all of the potential and some of
the virtual features? [15, pp. 302, 314]. At once we realize that
the interpretation of metaphor is not totally uncertain, yet it is
not as certain as the sentence "Peter is six feet tall" can be
true. In addition we feel it is not just a matter of intuition vs
reasonable thinking or experience. We know that our interpretation
of a metaphor depends on context, situation, culture and education,
personal age and historical period, just like everyday classifying
(see below) [36]. That is why for speakers of European languages
"my ducky", for example, may or may not be a nice thing to say to a
woman but "my little elephant" certainly is not (cf. the meanings
of head in English, French, German and Hungarian) [37].
The phenomenon of transgression of existing categories is common
both in poetic metaphors as well as in new inventions in sciences.
If one says "A wolf is an animal" he will classify animal as genus
and wolf as a species somewhere under the genus animal. But if he
says "A man is a wolf" he will not follow everyday or scientific
biological experience and we could say again that he has violated
the logical rules of classifying or a kind of tabula Porphyriana
based on it [38, pp. 202-250, 229]. Everyday and scientific
classifying themselves may also be totally different without being
really illogical. Everyday classifying, not unlike metaphorical
classifying, may depend on age, education, culture and social
status, period, genre and mental condition (see above).
When my 3-year-old daughter consistently called every animal,
even a fish on the kitchen table, bow-vow and every plant and
flower kertyschoo, the naming was funny yet the classifying
perfect, i.e. animal kingdom, vegetable kingdom [15, pp. 300-331;
39-45]. Similarly, when in Hebrew both
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Symmetry in metaphors 701
an eagle and a bee were called oph, that categorizing seems
naive to us at first glance because we translate oph as bird in our
system of categories. The ancient Hebrew system was unlike ours
however. The meaning of oph was "flying being with wings" and thus,
the classifying was again perfect [15, p. 317]. The same can be
found in the distinction of meat and fish (caro vs piscis) in
Catholic moral theology from the ancient times throughout the
Middle Ages up until modern times. From the viewpoint of fast
(Lent), common sense and even local tradition were authoritative in
deciding what was meat and what was fish [46]. Thus, every animal
that lived and breathed on the surface of the earth was looked at
as meat--mammals, birds etc. Every animal that lived in and around
water wasfish. Therefore, during Lent people were allowed to eat
frogs, turtles, cockles, shellfish, crayfish, beavers, wild ducks,
crakes, seagulls etc. This distinction, which included even mammals
in the termfish had nothing to do with science. Yet, there is a
clear logic in it: the place of life [1, p. 402]. Something similar
happens in verbal jokes as well [47].
As far as metaphorical language is concerned it provides a more
holistic view of man and his ideas in everyday life even though it
is not precise in a scientific way, not to mention the fact that it
was the unusual associations and unexpected relations which helped
develop natural sciences as well, as pointed out in the story of
Newton's apple. Every invention or new idea in science is a kind of
rebellion against and a violation of existing categories just like
the language of children, poets and early civilization myths. In
each case there is something in common: the introduction of new
categories as a result of a new system of classifying. Therefore, a
metaphor is much more than simply a break in the semantic isotopy
of a text I15, p. 312; 48-50]. "No advance was possible in the
intellectual life of man without metaphor." [51]
The importance and the problems of metaphor which I have tried
to sketch above may be responsible for the two extreme views on
interpretation: one says metaphors make language totally obscure,
while the other says they can be analyzed as exactly as facts in
sciences [15, p. 323]. In an attempt to reach a more differentiated
understanding of the problem of metaphor I introduced the
uncertainty principle to the question in 1981 [52].
Then I suggested that every manifestation of a human being,
first of all an artistic one, is potentia which is actualized, i.e.
interpreted, by the recipient, another human being (in case of
language). Consequently, what a man says is always polyvalent. It
is the circumstances (who, what, to whom, where, why etc.) that
make his utterance more or less definite. Let us try to compare
metaphorical language with scientific language. The latter tends to
be accurate, so that it expresses extremely little with one word
and thus achieves exactness and totally excludes ambiguity.
Metaphors, on the other hand, tell us a lot, but inexplicitly,
ambiguously and in an undefined manner. Abstract language is
subsidiary and artificial. Metaphors are not simply there to
decorate language but to achieve conciseness, serve totality in
cognition and reduce the number of signs. For instance, the wording
of the label on a bottle of Tokay wine "Rex vinorum et vinum regum"
(Wine of kings and king of wines) could be scientifically
explained, at least in theory, but the process would fill books.
Even in chemistry and physics approximations are often the only
practicable way. Thus, for example, to make an exact calculation
and provide a description of all possible wave functions of an iron
atom would fill an entire library and that of a uranium atom would
require more paper and ink than there is matter in the solar
system. Or take, for example, the term "electron cloud" in the
description of atomic structures which is one of the most telling
metaphors among the many used in natural sciences [53]. It is
important in my analogies here that metaphors are always "cloudy"
in common experience [35, p. 47].
There is an uncertainty in the question of metaphor as well. We
know exactly the two "names" (man-wolf), yet we cannot link them
adequately (Fig. 5). Therefore, a literary analysis or any everyday
interpretation cannot come near anything like a mathematical or
scientific one (except in the case of the uncertainty principle of
physics), which totally eliminates ambiguity and establishes
equivalences and equations. Any interpretation must retain some
degree of uncertainty. It sets only the limits within which
ambiguity may exist and alternatives (fierce, hostile etc.) may be
chosen. It offers end values (man and wolf) and the oscillation of
mind can spring into existence in any channel (fierce, hostile
etc.) between them. Consequently, the number of intepretations is
not unlimited [37]. Ambiguity and tension remain within certain
limits. For example in the famous metaphorical saying "Homo homini
lupus"--"Man is to man a wolf" Plautus: Trinummus II.4 [54, 38, pp.
202-250, 229], the channel can be wild, hostile, inimical, fierce
etc., but obviously not
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702 L. BENCZ~
Jove .. . . . . - ' :~" . , : '~ .~ : : : : ' ~eo.
~,,e , fierce . .
~: : ........ -,./~/~ hostile ~ : ~ ~
\
~" " """""" hate
Homo homini lupus. Homo homini aut deus, sut lupus.
Fig. 5. (Drawing: M. Barab~is.)
mild, friendly, serving, adoring etc. Otherwise it would perhaps
say: "Homo homini deus"- -"Man is to man a god", as Erasmus quotes
it as a proverb: "Homo homini aut deus, aut lupus". The oscillation
of mind here seems to correspond to connections between different
parts of the brain. A metaphor makes the whole man react. In
metaphorical thinking, the scholastic principle can be altered in
the following way: "Nihil est in intellectu quod simul non sit in
anima, corpore et sensibus"--Nothing is in the mind that is not
simultaneously in the soul, body and senses (see below also).
This can be illustrated by an analogy from chemistry, too. In a
molecule, which is constructed of atoms, we know that there are
certain electrons which are shared between atoms and that there are
others which belong to individual atoms, at least to a good degree
of approximation. In a metaphor, we also know which items of
meaning can be common (hostile, fierce etc.) and which cannot
(mild, nice etc.), but we can never be certain of the actual common
one or ones (hostile and/or fierce etc. and/or both and/or others).
This depends on the individual, his age, education etc. [38, p.
219]. So we must take into consideration both bonding and
nonbonding electrons, using the molecular language vs features of
meaning [10]. It seems much easier and certainly more clear-cut to
describe the affinity and repulsion of electron pairs with one
another than those in the meaning of a metaphorical expression.
Wolves may be fierce both toward other animals and toward each
other, may quarrel over prey and with each other etc. These
relations are also defined much more by education, common sense
etc. than biology. The two meanings in the metaphor remain the
same, just as the two nuclei remain unchanged in the chemical bond,
whereas the relationship between the two meanings is subject to
various conditions, just as the bonding between the two atoms can
be described, at best, by a probability distribution function of
the electrons, and is more sensitive to changes on various
conditions than the nuclear positions. While we know the number of
chemical bonds in a molecule, we do not even know the number of
features in a metaphor. We can speak of positions of greater and
smaller symmetries and this is why, for example, "my little
elephant" can be nice in one language and culture and insulting in
another. The problem of certainty and uncertainty in the nature of
metaphor can be revealed more closely if we take the concept of
symmetry into consideration in a more detailed way.
It is all the more necessary that we do this because metaphor
was discovered as an example of symmetry as early as, at least,
Shubnikov and Koptsik, though they share the common European
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Symmetry in metaphors 703
Fig. 6 Fig. 7
G
opinion of a narrow interpretation of the use of metaphor and
restrict it to poetic language (cf. the remarks above on
Quintilian):
"A specific feature of poetry such as the metaphoric content of
its language develops within a unified scheme of groups of
projective transformations. Writing the Aristotelian metaphor in
the form of ratio
What age is so evening is for life for day
we find that other tropes (poetic comparisons and contrasts) are
formed in an analogous manner." [23, p. 359]
The concept of antisymmetry in grammatical metaphors as the
unusual and parallel use of Hungarian plural suffixes was raised by
Frnagy [15, p. 310].
Scientific investigations of metaphor go back to Aristotle, just
as the concept of symmetry goes back to Greek thinking. The word ~
aotq~e~piot had various meanings, the most important of which were:
commensurability, due proportion, symmetry, one of the
characteristics of beauty and goodness, fixed proportion, suitable
relation, convenient size and harmony of life [55].
In today's literature of symmetry a kind of wider sense
corresponds to the Greek meanings: "A broader interpretation allows
us to talk about degrees of symmetry, to say that something is more
symmetrical than something else" [10]. In this sense we "call
objects equal in relation to some particular feature if both
objects possess this feature" [23, p. 1] and thus "we introduce the
idea of two objects being more or less equal" [23, p. 1]. This type
of symmetry is called "material symmetry" [9] and applies to
metaphor while the so-called "geometrical symmetry", "as a special
kind of geometric law" [23, pp. 4, 2] and geometric regularity does
not [4, 10, 56]. I use the terms bilateral, rotational,
translational and color symmetries as well as asymmetry in the
sense in which they are generally accepted and established in the
literature [2, 10, 23, p. 359; 57~50].
If we consider the symmetry of the sentence "A wolf is an
animal" from a logical point of view, i.e. we categorize the animal
as genus, the wolf as a species of it, we shall find reflectional
symmetry and asymmetry in their extensional relation as the set of
animals includes the set of wolves (Fig. 6). A similar symmetry and
asymmetry can be found in their intensional relation but in a
reciprocal way, as the set of features of a wolf includes a set of
animal features (Fig. 7). This symmetry and asymmetry is also
present in a simple sketch of the dichotomic structure or binary
oppositions of the so-called Tabula Porphyriana (or Arbor
Porphyrianus):
beings
/ living beings
J \ animal kingdom vegetable kingdom
J \ man other animals
\ inanimate beings
beings
/ \ living be ings inanimate beings ( + being ( + being +
living) - living)
The symmetry is in the feature being which exists in both; the
asymmetry, or at best antisymmetry (traditionally called
differentia specifica), is in the features living-inanimate, with
the feature living existing in one and missing in the other etc.
This is why it could also be looked at as antisymmetry.
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704 L. BENCZE
Now let us see what happens if we say "A man is a wolf". We
disregard the system of Tabula Porphyriana in this sentence,
regardless of whether our tabula is based on science or is
determined by culture, language etc. (see the examples offish, bird
etc. above), as if wolf were a genus and man a species of it:
wolf
\ \ \ \
man
while according to the common system, man and wolf are both
species somewhere under different generi, as can be seen quite
clearly even in a mere sketch:
animal kingdom
man other animals
J wolf
Yet, we cannot say that the sentence "A man is a wolf" is simply
illogical and violates the rules of thinking and of language
because we--in a European culture-can understand it without
difficulty. The solution to the problem, I think, is in the
existence of the above-mentioned uncertainty in the symmetry and
asymmetry of the meanings in the sentence, not to mention that it
is symmetrical and asymmetrical even in its acoustic or written
form:
I
I
A man is a wolf I
I
where the copula is is the axis of reflection or the border of
translation. Metaphorical relation is a kind of mirror which is
polished semantically, socially and culturally (cf. the example
"little elephant" above).
Now let us suppose that the two meanings (man-wolf) are two
different and amorphous objects opposite each other. They can both
be turned in space separately in every direction. Both have certain
parts on their surfaces which are identical or similar either in
shape or color (fierce, hostile etc.). Consequently, if we turn
them continuously there will be certain moments and stages when
identical or similar parts face each other (fierce-fierce etc.) or
are back to back. The two objects (man-wolf) in and of themselves
are asymmetric, but in the above-mentioned moments and stages
symmetries arise between parts. This is when we discover common
features of man and wolf(hostile, fierce etc.). The probability of
such turnings depends on the number of identical or similar parts,
on the speed and direction of the turnings and the cleverness of
the person who is turning them (cf. the problem of the Rubik cube,
and see Fig. 8). If one is clever, the probability of symmetrical
stages in an interval grows and the frequency and probability of
the returning of such stages will be more or less stabilized (cf.
the problem of certainty and uncertainty of metaphor as discussed
above). This means that a clever person can identify more common
features of man and wolf more quickly than others. We can make this
play more complicated and refined and put a lens between the
objects. In this case the work of the lens will also depend on the
distance of the objects from the lens and on the nature of lens
itself. Such lenses can be culture, education, age etc., as above.
Therefore, let us add omnidirectional motion in space to the
earlier rotation of the two objects. Then theoretically there will
be more possible stages of symmetry as the lens can enlarge or
reduce shapes, i.e. a square of this size [3, for example, can be
symmetrically adequate with this size [ ] etc. (see Fig. 9). If the
lens in question happens to be a fish-eye then a shape O can be
symmetrical with c:::~. That is why "my little elephant" can be
nice---depending on the cultural lens.
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Symmetry in metaphors 705
[ ] hostile
f ierce
etc. Fig. 8
The two meanings in metaphor are amorphous in comparison with
one another. Yet, there are more or less symmetrical items (fierce,
hostile etc.) in them while others are asymmetrical. The existence
of items belong to the possibility of the objective, external world
(cf. potentia above). Whether they appear or are thought or
recognized as symmetries (cf. actualization above) depends on two
main groups of conditions: one is the rotational and
omnidirectional motion, which is the brightness and cleverness of
the speaker; the other is the mirror or lens/lenses and the
objects, the type of lens, the type of amorphous object--which is
the individual's language, culture, education, age, historical
period, social status, context, situation etc. (cf. the
"circumstantiae" in classical rhetoric) [13, pp. 91,139, 377, 399
etc.]. These result various values which can be subdivided as
aesthetics, knowledge-invention, emotional tension, humor,
poeticity etc. The two main factors (motions and lens + object)
define the borders of metaphor-nonmetaphor in an exact and precise
way. Within these borders one stage, one moment (fierce or hostile
or wild etc.), i.e. the appearance of metaphor/symmetry as
metaphor/symmetry, is more or less uncertain.
By means of this model the nature, behavior and effect of
metaphor can be described--I am convinced--more precisely and
exactly than ever. It comprehends several different characteristics
of metaphor which have been emphasized separately by various
approaches, and provides an explanation of the tension,
oscillation, cognitive and emotional procedures, invention and
poeticity, and the role of science and art in our mind and life. It
also alludes to the relationship between the external world and the
world in language (cf. Pet6fi's TeSWest theory: text
structure--world structure) [61], which is a kind of symmetry as
complicated as symmetry in metaphor. Besides, it reminds us of the
external, formal symmetry of the shape of neocortex, which is the
material source of the metaphorical operations discussed above.
There may also be a functional connection between metaphoric
thinking and the structure and working of the brain.
Fig. 9
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706 L. BENCZE
Since Sperry's experiments the research of left and right
hemispheres has become fashionable [15, p. 324; 62, 63]. It is
widely known that the left hemisphere is the center of abstraction
and speech, while the right hemisphere is the center of music and
iconic thinking. It is also well-known that there has been a
contradiction in localizing certain functions in the brain.
Lashley's experiments seemed to prove there is no special place of
memory in the brain, while Penfield succeeded in connecting certain
senses to certain neurons [62, pp. 201-204]. I f certain parts of
the neocortex are cut out, other parts may take over their
functions--primarily in childhood. This contradiction and
uncertainty of definite localization and the possibility of the
changing place of functions seems to correspond to the
unpredictability in metaphorizing which is, at the same time,
predictable within certain limits in its special symmetry, as we
have seen above. The brain as a whole (including the limbic system,
the center of emotions and other parts) is the same in every man,
though not regarding the level of neurons and their connections. A
certain connection is established within one man's brain but not in
another's, though the neural possibilities are more or less equally
given (cf. determination by age, education, culture etc. above). I
f the neural connection is produced, it is not sure that the neural
route is the same. The length and number of intermediate
connections on it can be different and can exist in parallel [64].
This also seems to correspond to the special uncertainty and
symmetry of semantic features in metaphor which can be produced by
various rotations etc. in our model. Consequently, both the nature
of the brain and the nature of the metaphorizing mind include a
kind of risk, not unlike human life itself [65, pp. 1, 9], which is
not limitless in either case (see the introductory remarks to this
paper). Degrees of risk in finding symmetry in language and art
consist of a wide range of chances (cf. Figs 1-4). The use of
metaphor in language--as I hope I have proven-- is a "carefully
calculated risk" [65, p. 94] as metaphor connects known and unknown
as a means of requiring a knowledge of unknown via known [26, 38,
p. 217], art and inventions are also adventures into an unknown
part of the world with the purpose of making it known. In the
symmetry of metaphor- -one could say--the unknown is reflected by
the known. At the same time the concept and existence of symmetry
itself ensures the limits of risk. This anxiety and hope is
expressed by Black and Boyd:
"No doubt metaphors are dangerous--and perhaps especially so in
philosophy. But a prohibition against their use would be a willful
and harmful restriction upon our power of inquiry." [35, p. 47];
"The use of metaphor is one of many devices available to the
scientific community to accomplish the task of accommodation of
language to the casual structure of the world" [66].
This accommodation by metaphors belongs to the most routine of
human acts, so much so that it is taken to extremes even when used
without similarity, e.g. in the physics of quarks where there are
technical terms like "naked charm state" and "naked bottom state"
[1, pp. 381-413; 67]. That is why I think Petrfi is perfectly fight
in saying that "normal and figurative messages can be handled in
the same way" (see also the everyday and scientific classifying
above) [68]. I also hope that the introduction of the correlation
of the uncertainty principle and symmetry in metaphor may be
fruitful and stimulating for modeling facts in natural sciences.
The risk of certainty and uncertainty, the struggle to reduce it
and keep it to a limited extent, to evaluate and ramify it in
metaphor has removed the concept of metaphorical symmetry from the
geometrical one. Yet, the key to the enigma of metaphor may also be
the uncertainty principle in symmetry.
REFERENCES
1. L. Bencze, Conscious tradition, unconscious construction or
subconscious metaphors? Certain levels of text cohesion and
coherence. In Text Connexity, Text Coherence. Aspects, Methods,
Results (Ed. E. SSzer). Buske, Hamburg (1985).
2. I. Hargittai, Szimmetria egy KJmikus Szem~vel (Symmetry
Through the Eyes of a Chemist). Akad~miai Kiad6, Budapest
(1983).
3. L. A. Cummings, A recurring geometrical pattern in the early
renaissance imagination. Comput. Math. Applic. 12B, 981-997.
Reprinted in Symmetry: Unifying Human Understanding (Ed. I.
Hargittai). Pergamon Press, Oxford (1986).
4. Gy. Drczi, Seen and unseen symmetries: a picture essay.
Comput. Math. Applic. 1211, 39-62. Reprinted in Symmetry: Unifying
Human Understanding (Ed. I. Hargittai). Pergamon Press, Oxford
(1986).
5. V. Molnhr and F. Moln~ir, Symmetry-making and breaking in
visual art. Comput. Math. Applic. 1211, 291-301. Reprinted in
Symmetry: Unifying Human Understanding (Ed. I. Hargittai). Pergamon
Press, Oxford (1986).
6. R. Donnini, The visualization of music: symmetry and
asymmetry. Comput. Math. Applic. 121~ 435--463. Reprinted in
Symmetry: Unifying Human Understanding (Ed. I. Hargittai). Pergamon
Press, Oxford (1986).
7. B. Pavlovir, On symmetry and asymmetry in literature. Comput.
Math. Applic. 12B, 197-227. Reprinted in Symmetry: Unifying Human
Understanding (Ed. I. Hargittai). Pergamon Press, Oxford
(1986).
8. I. Hargittai, Degas' dancers: an illustration for rotational
isomers. 3". chem. Educ. 60(2), 94 (1983).
-
Symmetry in metaphors 707
9. I. Hargittai (Ed.), Limits of perfection. Comput. Math.
Applic. 12B, 1-17. Reprinted in Symmetry: Unifying Human
Understanding. Pergamon Press, Oxford (1986).
10. I. Hargittai and M. Hargittai, Symmetry Through the Eyes of
a Chemist. VCH, Weinheim (1986). 11. Pope Leo the Great, 1. Sermo
in Nativitate Domini. In Breviarium Congregationis Sancti Mauri
O.S.B. Pars Hyemalis,
pp. 230-231. Vindobonae, Ex Typogr. Mechitaristarum (1842). 12.
J. J. A. Mooij, A Study of Metaphor. On the Nature of Metaphorical
Expressions, with Special Reference to Their
Reference. North-Holland, Amsterdam (1976). 13. H. Lausberg,
Handbuch der fiterarischen Rhetorik. Eine Grundlegung der
Literaturwissenschaft, Band I-II. Zweite, durch
einen Nachtrag vermehrte Auflage. Hueber, Miinchen (1973). 14.
J. P. van Noppen (Ed), Metaphor and Religion. Vrije Univ., Brussels
(1983). 15. I. Frnagy, Metafora. In Vikigirodalmi Lexikon, Vol. 8.
Akadrmiai Kiad6, Budapest (1982). 16. W. A. Shibles, Metaphor: an
Annotated Bibliography and History. The Language Press, Whitewater,
Wise. (1971). 17. J. P. van Noppen (Ed.), Metaphor: a Bibliography
of Post-1970 Publications. Benjamin, Amsterdam (1985). 18. I.
Bywater, Aristotle, De Poetica. In The Works of Aristotle
Translated into English under the Editorship of W. D. Ross,
p. 1457b. Clarendon Press, Oxford (1946/1952). 19. Aristotle,
The Poetics. With an English Translation by W. H. Fyfe, p. 1457b.
Harvard Univ. Press, Cambridge,
Mass./Heinemann, London (1960). 20. I. A. Richards, The
Philosophy of Rhetoric. Oxford Univ. Press, New York (1936/1950).
21. A. Preminger (Ed.), Encyclopedia of Poetry and Poetics, p. 490.
Princeton Univ. Press, N.J. (1965). 22. P. Edwards (Chief Ed.), The
Encyclopedia of Philosophy, Vol. 5, pp. 284-289. Macmillan, New
York/The Free Press,
London (1967). 23. A. V. Shubnikov and V. A. Koptsik, Symmetry
in Science and Art. Plenum Press, New York (1974). 24. Quintilian,
The Institutio Oratoria of Quintilian. With an English Translation
by M. E. Butler, Vols I-II. Harvard Univ.
Press, Cambridge, Mass/Heinemann, London (1953/1960). 25. L.
Bencze, A metafora meghat~rozfisa 6s helye az arisztotelrszi
fogalomrendszerben (On the place and definition of
metaphor in Aristotle's conceptual system). Filol. Krzl. 29,
1-18, 273-284 (1983). 26. W. R. Roberts, Aristotle, Rhetorica. In
The Works of Aristotle Translated into English under the Editorship
of W. D.
Ross, p. 1410b. The Clarendon Press, Oxford (1946/1952). 27. M.
Black, Metaphor. Proc. Aristotelian Soc. New Ser. 55, 273-294
(1954-1955). 28. W. Abraham, A Linguistic Approach to Metaphor.
Peter de Ridder Press, Lisse (1975). 29. H. Kubczak, Die Metapher.
Carl Winter Univ. Heidelberg (1978). 30. S. R. Levin, The Semantics
of Metaphor. The Johns Hopkins Univ. Press, Baltimore, Md (1977).
31. J. R. Searle, Metaphor. In Expression and Meaning. Studies in
the Theory of Speech Acts, pp. 77-116. Cambridge Univ.
Press, Cambs. (1979). 32. A. Ortonv (Ed.), Metaphor and Thought.
Cambridge Univ. Press, Cambs. (1979). 33. P. Recoeur, The Rule of
Metaphor. Routledge & Kegan Paul, London (1978). 34. R. E.
Sanders, Aspects of figurative language. Linguistics 96, 56-100, 60
(1973). 35. M. Black, Metaphor. In Models and Metaphors. Studies in
Language and Philosophy. Cornell Univ. Press, Ithaca, N.Y.
(1962). 36. I. F6nagy, Reported speech in French and Hungarian.
In Direct and Indirect Speech (Ed. F. Coulmas), pp. 255-309.
de Gruyter, Berlin (1986). 37. I. Fbnagy, Nyelvek a nyelvben
(Languages in language). ,4It. Nyelv. Tanulm. 12, 61-105 (1978).
38. G. A. Miller, Images and models, similes and metaphors. In
Metaphor and Thought (Ed. A. Ortony). Cambridge Univ.
Press, Cambs. (1979). 39. B. Leondar, Metaphor and infant
cognition. Poetics 4, 273-278 (1975). 40. M. C. Beardsley,
Aesthetics. Problems in the Philosophy of Criticism.
Harcourt-Brace, New York (1958). 41. J. Bernicot, L'&ude
exprrimentale des mrtaphores. Annie psychol. 81, 465-484 (1981).
42, R. Brown, Words and Things. The Free Press, Glencoe, Ill.
(1958). 43. R. Brown, A First Language: The Early Stages. Harvard
Univ. Press, Cambridge, Mass. (1973). 44. J. Piaget, Six
Psychological Studies (Translated by A. Tenzer). Random House, New
York (1967). 45. B. Kaplan, Radical metaphor. Aesthetic and the
origin of language. Rev. exist. Psychol. Psychiat. 2, 75-84
(1962). 46. H. Noldin, Summa Theologiae Moralis iuxta Codicem
luris Canonici, XXVII edn (Recognovit et emendavit A. Schmitt);
Vol II, De praeceptis Dei et Ecclesiae. Oeniponte-Lipsiae, p.
III.I.II.I. 677b (1941). 47. I. Frnagy, He is only joking: joke,
metaphor and language development. In Hungarian General Linguistics
(Ed. F.
Kiefer), pp. 31-108. Benjamin, Amsterdam (1982). 48. A. J.
Greimas, Sbmantique Structurale. Larousse, Paris (1966). 49, J.
Dubois, Fr. Edeline, Ph. Minguet, J. M. Klinkenberg, Fr. Pire and
H. Trinon, Rh~torique Gknbrale, p. 220. Larousse,
Paris (1970). 50. J. Dubois, Fr. Edeline, J. M. Klinkenberg and
Ph. Minguet, Rh~torique de la Pobsie, p. 88. Ed. Complexes,
Brussels
(1977). 51. Miiller (Cited by W. A. Shibles), An Analysis of
Metaphor in the Light of W. M. Urban's Theories, p. 127.
Mouton,
The Hague (1971). 52. L. Bencze, On the metaphorical animal.
Annls Univ. Scient. bpest. Rolando Ertv6s nominatae. Sectio ling.
12, 215-222
(1981). 53. E. R. MacCormac, Meaning variance and metaphor. Br.
J. phil. Sci. 22, 145-159 (1971). 54. M. Black, More about
metaphor. In Metaphor and Thought (Ed. A. Ontony). Cambridge Univ.
Press, Cambs. (1979). 55. H. G. Liddell and R. Scott, A
Greek-English Lexicon. Clarendon Press, Oxford (1953). 56. A. L.
Mackay, But what is symmetry? Comput. Math. Applic. 12B, 19-20.
Reprinted in Symmetry: Unifying Human
Understanding (Ed. I. Hargittai). Pergamon Press, Oxford (1986).
57. J. Brandmiiller and R. Claus, Symmetry. Its significance in
science and art. lnterdiscipl. Sci. Rev. 7, 296-308 (1982). 58. J.
Rosen, Symmetry Discovered. Concepts and Applications in Nature and
Science. Cambridge Univ. Press, Cambs.
(1975).
-
708 L. BENCZE
59. N. Shejkov, Leben und Symmetrie. Urania, Leipzig (1982).
Hungarian translation: l~let bs Szi~metria. Gondolat, Budapest
(1987).]
60. H. Weyl, Symmetry. Princeton Univ. Press, N.J. (1952). 61.
J. S. Pet6fi, Thematisierung der Rezeption metaphorischer Texte in
einer Texttheorie. Poetics 15, 289-310 (1975). 62. St Rose, The
Conscious Brain. Weidenfeld & Nicolson, London (1973). 63. C.
Sagan, The Dragons of Eden. Speculations on the Evolution of Human
Intelligence. Random House, New York (1977). 64. B. Guly/ts (Ed.),
The Brain-Mind Problem., Philosophical an d Neurophysiological
Approaches. Leuven Univ. Press,
Leuven (1987). 65. N. Reseher, Risk, A Philosophical
Introduction to the Theory of Risk Evaluation and Management. Univ.
Press of
America, Lanham, Md (1983). 66. R. Boyd, Metaphor and theory
change. In Metaphor and Thought (Ed. A. Ortony), pp. 356-408,
358-359. Cambridge
Univ. Press, Cambs. (1979). 67. E. R. MacCormae, Religious
metaphors: linguistic expressions of cognitive processes. In
Metaphor and Religion (Ed.
J. P. van Noppen), pp. 47-70, 61. Vrije Univ., Brussels (1983).
68. J. S. Pet6fi, Metaphors in everyday communication, in
scientific, biblical, and literary texts. In Metaphor and
Religion
(Ed. J. P. van Noppen), pp. 149-179, 289. Vrije Univ, Brussels
(1983).