Likewise, Aristotle considered metaphors a sign of language mastery and genius, but he also deemed them ornamental, appropriate for poetry but too enigmatic for philosophical or scientific discourse. On the contrary, Max Black articulated an influential alternative to traditional views of understanding metaphors. Having rejected Aristotle’s comparison as too simplistic, Black argued that metaphor is a communicative phenomenon operating not at the level of mere word meaning, but at the (ostensibly) deeper level of conceptual structure. Lakoff and Johnson (1980) put forward that metaphors establish the modal method through which the mind represents concepts that are not sensorial or perceptual in nature. Their conclusion is:

“Metaphor pervades our normal conceptual system. Because so many of the concepts that are important to us are either abstract or not clearly delineated in our experience (the emotions, ideas, time) we need to get a grasp on them by means of other concepts that we understand in clearer terms (spatial orientation, objects). This need leads to metaphorical definition in our conceptual system” (1980, 115).

Conceptual Metaphor has been the prime concern for translation scholars, academicians, and students. Scholars have tried to map and analyze conceptual metaphorical aspects in poetry and novels for a long time. But somehow, they face a series of confusions regarding the meanings of some conceptual metaphorical phrases. As Newmark (1988) holds, whilst the central problem of translation is the overall choice of a translation method for a text, the most important particular problem is the translation of metaphor. Conceptual Metaphor is often fully employed in literary texts and it is regarded as a challenge to ESL students and academicians.

According to Tone Aksberg Bjerkmo Johansen (2007), the process that constitutes a conceptual metaphor is when the knowledge of one field is epitomized onto another field. Conceptual Metaphors are normally used when expressions that represent our thoughts in a conventional way are being systematically used in everyday language. An example of conceptual metaphor is a metaphoric concept such as “Theories are buildings,” where we can partially conceptualize “Theories” in terms of “Buildings.” According to Lakoff and Johnson, metaphor has the tendency to highlight and hide certain aspects of the target concept. Another example is “A relationship is a journey,” which ascertains that the metaphor is measuring the progress in a relationship, but it does not give any idea of how this progress can be achieved. Metaphor is only a partial mapping as “not all the features of the source have analogs in the target,”

According to Apps (1995), metaphors have proven useful after examining different approaches to learning in adult education. Young (1996) states that, “Metaphors form visual constructs through which we associate, interpret and organize thought. They dominate and delimit our consideration of experience and phenomena. Because one’s metaphor of teaching and learning interacts with fundamental issues such as the nature of knowledge and the nature of persons, it impinges directly on the way pedagogical decisions are made” (p. 79).

Postman and Weingartner (1969) suggested that many adult educators conceptualize teaching and learning through the use of metaphors. Winner and Engel (1980) used a matching task where the classification of one item in terms of recurring similarity to another item was scored as metaphorical. Furthermore, Vosniadou and Ortony (1983) asked their participants to complete similarity statements, including similes. The expressions tested “were often constructed idiosyncratic metaphorical expressions instead of actual natural language expressions.”

Waggoner, Messe, and Palermo (1985) found out that the recollection and the construction of meaning for both literal and metaphorical expressions depends on the supporting contexts, such as extended and appropriately structured stories. Stones (1989) used short stories with familiar concrete nominal metaphors as targets and he found out that participants perform better when they are asked to paraphrase rather than explain the meaning of the metaphor. However, this has one drawback for children, as the meta-cognitive abilities that paraphrasing required usually develop late in childhood. Thus, such reasons could prevent participants from scoring well in the task.

For students who do not have a cultural orientation of the western background, metaphors from English Linguistics or English Literature textbooks might create confusion. According to Brown, “cultural knowledge” is too vast to teach in the context of English Literature, thus, ESL students should be taught “explicit strategies for making inferences from language” (1990, 11-17). Furthermore, Murray (1985, 7) states that without the inculcation of such strategies, students will interpret the texts according to their own background. Murray’s recommendations are based on the “Schema Theory” (Adams Collins 1979), which is the body of research into reading comprehension. According to Adams and Collins (1979), a schema can be characterized as an “abstract knowledge structure” in the memory and it functions by interpreting, storing, and retrieving new information. This theory concludes that texts on their own do not provide meanings, but rather they direct to readers the construct meaning based on what they have acquired previously.

References

• (n.d.). The American Heritage Dictionary of the English Language (4th Ed.). Retrieved June 23, 2007, from Dictionary.com website.
• Kaal, Anna Albertha. 2012. Metaphor in conversation. VU University Amsterdam.
• Lakoff, George and Johnson, Mark. 1980. Metaphors We Live By. Chicago: University of Chicago Press.
• Lakoff, George. 1993. Metaphor and Thought. 2nd Ed. Cambridge University Press.
• Lakoff, George and Turner, Mark. 1989. More Than Cool Reason: A Field Guide to Poetic Metaphor. Chicago: University of Chicago Press.
• Lakoff, George. 1993. “The contemporary theory of metaphor.” In A. Ortony (Ed.) Metaphor and Thought. (pp. 202-251) Cambridge: Cambridge University Press [second edition]
• Lakoff, George and Johnson, Mark. 1980. “Conceptual Metaphor in Everyday Language.” (Vol. 7). The Journal of Philosophy.
• McGlone, Matthew S. 2006. What is the explanatory value of conceptual metaphor? The University of Texas.
• Erna. 1996. “The limits of literal meaning.” Danish Yearbook of Philosophy.
• Pierson, Cheri. 2008. “Reflections on Educational Metaphors for Teaching English as a Second Language to Adult Learners.” (Vol.17). PAACE Journal of Lifelong Learning.
• Short, Mick. 1996. Exploring the Language of Poems, Plays and Prose. Longman.
• Van, Engen Robert B. 2008. Metaphor: A Multifaceted Literary Device used by Morgan and Weick to Describe Organizations. (Vol. 1). Regent University.
• Winberg, Christine. 1994. The comprehension of figurative language in English literary texts. Rhodes University.

The Fountain of Living Waters frames Christian Scriptures from beginning to end. In Genesis, the first book of the Torah, in the very first verse, we read: “In the beginning, when God began to create, the Earth was without form and void, and the Spirit of God moved over the face of the deep.” The deep in Hebrew is tehom. Such depth is not only the literal vastness of the primordial ocean; tehom also points us to the truth that creation comes from chaos. Life begins in the waters of the womb; cosmos originates in chaos.

Then, in the very last verses of Christian Scriptures, the Book of Revelation, another water image appears. The author borrows from the Prophet Ezekiel to envision the new Jerusalem, the city of peace. This city comes down from heaven, and in its center is a river of life. This river contains crystal clear water, washing away all violence, so that “nothing any more shall be accursed.” Living Waters flow through Christian Scriptures from alpha to omega.

The Holy Bible practically drips; 692 verses refer to waters. Prophet Moses leads the people of Israel to freedom through the waters of the Red (or Reed) Sea. Prophet Jonah doesn’t think it’s such a good idea to preach repentance to the people of Nineveh, Israel’s enemy, and embarks on a boat going the opposite direction. But God swallows him up in the belly of a whale, and he returns to the waters of creation, the chaos of tehom. And what does he do there? He prays. His prayer brings him safely to Nineveh, where out of the waters he brings the enemy to repentance. Living Water, the Fountain, turns enemies to allies. This truth is beautifully conveyed in perhaps the most famous Psalm, Psalm 23:

The Lord is my Shepherd. I shall not want. He makes me lie down in green pastures. He leads me beside still waters. He restores my soul. Yea, though I walk through the valley of the shadow of death, I shall fear no evil, for Thou art with me. Thou preparest a table before me in the company of my enemies. My cup overflows. Surely goodness and mercy shall follow me all the days of my life.

The Fountain overflows with abundance, to invite even enemies to the table of justice and mercy.

But the Fountain of our Source also dissolves our petty, ego-driven associations. Prophet Amos puts this best. The people of Israel in his day were unjust. They treated the poor with callous disregard, they didn’t educate their youth, they were violent. But they were also pious, praying five times a day (or the ancient equivalent, anyway!)

And hear what God says, through Amos: “I hate, I despise your festivals. The noise of your solemn assemblies hurts my ears … But let justice roll down like waters, and righteousness like an ever-flowing stream.”

The Fountain of love is not just a gentle flowing stream. It’s also a tsunami of the power of love that sweeps away all our pretenses. The Fountain throws us unto the mercy of an infinite flood of justice.

Of course, for Christians like me, this merciful and just Fountain also points to, indeed is incarnate within Jesus. Jesus is Living Waters. The story that most clearly conveys this metaphor is in the Gospel of John, where Jesus meets a Samaritan woman by a well and asks her for a drink. She asks him what he’s doing there, for being at a well was woman’s work, and Jesus’ disciples are scandalized, because rabbis didn’t talk to women, much less Samaritans (who were racially “other”). And to make matters worse, this woman has been married five times, and she is now living with a man who is not her husband.

But Jesus tells her: “The water that you give me will only temporarily quench my thirst. But the water I give to you is living waters, and it will well up in you to eternal life.”

And this woman cries out: “Give me this water!” And Jesus says: “I am he.”

Jesus is innocent and perfect compassion. He is a drink of water on a hot day. He is mercy for outcasts, for the poor, for sinners like this Samaritan woman. And what he brings is the possibility that we, too, might live compassionate lives. So the woman goes and tells her neighbors: “I’ve met the Messiah!” She has been washed in the Fountain.

Once we lose our attachment to petty associations, we can live for others, out of true grace. “Whoever seeks to save one’s life,” Jesus teaches, “will lose it. But whoever gives up one’s life for my sake and for the sake of the good news (the gospel), will find true life.”

True life is a life lived for others. This doesn’t entail masochism, but instead offers fulfillment. Psychologists teach that when we are fully engaged in a task we lose the usual blinders of self-consciousness and enter into what they call “flow.” We’re “in the zone,” whether at work, at play, or in love. The point is this: when we love, we truly live.

This is why Lutheran Christians like myself celebrate the baptism of infants. Sometimes, baptism is misunderstood as a one-time event: you get dunked and you’re done. In fact, baptism is more like a first contact with the Fountain. Metaphorically, it can be experienced daily, even many times a day.

Whenever we wash, we can be reminded of our Source. Whenever it rains, we can remember the Fountain. Whenever we take a drink, we can give thanks to God for the mercy of compassion.

All in all, then, baptism is not unlike wudu—the washing of regeneration—that prepares us to pray. As the Apostle Paul urged us, “Pray constantly.” This doesn’t mean doing salat perpetually, it means being aware of our Source. Praying constantly means giving up petty attachments or associations, such as greed, anger, and violence. And praying constantly means giving ourselves away in acts of compassion. When we find the flow of love, we live.

Reading The Fountain as a Christian connects me not only to a magazine, but also to a profound metaphor. The Fountain reminds us of our Source, dissolves petty egoist attachments as we learn about our world, and invites us to join the flow of compassionate living. And isn’t that worth at least the price of a subscription?

In this article we will review these three concepts and the relations among them by giving examples from the realms of both physical and metaphysical concepts.

Even though there is no universally accepted definition of analogy, or metaphor, or literal similarity, the purpose of their use is unanimously defined as “throwing light on an unfamiliar concept or situation using a familiar one.” The past few decades have witnessed several attempts of redefining these terms or at least extending a definition that is somewhat agreed-upon to an all-encompassing one. In so doing, researchers tended to employ mathematical structures that are by no means simple. What seems to differ from one approach to another is the method used in the process of establishing a correspondence between the familiar and the unfamiliar. Our purpose is not to give a full account of these approaches here, as there are so many of them, but rather to adapt one that is more convenient for conveying our examples.

Analogy: The word analogy is derived from the Greek word analogia. Originally, this was a mathematical (actually a musical) term before becoming a grammatical and linguistic one, meaning “proportion” (Szabo 1978, 23). An example of Aristotelian analogy is “spine is to fish as bone is to animal.” This simple analogy is generally formulated as A:B = C:D. We say, in this case, A and C are analogous. The sense in which A and C are analogous could be a property they have in common as well as the similarity between their relations to B and D, respectively. In the spine and bone example above we observe both. In the analogy “feet are to animal as wheels are to automobile,” however, feet and tires have virtually nothing in common, but they are analogous with respect to their functions within the bodies that they are part of, i.e., both are used as a means of transportation. Therefore, common relations are essential to analogy, but common objects are not. (Gentner-Markman 1997, 46).

One of the recent approaches to analogy which is widely used is the structure-mapping theory (SMT) (Dedre Gentner, 1983). It presumes a mapping between the familiar (domain or base) and the unfamiliar (target). The domain and the target consist of objects and relations among objects. SMT establishes a one-to-one correspondence between the objects of the domain and the target in a way that preserves the relations between objects (Those who are familiar with the category theory in mathematics will notice the resemblance of this mapping to a “covariant functor” between two “categories”). This is a “structural alignment” between the domain and the target (Gentner-Markman 1997, 47). In the “feet and wheels” example the mapping occurs between a body and an automobile. It maps feet to wheels and the relation TRANSPORT (feet, body) to the relation TRANSPORT (wheels, automobile). One can find more matching elements between a body and an automobile. For instance, we can match the heart of the body to the engine of the vehicle and observe that the relations RUN (heart, body) and RUN (engine, automobile) are preserved.

One might ask where do the arms get mapped? The answer is “nowhere.” We do not expect this mapping to match every object in the domain to an object in the target. The “power of the analogy” is not in the number of objects that are matched or the common attributes that the objects share. It is rather the degree of matching among relations that makes an analogy more powerful (Gentner 1982, 110).

Having introduced the concept of analogy by using some simple physical examples let’s now consider a not-so simple metaphysical situation.

In the 1920’s two mathematicians proved a very interesting but at the same time very puzzling theorem, known as the Banach-Tarski Paradox. In plain English, the theorem states that it is possible to divide a solid ball into a few pieces and reassemble those pieces together to make two balls, each of which has the same size as the original ball that was divided. A more striking consequence of their theorem is (you may want to sit down before you read this) a solid ball the size of a small pea can be cut into a number of pieces and reassembled into a new ball the size of the sun! Strange as it may sound, it is a valid mathematical argument, not a myth. (We have to note that it is not something one can do at home using a knife and a cutting board, because some of the pieces have no volume!) The analogy that we would like to establish under SMT is to map that solid ball of the theorem to a small amount of water which could quench the thirst of an army of about 30,000 in Tabuk in year 631. This was a miracle given to Prophet Muhammad, peace be upon him. A similar miracle of Prophet Jesus, peace be upon him, is described in the Bible, Matthew 14:21 (Volker Runde, in the Sky 2 (2000), 13–15).

Metaphor: The essence of metaphor is understanding and experiencing one kind of thing in terms of another. (Lakoff & Johnson 1980, 104) Simple examples are “What a sweet baby!” “Your car is a lemon, let’s take mine.” Obviously babies are not candies, nor are vehicles some sort of fruit. We use this sort of “identification” in order to communicate our ideas/feelings in a more striking way. Here are more examples of metaphors: “he is the apple of my eye,” “it’s raining cats and dogs,” “he has a golden heart,” “she cried rivers” etc. As these examples show, the distinguishing characteristic of metaphors is substitution, for example, rivers taking the place of tears in the last example. And this substitution takes place between different domains. If we say “a nightingale is a bird,” that’s not a metaphor; it’s a literal categorization, as both nightingale and bird signify the same domain (Gentner 2005, 200).

As long as the correspondence is not purely attributional, but some relations are also preserved we can also talk about structural alignment for metaphors (Gentner 88, 49). From this perspective, many metaphors are in fact analogies, but it’s the form of the language that helps us differentiate them. For example, “the engine is the heart of an automobile” is a metaphor, but it uses the same structural alignment of the analogical comparison that we mentioned above.

Nonetheless, not every metaphor is of this sort. Consider, for example, the verse (48:10) “God’s hand is over their hands” from the Qur’an; this was revealed in connection to some 1,400 believers’ pledging allegiance to Prophet Muhammad, peace be upon him, under a tree in Hudaybiyah in year 628 by giving their hands to him. Whatever “God’s hand” in this verse refers to, whether it is to His power, His victory, His protection and blessings for the believers, or His acceptance of their pledge, it is far from being a physical hand. Therefore, we can not imagine a relation between dissimilar objects (Gentner 1982, 109; Gentner 2001, 204) that is mapped to the relation (Hand, God) under a structural alignment using SMT.

Literal similarity: If there is a considerable number of common attributes that are shared by the objects of the domain and the target then the comparison is more likely to be a literal similarity (Gentner 1982, 110). For example the comparison in the following verse of the Qur’an is a literal similarity: “Indeed, the example of Jesus to God is like that of Adam. He created him from dust; then He said to him, “Be,” and he was” (3:59). In this example there are a great number of attributes that Jesus and Adam (peace be upon them) share but only one of them is the subject of the comparison here, which is that both Jesus and Adam had no father. If Jesus also had no mother this would be an “identity,” not a similarity (Gentner 1982, 110).

The statement “Jesus is like Adam” makes much more sense than “Jesus is Adam,” even if we make it clear in what sense we use this identification. Typically metaphors use the word “is” and literal similarity comparisons (similes) use either of the words “like” or “as.” Mathematically speaking, if metaphors are equalities, then similes are approximations (Casnig).

Even though metaphors are substitutions, they are not necessarily “two-way” identifications. In other words, most of the times they are asymmetric; i.e., there is a sense of direction in the “identification.” For example, we never substitute a car in the place of a lemon and say “this lemon is a car.” This is because the first and foremost requirement of any comparison is that it be informative. What information do we obtain from the statement “rose is love” or “iron is fist”? In that respect many metaphors are irreversible, like similes: “a butcher like a surgeon” is quite different than “a surgeon like a butcher.” One is a compliment but the other is not! (Gentner 2001, 224). Perhaps irreversibility can also be taken as a distinguishing character of (at least attributional) metaphors.

Mathematical and metaphysical examples: Although there is no consensus on how mathematical ideas come about, it is certain that they are introduced into our world of knowledge by symbolism. Whether we associate a symbol to something physical, such as the symbol 70 to the weight of an object or the letter g to gravitational force, or to an abstract mathematical concept, such as the letter i to √–1, we are substituting one thing to mean another thing. We even associate symbols to concepts we cannot even describe, such as the concept of infinity and the symbol ∝ that is used to represent what it signifies in mathematics. From this perspective, mathematical symbols can be viewed as metaphors (Pimm, David 1981).

On the other hand mathematical formulas preserve the relations among the objects or concepts that they represent. In that respect, it is possible to see them as analogies as well. Therefore, they can be subjects of structural alignment. In the next example we will use SMT to form an analogical comparison between infinity and human life in order to better understand a Qur’anic verse.

In verse (5:32) of the Qur’an reads: “…he who kills a soul unless it be (punishment) for murder or for causing disorder and corruption on the earth will be as if he had killed all humankind; and he who saves a life will be as if he had saved the lives of all humankind…”

In a sense this verse means “one equals many.” How can that be? How can one be equal to a million? Or a billion? Those who know something about mathematics with infinities will remember that it is a quite different thing from mathematics with ordinary numbers. For example, if we add two infinities we still get infinity, i.e., ∝+∝=.∝=∝, something that never happens with any finite number, except for 0 (0+0=2.0=0). Likewise, if we add any number of infinities together we still get infinity: ∝+∝+∝+…∝=∝.Therefore, for any positive number m if we write m.∝=∝ it would be a perfectly acceptable mathematical statement.

Now, everyone will agree that there is no value one can associate to human life. Therefore, it’s fair to say that the value of human life is infinite. Let’s map “∝” to “saving the life of one person” under a structural alignment and let counting people in the target correspond to adding infinities in the domain. Now, if m represents the total number of lives on earth then what element should we associate to saving them altogether? The answer is m infinities added together, in other words m.∝ But seeing that m.∝ is equal to ∝ we can say that saving the lives of all people on earth is no different than saving the life of one individual! That’s how one can equal many. Now, if we map “killing an innocent person” to “–∝” then we clearly see that the mathematical statement m.(-∝)=-∝translates into “killing all innocent people on earth is as grave a sin as killing one.”

Note that this “one equals many” situation is not a violation of the requirement that structure mapping be one-to-one (Gentner-Markman 1997, 47). It’s a relation that occurs between the objects of the domain and the objects of the target and that relation is preserved under a one-to-one structure mapping.

Another relation between infinities is that “∝-∝” is indeterminate. In particular “∝-∝” is not necessarily 0. Using the analogy we just constructed we can translate this as “killing one innocent person and saving the life of another does not balance out.” Then, “∝-∝” is indeterminate” translates as “we cannot know if God will forgive that person for saving a life or punish him/her for taking one; it depends on which ∝ is greater!” Indeed, those who have taken calculus will remember that “∝-∝” sometimes turns out to be a positive number and sometimes a negative number; as well as 0 or ∝ or -∝

One could ask, what about m.0=0? Isn’t this also true? Yes, indeed “the sum of m zeros is equal to zero” is another mathematically accurate statement. Then, what meaning could this equation be given? Perhaps this would be the “murderer’s” version of the Qur’anic principle that we mentioned above: “When the life of an individual has “no value” in your heart, killing one person or a million people should be equally disheartening (!)”

Another mathematical tool that would be helpful in interpreting the above-mentioned principle is a technique that is used in mathematical proofs. When proving a fact about a set of elements in mathematics one proves it for an arbitrarily chosen member of the set and it is automatically generalized to the rest of the elements in the set. For example, in order to prove the statement “the square root of every prime number is irrational” we choose a prime number, say p, arbitrarily and prove the statement for it. Once we do that it is as if we proved that √2 is irrational, √3 is irrational, √5 is irrational etc. It covers all the numbers in the form √p, where p is a prime number. In the same way, when one kills an innocent person the message that it is acceptable to kill “any” innocent person is given, as the choice of person has been made arbitrarily. Therefore, this can be likened to killing all of mankind because being able to kill one person is simply generalized to all people who could be in that person’s shoes.

Summary: In this article we have given examples of analogy, metaphor, and literal similarity and have tried to indicate some distinguishing characters that set them apart. We included some uncommon metaphysical phenomena which have been placed in analogical correspondence with mathematical quantities with the intention of showing that mathematics can be used to shed light on purely religious concepts as well.

Yusuf Ziya Gurtas is an assistant professor of mathematics in Queensborough Community College, CUNY.

References

• Casnig, John D. 1997–2009. A Language of Metaphors. Knowgramming.com. Kingston, Ontario, Canada.
• Gentner, Dedre. 1982. “Are scientific analogies metaphors?” in David S. Miall (Ed.), Metaphor, Problems and Perspectives, Brighton, England: Harvester Press, pp. 106–132.
• –. 1983. “Structure-Mapping: A Theoretical Framework for Analogy.” Cognitive Science, 7, pp. 155–170.
• –. 1988. “Metaphor as Structure Mapping: The Relational Shift.” Child Development, 59, 47–59.
• Gentner, Dedre & Markman, Arthur D. 1997. “Structure Mapping in Analogy and Similarity.” American Psychologist, 52, 45–56.
• Gentner, Dedre, Bowdle, B., Wolff, P., & Boronat, C. 2001. “Metaphor is like analogy” in D. Gentner, K. J. Holyoak, & B. Kokinov (Eds.), The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: MIT Press, pp. 199–253.
• Gentner, Dedre & Bowdle, Brian F. 2005. “The Career of Metaphor.” Psychological Review, 112, pp. 193–216.
• Lakoff, G., & Johnson, M. 1980. Metaphors We Live By. Chicago: University of Chicago Press.
• Pimm, David. 1981. “Metaphor and Analogy in Mathematics.” For the Learning of Mathematics, 1, 47–50.
• Runde, Volker. 2000. “The Banach-Tarski Paradox or What Mathematics and Miracles Have in Common.” in the Sky, 2, 13–15.
• Szabo, A. 1978. The Beginnings of Greek Mathematics. Dordrecht, Holland: Reidel.

Metaphors also play an important role in science. Cognitive scientists, who continue to research how language evolved and which tools the mind uses during this process, state that metaphors are widely used tools. Scientists use language, as well as graphs and equations, to explain their models. Therefore metaphors are essential in learning and teaching science. In this article, we will present a few examples of metaphorical thinking in science and how it guides science in new directions that could lead to breakthroughs. We will be concerned mainly with the machine metaphor that affected the way we picture the world.

A short history

Metaphor derives from the Greek verb methaphora (to transport or transfer). George Lakoff, professor of linguistics at the University of California”Berkeley, and philosopher Mark Johnson explain the essence of metaphor as understanding and experiencing one kind of thing in terms of another. We generally use analogies to make less familiar things appear in guises that are more familiar to us. For example, we try to picture time by associating it with a river. Chemists extend their knowledge of a poorly understood compound by finding similarities with familiar compounds. Biologists use biological mechanisms found in organisms to understand similar mechanisms in others. Luigi Galvani associated the transmission of nerve pulses to an electric current.

Metaphor can be defined as the mapping of a source domain onto a target domain. Throughout the history of science, water waves were used prototypically for understanding light waves. People tried to understand light (target domain) in terms of water waves (source domain). This mapping forced scientists to search for a medium”ether”that could propagate light waves, for water waves were propagated in water.

According to the English physicist Norman Campbell, every scientific theory requires the use of models to understand theoretical terms. For example, in order to comprehend the kinetic theory of gas, we must resort to an analogue model gas behaving as if it were composed of point particles randomly moving in a vessel. Metaphorical models help to improve the scientific imagination. But for scientists to take a model seriously, it must be expressible in terms of mathematical equations.

Sometimes, the symbolic representation of a mathematical relation can lead to a metaphor. For example, the space is time metaphor has an interpretation in molecular biology where millions of years (time) are encoded and contained in DNA (space). In addition, metaphors offer insight into mathematical phenomena. The basic example is the number line, which is the result of imagining numbers as points on a line.

The machine metaphor

From the seventeenth to the nineteenth centuries, the dominant metaphor was the machine metaphor: The world is a machine. This connection was made by Galileo (d. 1642), Descartes (d. 1650), Boyle (d. 1691), and Newton (d. 1727). They imagined the universe as a static, predictable machine. This worldview influenced our beliefs and psyche, as well as the way scientists, philosophers, and other intellectuals thought. Scientists started to think of everything in terms of a machine. Muscles were considered to be force-generating machines, nerves to be electronic machines, and photosynthesis to be a solar-powered machine. Lord Kelvin (d. 1907) characterized the universe as a galactic heat engine.

The machine metaphor led to reductionism in philosophy: If we wish to understand how a machine works, we look into its component parts. Descartes’ analytical method of reasoning is based on the assertion that complex phenomena can be understood by reducing them to simple phenomena. Biologists tried to understand living organisms, as well as bodily motions and functions, by reducing them to their constituents. More research was devoted to understanding the nature of genes. Physicist reduced gases’ properties to the motion of atoms or molecules. Locke (d. 1704) attempted to understand society by observing the behavior of individuals.

With the picture of a perfect world-machine, belief in a Creator became a logical necessity, since the machine implies an engineer. Even children know, as a part of their personal experience of reality, that a house implies a builder and a watch a watchmaker. As they study the more intricately complex nature of the human body or the ecology of a forest, it is highly unnatural to tell them to think of all these systems as chance productions of irrational processes.

Theologian William Paley (d. 1805) expressed this creationist view on page 98 of his Natural Theology as: There cannot be a design without a designer; contrivance without a contriver; order without choice; arrangement without a thing capable of arranging … Arrangement, disposition of parts, subserviency of means to an end, relation of instruments to use, imply the presence of intelligence and mind. This Cartesian philosophy connoted the idea that The Hand of God had set the machine in motion at the beginning of creation. As everything had been determined by God already, nothing could be the result of chance. This view is known as determinism.

The computer metaphor

The computer, the current dominant machine, has become the modern era’s dominant metaphor. Visionary physicist Edward Fredkin characterizes the universe as a cosmological computer. The universe appears as a network of a dynamic whole whose parts are essentially interrelated. Modern physicists do not consider the atom a basic building block; rather, it is a web of relations that includes human consciousness in an essential way. Modern biologists describe cells as distributive real-time computers. Making good use of the computer metaphor, they focus more on how neurons work together and how each cell interacts with its environment.

Sociologists study individuals and their social relationships. Psychologists and cognitive scientists use the analogy of a computer to understand the mind. Artificial intelligence is just one consequence of such modeling. The universe is no longer seen as a simple mechanical machine, but as a more complex high-tech computer system.

The computer metaphor supports the view of a dynamic universe more than Newton’s static universe. James Maxwell’s (d. 1879) electrodynamics, the second law of thermodynamics (entropy), and Darwin’s (d. 1882) theory of evolution all involve dynamic concepts. Entropy describes the evolution of inanimate matter and states that inanimate systems tend to go from order to disorder. Entropy is an increase in disorder became a root metaphor at the beginning of the nineteenth century.

Biologists describe evolution as a movement toward increasing order and complexity. Darwinian theory attributes biological complexity to the accumulation of mutations by natural selection. One factor that makes Darwinian theory a naturalistic philosophy more than an empirical science is its claims that all of these dynamic processes are a result of random chance. Natural selection is introduced as the mechanism that minimizes the effect of chance. According to Darwinism, probability governs the universe and there is no need for God.

There are probabilities in the quantum world as well. However, probability and uncertainty show the unpredictability of the outcomes of quantum measurements from a human perspective. This probabilistic vision of universe, contrary to Darwinian theory, deepened the consequences of the machine metaphor: God not only set the machine in motion eons ago, but is still governing the process of creation and changing the probability pattern.

Metaphors and paradigm shifts

According to Thomas Kuhn (d. 1996), metaphorical thinking becomes crucial at periods of scientific revolution and gives way to a paradigm shift. Distant analogies are probably the most useful in times of scientific revolution: Newton’s metaphor of an apple is a moon is of this kind. However, this metaphor became literal after it was understood that the same gravitational force that holds the apple to Earth is the same one that holds the moon in its orbit around Earth.

Kuhn’s paradigm shift and use of metaphors can best be seen in the history of exploring the atom. The atom was conceived first by Democritus (d. c. 370 BCE) as an impenetrable sphere. This analogy was used to explain the behavior of matter until the nineteenth century. Spherical analogy was discarded in favor of Ernest Rutherford’s (d. 1937) analogy between the solar system and the hydrogen atom.

The following interpretations followed the planetary model: The nucleus is more massive than the electron (just as the sun is more massive than the planet), the nucleus attracts the electron, this plus the mass relation causes the electron to revolve around the nucleus, and so on. Object descriptions are disregarded, for there is no attempt to match the nucleus with the sun in color, size, or temperature. Then, the atomic nucleus was analogized to a drop of water instead of to a body like the sun.

Now, in quantum mechanics, every particle is considered to be a probability wave, which is an abstract mathematical quantity. Scientists have not yet been able to put these waves into a metaphorical pictorial model, which makes them difficult to comprehend.

Metaphors in revealed texts

The following Qur’anic verses illustrate the use of metaphors in the Qur’an. Speaking of hypocrites who do not believe in God but nevertheless claim to believe, it states: Their parable is like the parable of one who kindled a fire, but when it had illumined all around him, God took away their light and left them in utter darkness”they do not see. Deaf, dumb (and) blind, so they will not turn back. Or like abundant rain from the cloud in which is utter darkness and thunder and lightning. They put their fingers into their ears because of the thunder peal, for fear of death, and God encompasses the unbelievers. The lightning almost takes away their sight. Whenever it shines on them they walk in it, and when it becomes dark to them they stand still. If God had willed, He would have taken away their hearing and their sight. God has power over all things. O people, serve your Lord, Who created you and those before you so that you may guard (against evil) (2:17-21).

Conclusion

Logic and mathematics are not enough to understand science. We need internal mental pictures to grasp new phenomena. When trying to understand unfamiliar phenomena, the mind thinks of them in metaphorical terms. This not only helps to explore new realms for scientific theories, but also can change the view we hold of the world.

References

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• Hesse, Mary. Models and Analogies in Science. University of Notre Dame Press: 1966.
• Belal A. Baaquie and Lai Choy Heng, Department of Physics, National University of Singapore Method and Anti-Method in the Sciences: Metaphors and Scientific Creativity. http://www.scholars.nus.edu.sg/natureslaw/methodology/anti_method/11.html
• Lakoff, G. and Johnson. Metaphors We Live By. University of Chicago Press, 1995.
• Morris, Henry, ed. Scientific Creationism. 2d ed. Word Publishing: 1974.
• Paley, William. Natural Theology; or, Evidences of the Existence and Attributes of the Deity. Online at: www.hti.umich.edu.