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.

There are seven chapters in the book. The first chapter summarizes the basic tenets of the classical narrative, then criticizes it listing many questions which the classical narrative cannot satisfactorily answer. Islamic civilization’s contribution to the development of modern science is so immense that it is impossible to completely ignore this part of the history in any serious discussion of the general history of science or civilization. The problem arises in assessing the importance and the nature of Islamic science. Generally accepted views of the classical narrative go something along these lines: Islamic civilization was a desert civilization and began to develop scientific thought only when it came in contact with more advanced civilizations (Persian, Indian and Greek and most importantly Greek). A vital component of the rise of science in Islamic civilization was the remarkable translation movement that took place during the early period of Abbasid times (750–900 CE), in which many important scientific books of other civilizations, particularly those of ancient Greeks, were translated into Arabic. The classical narrative says by learning Greek science through this translation activity, Islamic science reached its golden age while Greek science was neglected under Byzantine rule. Adherents of the classical narrative generally assume that Islamic civilization did not go much beyond translation, did not make original contributions to scientific knowledge or produced any new science of its own. They also assume this period of the golden age did not last long and came to an end with Ghazali’s “attack” on philosophers in his major work Tahafut al-Falasifa (The Incoherence of Philosophers). They assume that Islamic science began to decline with Ghazali while there was an awaking in Europe, sometimes called the Renaissance of the twelfth century, when Europeans began to translate major Arabic philosophical and scientific texts into Latin. Some of these texts had already been translated from much earlier Greek and Sanskrit texts into Arabic. So, they reconnected with their Greco-Roman legacy. The classical narrative says from that point on Europe had no need for Islamic science, hence the role of Islamic civilization was to simply translate and preserve the ancient Greek science and make it available to Europeans later. Thus, according to this view all the roots of modern science were European. The classical theory also attempts to explain the process by which the acquisition of Greek science by the Muslim world occurred. There are a few versions of this proposal which are called “contact theory,” “pocket transmission theory,” and “translation through Syriac medium first.”

In this first chapter of the book, Saliba argues that the classical narrative is an oversimplification of what actually happened in reality and fails to answer many fundamental questions. The first problem is about origins. He argues none of the proposed methods of translation is convincing to explain the reasons why, how, and when Muslims acquired Greek science. In terms of the nature and quality of translations, Saliba gives examples of sophistication and maturity exhibited by the Muslim scientists that is well beyond what would be expected from an early generation of translators who are struggling to understand a foreign science. Moreover, already in the early period of the translation movement Muslim scientists produced original new science such as algebra by al-Khwarizmi (830 CE), remarkable advances by Habash a-Hasib (850 CE) in the field of trigonometry and mathematical projections that go far beyond what was known from Indian and Greek sources, and developed decimal fractions. He argues such advances could not happen suddenly. There must be a longer tradition of scientific activity in the Islamic world and real motivations for the rise of science which cannot be explained by the classical narrative.

Not only does the classical narrative fail to explain beginnings but also more recent developments as well. Saliba gives many examples from various scientific disciplines to show that the Islamic science did not decline after Ghazali. Astronomy is a perfect counterexample to this thesis of the classical narrative, and it is not the only one. In fact, there were so many advances in astronomy in the Islamic world after Ghazali that Saliba calls the post-Ghazali period as the golden age of Islamic astronomy. Recent research in the second half of the twentieth century shows that astronomy has particularly interesting connections to the European Renaissance. Saliba comments that post-Ghazali works by the Muslim scientists were not sufficiently considered by the adherents of the classical narrative because of their pre-supposition that no significant science of any interest could have been produced in this period. This caused unfortunate damage in terms of understanding the post-Ghazali period in the Islamic world as well as the European Renaissance itself.

In the second chapter, Saliba proposes an alternative thesis/narrative to the classical narrative in terms of the beginnings of the rise of scientific activities in the Islamic world. His thesis is based on the writings of Al-Nadim (full name Abu al-Faraj Muhammad b. Abi Ya’qub Ishaq al-Nadim) who wrote about intellectual history of the early Islamic period. Saliba also supports his thesis with well known historical facts. In summary, the alternative narrative proposes that there was already a significant amount of interest and activity in the nascent Islamic civilization before the translation movement began. Rather than learning science from others (Greeks) just because they came into contact with them, the Islamic world actively sought those sciences because of a keen interest to advance their own scientific knowledge. Unlike the classical narrative, the alternative thesis argues that Muslim scientists already had a high level of knowledge and maturity when the translation activities began. This is evidenced by the high quality of translations of highly technical materials, and corrections of errors in the original sources. The main societal factors for the rise of science in the new civilization are listed as a) the need for people (bureaucrats) with a high level of scientific knowledge in administrations, and b) competition between those people to acquire higher levels of scientific knowledge to be able to advance in the ranks of governments.

In the next chapter, Saliba gives detailed examples, mostly from astronomy, to show how critically Muslim scientists received and reacted to the Greek science. They noticed observational errors and internal inconsistencies in Greek texts. They also pointed out more philosophical and foundational errors and contradictions. Muslim scientists showed a high level of sophistication, maturity and critical spirit. They had a comprehensive look at the Greek texts they translated and studied them in relation to one another. Saliba argues that it is not possible to explain these phenomena with the classical narrative. Moreover, Muslim scholars went beyond just criticizing these errors and made many novel contributions to exact sciences. In the process, they realized the proper place of mathematics in the natural sciences. Saliba also comments that Muslim scientists continued to make original contributions to astronomy and other mathematical sciences long after Ghazali, when the classical narrative would preach the death of Islamic science.

In chapter four, Saliba gives examples of critical innovations by Muslim astronomers. He remarks that the interest of the Islamic society in astronomy was very strong due to many religious requirements that need to be answered by astronomy, such as visibility of the moon, daily prayer times, and qibla (direction of worship) etc. Such problems were not considered by Greeks before. Muslim astronomers could not ignore absurdities in Ptolemaic astronomy where mathematical models in Almagest violated the fundamental cosmological assumptions in Planetary Hypotheses. Although Ptolemy’s mathematical models usually made good predictions computationally, it was not satisfactory for the scientists in the new civilization to allow those models to violate the physical properties of the celestial bodies. They took it upon themselves to propose alternative mathematical models that satisfied both requirements. They were highly successful in that quest. The solution of this problem required some new mathematical theorems. Two of the most important of such theorems were Urdi’s Lemma and Tusi couple invented by Urdi and Nasir al-Din al-Tusi in the thirteenth century. Both of these were fecund and fundamental theorems that were used repeatedly by many astronomers who followed them for a long time. Renaissance astronomer Copernicus was among those who made use of these theorems. Also noted in this chapter is Shams al-Din al-Khafri’s understanding of the role of mathematics in describing the physical phenomena.

The title of chapter five is “Science between Philosophy and Religion: the Case of Astronomy,” wherein Saliba considers the relationship between the religion of Islam and scientific developments in astronomy. He explains that religious motivations led to the creation of new disciplines such as ilm al-hay’a (science of configuration) and advances in trigonometry. He states that astronomy and trigonometry are the best examples which demonstrate the intersecting interest between the practice of a religion and scientific thinking that need to be developed as a result of that practice. Many important scientists in medieval Islam were at the same time religious authorities. A few examples among such scholars are Ibn al-Nafis, Nasir al-Din al-Tusi, Qutb al-Din al-Shirazi and Ibn al-Shatir. Saliba also notes that the European paradigm of conflict between science and religion does not exist in the Islamic world.

“Islamic Science and Renaissance Europe: The Copernican Connections” is the title of chapter six. Researchers in the second half of twentieth century first realized that many of the astronomical models of Copernicus were identical to that of Ibn al-Shatir from three centuries earlier. This surprising discovery, which contradicted the view that Renaissance science was a European self-contained creation, opened the door for further investigations which revealed more surprising outcomes. The mathematical theorem called the Tusi couple that is mentioned above plays an important role in Copernicus’s model. Copernicus stated the theorem and proved it in 1543 without mentioning that he invented a new theorem or saw it in any other source. The theorem was first invented and proved by Tusi in the middle of the thirteenth century. By comparing the two proofs, W. Hartner noticed in 1973 that Copernicus’s proof was identical to Tusi’s. He even used the same letters for essential geometric points. That is where Tusi used the Arabic letters “alif,” “ba” etc. Copernicus used the corresponding Latin letters “A,” “B” etc. This discovery makes it pretty certain that Copernicus knew about Tusi’s work.

Saliba shows Copernicus’s case is not an isolated instance and gives more evidence in this chapter of the phenomenon that “there are much too many coincidences of ideas appearing first in Arabic texts usually written between the 12th and 15th centuries, which reappear, without much explanation, in Latin sources of the 16th and 17th centuries.” Saliba’s explanation of this phenomenon is that by the Renaissance time men of science themselves learned Arabic and no longer needed translations. There are many examples that show European reliance on Arabic sciences in the post-Copernicus period when the whole worldview was supposed to have been changed by him. Renaissance men of science had a high regard for the Islamic sciences and were looking to the Islamic world for the latest in scientific activities rather than the classical Greek sources.

In the last chapter Saliba discusses the age of decline in Islamic science. He starts by rejecting the two main reasons proposed by the advocates of the classical narrative and argues that it did not start after Ghazali (eleventh century) or the destruction of Baghdad by Mongols in 1258. Saliba says that those who believe the first reason look at the Islamic civilization as a source of religious thought only and operate under the assumption that the European paradigm of conflict between religion and science applies to Islamic world as well. Saliba argues that this assumption is not true for the Islamic world and that scientific activities did not decline after Ghazali. Those who think the main reason was the destruction of Baghdad by Mongols saw the Islamic civilization mostly in political terms and paid little attention to its intellectual history. Saliba gives many examples of high quality and sophisticated scientific production in the Islamic world, mostly in astronomy but in other areas as well, well after both of these events. He says those examples were ignored or not properly read by the adherents of the classical view who did not expect to find any important scientific production in the Islamic world after the thirteenth century.

There still remains the problem and timing of decline of science in the Islamic world. When did it happen? Saliba notes that decline is a relative concept. What actually happened was the European science advanced more rapidly than the rest of the world after the sixteenth century. Hence it looked like science declined elsewhere, including the Islamic world. According to Saliba the main reason for these rapid developments in science in Europe was related to the discovery of the “new world.” He argues that the wealth and resources obtained by Europeans as a result of discovery of new lands helped them fund scientific activities. Europe witnessed the rise of royal and scientific academies where most educated men of the time were assembled and engaged in scientific research without having to worry about financial needs. Healthy competition among these institutions led to new scientific discoveries. Western superiority in science continues to this day and the constant brain drain that feeds the West at the expense of the developing and third worlds does not help to change the balance.

In summary, this book presents fundamental challenges to many of the commonly held views about the intellectual and scientific history of the Islamic world and proposes alternative explanations. The science of astronomy is used as a template to test and justify these claims. The author invites researchers to subject his proposals to the test of historical data in other disciplines as well. This book is highly recommended to all interested in the general history of science, and that of the Islamic world and the Renaissance period in particular.

Nuh Aydin is an associate professor of Mathematics at Kenyon College, Ohio, USA.

Use of redundancy in human communication

We make use of redundancy that is present in human language to correct errors. This happens in both oral and written communication. For example, if you read the sentence “There is a miscake in this sentence,” you can tell that something is wrong. So we can detect an error. Moreover, we can even correct it. We are achieving two things here: error detection and error correction. What are the principles that we are using to achieve these goals? First, because the string “miscake” is not a valid word in English, we know that there is an error. Here, the redundancy manifests itself in the form of the fact that not every possible string is a valid word in the language. In a sense, some strings are wasted: potentially they could have been used as words of a language but they are not. The benefit of this “wastefulness” is that it lets us detect or correct errors in communication. Secondly, the word “miscake” is closest to the valid word “mistake” in the language, so we conclude that it is the most likely word intended. Of course, we can also use the context and meaning to detect and correct errors but that is an additional feature, not available to computers. If you enter the string “mistaky” to Merriam-Webster online dictionary, ¹ it cannot find an entry for it; however, it comes up with a list of suggested words, first of which is “mistake.” So the computer is telling us that “mistake” is the most likely word intended because it is closest to the given string. This is called the maximum likelihood principle. As I type this article on my computer I witness many instances of this principle used by my word processor. For instance, when I mistakenly typed “fisrt” it automatically corrected it to “first.”

There are also other ways redundancy is used in natural languages. As already pointed out above, redundancy in context often enables us to detect and correct errors, vagueness and ambiguities. When humans communicate, redundancy, either explicitly introduced by the speaker or author or built into the language, comes into play to help the audience understand the message better and to overcome such obstacles as noise, accent, hearing difficulties, and so on. Shetter [4] gives a number of examples in which redundancy is manifest and useful in languages. We include a few interesting examples from his article here.

1. If we strike out all the vowels in a sentence, “xt slxws yxx dxwn bxt thx sxntxncx xs stxll lxgxblx, xsn’t xt”? (Can you read the part in quotes?) Since the consonants seem to be giving us most of the information we need, there must be a lot of redundancy here too.

2. The sentence “These three dogs are retrievers” shows grammatical redundancy in forms: plurality is expressed multiple times. Examples in other languages are just as easy to find, for instance, obligatory gender agreement in a language such as Spanish: La unica otra senora venezolana “The only other Venezuelan lady.”

3. A language’s stock of words (called the lexicon) shows a lot of redundant overlapping. To be convinced of this, all you have to do is to grab a thesaurus and look up a few words (big, little, fat, to die) that have lots of near-synonyms with only small stylistic differences.

4. Even the way languages are written is highly redundant. Try another experiment: take a piece of paper and cover up the LOWER HALF of all the letters in any sentence you have not read yet. If it is not significantly harder to read, that means that a lot in the shapes of the letters is redundant (could you still manage to read with 2/3 covered?).

Mathematical use of redundancy in digital communication

As we see, redundancy is present and useful in human languages in a number of different ways. Engineers have considered the question of whether computers can use some of the same principles to achieve error detection and correction in digital communication. Since computers have very limited capabilities compared to humans, for example they cannot make sense of words, it is the method of explicitly adding redundancy to original messages (as opposed to using the context) that can be used to achieve this goal in computers using the precise language of mathematics.

To illustrate the use of redundancy in a mathematical way in digital communication systems, consider the following example. Suppose we want to communicate with another party in a simple manner: sending messages that represent Yes or No, Let us agree that a 1 represents Yes and a 0 (zero) represents No. Unfortunately, there is often noise in the communication channel which may distort messages by flipping the binary bit (a 0, or a 1). If we just send the messages as they are, do we have any way of knowing if an error occurred during the transmission? Note that the reason we can do nothing against errors is that all possible strings (that all have length 1 in this simple example) are valid codewords. Codewords in digital communication correspond to valid words in a language. Compare this to the earlier example about correcting the typo in the word “miscake.”

Data of any kind is stored and processed as binary strings, that is strings of 0s and 1s, in computers. Every letter has an ASCII code. For example, the ASCII code of the letter “A” is 01000001. Typically, data consists of billions of bits. A bit is a 0 or a 1. To employ redundancy, data is broken into blocks of a fixed length. We now consider and compare several encoding schemes where the block size is 4.

Scheme 1: Perhaps most intuitive way of adding redundancy is simply to repeat the original message. Instead of sending 1011, we send 10111011. Here 1011 is the original message and 10111011 is the codeword. The string obtained after adding redundancy is called a codeword. What does this scheme buy us? Do we get any error detection or correction capability? If you think about this for a moment, you can see that if there is a single error, then it can be detected. We simply break the received word in half, and compare the two halves. If there is exactly one error, the two halves will not be the same. We also note, however, that we cannot correct any errors. Also, if the number of errors is 2 (or even) we may not be able to detect that, depending on the location of the error.

To quantify what we gain by employing an encoding scheme, let us assume that the probability of a bit error for a channel is 0.001, and there are about 3000 bits on a page. If we do not employ any encoding scheme, we expect to have an average of 3 words in error per page. If we employ this scheme though, there must be at least 2 errors per word in order for an error to go unnoticed. This improves the expected number of incorrect words to 1 in about 50 pages. Can we do better?

Scheme 2: This scheme repeats everything 3 times. So the original message 1011 is encoded as 101110111011. What are the pros and cons of this scheme? It is not hard to see that not only can we detect single or double errors; we can also correct single errors by using the “majority opinion.” This improvement comes with a cost though: only 1 out of 3 bits sent are information bits (so 2 out of 3 are redundancy bits). We say that the rate of this code is 1/3. The rate of the previous code was 1/2. With this improved error correction capacity, the expected number of incorrect words is 1 in about 6250 pages.

Scheme 3: This is a well-known and commonly used encoding scheme that adds a single parity check bit at the end so that the number of 1’s in the resulting codeword is even. Therefore, the original information 1011 is encoded as the codeword 10111. Another way of describing this method is that the modulo 2 sum of all bits (including the redundancy bit) is 0. In modulo 2 arithmetic 1+1=0. It is easy to see that this scheme detects any single errors, but cannot correct any.

Scheme 4: This is also a well-known example of an error correcting code that was one of the earliest codes designed. It was discovered by R. Hamming [1]. In this scheme 3 bits of redundancy are added to the information bits. The first redundancy bit, or the fifth bit of the codeword, is the sum of the first, second, and fourth bits. The next redundancy bits are the sum of the first, third, and fourth bits. The last bit is the sum of the second, third and fourth bits. All sums are modulo 2. According to this scheme, the information bit 1011 is encoded as 1011010. Although it is not obvious, this code can correct any single error. Therefore, compared to the second scheme above, the Hamming code achieves the same error correction ability in a more efficient way: The information rates are 1/3 vs. 4/7.

Although codes used in practice are longer and more sophisticated, the basic principles are the same. These examples show that there are different ways of employing redundancy, some more efficient than others. The question is, therefore, not whether or not redundancy can be useful but how best to use it. Error correcting codes are used in a wide range of communication systems from deep space communication, to quality of sound in compact disks and wireless phones. Researchers are still looking for more efficient codes to make use of redundancy in more clever and useful ways. It is remarkable and surprising that a lot of theoretical mathematics can be used in the design of good codes. Some seemingly useless and abstract parts of mathematics are being used in very practical applications.

Other examples of “redundancy”

We have looked at the use of redundancy mainly in communication systems. But there are apparent redundancies in other places as well. For instance, the so called “vestigial organs” in humans and other living beings are an interesting topic of controversy. Initially, these organs were thought to be useless and non-functional. However, some functions of these organs have since been discovered. The German Anatomist R. Wiedersheim made a list of vestigial organs in 1895 which included approximately 100 organs, including the appendix and coccyx. As science progressed, it was discovered that all of the organs in Wiedersheim’s list in fact had very important functions. For instance, it was discovered that the appendix, which was supposed to be a “vestigial organ,” was in fact a lymphoid organ that fought infections in the body. This fact was made clear in 1997: ²

Other bodily organs and tissues-the thymus, liver, spleen, appendix, bone marrow, and small collections of lymphatic tissue such as the tonsils in the throat and Peyer’s patch in the small intestine-are also part of the lymphatic system. They too help the body fight infection. ³

It was also discovered that the tonsils, which were included in the same list of vestigial organs, had a significant role in protecting the throat against infections, particularly until adolescence. It was found that the coccyx at the lower end of the vertebral column supports the bones around the pelvis and is the convergence point of some small muscles and for this reason, it would not be possible to sit comfortably without a coccyx. ⁴

Another important example we would like to consider is repetitions in the Qur’an, the Muslim holy book. There are several historical events or divine decrees and commands that are repeated in many places in the Qur’an. Some have criticized this as redundant. However, this is a superficial view. The Qur’an is the word of the All-Wise Creator, who has wisdom in everything He does. So, there must be some wisdom behind these repetitions. Seventh-century Arabs were very skilled in literature and poetry. The literary masters of Arabic admitted and appreciated the miraculous eloquence and literary power of the Qur’an. The Qur’an challenged them to make something similar to it:

And if you are in doubt about what We have revealed to our servant, then produce a sura (chapter) like it. (Baqara 2:23)

They have since been unable to meet the challenge. They used to hold literary competitions where the best poems were chosen and exhibited on the walls of the Ka‘ba, and called the Seven Hanging Poems. The Qur’an demonstrated such eloquence that it caused Labid’s daughter to remove the poems from the walls of the Ka‘ba. She declared while doing so, “Besides the verses of the Qur’an these no longer have any value” [3]. When a Beduoin poet heard verses from the Qur’an, he bowed down in prostration before its eloquence despite the fact that he did not convert to Islam. All of this should make us search for the reasons and wisdom behind the repetitions in the miraculous divine book. Nursi gives a number of such reasons in The Words [3]. He says that since the Qur’an is a book of invocation, prayer and summons, the repetition is desirable, even necessary. Also, it speaks of such mighty matters of extraordinary importance that their repetitions are most appropriate. Two examples of verses that are repeated many times in the Qur’an are Which of the favors of your Lord will you deny? (55:13, repeated thirty times in Sura al-Rahman) and Woe on that day to the deniers (77:15, repeated ten times in Sura al-Mursalat). These verses proclaim before Earth, the heavens, the ages, and in the face of humanity and jinn, their ingratitude, unbelief, and wrongdoing. They also proclaim their violation of the rights of all creatures, which brings the heavens and Earth to rage, spoil the results of the universe’s creation, and indicate contempt and denial of Divine Sovereignty’s majesty. If these two verses were repeated thousands of times, in a universal teaching related to thousands of issues, a need for them still would remain. It would be conciseness in majesty and miraculousness of eloquence in grace and beauty [3]. For a more detailed account of the reasons behind repetitions in the Qur’an, we refer the reader to Nursi’s The Words [3].

Conclusion

We have seen many examples where redundancy is very useful. We have seen redundancy is inherently built into the natural languages we speak, and it serves a purpose. Inspired by this fact, we introduce redundancy explicitly into digital communication systems when we want to be able to correct errors caused by noise. We have seen other examples where what appears to be redundant or unnecessary at a first glance really serves a purpose, and hence is not really redundant. We have seen that there are repetitions in the Qur’an but they too serve a purpose. The Qur’an and the universe reflect each other. We see apparent redundancies in both, but in the end we understand that there is a purpose behind everything that may initially appear to be redundant; hence, we cannot really find anything in the universe that is truly redundant. Therefore, we should keep in mind that apparently redundant or useless things in the universe may have hidden treasures behind them. Given that the creator is All-Wise and has wisdom in everything He does, it is our duty to go beyond the surface and seek that wisdom.

Nuh Aydin is an associate professor of Mathematics at Kenyon College, in Ohio, USA.

Notes

1. http://www.m-w.com
2. http://www.darwinismrefuted.com/embryology_02.html#313.
3. The Merck Manual of Medical Information, Home edition, Merck & Co., Inc. The Merck Publishing Group, Rahway, New Jersey, 1997.
4. http://www.darwinismrefuted.com/embryology_02.html#313.

References

Richard W. Hamming, 1950. “Error-detecting and error-correcting codes”. Bell System Technical Journal. 29: 147-160

R. Pinch, “Coding theory: the first 50 years” http://pass.maths.org/issue3/codes/

Bediuzzaman Said Nursi, The Words, Sozler, 1992.

William Z. Shetter, “This essay is redundant”

http://mypage.iu.edu/~shetter/miniatures/redund.htm

The innovations implemented in nature have the potential to improve the way we do everything, from desalinating water, gluing things together, to streamlining cars. Where there is a design problem, there is a solution for it in nature created by nature’s Designer. We can distinguish the levels in biology that technology can be modeled after as i) mimicking the natural methods in the manufacture of chemical compounds to create new ones, and ii) imitating mechanisms found in nature. There are a few examples of biomimetic materials that are already part of our daily lives. Velcro, for instance, is a brand name of a fabric that consists of hook and loop fasteners used to connect objects. It was invented by Georges de Mestral, a Swiss engineer/inventor. The idea came to him after he took a close look at the Burdock seeds which stuck to his clothes and his dog’s fur on their daily walk in the Alps. He closely examined the hook-and-loop system that the seeds used under a microscope, and realized that the same approach could be used to join other things together. Velcro is commonly used in many different areas, such as in the automotive industry, clothing, shoe making, and for bringing rigid or soft surfaces together. The lotus, which possesses tiny wax crystals on the surface of its leaves, remains pristine and white, even in the midst of swampy, contaminant-rich conditions. For some, the lotus plant is even a symbol of cleanliness.

The lotus effect in material science is defined as the observable self-cleaning property found in the lotus plant. The characteristics of the lotus brought about a new application of biomimetics to the self-purification of surfaces, such as paints and roof tiles that maintain a clean surface like the lotus, by creating a surface that is similar to that of the lotus plants.1 The figure shows that dirt particles are unable to adhere to the paint and simply flow away with the rain. Everybody knows about the vivid colors of butterflies. But where does this color come from? One would naturally think that butterflies must use pigments, as in the paint industry. Actually, there are two fundamental mechanisms by which color is produced on butterfly wings. One leads to what we call ordinary color, and the second leads to the spectacular iridescent color. The ordinary color is due to the presence of chemical pigments, which absorb certain wavelengths and transmit or reflect others. The iridescent color is produced not by pigmentation, but by the interference of light due to multiple reflections within the physical structure of the material. The parts of a butterfly wing are shown in the Figure 3 in the following order, from left to right: Wing > Scales > Veins > Ridges. The size and periodicity of arrangement of the features on the wings causes interference with the visible light, creating color. Using this concept, structures and physical mechanisms that produce a shining color, like that found on the wings of butterflies, have been reproduced in carbon by an international team based at Allied Signal in Morristown, N.J. These highly periodically patterned novel carbon materials possess unique and potentially useful properties. 2 Another striking example that inspires design principles is the box-fish. These are rigid-bodied marine fish that live predominantly in shallow-watered, highly energetic, tropical reef environments. They are remarkably stable and agile swimmers.

They are able to maintain smooth swimming trajectories with minimal pitching, rolling, or yawing, even in highly turbulent waters. Moreover, they are capable of swimming rapidly (> 6 body lengths s-1), can spin around with a minimal turning radius, and can maintain precise control of their position and orientation.3 What applications could these types of properties be used for? In fact, one of the leading car manufacturers produced a bionic concept car that is based on the contours of the boxfish carapace and takes advantage of its drag reduction benefits. Not only the shape, but also the organizational composition of living organisms is highly advanced.

Therefore, great efforts are made to study and understand the formation of the hierarchical structures of these creatures. The shell of the abalone, for instance, is known for being exceptionally strong. It is made of microscopic calcium carbonate tiles that are stacked like bricks. Between the layers of tiles is a sticky protein substance. Even though calcium carbonate is one of the softest materials in nature, when the abalone shell is struck, the tiles slide, instead of shattering and the protein stretches to absorb the energy of the blow. Material scientists at the University of California, San Diego are studying the tiled structure for insight into stronger ceramic products, such as body armor. Researchers at Princeton, working on a grant from NASA, are analyzing the remarkable strength of abalone shells to help make impact-resistant coatings for thermal tiles. There are numerous groups that are working towards a better understanding of the structure and the governing mechanisms involved in the assembly of natural composite systems that have amazing mechanical properties. In synthetic composite structures, the hardness of the material is proportional to the inorganic/mineral content. However, there are striking examples of design in nature in which almost negligible amounts of minerals are used in a specially tailored environment, and very high levels of hardness, comparable to human dentine, can be achieved. An interesting example is sea-worms. Although mainly consisting of soft tissue, these worms have very hard jaws that have an exceptionally low amount of inorganic consistency. The jaw material is of particular interest because of its hard, lightweight and abrasive-resistant properties due to some gradient elements. The chemical surrounds and forms of these elements are not clear enough to be able to identify or mimic the arrangement/structure. These jaws, in addition to their extraordinary mechanical properties, are very good examples of natural gradient materials that have a perfect interface between the hard and soft tissues. Although many high-tech analysis techniques have been devised to understand how such a composite could be formed, particularly in highly unfavorable salty sea or ocean water, and how they have such great mechanical strength, the findings are still incomplete.

The information gathered is like the scattered pieces of a puzzle; to finish the puzzle, the missing pieces must be found with new advancements in analytical tools. What about mussels then? “If we have Batman and Spider-Man, why don’t we have any mussel super heroes?” asks Professor Herbert Waite of the University of California, Santa Barbara. Mussels may not be the biggest or the flashiest creatures in the sea, but they do one thing exceedingly well. They make a glue that lets them anchor themselves firmly to a rock and remain there-drenched by water, buffeted by the ocean’s waves. “I don’t know any other adhesive that can do that,” says Waite.6 Not only the glue, but the threads they make to attach themselves to the rocks are very significant in terms of both their composition and complexity, according to Niels Holten, who is conducting research on these systems at the University of California, Santa Barbara. These threads can elongate and relax with extraordinary mechanical flexibility under great impacts from ocean waves. The Waite group research on these thread cuticles reveals a very important aspect of material science, the significance of which has only very recently been understood: interface engineering. These threads have a very low amount, ca. 1-2 wt%, of metal ions in a polymeric matrix holding together large polymeric chains, which is possibly what gives the structure its flexibility and extensibility. Man-made structures cannot compete with the mechanical performance of these threads, especially at such a low volume of metal ion ingredients.

The ultimate goal of ongoing research is to understand the formation principles of these features so that similar structures can be made, using the same set of principles in laboratory conditions. In fact, the perfections of designs that are implemented in nature turn out to be an enormous fountain of ideas. Jewel beetles, which lay their eggs in freshly charred trees, can detect fires from miles away; the defense industry is studying these beetles for clues to design new low-cost, military-grade infrared detectors. Meanwhile, one of the leading car manufacturers is tapping the locusts’ famed ability to fly in dense swarms without colliding for a possible key to anti-collision devices in cars. And the Defense Advanced Research Projects Agency is funding development of a robot that can climb vertical surfaces, using the same principle that geckos use to walk up walls and saunter upside down across ceilings. There are several examples that could be given on this matter, but, due to limited space, we can only briefly summarize some of them. However, our understanding of the mechanism in nature is very limited, and it is expected that better insight will be gained with the advancement of available analytical tools. The great diversity of product designs in nature is produced from only a few common components, whereas we use a great number of materials and components to achieve new designs. Such high control and hierarchy in design in nature can only be attributed to an artist or designer who hides the perfection of his creation in the details. It is up to us to find out, see, and appreciate these perfections. Material scientists, of course, have the duty of transferring the findings from nature for the service of humankind by turning them into applicable forms in our daily lives.

Notes

1. Lotusan Paints. (2002). Retrieved 12 Nov, 2003, from http://www.lotusan.de Translated by http:// www.google.com.
2. Anvar A. Zakhidov et. al., Science, 282, 897 (1998).
3. URL: http://www.gharib.caltech.edu/bioinspired_ design/index.html
4. http://www.daimlerchrysler.com/dccom/0-5-7154-1-503504-1-0-0-503518-0-0-135-7145-0-0- 0-0-0-0-1.html
5. http://en.wikipedia.org/wiki/Abalone#_note-0
6. Anne Underwood, “Nature’s Design Workshop,” Newsweek, U.S. Edition, September 26 (2005).

What would it have to fear of the dogs or their barking?

The dogs continue to do what they are supposed to do

And the moon continues to beautify the face of the night.

A bit of weed floats on water

Yet the water does not lose its purity.

Mustafa¹ splits the moon in half

While Abu Lahab² utters silly curses.

Jesus revives the dead

While his enemies pull their beards out of hatred.

The sound of the dog never reaches the ear of the Moon,

If that moon is a friend of God”³

— M.J. Rumi, Mathnawi, “The Candy Seller Child (The Debtor Sheikh).”

The true “friends” of God reflect His light in their hearts, which have become like mirrors. Like the full moon on a bright night, they illuminate everything within their reach. They do not discriminate anyone; they can be called “champions of compassion without frontiers.” It is so difficult to contain light in a closed place, it seeps out and illuminates. Likewise, it is hard to confine the compassion of such people when they come in contact with others, their compassion and love touches, affects and transforms them. You cannot find any trace of the stereotypes of the idle or the harsh reactions of the conceited in them. They reach out and embrace. And the hatred, the misdemeanors, the biases, the bad habits, the doubts all dissolve and disappear within this embracing. In this article, we will present two examples of radiating compassion and love from the life of a famous scholar of Islam and a person of devotion, Bediuzzaman S. Nursi, and then turn to his inspiration for such outpourings.

Who was Bediuzzaman?

Said Nursi, also known as “Bediuzzaman” or “the wonder of the age” by his contemporaries, was born in eastern Anatolia (in modern Turkey) in a turbulent era towards the end of the nineteenth century.⁴ Earlier in his life, he was noted for his genius, unmatched scholarship and his balanced combination of Islamic spirituality with the duties of contemporary life. Over the course of his life, he inspired hundreds of thousands of students. Since his passing away in 1960, he has continued to inspire millions and his books remain as the bestsellers of all times in Turkey, as well as being translated into several languages. His main work, Risale-i Nur Collection (The Treatises of Light) is a collection of books that consists of more than 6,000 pages. This collection deals with topics such as logical arguments concerning the pillars of faith, the importance of worship, the significance of the Prophetic Tradition, the miracles of the Qur’an and the Prophet (peace and blessings upon him), consolation for the sick and elderly, treatments of perceived conflicts between science and religion, reflections on natural phenomena and the signs of the Hereafter, as well as perspectives of the believer and the disbeliever on the world and the consequences of these, among other matters.

The noteworthy stances of Bediuzzaman include his championing of representative democracy over monarchy and despotism among the tribes in Eastern Anatolia, as well as his support for republicanism, the marriage of natural sciences and theology, the complete rejection of gifts or donations, and his advocacy for dialogue among people of different faiths. He succeeded in securing funds from the Ottoman government of Sultan Reshad, as well as the subsequent Turkish Republican parliament, for the establishment of a university in eastern Turkey where theological and natural sciences would be integrated in a single curriculum.

Although Nursi supported the Anatolian resistance through his efforts in Istanbul, during the early years of the Turkish Republic, he was exiled by the government in fear that he might exert his influence on the people around him against the government. Though subsequent investigations failed to show any evidence for such political intentions, he ended up spending 25 years of his life in jail or in exile. In a piece he wrote later about these painful years, he said that he would not seek justice from God in the Divine court of the Hereafter if the people who had inflicted suffering on him had benefited from his works and died as believers.⁵ During these years, neighbors and witnesses reported in a collection of interviews published in Turkish that he used to spend most of his nights in prayers and remembrance, sometimes crying. In the prisons where he was held it was noticed that former criminals and killers, such as the so-called “Butcher Tahir” in the city prison of Afyon, were transformed into individuals who took care not to step on ants.⁶

In the following two stories, we will see examples of how this friend of God embraced people of diverse backgrounds and led them to become friends and fellow worshippers of God.

Bediuzzaman and the Two Famous Outlaws

During his exile in the city of Kastamonu, Bediuzzaman and his student from that town, Mehmed Feyzi, were climbing the skirts of the Karada€ (Black Mountain). Two famous outlaws had stopped to have something to eat by the road. Although these persons had been born into a Muslim community, they were living a wretched life full of crime and harassment. Mehmed Feyzi knew these people. They were notorious for their crimes around the city. Nobody dared say anything to them. Mehmed was worried about the safety of Bediuzzaman; so, he was praying silently for God to protect him.

Bediuzzaman walked by the men slowly, without saying anything to them.

The two outlaws looked at each other in surprise and one of them spoke:

–”Do you recognize this scholar?”

–”I do, indeed. I have heard that he is fearless. He is known for telling all the commandments of the Qur’an without hesitation.”

–”If that’s the case, how come he did not say a word to us?”

–”I think he thought it is of no use to try to teach anything to us. What does that tell you my friend? We are finished. We are doomed.”

The other one immediately grabbed the table with the liquor on it and threw it with all his power towards the mountain. And he proclaimed:

–”No my friend! We are Muslims and we will remain Muslims. We will clean ourselves of these sins; we will turn to God and obey His commandments. We will never mix in such dirty affairs again. Come, let’s go.”

The two men stood up and went to the public baths. After cleaning themselves they went straight to a mosque and sat down.

The members of the congregation were puzzled. They were pointing to the men and asking each other silently: “What are these guys doing here? What are they up to?” One of them asked the muezzin about them. The muezzin had heard about the incident on the mountain. He calmed them down and said: “Don’t worry. They have repented. They saw Bediuzzaman on his way to the mountain. They regretted what they have done and have come here to worship.”

Upon hearing these words, the congregation calmed down and continued with their duties. They had thought originally that these criminals had come to the mosque to kill people; they had not realized that the men had changed their lifestyle.

Bediuzzaman and the Gypsies

Bediuzzaman was exiled to the town of Emirda€. As they did every spring, the gypsies came from their dwelling places to the town and knocked on the doors, begging. Some of them were offered plastic utensils for laundry or household chores, goods that were no longer needed. They knocked on every door and asked, “In the name of God, please give us something.” They knocked on Bediuzzaman’s door as well. They did not know that the man who lived here was an old man exiled to the town with very little to live on.

Bediuzzaman opened the door and upon seeing who was there, he smiled. He gave them a piece of bread.

The next day, he was walking in the countryside with one of his students. He saw the gypsy tents and approached them. They immediately surrounded him and tried to kiss his hands. Some of them knew who he was. An older man among them approached Bediuzzaman and said: “Our teacher! We heard that you are a guest in this town. Please pray for us. We love you.”

Bediuzzaman replied: “Yes my brother. Indeed I love you too.” He put his hand on the old man’s back and continued: “You are among those who understand that this world is transitory. As nomads, you are my fellow travelers. I am a nomad like you.”

Upon reading incidents like the ones here, one wonders: Was Bediuzzaman the first devout Muslim to display such acts of compassion? Or did he have a teacher? And the answer is simple: He valued and championed the importance of the prophetic tradition of Muhammad, peace and blessings upon him; it was that very tradition⁷ that provided him with the source of his compassion that had no frontiers. Here is a striking example from the life of Prophet that shows the depth of this compassion:

The Mock Call to Prayer

Abu Mahzura tells his story:⁸ We were a group of 12 people and came across God’s Messenger on the road to Hunayn. When the time for prayer came, a muezzin began to recite the call for prayer. As he was reciting the words, we mocked him by repeating his words in a funny manner. I was leading the ridicule. The Prophet heard us and summoned us.

“Whose voice was it that I heard?” he asked. Nobody answered. He then listened to each of us individually and discovered that mine was the leading voice. He signed to the others to leave. He then turned to me and said: “Go ahead and recite the call to prayer.” I stood up with my head bowed down, but could not say anything as I did not remember the words. At that moment the Prophet was the worst person in my mind and the thing he was asking me to do was the worst thing to do. After seeing my silence, the Prophet taught me the words of the call to prayer, one by one. Then he gave me some money. He caressed my forehead, my face and breast and prayed “May God bless and protect you.” Then I asked, “O Messenger of God, would you allow me to make the call to prayer in Makka?” he answered, “I give you that permission.” At that moment, he was the most beloved person on earth to me.

This story illustrates beautifully the transformation of a man who was ridiculing something sacred to the believers into a different man devoted to serving the faith. With his compassion and patience, God’s Messenger had no trouble discovering and polishing a jewel. We can see a similar transformation in the incident of the man who urinated in the Prophet’s mosque.

The Man Who Urinated in the Mosque

In the Qur’an, God tells His Messenger: If you had been rough and hard-hearted with them, they would certainly have dispersed from around you (Al Imran 3:159). Indeed, the Prophet was known as the most compassionate and loving member of the community, and was able to balance these traits with his other roles as community leader and statesman. Abu Hurayra reported:⁹ A bedouin urinated in the mosque and some people rushed to beat him. The Prophet said: “Leave him alone and pour a bucket of water over it. You have been sent to make things easy and not to make them difficult.’’ Afterwards the Prophet called the man and gently explained to him that this was a place of worship and that it should be kept clean. Apparently, this person understood the point, for he was later observed in the mosque in his best clothes.

Conclusion

We have seen two examples of radiating compassion and love in a 20th century student of an eternal teacher and two examples from the life of his teacher. These examples are intended to show only the tip of an iceberg for those who are interested in exploring the spiritual dimension of Islam. At a time when this faith is associated with heinous crimes against humanity, it should be the duty of the inquisitive mind to transcend common stereotypes and explore the depth of spiritual richness in this source, which has produced world-renowned spiritual masters such as Rumi, the author of the verses at the beginning of this article, and continues to inspire hundreds of millions of people.

Notes

1. Referring to Prophet Muhammad, peace and blessings be upon him, whose other name is Mustafa, or the chosen one, and to his miracle of splitting the moon in half, as mentioned in the chapter “The Moon” of the Qur’an.
2. Referring to the uncle of the Prophet who was one of the fierce enemies of Islam, and who strove in vain to undermine the Prophet’s mission.
3. Translation by the author from original in Turkish.
4. Vahide, S., Islam in Modern Turkey, State University of New York Press, New York: 2005.
5. ibid.
6. Necmeddin Sahiner, Son Sahitler Bediuzzaman Said Nursi’yi Anlat›yor (Last Witnesses Tell of Bediuzzaman Said Nursi), Nesil Yayinlari, Istanbul: 2005.
7. Gulen, M. F., The Messenger of God, The Light, Inc., Izmir: 2005.
8. Hadith Encyclopedia, Harf Information Technology, Cairo: 1996.
9. Khan, M., Sahih al-Bukhari: The Translation of the Meanings, Darussalam Publishers, 1997.

References

• E.H. Whinfield (Translator), The Mathnawi: The Spiritual Couplets of Maulana Jalalu-D-Din Mahammad I Rumi, Watkins Publishing Ltd., 2002.
• Reynold A. Nicholson (Editor), Mathnawi of Jalaluddin Rumi, Gibb Memorial Trust; Set of 3 Books edition (June, 1990).
• C.Barks, Essential Rumi, Harper San Fransisco, 1997.
• Abdulbaki Golpinarli, Mesnevi Tercemesi ve Serhi (In Turkish), Inkilap Kitabevi, Istanbul, 1990.

Indeed, We have offered in this Qur’an every evidence and lesson by way of parables and examples for people so that they may think and take heed (Zumar 39:27)

So God propounds parables for human beings, that they may reflect on them and infer the necessary lessons. (Ibrahim 14:25)

Parables are short stories that may or may not represent an actual event that are designed to convey a truth or a moral lesson (Flexner 92). If we accept this definition of what a parable is then there are approximately 40 parables in the Qur’an. Some scholars define parables to include other narratives, such as stories of past prophets and their people, and thus find more parables in the Qur’an.

Parables help people understand abstract concepts by alluding to shared experiences and by allowing the readers to emphasize with participants or to feel as if they are direct observers in these experiences. By using carefully selected or crafted parables, remote and abstract truths can be made nearer and more comprehensible. Topics with a variety of sub-topics can be organized into a harmonious unity (Risale-i Nur).

Human beings are visual creatures. About 80% of the input to our brain comes through our eyes. Hence, important parts of the brain are dedicated to the processing, storage, and recall of visual information. Parables help activate our imagination, the eye of the mind, and enable us to comprehend a general truth or principle in a particular circumstance (Ozsoy). Parables help the power of imagination and inner senses to assist the mind/intellect in comprehending or internalizing the message. The parables of the Qur’an are another way in which the Qur’an uses human language to explain things that are beyond human capacity; this has been recognized even by non-Muslim experts, such as one of translators of the Qur’an, N. J. Dawood, who calls the Qur’an a “literary masterpiece.”

Those Who Associate Partners with God

The most important message of the Qur’an is the unity of God. As God is one and has no partners, there can be no partners associated with Him nor can any worship, including prayers, be directed toward others to seek help and protection. The very first chapter of the Qur’an emphasizes this fact in the form of a prayer; believers are instructed to say: You alone do We worship and from You alone do we seek help (Fatiha 1:5). In many verses, God challenges those who worship other objects or beings to bring proof that these are worthy of worship, and asks what those objects have produced that can be understood as a sign of their status. The following parable is an example:

O humanity! A parable is set forth, so pay heed. Those whom, apart from God, you call upon as gods will never be able to create even a fly, even if all of them were come together to do that. And if a fly snatches away anything from them, they cannot recover it from the fly. Powerless indeed is the seeker, and (powerless) the sought! They have no true judgment of God as His being God requires. God is certainly All-Strong, All-Glorious with irresistible might. (22:73-24)

Another example emphasizes the same message:

To Him alone is made the call to truth and the true prayer. Those (powers and persons) to whom they pray and call others, apart from Him, cannot answer them in any way-meaning nothing more than the action of he who stretches out his open hands in dire need toward the water so that it may reach his mouth; yet the water never reaches him. The prayer of the unbelievers is destined to go to waste. (13:14)¹

Those Who Forget God and Think of Themselves as Self-sufficient

In the Qur’an the reason why humanity was created is to worship God. According to this teaching, humans have been created to recognize their Lord, to strive to learn His attributes, to learn what code of conduct is pleasing to Him and to worship him in the way He desires. An important aspect of this worship is thanksgiving. Various verses of the Qur’an emphasize the importance of recognizing God’s bounties and being thankful for them. In particular, the chapter Al-Rahman (The All-Merciful) the following verse is repeated numerous times: Then, (O humankind and jinn,) which of the favors of your Lord will you deny? (Rahman 55:13) In the following parable, the Qur’an illustrates the events that happen to two people, one of whom is a grateful believer, and the other who abstains from recognizing the Giver of all bounties:

“…Tell them as an example the story of two men: for one of them We made two vineyards and surrounded both with date-palms, and placed a field of grain in-between. Both of the vineyards (including the date-palms and grain) yielded its produce, without failing in the least therein. We had also caused a stream to gush forth in their midst. So both of the vineyards including the date-palms and grain) yielded its produce, without failing in the least therein. We had also caused a stream to gush forth in their midst. The man had fruit in abundance, and one day he said to his friend, bandying words with him: “I am more than you in wealth, and more esteemed and stronger in respect of men.” He went into his vineyard in self-wronging (puffed up by worldly successes which had led him to conceit and unbelief). He said: “I deem not that all this will ever perish. Nor do I deem that the Last Hour will ever come. Even if (it should come, and) I am brought back to my Lord, I shall surely find (there by virtue of my own abilities and as my deserts) something even better than this as a resort.” His friend said to him, in the course of the argument with him: “Do you blaspheme (in such ingratitude as this) against He Who has created you out of dust, then out of a sperm-drop, then fashioned you into a complete man? But I believe for my part that He is God, my Lord, and none can I associate with my Lord as partner (in His Lordship-His bringing up, providing, sustaining and protecting). Alas, if you had but said, on entering your vineyard, “Whatever God wills will surely come to pass. How perfectly He creates and how mercifully He provides! There is no strength save with God.” Though you see me as less than you in wealth and children, (this is no problem at all, for it is God Who does what He will, and He is All-Compassionate toward His servants). Yet it may well be that my Lord will give me something better than your vineyard, just as He may send a calamity upon your vineyard from Heaven, so that it becomes a barren waste. Or its water sinks deep into the ground, so that you will never be able search for and find it again.” So eventually all his produce was encompassed by ruin, and there he was, wringing his hands with grief over all that he had spent on it, when now it was all ruined on its trellises, and he could but say, “Oh, would that I had never associated anyone with my Lord as partner (in His Lordship).” And he had, apart from God, none, no troop of men to help him, nor could he be of any help to himself. For thus it is: all protective power and authority essentially belongs to God alone, the True One. He is the best to reward, and the best to determine the end of things. (Kahf 18:32-44)

The Transience of the Bounties of the World

The Qur’an presents three views of this world: (1) As a place to plant good deeds as seeds that will blossom in the Hereafter, (2) as a wonderful display of God’s names, and (3) as a place of enjoyment. While the world carries enormous significance with respect to the first two aspects, with the third it carries little weight in God’s sight. This is illustrated by the following parable:

The present, worldly life (which you pursue) is like this: We send down water from (the direction of) the sky, and with it the plants of the Earth grow rich and dense, mingling so that human beings and animals can eat of them, until, when the Earth has taken on her ornaments and has been embellished, and its inhabitants believe that they can do with it whatever they want, Our command comes upon it by night or day unexpectedly, and We cause it to become like a field mown down, as if it had not flourished the previous day. Thus We display in detail the signposts of Our way and the relevant Revelations (included in the Qur’an) for a people who will reflect (on them and draw the necessary lesson). (Yunus 10:24)²

Sincere Charity versus the Pleasure of Acknowledgement

The Qur’an encourages spending in the way of God to help the poor and the needy without embarrassing or insulting recipients. Any feeling or display of pride in giving nullifies its meaning. These are made clear in the following parables: The example of those who spend their wealth in God”s way is like that of a grain that sprouts seven ears; in every ear there are a hundred grains. Thus God multiplies for whomever He wills. God is One Who embraces all (with His mercy), All-Knowing. (Baqara 2:261) O you who believe! Render not in vain your almsgiving by placing under obligation and taunting like he who spends his wealth to show off to people and to be praised by them, he who does not believe in God or the Last Day. The example of his spending is that of a rock on which there is soil; a heavy rain falls upon it, and leaves it barren. They derive no gain (pertaining to the Hereafter) from their almsgiving, nor do they succeed in preserving it if they can derive any. God guides not such people of the unbelievers (to attain their goals). (Baqara 2:264) The example of those who spend their wealth in pursuit of where God”s good pleasure lies and who strive to make belief firmly established in their hearts is that of a garden on a hilltop; a heavy rain falls upon it, and it yields its produce twofold; even if no heavy rain falls upon it, a light shower suffices. Whatever you do, God sees it well. (Baqara 2:265)

The Good Deeds of Disbelievers are in Vain

One aspect Islamic belief that is misunderstood is the relationship between faith and deeds. In Islam, faith is the essential ingredient for success in this world and in the Hereafter. Deeds are important and have a symbiotic relationship with faith. Deeds both reflect and affect our faith. Through sincere worship we can connect with God in a way that would be impossible through intellect on its own. Conversely, a person who constantly behaves in opposition to their belief may risk losing their belief. As important as deeds are, they cannot qualify anybody for eternal success. In other words, nobody can “earn” Paradise through good deeds alone. In particular, those who do not believe in God or life in the Hereafter will receive the reward for whatever good they do in this world. The following parable illustrates these concepts very clearly: This is a parable to be set forth for those who disbelieve in their Lord: all their work is as ashes which the wind blows hard on a stormy day. They have no control of anything that they have earned (from which to benefit). That indeed is straying very far and extreme failure. (Ibrahim 14:18)³

The Ability of Humans to Transcend their Environment

The Qur’an gives examples of women who transcend their environment (both in good and bad ways) to choose a course of action. In the first example, the wives of Noah and Lot are shown as examples of people who, despite being in an environment of enlightenment, chose falsehood over the truth. The other examples illustrate two women who transcended the conditions of their environment to accept truth and live piously. While these examples are not exactly the same as the previous parables, nevertheless the iconization of the women as prototypes follow the same literary and educational style: God propounds the wife of Noah and the wife of Lot as an example for those who disbelieve. They were married to two of Our righteous servants, yet betrayed them (by rejecting the Messages they brought from God and collaborating with the unbelievers). But they (their husbands) availed them in nothing against God and it was said to them: “Enter the Fire with all those who enter it!” And God propounds the wife of the Pharaoh as an example for those who believe. She prayed: “My Lord! Build for me a home in Paradise in nearness to You, and keep me away and save me from the Pharaoh and his deeds and save me from the people of wrongdoing.” And also Mary, the daughter of “Imran, who guarded her chastity and so We breathed into him out of Our Spirit, who confirmed the words of her Lord (manifested as His Revelations—commandments, promises and warnings—to His Messengers), and His Books, and she was one of those who are devoutly obedient to God.” (Tahrim 66:10-12)

The Infinite Knowledge of God

In the Qur’an some historical accounts and important lessons are repeated; there are a variety of purposes for why this is done. Since most people find it hard to frequently read the Qur’an in its entirety, the major messages are repeated throughout the Qur’an. Also, the fact that the Qur’an serves not only as a reminder, but as a book of prayer, a book of remembrance, and a book of invitation/prohibition (in addition to its other roles), the repetitions fulfill subtle functions. These repetitions are not verbatim in each case, but rather, depending on the context, they display a subtle variance that emphasizes a certain aspect of the message in addition to the others or reveal a meaning that might not be obvious in other contexts. The following parable for instance, responds, in part, to the pagan Arabs” attribution of the frequently repeated messages or historical accounts being caused by the scarcity of God”s knowledge. If all the trees on the Earth were pens, and all the sea were ink, with seven more seas yet added to it, the words of God (the acts of all His Names and Attributes manifested as His commandments, and the events and creatures He creates) would not be exhausted in the writing. (Luqman 31:27)

Parables on Other Topics

In addition to the examples given above, parables in the Qur’an discuss such topics that depict God as the light of the Heavens and the Earth (24:35), the persistence of the truth and the transience of the falsehood (31:17), the Messenger of God and his Companions (48:29), the abundance of good and scarcity of evil (14:24), the hypocrites (2:17, 59:15), the responsibility that comes with knowledge (62:5, 7:175), the peoples who have slandered their messengers (16:112), the weight of the message of the Qur’an (59:21), belief versus unbelief (6:122, 7:58, 11:24, 16:75, 28:61), the hardening of the hearts (2:74), the attitude of unbelievers against the message (2:171), the situation of those who have forgotten God and have refrained from spending in good causes (68:17-33), and the resurrection and life after death (2:259, 35:9).

Conclusion

The parables of the Qur’an exemplify the unique literary aspects of this miraculous book. The parables are there to help readers understand complex and abstract topics. They also facilitate the involvement of the human imagination and inner senses to internalize the messages within the stories. Such characteristics are among many that made those who opposed the Qur’an in the early days of Islam resort to violence; the Qur’an puts forward the challenge to the non-believers to produce something similar if they are intent on proving that the Qur’an was written by a human. They were unable to produce the like, so instead they used violence to try to suppress the Muslims at that time. If they had been successful, the Qur’an would have become irrelevant for society. The fact that they preferred opposition by sword to a verbal or written response illustrates the fact that they were unable to challenge the Qur’an on the grounds of language.

Notes

1. For other parables on this topic, see Qur’an 22.31, 29.41, 30.28, and 39.29.
2. Other parables on this topic include 18.45 and 57.20 of the Qur’an.
3. Other parables on this topic include 3.117 and 24.39.

References

• Flexner, S. B. et al., The Random House Dictionary, Random House, NY: 1992.
• Ozsoy, O., Guler, I., Konularina Gore Kur’an, Fecr Yayinevi, Ankara: 2003.
• Celik, M., Kur’an’in Ikna Hususiyeti, Caglayan, Izmir, 1996.
• Nursi, S., Risale-i Nur Kulliyati (The Risale-i Nur Collection), Sikke-i Tasdik-i Gaybi.
• Dawood, N. J., The Koran, Penguin Classics, Penguin Books: 2000.

Cultural diversity has two vital benefits. First, individuals from different groups and cultures get to know each other, which engenders respect and consideration for each one’s beliefs, values, and ways of life. Achieving such a goal is a must for countries like America, which hosts many different cultures and groups. Such an understanding is becoming crucial for all nations, even for quite homogenous ones, as all are quickly becoming dwellers of the same global village. Humanity needs examples of successful multicultural societies. The second benefit is the exchange of knowledge and experience. This article elaborates on the second benefit.

Today, in many American-made movies and television serials (such as Kung Fu), we see a wise Asian man who is always calm, never panics, and brings such unique, humanitarian solutions to problems that the Americans on the scene are amazed. Although these are not real stories, they give the flavor of possible benefits to be derived from exploring different perspectives and philosophies.

The fact that all individuals living in the vast variety of societies found on our planet are human beings is often overlooked by individuals, communities, and even social science professionals, depending on the rate of their self-containedness. All individuals living in different societies are, without doubt, human beings; the differences separating them are merely external elements. Thus everyone, regardless of his or her society, experiences common problems; only the context changes. For example, a beggar and a king both feel anger at times. The beggar’s anger may lead him to hit his wife, whereas the king’s anger may cause him to engulf the nation in war. Another analogy is that of a pickpocket to a computer hacker illegally transferring funds.

Throughout history, human cultures and groups have dealt with the same characteristics and problems as we, the people welcoming a new millennium, are dealing with now. As contemporary cultures reflect inherited perspectives and philosophies, centuries-old cultures and civilizations may be invaluable resources for finding new points of view and approaches to our problems.

The emphasis placed on such a cultural exchange by both American individuals and institutions at all levels is not as great as that which has been placed on other, but less important, issues. For example, a typical American secondary school student’s knowledge of world geography and foreign languages has long been inferior to that of his or her European counterpart. This indicates a lack of interest toward the rest of the world.

The same indifference can be observed in American nightly news programs, even on national television channels. For example, the “World Report” news programs usually give domestic news (unless there is a war going on in which America is heavily involved). Might such an ethnocentric view of the world stemming from being the sole superpower be responsible for this attitude?

Sometimes people living in a system, even a well-functioning system, cannot solve their social and individual problems because they cannot raise themselves above the flow of events. The most frequently used tool to solve any problem is power, especially if it is abundant and readily available. Power often is seen as the best shortcut to the solution due to the deceiving ease of its exertion, which also allows its user to ignore or to not consider its potentially serious side effects.

The power applied may be physical, economic, military, or technological, depending on the nature of the problem. However, its exercise is not always the key to the solution. A mighty lion caught in a hunter’s net should have the modesty to request help from a tiny mouse, for the latter’s sharp teeth may work where the lion’s devastating paws cannot. One should have the wisdom to know a gallon of gas cannot attract that which can be attracted by a teaspoonful of honey.

A simple but enlightening example of how different perspectives can help to solve problems is given below. During the heated negotiations between two political parties for a coalition in Turkey, a simple but totally satisfactory suggestion by a Turkish newspaper columnist attracted my attention. The two parties, having an almost equal number of representatives in Parliament, could not share the ministries, for ministries have varying degrees of political weight. The columnist’s suggestion was not inspired by a similar case from a contemporary democracy, but from a parable describing King Solomon’s approach to a similar problem: Two heirs could not agree on how to divide their inheritance equally, because they could not agree on the value of the items to be inherited. King Solomon suggested that one heir divide the inheritance into two equal halves, after which the other heir would have the first choice. Thus, an ancient parable offered a practical solution to a conflict in a contemporary democracy. Whether his suggestion was considered or not is beyond our concern here.

One can find books of ancient and contemporary philosophers and different cultures in bookstores, but who reads them? The general public, especially the youth, should be made aware of these resources and directed to make use of humanity’s historical experience. For example, various herbs used in some parts of the world for centuries to treat specific illnesses are now preferred over drugs developed in laboratories, for they are all-natural, non-addictive, and have no side effects. Obviously, cultures and civilizations have much more to offer each other than herbs. I wish that Americans would look sincerely for the wisdom that different civilizations and cultures have to offer.

Note: Since this article is intended to reflect a broad perspective, I gave no specifics about the methodology to realize the goals indicated and no thorough examples. Such examples in different fields, along with their methodologies, can serve as the content of separate articles.