<?xml version="1.0" encoding="UTF-8"?><rss version="2.0"
	xmlns:content="http://purl.org/rss/1.0/modules/content/"
	xmlns:wfw="http://wellformedweb.org/CommentAPI/"
	xmlns:dc="http://purl.org/dc/elements/1.1/"
	xmlns:atom="http://www.w3.org/2005/Atom"
	xmlns:sy="http://purl.org/rss/1.0/modules/syndication/"
	xmlns:slash="http://purl.org/rss/1.0/modules/slash/"
	>

<channel>
	<title>domain &#8211; Fountain Magazine</title>
	<atom:link href="https://fountainmagazine.com/tag/domain/feed/" rel="self" type="application/rss+xml" />
	<link>https://fountainmagazine.com</link>
	<description></description>
	<lastBuildDate>Sat, 01 Nov 2014 00:00:00 +0000</lastBuildDate>
	<language>en-US</language>
	<sy:updatePeriod>
	hourly	</sy:updatePeriod>
	<sy:updateFrequency>
	1	</sy:updateFrequency>
	<generator>https://wordpress.org/?v=7.1</generator>
	<item>
		<title>Becoming a &#8220;Good&#8221; Foreign Language Teacher: Knowledge, Skills, and Dispositions</title>
		<link>https://fountainmagazine.com/all-issues/2014/issue-102-november-december-2014/becoming-a-good-november-2014/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Sat, 01 Nov 2014 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 102 (November - December 2014)]]></category>
		<category><![CDATA[Advocacy]]></category>
		<category><![CDATA[Assessment]]></category>
		<category><![CDATA[competent]]></category>
		<category><![CDATA[content]]></category>
		<category><![CDATA[cultural]]></category>
		<category><![CDATA[development]]></category>
		<category><![CDATA[diversity]]></category>
		<category><![CDATA[domain]]></category>
		<category><![CDATA[Education]]></category>
		<category><![CDATA[effective]]></category>
		<category><![CDATA[Instruction]]></category>
		<category><![CDATA[knowledge]]></category>
		<category><![CDATA[language]]></category>
		<category><![CDATA[Language learning]]></category>
		<category><![CDATA[learners]]></category>
		<category><![CDATA[learning]]></category>
		<category><![CDATA[methods]]></category>
		<category><![CDATA[Professionalism]]></category>
		<category><![CDATA[programs]]></category>
		<category><![CDATA[skills]]></category>
		<category><![CDATA[students]]></category>
		<category><![CDATA[teachers]]></category>
		<category><![CDATA[teaching]]></category>
		<category><![CDATA[theories]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2014/issue-102-november-december-2014/becoming-a-good-november-2014/</guid>

					<description><![CDATA[Most language educators would agree that the ultimate goals of a foreign/second (L2) language education are trifold: language skills, cultural knowledge, and academic achievement. The needs and expectations of L2 learners can no longer be defined in terms of grammar knowledge, or translation skills; rather, proficiency in an L2 is considered a phenomenon that entails [&#8230;]]]></description>
										<content:encoded><![CDATA[<p>Most language educators would agree that the ultimate goals of a foreign/second (L2) language education are trifold: language skills, cultural knowledge, and academic achievement. The needs and expectations of L2 learners can no longer be defined in terms of grammar knowledge, or translation skills; rather, proficiency in an L2 is considered a phenomenon that entails ability to communicate one&#8217;s self authentically in a linguistically and culturally diverse world. To be able to do that, learners must be taught an L2 differently than they would have been taught 40 or 50 years ago. As the world changes, the communication needs of L2 learners also change. As a result, L2 teachers need to adapt to these changes while also constantly updating their professional knowledge, skills, and dispositions to be able to effectively serve their students. Below, I outline and describe the basic professional competencies of a well-trained foreign language teacher.</p>
<p><span id="more-1722"></span></p>
<p>What are the basic traits that a teacher should have to be able to help students attain necessary language skills and cultural knowledge in an L2? As language educators, we receive this question all the time. Unfortunately, the answer to this question is not an easy one because research involving curriculum analyses, both in the United States and in Europe, has revealed a significant amount of variation in the number of domains and competencies covered in L2 teacher education programs (Richards, 2008). While some programs have predominantly focused on language and L2 acquisition research and theory, others have taken a more linguistics and methods-orientated direction. In general, though, most experts in the field would agree on a number of fundamental competencies.</p>
<p>Competent L2 teachers know who their learners are (1), what language is (2), how it is learned (3), and how it should be taught (4). Furthermore, they have a solid background about the foundations of L2 curriculum (5), the selection and development of instructional materials (6), and the design of a learning environment (7) that is sensitive to socio-cultural differences (8). They also know how to use the L2 as a tool for L2 learners to gain access to academic content knowledge (9). While they are also able to situate the whole language learning and teaching experience within broader learning theories (10), and competently assess and evaluate L2 development and proficiency (11), they are well aware of their professional roles and responsibilities as advocates for successful L2 education in its entirety at all levels, including institutional, national, and international. Indeed, these competencies have been categorized under the five domains of (I) Language Learning, (II) Learners, (III) Instruction, (IV) Assessment and Evaluation, and (V) Professionalism and Advocacy. Before any further ado, let&#8217;s take a look at what each competency entails.</p>
<h3><b>Domain I: Language learning</b></h3>
<p>This domain includes background knowledge and skills in (1) linguistics, (2) general learning theories, and (3) first and second language acquisition theories. First, L2 teachers need to be highly proficient in the language that they teach. Competent L2 teachers understand the nature of language and basic concepts of language systems such as phonology, morphology, syntax, lexicon, semantics, discourse, and pragmatics. They are also familiar with socio-linguistic, psycho-linguistic, and neuro-linguistic factors in L2 learning. Furthermore, they know the functions and register of the L2, including the conventions of written and spoken language, and the pedagogical implications of differences between basic interpersonal communication skills (BICS) and cognitive academic language proficiency (CALP) (Cummins, 1984). In addition, they understand the interrelatedness of receptive (listening, reading), productive (speaking, writing), and complementary (grammar, vocabulary, pronunciation) language skills.</p>
<p>Second, competent L2 teachers are familiar with the basic theories and concepts about first (L1) and L2 acquisition, including the language universals (Chomsky, 1965), and the role L1 plays in L2 development. While they understand differences between the processes of L1 and L2 acquisition, they have a solid background in second language acquisition (SLA) theories. For example, they know how to use different ways to maximize the comprehensible input (Krashen, 1987) opportunities for their students through authentic tasks and activities. More importantly, they know that the greatest bulk of an L2 is acquired through self-exposure and social interactions, not learned in strictly structured and inauthentic classroom settings. Finally, competent L2 teachers are able to situate SLA theories within the broader learning theories. For instance, they understand behaviorist (memorization) versus cognitivist (information processing) versus socio-constructivist (socio-cultural factors) views (Pavlenko &#8211; Lantolf, 2000) about L2 learning and development.</p>
<h3><b>Domain II: Learners</b></h3>
<p>Current SLA research has revealed that socio-psychological factors affect success in learning an L2. This domain covers teacher knowledge about (1) differences among language learners and (2) their levels of socio-cultural awareness. Individual differences, such as motivation, attitudes, anxiety, identity, learning styles, pedagogical beliefs, socialization patterns, and learning and communicative strategies affect success in learning an L2. For example, many scholars have found that high motivation has a positive effect on L2 learning (Dörnyei, 2005) while learners with high levels of anxiety do not seem be successful language learners (Horwitz, 2008). In fact, researchers have found that learners who strongly identify with the L2 community attain a more native-like accent than those who strongly identify with their native-speaking communities Dörnyei &#8211; Ushioda, 2009). Competent L2 teachers know about the role these factors might play in L2 attainment and plan the learning experience for their students accordingly.</p>
<p>Other learner-related factors concern the socio-cultural differences. L2 learners come from different families and geographical regions with different socio-economic and educational backgrounds, demonstrating a significant amount of cultural diversity. Culturally responsive L2 teachers understand the role of diversity &#8211; namely cultural products, perspectives, and practices &#8211; in L2 attainment. They know not only how to construct culturally-sensitive learning experiences to facilitate the most effective learning, but also what strategies to apply to create among students an awareness of and respect for cultural diversity. Indeed, culturally competent teachers effectively apply skills for communicating and collaborating effectively with the parents/guardians, the community members, and local resources to enhance their students&#8217; learning. For example, such teachers not only genuinely value cultural diversity and incorporate it into the curriculum, but also organize extra-curricular activities in appreciation of diversity as an added value for advancement.</p>
<h3><b>Domain III: Instruction</b></h3>
<p>Under this domain, we have instructional competencies including (1) foundations of curriculum, (2) methods of language teaching, (3) learning environment, (4) instructional materials, and (5) language and content area integration. First, competent L2 teachers know the history and policy foundations of L2 education and use this knowledge to plan and implement effective L2 programs (Richards, 2001). They are able to select the most effective types of programs that are appropriate for the needs of a particular learner profile in a particular setting. For example, while most scholars agree that bilingual and immersion programs are the most effective, the most common English as a second language (ESL) programs in the U.S. are the pull-out ones, also known as the least effective programs that are primarily based on the development of BICS skills while neglecting the teaching of CALP via content-based curricula.</p>
<p>Second, competent L2 teachers are also able to choose and implement the most appropriate and current methods of language teaching. Such teachers know that we have come a long way since the grammar translation and audio-lingual method (Richards &#8211; Rodgers, 2001), however, we no longer adhere to one particular method because we live in the beyond-methods&#8217; era (Kumaravadivelu, 2006). Nonetheless, this does not imply a senseless, eclectic approach; rather it entails being flexible within a consistent theoretical and pedagogical framework often referred to as &#8220;principled eclecticism&#8221; (Larsen-Freeman, 2003). Third, as the current ecological L2 learning theories would suggest (Brown, 2006), just as only a balanced amount of sun, water and care, in a nurturing environment, can lead to the healthy growth of a flower, instructional methods can lead to success in L2 learning only if the learning environment is meticulously designed.</p>
<p>Last but not least, an important part of what constitutes a nurturing environment is the availability of effective instructional resources. Competent L2 teachers are not only well-informed about the strengths and weakness of commercial and authentic materials but also possess the necessary skills to select, adapt, or develop their own materials based on the specific needs and goals of their students. Indeed, competent L2 teachers use the instructional materials that integrate the language and content area goals, supporting L2 learners&#8217; BICS, CALP, and academic achievement (Cummins, 1984). For example, most English-medium universities overseas have English preparatory programs to prepare students to be able to receive, say, engineering or economics content in English; however, instead of conducting a needs analysis and basing their EFL instruction on the content of these majors, most of these programs select generic commercial materials that often times include linguistic input predominantly about shopping, holidays, food, and friendship.</p>
<h3><b>Domain IV: Assessment and evaluation</b></h3>
<p>This domain covers knowledge and skills about the assessment and evaluation of L2 learners&#8217; language development. It includes background in L2 testing skills related to the placement, diagnostic, achievement, and proficiency of L2 learners. Competent L2 teachers know the commonly used national and international standard assessment tools, such as TOEFL. Such teachers also know the basic concepts and practices related to test design, development, and interpretation. In addition to understanding the validity and reliability of testing methods and tools, they understand potential relationships among the national standards, instruction, and L2 testing. More importantly, in their classrooms, they effectively apply knowledge of formal/informal, direct/indirect, and dynamic and authentic assessment. Most importantly, however, competent teachers are familiar with the construct of the &#8220;backwash effect&#8221; &#8211; the effect testing might have on student learning (Hughes, 2003). Successful learning will not take place if teaching and testing goals and/or methods are incongruent. For example, if writing skills are tested by multiple choice tests, students will invest their time and effort in developing their skills to respond to such questions, not in working on actual writing skills that they will need in real-life tasks.</p>
<h3><b>Domain V: Professionalism and Advocacy</b></h3>
<p>As part of the last domain, L2 teachers are required to possess certain professional qualifications and individual characteristics to be able to support L2 learners&#8217; linguistic, cultural, and academic development. This domain lies at the heart of the profession. Competent L2 teachers demonstrate knowledge of the history of L2 teaching, keep up-to-date with new trends and current educational research, and follow domestic and international issues related to language planning and policy, as well as other advances in L2 education. Moreover, considering language learners spend only a limited amount of time with language teachers, it is very important that L2 teachers collaborate with the mainstream teachers and build partnerships with outside resources and parents to support the linguistic, cultural, and content areas of development. Also noteworthy is that such teachers claim responsibility for L2 learners and are able to apply effective strategies to advocate educational and social equity for their students, both at the institutional and broader community levels (Crawford, 2004). For instance, such teachers serve as a resource to promote a school environment that values cultural and linguistic diversity, and they advocate for equitable access to resources for language learners by becoming members of organizations (e. g.: TESOL) that support L2 learning and teaching.</p>
<p>Furthermore, in order for teachers to apply these professional competencies in actual classroom practices, they need to posses certain individual characteristics and dispositions that complement their professional qualifications. Unlike learning other subjects, language learning requires a great deal of patience and perseverance. Hence, L2 teachers need to be caring, compassionate, understanding, self-sacrificing, and patient. They need to establish a good rapport and empathy with their students, offering them timely motivational support. Only by doing so can they understand their students&#8217; socio-psychological well-being and invest additional personal time and effort in students&#8217; learning.</p>
<p>Last but not least, L2 teachers need to remain positive and enthusiastic about their students&#8217; progress, because the process of L2 development is a bumpy road with lots of ups and downs. To help their students, teachers need to be able to identify their students&#8217; struggles correctly and provide them with developmentally appropriate support. In addition, they need to be fair and treat all of their students equally. In doing so, they need to know their students very well and think outside the box, supplying innovative in-class and self-study strategies. Finally, in order for L2 teachers to be able to competently demonstrate these personal traits, they need to have effective communication skills. While such teachers are very good and empathetic listeners, they also need to be able to communicate their thoughts and feelings effectively, and with mutual respect and appreciation, to support their students&#8217; learning.</p>
<p><em>Saban Cepik is Assistant Professor/Department Chair, ELT, Zirve University. </em></p>
<h3><b>References</b></h3>
<ul>
<li>Brown, D. H. (2006). Principles of Language Learning and Teaching (5th Edition). New York: Pearson ESL.</li>
<li>Chomsky, N. (1965), Aspects of the Theory of Syntax. Cambridge, Massachusetts: MIT Press</li>
<li>Cummins, J. (1984) Bilingualism and special education: Issues in assessment and pedagogy. Clevedon, England: Multilingual Matters.</li>
<li>Crawford, J. (2004). Educating English Learners: Language Diversity in the Classroom. (5th ed). Los Angeles, CA: Bilingual Education Services.</li>
<li>Dörnyei, Z. (2005). The psychology of the language learner. Mahwah, NJ: Lawrence Erlbaum.</li>
<li>Dörnyei, Z. &#8211; Ushioda, E. (Eds.). (2009). Motivation, Language Identity and the L2 Self. Bristol: Multilingual Matters.</li>
<li>Horwitz, E.K. (2008). Becoming a language teacher: A practical guide to second language learning and teaching. Boston, MA: Allyn &#8211; Bacon, Inc.</li>
<li>Hughes, A. (2003). Testing for language teachers. Oxford: Oxford University Press.</li>
<li>Krashen, S.D. (1987). Principles and practices in second language acquisition. New York: Prentice-Hall.</li>
<li>Kumaravadivelu, B. (2006). TESOL methods: Changing tracks, challenging trends. TESOL Quarterly, 40, 59-81.</li>
<li>Larsen-Freeman, D. (2003). Teaching language: From grammar to grammaring. Boston: Thompson-Heinle.</li>
<li>Pavlenko, A., &#8211; Lantolf, J. P. (2000). Second language learning as participation and the (re)construction of selves. In J. Lantolf (Eds.), Sociocultural theory and second language learning: Recent advances (pp. 1545-177). New York: Oxford University Press.</li>
<li>Richards, J. C. (2001). Curriculum development in language teaching. NY: Cambridge University Press.</li>
<li>Richards, J. C. (2008). Second language teacher education today. RELC Journal, 39: 158-177.</li>
<li>Richards, J., &#8211; Rodgers, T. (2001). Approaches and methods in language Teaching (2nd ed.). Cambridge: Cambridge University Press.</li>
</ul>
]]></content:encoded>
					
		
		
			</item>
		<item>
		<title>Metaphors, Metaphysics, Mathematics, etc.</title>
		<link>https://fountainmagazine.com/all-issues/2011/issue-80-march-april-2011/metaphors-metaphysics-mathematics-etc/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Tue, 01 Mar 2011 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 80 (March - April 2011)]]></category>
		<category><![CDATA[analogy]]></category>
		<category><![CDATA[domain]]></category>
		<category><![CDATA[examples]]></category>
		<category><![CDATA[gentner]]></category>
		<category><![CDATA[jesus]]></category>
		<category><![CDATA[life]]></category>
		<category><![CDATA[mapping]]></category>
		<category><![CDATA[mathematical]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[metaphor]]></category>
		<category><![CDATA[metaphors]]></category>
		<category><![CDATA[number]]></category>
		<category><![CDATA[objects]]></category>
		<category><![CDATA[person]]></category>
		<category><![CDATA[relation]]></category>
		<category><![CDATA[relations]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[statement]]></category>
		<category><![CDATA[target]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2011/issue-80-march-april-2011/metaphors-metaphysics-mathematics-etc/</guid>

					<description><![CDATA[Analogies, metaphors, and similes are essential elements of human cognition and this makes them an indispensable tool in education, science, and literature. When it comes to explaining metaphysical concepts, however, these are pretty much the only tools that we have at hand. In this article we will review these three concepts and the relations among [&#8230;]]]></description>
										<content:encoded><![CDATA[<p>Analogies, metaphors, and similes are essential elements of human cognition and this makes them an indispensable tool in education, science, and literature. When it comes to explaining metaphysical concepts, however, these are pretty much the only tools that we have at hand.</p>
<p>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.</p>
<p>Even though there is no universally accepted definition of analogy, or metaphor, or literal similarity, the purpose of their use is unanimously defined as &#8220;throwing light on an unfamiliar concept or situation using a familiar one.&#8221; 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.</p>
<p><b>Analogy:</b> 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 &#8220;proportion&#8221; (Szabo 1978, 23). An example of Aristotelian analogy is &#8220;spine is to fish as bone is to animal.&#8221; 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 &#8220;feet are to animal as wheels are to automobile,&#8221; 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).</p>
<p>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 &#8220;covariant functor&#8221; between two &#8220;categories&#8221;). This is a &#8220;structural alignment&#8221; between the domain and the target (Gentner-Markman 1997, 47). In the &#8220;feet and wheels&#8221; 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.</p>
<p>One might ask where do the arms get mapped? The answer is &#8220;nowhere.&#8221; We do not expect this mapping to match every object in the domain to an object in the target. The &#8220;power of the analogy&#8221; 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).</p>
<p>Having introduced the concept of analogy by using some simple physical examples let’s now consider a not-so simple metaphysical situation.</p>
<p>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).</p>
<p><b>Metaphor:</b> The essence of metaphor is understanding and experiencing one kind of thing in terms of another. (Lakoff &amp; Johnson 1980, 104) Simple examples are &#8220;What a sweet baby!&#8221; &#8220;Your car is a lemon, let’s take mine.&#8221; Obviously babies are not candies, nor are vehicles some sort of fruit. We use this sort of &#8220;identification&#8221; in order to communicate our ideas/feelings in a more striking way. Here are more examples of metaphors: &#8220;he is the apple of my eye,&#8221; &#8220;it’s raining cats and dogs,&#8221; &#8220;he has a golden heart,&#8221; &#8220;she cried rivers&#8221; 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 &#8220;a nightingale is a bird,&#8221; that’s not a metaphor; it’s a literal categorization, as both nightingale and bird signify the same domain (Gentner 2005, 200).</p>
<p>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, &#8220;the engine is the heart of an automobile&#8221; is a metaphor, but it uses the same structural alignment of the analogical comparison that we mentioned above.</p>
<p>Nonetheless, not every metaphor is of this sort. Consider, for example, the verse (48:10) &#8220;God’s hand is over their hands&#8221; 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 &#8220;God’s hand&#8221; 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.</p>
<p><b>Literal similarity:</b> 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: &#8220;Indeed, the example of Jesus to God is like that of Adam. He created him from dust; then He said to him, &#8220;Be,&#8221; and he was&#8221; (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 &#8220;identity,&#8221; not a similarity (Gentner 1982, 110).</p>
<p>The statement &#8220;Jesus is like Adam&#8221; makes much more sense than &#8220;Jesus is Adam,&#8221; even if we make it clear in what sense we use this identification. Typically metaphors use the word &#8220;is&#8221; and literal similarity comparisons (similes) use either of the words &#8220;like&#8221; or &#8220;as.&#8221; Mathematically speaking, if metaphors are equalities, then similes are approximations (Casnig).</p>
<p>Even though metaphors are substitutions, they are not necessarily &#8220;two-way&#8221; identifications. In other words, most of the times they are asymmetric; i.e., there is a sense of direction in the &#8220;identification.&#8221; For example, we never substitute a car in the place of a lemon and say &#8220;this lemon is a car.&#8221; This is because the first and foremost requirement of any comparison is that it be informative. What information do we obtain from the statement &#8220;rose is love&#8221; or &#8220;iron is fist&#8221;? In that respect many metaphors are irreversible, like similes: &#8220;a butcher like a surgeon&#8221; is quite different than &#8220;a surgeon like a butcher.&#8221; 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.</p>
<p><b>Mathematical and metaphysical examples:</b> 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 &amp;#8730;–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).</p>
<p>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.</p>
<p>In verse (5:32) of the Qur’an reads: &#8220;…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…&#8221;</p>
<p>In a sense this verse means &#8220;one equals many.&#8221; 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: ∝+∝+∝+&#8230;∝=∝.Therefore, for any positive number <em>m</em> if we write m.∝=∝ it would be a perfectly acceptable mathematical statement.</p>
<p>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 &#8220;∝&#8221; to &#8220;saving the life of one person&#8221; 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 &#8220;killing an innocent person&#8221; to &#8220;–∝&#8221; then we clearly see that the mathematical statement m.(-∝)=-∝translates into &#8220;killing all innocent people on earth is as grave a sin as killing one.&#8221;</p>
<p>Note that this &#8220;one equals many&#8221; 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.</p>
<p>Another relation between infinities is that &#8220;∝-∝&#8221; is indeterminate. In particular &#8220;∝-∝&#8221; is not necessarily 0. Using the analogy we just constructed we can translate this as &#8220;killing one innocent person and saving the life of another does not balance out.&#8221; Then, &#8220;∝-∝&#8221; is indeterminate&#8221; translates as &#8220;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!&#8221; Indeed, those who have taken calculus will remember that &#8220;∝-∝&#8221; sometimes turns out to be a positive number and sometimes a negative number; as well as 0 or ∝ or -∝</p>
<p>One could ask, what about m.0=0? Isn’t this also true? Yes, indeed &#8220;the sum of m zeros is equal to zero&#8221; is another mathematically accurate statement. Then, what meaning could this equation be given? Perhaps this would be the &#8220;murderer’s&#8221; version of the Qur’anic principle that we mentioned above: &#8220;When the life of an individual has &#8220;no value&#8221; in your heart, killing one person or a million people should be equally disheartening (!)&#8221;</p>
<p>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 &#8220;the square root of every prime number is irrational&#8221; 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 &amp;#8730;2 is irrational, &amp;#8730;3 is irrational, &amp;#8730;5 is irrational etc. It covers all the numbers in the form &amp;#8730;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 &#8220;any&#8221; 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.</p>
<p><b>Summary:</b> 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.</p>
<p><em>Yusuf Ziya Gurtas is an assistant professor of mathematics in Queensborough Community College, CUNY.</em></p>
<p><b>References</b></p>
<ul>
<li>Casnig, John D. 1997–2009. A Language of Metaphors. Knowgramming.com. Kingston, Ontario, Canada.</li>
<li>Gentner, Dedre. 1982. &#8220;Are scientific analogies metaphors?&#8221; in David S. Miall (Ed.), Metaphor, Problems and Perspectives, Brighton, England: Harvester Press, pp. 106–132.</li>
<li>&#8211;. 1983. &#8220;Structure-Mapping: A Theoretical Framework for Analogy.&#8221; Cognitive Science, 7, pp. 155–170.</li>
<li>&#8211;. 1988. &#8220;Metaphor as Structure Mapping: The Relational Shift.&#8221; Child Development, 59, 47–59.</li>
<li>Gentner, Dedre &amp; Markman, Arthur D. 1997. &#8220;Structure Mapping in Analogy and Similarity.&#8221; American Psychologist, 52, 45–56.</li>
<li>Gentner, Dedre, Bowdle, B., Wolff, P., &amp; Boronat, C. 2001. &#8220;Metaphor is like analogy&#8221; in D. Gentner, K. J. Holyoak, &amp; B. Kokinov (Eds.), The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: MIT Press, pp. 199–253.</li>
<li>Gentner, Dedre &amp; Bowdle, Brian F. 2005. &#8220;The Career of Metaphor.&#8221; Psychological Review, 112, pp. 193–216.</li>
<li>Lakoff, G., &amp; Johnson, M. 1980. Metaphors We Live By. Chicago: University of Chicago Press.</li>
<li>Pimm, David. 1981. &#8220;Metaphor and Analogy in Mathematics.&#8221; For the Learning of Mathematics, 1, 47–50.</li>
<li>Runde, Volker. 2000. &#8220;The Banach-Tarski Paradox or What Mathematics and Miracles Have in Common.&#8221; in the Sky, 2, 13–15.</li>
<li>Szabo, A. 1978. The Beginnings of Greek Mathematics. Dordrecht, Holland: Reidel.</li>
</ul>
]]></content:encoded>
					
		
		
			</item>
		<item>
		<title>Need a Third Eye?</title>
		<link>https://fountainmagazine.com/all-issues/2009/issue-71-september-october-2009/need-a-third-eye/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Tue, 01 Sep 2009 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 71 (September - October 2009)]]></category>
		<category><![CDATA[death]]></category>
		<category><![CDATA[dimensional]]></category>
		<category><![CDATA[domain]]></category>
		<category><![CDATA[existence]]></category>
		<category><![CDATA[good]]></category>
		<category><![CDATA[human]]></category>
		<category><![CDATA[life]]></category>
		<category><![CDATA[objective]]></category>
		<category><![CDATA[people]]></category>
		<category><![CDATA[person]]></category>
		<category><![CDATA[Perspectives]]></category>
		<category><![CDATA[sees]]></category>
		<category><![CDATA[ship]]></category>
		<category><![CDATA[side]]></category>
		<category><![CDATA[space]]></category>
		<category><![CDATA[subjective]]></category>
		<category><![CDATA[subjectivity]]></category>
		<category><![CDATA[universe]]></category>
		<category><![CDATA[view]]></category>
		<category><![CDATA[world]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2009/issue-71-september-october-2009/need-a-third-eye/</guid>

					<description><![CDATA[“For he who has but one tool, the hammer, the whole world looks like a nail.” Since the time of Copernicus, natural philosophers have commonly assumed there is a real, physical world that exists prior to and independent of the human mind, and they have set themselves the task of penetrating “beyond the veil” of [&#8230;]]]></description>
										<content:encoded><![CDATA[<blockquote>
<p><em>“For he who has but one tool, the hammer, the whole world looks like a nail.”</em></p>
</blockquote>
<p>Since the time of Copernicus, natural philosophers have commonly assumed there is a real, physical world that exists prior to and independent of the human mind, and they have set themselves the task of penetrating “beyond the veil” of subjective impressions to that external “objective” world. Thus, the real world is viewed as something devoid of subjective experience. On the other hand, though the causes of experiences are thought to be objective and available to everyone, the experiences themselves are only available to the person experiencing them. This makes it almost impossible to draw a clear boundary between what constitutes objective or subjective experience.</p>
<p>Paulson, in his article “The Nearing Death Process and Pastoral Counseling,” proposes the acknowledgement of multiple domains for humans. He argues that reducing everything into one domain, either into the objective or subjective domain, causes problems: “This situation was illustrated by Viktor Frank through the aid of a three-dimensional model. In three-dimensional space, a cylinder is a cylinder, containing both rectangular and spherical components. But, when presented in two-dimensional space, the cylinder provides two conflicting views: it is either a sphere or a rectangle. One must be right and the other wrong (Fig. 1). In life, when a subject is reduced to the objective domain, consciousness, thoughts, feelings, and perceptions are viewed merely as biochemical reactions. That is, under the laws of science (physics, biology, and biochemistry), conscious thoughts, feelings, and perceptions cannot exist, whereas they do. Conversely, many postmodern philosophers reduce both subjective and objective domains into the cultural domain of shared meaning. In this view, the world we live in is completely relative.”</p>
<p>Attaining empirical knowledge through one’s sense-based experiences, one frames an individual view of the colorful face of creation. The constant flow of views and perceptions maps the external world in the human mind on two axes, one subjective and the other objective. This mapping process causes every individual living under the same sky to have a world of their own. For example, a despairing, lamenting, weeping person sees beings as weeping and in despair, while a cheerful, optimistic, merry person sees the universe as joyful and smiling.</p>
<p>This brings subjectivity to our attention. One can use this subjective point of view with the aim of strengthening faith in God’s existence and regarding every creature as part of the great fellowship of this faith, worshipping God. For a reflective person who is engaged in solemn worship and glorification discovers and sees to a degree the certain, truly existent and worship and glorification performed by all beings, while a person who abandons worship through neglect or denial sees beings in a state of idleness, as playthings in the hands of coincidence and mere accidents.</p>
<p>One should sometimes take the side of subjectivity to be able to feel joy and happiness in this worldly life. Although there is seemingly a dark and ugly face of existence, everything, stemming from Divine beauty, will eventually return to the same source. Although not everyone can fully understand this reality, everybody should always look at the brightest side of existence. As the famous scholar, Said Nursi, points out, “Those who attend to the good side of everything contemplate the good. Those who contemplate the good enjoy life.”</p>
<p>There is no doubt that all of us should view the created with an educated look. Eyes are the windows through which the soul sees outer space. One should be selective when it comes to where one opens those windows to. The thinking mechanism generates outputs depending on the inputs it receives. Everything is beautiful in itself or in its outcomes, thus the explorer of the universe should always beam his censors towards this beautiful side of the existence. One should support this subjective perception of the universe by every possible means, tolerating his ignorance and shortcomings in seeing the objective beauty of the universe.</p>
<p>As we all are human beings, we all have our own weaknesses in our personal realms. We can categorize the weaknesses embedded in our natures as follows: worldly ambition (that can result in forgetting about the Creator), greed, fear (which can make us sacrifice even our honor and integrity), racism and negative nationalism (which can mean one only feels satisfied at swallowing the rights of other nations), and selfishness. The main source feeding these weaknesses is thinking that one will live forever in this worldly life. This thought or feeling is completely subjective. None of us applies the concept of “death” to ourselves; everyone thinks it only applies to others. We see the mountains as stable, our surroundings as unchanging, and this observation leads us to think we will also remain unchanged. This deceptive subjectivity paralyzes sincerity and opens ways to the corruption and moral suicide of society. Explorers of the universe should spoil the poisonous sweetness of this subjectivity with the bitter taste of the contemplation of death itself. The reality of death is so vivid that it cannot be denied.</p>
<p>The example of a man in a small room of which four walls are mirrors can demonstrate this fact further. The man thinks that the small room is an infinitely large space, looking at its reflections in the mirrors. When the man stretches out his hand, touches the surface of the mirror and breaks it, he understands the inevitable reality. There is death, an end to unlimited wants and wishes for eternity on the earth. This objective fact exists regardless of what human minds think about it.</p>
<p>Human beings exist in impotence on this earth. It is as foolish to say that nature obeys our will or command as to say that a baby’s parents serve him due to his own power. Whenever delusions cause humans to think that they have a godly existence, they should remember Pharaoh’s fate and never forget that even a tiny microbe can defeat and force them to lie down for weeks. Hospitals, prisons and graveyards tear off this subjective mask of power and show the objective pure face of human beings’ underlying impotence.</p>
<p>Another important drawback of subjectivity is “familiarity.” Our lack of information and knowledge about a particular topic is our ignorance on that topic. However, if we do not even know that we lack that knowledge, this is called “compound ignorance.” For example, the rising and setting of the sun every day and spring’s appearing with bouquets of flowers at our doorsteps every year are not understood or appreciated by most people, as these natural events happen continuously without any interruption. People become blinded by a veil of “subjective familiarity.” They do not see the true value of events which appear to be usual and ordinary but in fact are extraordinary.</p>
<p>Another misuse of subjectivity is seen in the ways that people put a distance between each other and build a solid wall of enmity that blocks the way to peace and harmony in society. The reasons for putting up these barriers are far from being objective; they are only the dark shadows of our subjective caprices. Let us say that there is a ship carrying ten people out of whom nine are murderers and one is innocent. No one with right thinking would try to sink that ship in order to get rid of the nine murderers at the expense of the life of the one innocent. A judge looking at the incident through the lens of objectivity would demand the securing of the rights of the innocent.</p>
<p>Similarly, every human being on this earth is a spectacular ship built by the Creator. Everybody has good and bad sides. Nobody has the right to hate another person just because that person has some bad qualities. Hatred means sinking that hated ship of the individual in the eyes of the one committing the deed of hatred. Most of the arguments people use to support turning their backs on one another are as small as a pebble compared to arguments that are as great as mountains and that would bring apparently opposing sides together. All of us were created by the same God. This is a reason –for most- for fellowship stronger by far than the relation between the children of the same father. All of us are sharing the same slice of time out of thousands of years, a very small probability if one thinks of the millions of years since the beginning of creation. We all have a longing for love, tenderness, warmth, openness, honesty, and integrity. We are all afraid of clashes, tears, fears, the unpredictability of darkness, and sorrows. We, as fellow human beings, have so much in common.</p>
<p>The human being’s objective and subjective view of the universe should be a perspective illuminating both the soul and body. That perspective adds a third dimension to the two-dimensional picture in most of our minds. It highlights the wonders of this universe and the depth and richness hidden under the flat, quiet, calm ocean of creation.</p>
<h3><b>Notes</b></h3>
<ol>
<li>Wallace, B.Alan, , “The Intersubjective Worlds of Science and Religion,” from Science, Religion and Human Experience, Oxford University Press, 2005.</li>
<li>Frankl, V. E. (1959). The will to meaning, New York: New American Library</li>
<li>Paulson, Daryl S, “The Nearing Death Process and Pastoral Counseling,” Pastoral Psychology, Vol. 52, No. 4, March 2004.</li>
<li>Nursi, Said, The Letters, NJ: Tughra Books, 2007, p. 450.</li>
<li>For more discussion on human weakness see Nursi, 2007, pp. 399–413.</li>
<li>See Nursi, 2007, p. 282.</li>
</ol>
]]></content:encoded>
					
		
		
			</item>
	</channel>
</rss>
