In reality, people who habitually go to sleep very late at night have difficulty waking up in the morning. This happens because of disturbances in the body’s internal clock or circadian rhythms. Circadian rhythms are important in determining the sleeping and feeding patterns of all creatures.

There are clear patterns of brainwave activity, hormone production, adjustments to body temperature, blood pressure and many other biological activities linked to this daily cycle.

It is known that melatonin, a hormone with a high level of concentration at night and low levels during daytime, regulates the circadian rhythm.2 However, there are other factors that activate or inhibit the internal body clock and several studies have demonstrated that light on the eye’s retina is a more powerful influence on human circadian rhythms.

Blue light

As light that is radiated from the sun travels through the atmosphere, some shorter wavelengths of light, such as violet and blue, are absorbed by gas molecules and then scattered all around the sky. This gives the sky a blue appearance. According to Dr. Mark Rea, director of the Lighting Research Center, our daily rhythms are in fact blue sky detectors, and he notes, “Blue sky is ideal for stimulating the circadian system because it’s the right color and intensity, and it’s ‘on’ at the correct time for the right duration, the entire day.”3

Researchers have used light for jet-setters, sleep-troubled patients, and shift workers to set their body clocks and solve sleep problems. Moreover, they claim the dogma that the 24-hour biological clock is set by light alone is a misconception that many scientists have believed for years.4 Steven Lockley of Brigham and Women’s Hospital, a Harvard research and teaching affiliate says, “The visual system in humans is most sensitive to green light, but when we exposed twelve healthy young men and women to the same amount of either green or blue light, their 24-hour rhythms shifted twice as much with blue than with green.”5 After exposure to blue light, their body clocks were rearranged by three hours, whereas the effect of green light was a change of about 1.5 hours. So, if your eyelids get heavy around 11 p.m., 6.5 hours of exposure to blue light will keep you up until 2 a.m. Since television and computer screens produce blue light, watching them too much at night may inappropriately affect the sleep cycle.6 However, if a change in shift makes you sleepless at 4 a.m., proper blue light therapy might help you sleep three hours longer.

To reduce the impact of synthetic light on our biological system, lighting manufacturers have been developing dynamic lighting control led by computer based systems. For example, to perk people up in the morning, the lamp increases the blue light concentration. After lunch, it again produces more blue light to counter afternoon sleepiness. In Europe, such systems have already been installed in some places including some hospitals, business offices, town halls and traffic-control centers.

Keeping all this in mind, we see how blue light affects our daily life. So, sleeping in some parts of the daytime can have advantages and disadvantages for sustaining optimal performance.

Daytime sleep in Prophetic tradition

If we turn our attention to the life of the Prophet Muhammad, (peace and blessings be upon him) we see how he successfully set an example for his Companions. It was the practice of the Prophet and his Companions not to sleep after the dawn prayer, the first of the five daily prayers, as it is a time of blessing. He would read some parts from the Qur’an and reflect on the universe and its Creator at a time when concentration is at its peak and the mind is clear of daily worries. Once dawn broke, the Prophet would pray and then speak with people who stayed behind for some time. Therefore, some of the early Muslims disliked the idea of sleeping immediately after dawn because being awake at this time was encouraged. In his Risale-i Nur collection, Bediuzzaman Said Nursi explains the three types of daytime sleep as follows:

The first is “ghaylula.” This is from pre-dawn to forty minutes or so after the sun has risen, the time when prayer is lawful but reprehensible. Sleep at this time is contrary to the practices of the Prophet, since according to hadiths, it leads to a decrease in one’s livelihood and to its being unfruitful. The time most appropriate for preparing to labor for one’s sustenance is when it is cool. When this time has passed, lethargy descends. It has been established through numerous experiences that just as this is detrimental to that day’s labor and indirectly to one’s livelihood, so also is it the cause of unfruitfulness.

Based on our limited knowledge about blue light, by sleeping at this time we may cause our biological rhythms to delay because of missing the right blue intensity at the correct time, which can result in a shift in sleep period and other shifts in daily cycles.

Nursi goes on:

The second is “faylula.” This is from the afternoon prayer till sunset. This sleep leads to a diminution of life, that is, it makes life that day shorter and makes it pass in a state of semi-sleep due to drowsiness, thus causing a physical deficiency to life. So too in an immaterial aspect, since most of the results of that day, material and immaterial, become apparent after the afternoon prayer, to pass that time in sleep as though prevents those results being seen and makes the day as though not lived.

The third is “qaylula,” which is in accordance with the Sunna of the Prophet. It is from mid-morning to just past noon. This sleep is part of the Sunna since it allows a person to rise at night to pray. So also in the Arabian Peninsula to rest from work at noon when it is intensely hot is the custom of the people and of the area, so has further strengthened this Practice of the Prophet. This sleep increases both life and sustenance. For half an hour’s qaylula sleep is the equivalent of two hours’ sleep at night. That means it adds one and a half hours to a person’s life every day. It saves one and a half hours from the hand of sleep, the brother of death, and makes it live, adding it to the time of working for one’s livelihood.8

Recently, this type of sleep or nap has been strongly advised for health and for enhancing daily performance. “When I was at NASA we gave the pilots a planned nap in the cockpit,” says Rosekind, a board member of the National Sleep Foundation. “While two pilots flew the plane, the third would have forty minutes to nap. We found they would sleep for twenty-six minutes, which boosted their performance by 34% and their alertness by 54%.”9 He explains that the pilots were able to improve their performance significantly, and he adds that the effects of a short nap of less than a half hour lasted for two to three hours. Similar research shows that in this way you can make yourself more alert, reduce stress, and improve cognitive functioning, which means more patience, less stress, better reaction time, increased learning, and more efficiency.

Each day our daily life gets faster and we unintentionally ignore our body and its need for rest, which leads to sleep deprived eyes, disturbed sleep cycles, stress, and so on. Sleeping well keeps us alive longer. But this does not mean sleeping for a long time, which increases the risk of death. What we learn from the Prophetic tradition and research into the effects of light on our biological clocks can help us to find and to arrange proper times for sleeping and coordinating our daily activities. Once we achieve this, benefits in spiritual life, health, social interactions, learning and thinking clearly will follow.

Notes

1.National Sleep Foundation

2.Cimo M, “New Math: Two Plus Two Equals Three,” Lighting Research Center News, January 23, 2006; Arendt J, Melatonin, “Circadian Rhythms, and Sleep,” The New England Journal of Medicine (2000) Vol. 343, No. 15.

3.Cimo, 2006.

4.Cromie J.C, “When light has you singing the blues,” Harvard University Gazette, Sept 23, 2003.

5.Ibid.

6.Raloff J, “Light Impacts,” Science News Online, May 27, 2006.

7.Bediuzzaman Said Nursi, The Flashes, Twenty-eighth Flash, Sözler Publications, Istanbul: 2000, p. 367.

8.Ibid.

9.Hatfield H, “The Power of Napping,” WebMD Feature; Bill Anthony, PhD, author, Art of Napping; professor, Boston University. James Maas, PhD, professor of psychiatry, Cornell University, Ithaca, N.Y. Mark Rosekind, PhD, president, chief scientist, Alertness Solutions; board member, National Sleep Foundation, Cupertino, Calif.

Every part of creation is a mirror displaying various names and attributes of God in unique combinations and degrees. The human being is merely the brightest mirror reflecting God’s divine names and beauty even more gracefully than the whole universe. What separates us from Him is our minds, hearts, and egos that claim to have a separate existence. For those who see pointers to Him in every being, it is not possible to be far from Him. They do not expect Him to “come down to establish a loving relationship with His creation” as He is never away from His creation. We can feel that proximity only through losing our partial existence in the Whole. When the “self” disappears in God’s all-encompassing presence, then all existence besides God quickly loses significance.

The mainstream theological school of Islam distinguishes between two categories of existence. The first is the necessarily existent (wajib al-wujud), which defines the existence of God the Most High. God the Most High exists independently through Himself and His existence is necessary for the existence of all other things. None of His creation shares in His existence. The second category is contingent existence (mumkin-il wujud). This defines the existence of created things that may or may not exist. Created things have no independent being and their existence is not necessary.

God the Most High brought them into being through His will, power and knowledge, and if He willed they would have no existence. Creation only exists through Him giving it being, so in this sense it exists through Him, but doesn’t share in His independent, necessary being. The core concept of the spiritual tradition of Islam is ihsan, that is living in the constant consciousness of God’s presence. This concept is described in a famous and authentic prophetic tradition narrated by Abu Dawud where the archangel Gabriel appears in a meeting of Prophet Muhammad, peace and blessings be upon him, as a traveler, sits down close to the Prophet and asks him three questions: [The stranger] said, “Tell me about iman (faith).” [The Prophet] said: “It is that you affirm God, His angels, His books, His messengers, and the Last Day….” [The stranger] said, “Muhammad, tell me about Islam (submission to God).

”The Messenger of God, may God bless him and grant him peace, said, “Islam is that you bear witness, testifying that there is no object of worship aside from God, and that Muhammad is the Messenger of God; and you establish the ritual prayer; and you give the prescribed alms; and you fast in the month of Ramadan; and you perform the pilgrimage to the House if you are able to find a way to do so.

”Finally, he said, “Tell me about ihsan.” [The Prophet] said, “It is … that you worship God as though you see Him, for though you do not see Him, truly He sees You.” The ultimate goal in some Sufi schools is to achieve a state where one is so immersed in the presence of God that he or she regards the creation as nothing but a collection of pointers to Him. Wherever such a seeker looks, (s)he sees nothing but reflections of God’s Names. In a sense, the seeker “annihilates” his self in the presence of God. God’s transcendence If the Whole is likened to the Ocean, and the part to a drop, the Sufi says that witnessing the Ocean with the eye of a drop is impossible. However, when the drop becomes immersed in the Ocean, it sees the Ocean with the eye of the Ocean. It is true that God is transcendent and His Essence is a mystery to us. He exists in His unique way which is impossible to grasp for the human mind. However, God has chosen human beings, the most glorious of creation (ashraf al-mahluq), to get to know Him. He wanted to be known by us and granted us vehicles to understand His names and attributes. This vehicle is the “ego.” This vehicle is given to humankind to understand the Lordship of God and to feel our Oneness with the God. Ironically, human beings use this vehicle to distance themselves from God, and to question God’s closeness to them.

Ego: Both the remedy and the venom

Human beings can only know God with the help of their ego, which constitutes a hypothetical bounding line (wahid- i qiyasi) to understand God’s immenseness. It is the key that can open the secret treasures of God’s names and the enigmatic meaning of the universe. How? The great Islamic scholar Nursi answers this question as follows: “An absolute and all-encompassing entity has no limits or terms, and therefore cannot be shaped or formed, and cannot be determined in such a way that its essential nature can be comprehended. For example, light undetermined by darkness cannot be known or perceived.

However, light can be determined if a real or hypothetical bounding line of darkness is drawn. In the same way, the Divine Attributes and Names (e.g., Knowledge, Power, Wisdom, and Compassion) cannot be determined, for they are all-encompassing and have no limits or like. Thus what they essentially are cannot be known or perceived. A hypothetical boundary is needed for them to become known. In our case, this hypothetical boundary is our ego. Ego imagines within itself a fictitious lordship, power, and knowledge, and so posits a bounding line, hypothesizes a limit to the all-encompassing Attributes, and says: ‘This is mine, and the rest is His.’ Ego thus makes a division. By means of the miniature measure it contains, ego slowly comes to understand the true nature of the Divine Attributes and Names. Through this imagined lordship, ego can understand the Lordship of the Creator of the universe. By means of its own apparent ownership, it can understand the real Ownership of its Creator, saying: ‘As I am the owner of this house, the Creator is the Owner of this creation.

Through its partial knowledge, ego comes to understand His Absolute Knowledge. Through its defective, acquired art, it can intuit the Exalted Fashioner’s primary, originative art.

“Our Creator knows that we need a God that is close to us. He knows that when we feel that He is not close to us we won’t be satisfied. That is why he has chosen us and furnished us with the necessary tools to know Him. He granted us a magical key to unlock the mysteries of His Essence and His Creation. Yet, while the key is meant to be the remedy, it also has a potential to turn into a poison that blurs our consciousness and detaches us from the Essence. An illusory individuation, a deceptive wisdom and knowledge covers our sight and conceals the truth; the truth that “There is no existent but He.”

Counterargument to: “Islam is about man trying to please God by obeying His will”

“And I have not created the Jinn and the men except that they should serve Me.” (Dhariyat 51:56) “And that you should serve Me; this is the right way.” (Ya Sin 36:61) According to the Islamic view, serving God, obeying His will and worshipping are the human being’s fundamental obligations. However, the purpose of worshipping is to grow in faith, knowledge and love of God and to feel His proximity. Seeking God’s pleasure in one’s worship, conduct and life in general is seen as a necessary outcome of one’s growing love of God. Worshipping God to attract God’s reward or to avoid punishment is seen as an inferior level of faith. If we accept that the main purpose of worshipping God is to get close to Him, or more accurately to “be aware of our closeness to Him,” then the main purpose of human beings in this world emerges as removing obstacles that we put up between ourselves and God who is always close, and attaining His consent by doing that. Anything that brings about this proximity or guides in that direction is praiseworthy and it is considered as worship. One of the means to help man in his journey towards God is knowledge; accordingly, a prophetic saying (hadith) reveals that gaining knowledge is considered as worship: “God can be worshipped and served by means of knowledge; bliss in this world and hereafter comes through knowledge; and adversity of this world and hereafter lies in ignorance.

”The purpose of God’s commandments and all the obligatory worship is to seek proximity to God. And it is only God’s mercy that He shows us the way that will lead us to Him. Through prayer, contemplation, fasting, and purification of the soul by begging His forgiveness, the “ego” abandons his vice and arrogance. The ego realizes the Truth and becomes aware of his proximity to God which was concealed from him by claiming a separate existence.

The basis of attaining closeness and proximity to God is through seeking (talab) Him, and this seeking is manifested in the form of practice and actions that allows one’s level of closeness to increase. By sending us down to this worldly realm and making us in our bodily forms, God placed within us a capacity to perform actions through which the doors of the levels of proximity were fully opened.

It is us who should attain a proximity to God, because He already is close to us. Such an awareness and appreciation are what makes people “friends to God” (wali). One way of attaining this awareness is through being an “abd” to God which means acknowledging your position as a servant. However, attaining proximity to God is an endless journey. There are levels of proximity (qurb) that awaits us, without boundaries. This is why even the Prophet Muhammad, peace be upon him, whose proximity to God is unimaginable and unattainable by the rest of the creation, was commanded to supplicate with “Oh God, increase my knowledge.” The connection between knowledge and proximity is clear in that the former increases the latter.

Yet, since knowledge is infinite, so is proximity, thus reaching a “finish line” is impossible. It is mentioned in an authentic prophetic tradition that God Most High said: “When the servant draws close to Me a hand’s span, I will draw close to him an arm’s length. And when he draws near to Me an arm’s length, I will draw near to him a fathom’s length. And when he comes to Me walking, I will go to him running.”2 God the Most Merciful tells us that our intention to seek Him is what He is expecting from us and the levels of closeness will be ascended quickly if we are eager to feel the proximity. Since He is already close to us, it is our choices and intentions that will either allow us feel the “oneness of being” or keep us away from Him as a result of our unwillingness to get rid of the illusory wisdom and arrogance. The spiritual life in Islam begins with the inner struggle with the ego. It is the fist stage in the journey that will make us aware of our position in front of God, to know God, love God and be a drop in the Ocean of oneness. Distracted and polluted by worldliness, the lower self has a tendency to drag the human creature down into arrogance and vice. Only by a genuine effort of will can the sincere seeker of Truth achieve the purity of soul which enables him to reach total “awareness” of God’s closeness.

Sophia Gallant is a sociologist in Houston, Texas. Yuksel A. Aslandogan is the Vice President of Institute of Interfaith Dialog, Houston, Texas.

Notes

1. Bediuzzaman Said Nursi, The Words, Thirtieth Word, The Light, Inc., NJ:2005, pp.552-3.
2. Bukhari from Abu Hurayra and Anas. Also narrated by Muslim, Tirmidhi and Ibn Majah.

Let us consider the case of the “heap” to understand the idea of vagueness in fuzzy logic. What is a heap? What do we mean when we are talking about a heap of dresses, for example? Assume that we have a heap of clothes and we begin to put them into a wardrobe by taking each item of clothing separately out of the heap. We take first the socks, then the shirts, and so on. In doing this, we observe that the heap disappears slowly. Finally, when we take the last of the items of clothing, there is nothing left. So, at what stage of this activity does the heap disappear? Does the heap disappear when we have taken away half of the clothes, or one third of them, or all of them? These questions are very important in terms of the logical characterization of this case. Classical logic, which depends on two truth values, namely true-and-false, does not answer these questions because there is no clear boundary between being a heap of clothes and not being a heap of clothes in this case. If we consider the constantly changing flow of events in the universe, we face similar cases all the time. Another outstanding example is the spectrum of light. There are no clear boundaries between colors. Where exactly is the boundary between yellow and light yellow? The indeterminacy of boundary can be observed in social area as well. Political ideologies range from the most radical right wing to the most radical left wing, and we can observe many different variations of ideologies in this range. For example, sometimes we may have difficulty in identifying the position of a particular political movement if it is between moderate right wing and moderate left one.

This is a special case of indefiniteness which we call “fuzziness” or “vagueness,” but there are different types of indefiniteness. For instance, when we use the term “bank” unqualifiedly, we can either mean a financial institution or a place to sit. We call such cases “ambiguous.” Whether it will rain next week or not is another indefinite case related to our ignorance of future.

The indefiniteness, which we deal with in fuzzy logic, is vagueness. The problem of vagueness is as old as humanity. It is discussed under the name of “sorite paradoxes”in ancient Greek and under the term “fuzzy logic” today.

Fuzzy logic proposes a systematic model to solve problems in vague cases. This model depends upon mathematical symbolization. It seems that fuzzy logic presents a better way to deal with vague cases than the way suggested by classical logic. Let us see why this is so.

Classical two-valued logic

Classical logic has two truth values, namely true and false. Both Aristotelian logic and symbolic logic have two truth values even though there are important differences between them. For that reason, both of them are treated under the name of “classical logic.” Aristotelian logic analyzes sentences by dividing them into subject and predicate. Consider the following sentence: Tom played tennis with John. “Tom” is the subject in this sentence and “played tennis with John” is the predicate. On the other hand, in symbolic logic, this sentence is analyzed in a different way. According to symbolic logic, there are two subjects in this sentence, namely Tom and John. The predicate of the sentence is a relation between these two subjects, namely “played football.” Furthermore, since Aristotelian logic is very close to metaphysics, it has a very strong existential import. For instance, if we assert the sentence “All dogs bark,” we also imply that there are dogs, according to Aristotelian logic. However, there is no such existential import in symbolic logic. In the view of the latter, we cannot say anything about the existence of dogs when we assert the above-mentioned sentence. What we mean by that sentence is that if something is a dog, then it barks. Nothing more, nothing less.

Although there are some differences between Aristotelian and symbolic logic, both of them are two-valued logics. However, we cannot call classical logic the logic of “white-and-black” because it has two values. This is a common mistake stemming from not appreciating exactly to what these two values refer. White-black duality ignores the grey tones between white and black. However, classical logic covers all tones between white and black. The duality here is between whiteness and non-whiteness or between blackness and non-blackness. So non-whiteness encompasses the grey tones.

The problem in classical logic is not exclusion of the grey tones but its insufficiency in representing them adequately. We have a problem in determining the boundary between whiteness and non-whiteness, and this is the problem of vagueness. Therefore, classical logic is inapplicable to vague cases, but clear cases lie in the area to which classical logic is applicable. Think of mathematics. A number is either even or odd, and this is clear for any number in question. There is a clear boundary between odd and even numbers. In comparison to classical logic, fuzzy logic claims that it has wider range of applicability. Let us examine fuzzy logic in detail.

Fuzzy logic

There is a discussion as to whether a logical system for vague concepts can be established or not. Gottlob Frege, one of the founders of symbolic logic, thought that logic cannot be applicable to fuzzy concepts and restricted logic to the area including clear concepts. The fundamental problem in vague concepts is determining the boundary between a concept and its negation. Assume that this problem cannot be solved by a two-valued logical system. Does it mean that the problem in question cannot be solved by three- or many-valued logical systems either?

Now, let us examine a three-valued logical system and see whether it solves the problem or not. In 1920, a Polish logician, Lukasiewitcz, presented a three-valued logical system whose values are true, false and indeterminate.

Assume that “This object is white” is true, “This object is black” is false and “This object is grey” is indeterminate in this logical system. Does presenting the grey area as indeterminate solve the problem of vagueness or make it more complex? In fact, the problem becomes more complex. The complexity arises from the question as to whether there is a certain, clear boundary between white and grey or between black and grey. Again here, we cannot claim that there is such a clear boundary. Vagueness is observed not only between black and non-black but also between black and grey. The problem of vagueness does not disappear if you increase the number of truth values in a logical system. For instance, postulating twenty truth values, instead of three, does not bring a solution to this problem. However, if you establish a logical system that includes infinitely many truth values, then the problem of vagueness seems to disappear. In that case, all colors with their tones can be analyzed by a scale of real numbers between 1 and 0. The infinitely many real numbers in this scale correspond to a truth value and so we can postulate a truth value for every tone of a color. For instance, “1” refers to pure blackness, “0” refers to pure whiteness, “0.5” refers to whiteness and blackness, “0.2” refers to a color whose whiteness overweighs its blackness. Since there are infinitely many truth values, you can give a truth value for any place in the light spectrum. In this way, we can get rid of determining clear boundaries.

The first serious study on fuzzy logic was carried out by Lotfi Askerzade Zadeh in 1965. He published an article called “Fuzzy Sets” when he was a professor of electrical engineering in the USA. Fuzzy logic was then improved by Zadeh, Joseph Gougen and many other scholars.

Fuzzy logic has a wide area of applicability in technology today ranging from washing and dishwasher machines to computers. Since it brings the advantage of flexibility, it increases productivity. Fuzzy logic is also used in the research program of artificial intelligence and modeling the human mind in computers.

If we come back to the internal structure of fuzzy logic, we observe that some of the fundamental principles of classical logic, such as the principle of non-contradiction and the law of the excluded middle, are not valid in fuzzy logic. For instance, if the proposition that this man is bald is true to a degree of 0.3, we say that this man is neither completely bald nor completely non-bald. The position of this man is the intersection point of baldness and non-baldness to a degree of 0.3. This man belongs to the set of baldness to a degree of 0.3 and to the set of non-baldness to a degree of 0.7.

An Islamic evaluation of vague cases

Said Nursi was one of the outstanding Muslim scholars of the twentieth century. He considers vague cases which give rise to relative truths to be important in terms of understanding divine activity in nature and knowing God’s Names and Attributes:

. . . God, the Eternal All-Wise and as the requirement of His Eternal Grace and Wisdom, has created this world as a testing arena, a mirror to reflect His Beautiful Names, a vast page upon which to write with the Pen of His Destiny and Power. People are tested here to develop their potentialities and to manifest their abilities. This emergence of abilities causes relative truths to appear in the universe, which, in turn, causes the Majestic Maker’s Beautiful Names to manifest their inscriptions and make the universe a missive of the Eternally-Besought-of-All.1

So, relative truths play an important role in knowing God. They are relative because they do not correspond to clear and fixed cases. As we remember from the analysis of fuzzy logic, these truth values are between 1 and 0. All values between 1 and 0 are relative because the case represented with such values belongs to two different sets with different values and the value depends on the perspective from which you are looking at it. If the truth value of “This man is bald” is 0.3, then the truth value of “This man is not bald” is 0.7.

According to Nursi, God gives rise to vague cases by mixing opposites. He mixes goodness with badness, beauty with ugliness, and so on. By this mixture, there occur infinitely many levels of beauty, goodness, and other qualities.

On the other hand, there is a famous saying of the Prophet Muhammad, peace be upon him, which suggests a criterion for human actions in fuzzy cases: “What is permitted is clear, what is forbidden is clear as well. There are doubtful cases between these two cases. Whoever avoids the doubtful things, his religion remains clean. Whoever approaches the doubtful cases, he approaches the forbidden cases as well.” Prophet Muhammad points out the vague cases between forbidden and unforbidden cases. In Islamic jurisprudence, scholars suggested many categories to represent these vague cases. Some cases are close to the forbidden ones, and some are not. They named each case separately. Fuzzy logic can be used in this regard to represent these different levels better than classical logic’s representation. Think of the following case. Grape juice is permitted in Islam. However, wine, which is prepared from grapes, is forbidden. More interestingly, there is a stage of fruit juice which is permitted but very close to the forbidden case. This stage is called “must” (unfermented grape-juice). After this stage, it gradually becomes closer to the forbidden case and we cannot exactly determine where the boundary between permitted and forbidden cases is. The Hadith emphasizes this point and suggests that we avoid such cases.

Conclusion

Fuzzy logic represents a wider area of cases than classical logic does. By representing vague cases in a symbolic and systematic way, fuzzy logic functions better than classical logic. However, fuzzy logic is not the ultimate system of thought which has been established by human mind. We should not exaggerate its importance by claiming that it can represent any case no matter what it is. For instance, fuzzy logic is inadequate to represent the logical relations between concepts including the notion of infinity. To deal with cases of infinity in mathematics, a different type of logic is proposed, namely intuitionistic logic. All of these systems show that the human mind is powerless or unable to grasp or establish a system which represents all cases and any case no matter what it is.

Notes

1. Nursi, Bediuzzaman Said, The Words, Twenty-ninth Word, The Light, Inc. NJ: 2005, p. 546.

References

Williamson, Timothy. Vagueness. New York: Routledge. 1994.

Mukaidono, Musao. Fuzzy Logic for Beginners, New Jersey, World Scientific, 2001.

In modeling atmospheric convection in the 1960s, a meteorologist and mathematician at MIT, Edward Lorenz, came up with a mathematical model showing that small perturbations in input parameters result in huge deviations in output, the “butterfly effect.” In other words, in theory, a butterfly flapping its wings in China could bring about a storm in New York City. This is another way to express sensitive dependence on initial conditions. Getting up two minutes late, one may end up missing the bus, which in turn costs one the job interview. As a result of pushing the brake pedal one second earlier a person’s life can be saved. Such slight changes in daily actions are actually signs of how tiny changes are relevant with our lives and how sensitive the future is to the present. Such dependence is called nonlinearity and many scientific problems, such as the well-known Navier-Stokes equations, have been awaiting a solution because of this complexity. In contrast to a deterministic approach, which is based on the idea that the knowledge of the past enables one to make future prediction, a nonlinear (or chaotic) approach claims that the future is not that straightforward.

In contrast to what we used to believe, chaos does not mean complete disorder. Some complicated long-term events may have a hidden order. Being bound by time prevents us from knowing the future. It is in this sense, that time can be said to be another dimension, so that together with the other three, our living environment is formed. To be able to control or observe time-dependent events, the individual of this four-dimensional space may need to move outside of time. To understand this idea better we may analyze the well-known butterfly example. In Figure 1, the behaviors of three different variables are shown on the horizontal time axis, where they are very irregular, complicated and chaotic. However, when the same motions are transformed into another space where time is hidden, what we see is an interesting order between these three variables.

Chaos and spiritual life

The human being’s spiritual life is also sensitive to small changes. We are continuously exposed to our personal desires and Satan’s whispers. One small sin is an invitation to worse ones which eventually accumulate and trouble the soul. Similarly, every good deed, no matter how small, has the potential to become a ticket to paradise. It just depends upon the situation in which it was performed and the level of sincerity in our heart. Giving water to a thirsty dog is not an extraordinary act, but in the particular case mentioned in a tradition of the Prophet Muhammad, peace be upon him, this sincere act was significant enough to purify a very sinful person, while another went to hell because of letting a cat starve. In another tradition, the Prophet says, “When a person first commits a sin, it falls as a black dot in (the clean slate of) his heart; if he refrains, repents, and seeks forgiveness, it is however erased; if, on the other hand, he were to persist in sin, the dot will gradually expand until it covers the entire heart.” The Prophet then explained, “This is the state of sealing the hearts that God warned (us) of in the Qur’an: Nay the sins they have accumulated have covered their hearts like a seal” (Mutaffifin 83:14). Likewise, in his Risale-i Nur collection Nursi says, “Sin, penetrating the heart, will blacken and darken it until it extinguishes the light of belief. Within each sin is a path leading to unbelief. Unless that sin is swiftly obliterated by seeking God’s pardon, it will grow from a worm into a snake that bites the heart.”1 Likewise, initial tiny scruples can grow exponentially and destroy hope in the heart in an unexpected way. Nursi explains this in the following way:

O you afflicted with involuntary evil thoughts and fancies, such things resemble a misfortune. The more you dwell on them, the more they grow. If you ignore them, they dwindle away; if you exaggerate them, they swell; if you belittle them, they die down. If you fear them, they become grave and make you ill; if you do not fear them, they become slight and remain hidden. If you do not know their real nature, they persist and become established; if you recognize their nature, they disappear.

. . .

Satan first casts a doubt into the heart. If the heart does not admit it, he offers a blasphemy and causes the mind to recall some unclean memories and pictures, some ugly scenes that resemble blasphemy. This causes the heart to despair. People experiencing such thoughts think that they are acting wrongfully toward their Lord and so feel great agitation and anxiety. To free themselves, they flee from the Divine Presence and want to plunge into heedlessness and forgetfulness.2

From the human being’s perspective, each time-dependent event can have very complicated consequences but it always bears God’s signature and His divine order. He is the only One Who knows the future, as stated in the verse: “They said, ‘Why hasn’t a miracle come down to him from his Lord?’ Say, ‘Only God knows the future.’ Therefore, wait, and I will wait along with you” (Yunus 10:20). It may not be possible to see tomorrow, but we should be aware that each small change we make affects our future. Many scholars lived in such a way that they were always carefully watching their hearts to take immediate action on small deeds or scruples. For every event or option we face, the decision is up to us to, like whether we smoke or not, whether we lie or not, whether we get up early or not and so on. These sets of small decisions play a role in terms of the future we do not know. Although they are small, they have such a big impact and should not be underestimated. Even reading this article was one of these small things you had the choice to do or not to do!

Notes

1. Bediuzzaman Said Nursi, The Flashes, The Second Flash, Sözler Publications, Istanbul:2000, p. 22.

2. Nursi, The Words, Twenty-first Word – Second Station, The Light, Inc., NJ: 2005, p. 288.

References

Gleick, J., Chaos: Making a New Science, New York: Penguin.

Lorenz, E. N. “Deterministic Nonperiodic Flow.” J. Atmos. Sci. 20, 130-141, 1963.

Strogatz, S., Nonlinear Dynamics and Chaos. Perseus Publishing.

]]> https://fountainmagazine.com/all-issues/2008/issue-61-january-february-2008/beware-of-others/ Tue, 01 Jan 2008 00:00:00 +0000 http://107.21.79.195/all-issues/2008/issue-61-january-february-2008/beware-of-others/ In My Fair Lady, a satirical movie based on George Bernard Shaw’s Pygmalion, Henry Higgins makes a wager with his friend that within six months he can transform a coarse Cockney flower girl, Eliza Doolittle, into a lady who can take her place in high society. After making his bet, Higgins starts his experiment simply by getting her to have a bath and change her dirty clothes. Immediately afterwards, he begins working on her vulgar accent; as he believes that diction is what really sets the classes apart. He has no doubt that as soon as she acquires perfect upper-class diction, she will be ready to deceive others and disclaim her plebeian origins.

Upon brief contemplation of the relationship between language and identity, it is not easy to deem Higgins totally unjust in classifying people according to their diction, since there is a strong relationship between the language we use and the personal and social identity we have. A Harvard graduate, who also studied at Columbia and the Sorbonne, David S. Thomson, confirms this: “No one can speak without broadcasting his origins, his role in life, and ultimately his identity. For the language that every individual uses is the product of the entire social forces that affect his behavior: the society in which he lives, his class, his occupation, and his own unique experience“ (p.109).

Here, Thompson summarizes how we acquire our language, verifying that to classify people based on their way of speaking is not completely inappropriate.

On the other hand, how we are perceived in the eyes of others, namely our perceived identity, is also shaped by the language we use. In other words, just as language is a product of our social and personal identity; our identity is formed and molded in accordance with the way we use language. On the whole, language is a distinctive characteristic that reveals the social status of people and affects who they are and whom they are seen to be. Most people automatically start judging a person favorably or unfavorably as soon as they hear them talking and when they detect a certain kind of accent or dialect, it is usually enough to deduce whether they belong to a higher or lower status in society. According to the studies of Colin Baker, the author of Attitudes and Language, “people’s attitudes toward dialects and their speakers consistently reveal that speakers of the standard dialect are considered more intelligent, better looking, and wealthier than speakers of nonstandard dialects” (in Dubrow and Gidney p.109).

Even so, there is not always a direct parallelism between people’s accents and the personal and social identities they have. Neither classifying a person who speaks with a standard accent as educated and intelligent, nor labeling others whose speech have traces of a non-standard language variations as unlettered and substandard would be right. Furthermore, when the linguistic characteristics of people are manipulated in order to produce stereotypes based on their national or social affiliations, it turns into an issue that needs careful attention.

Noticeable examples of such stereotypical representations are not scarce in many animated movies, in which language variations are widely used as a quick way to build character and affirm stereotype. They are frequently used to represent national tensions through portrayal of villains and not-so-likeable characters. In a broader picture, it would be true to argue that many movie producers use language variations in a stereotypical fashion which teaches children to discriminate ethnocentrically and maintains the status quo by creating fear of “the other.”

Due to the nature of animation, the majority of animated movies rely heavily on language to mark characters’ personalities. To build characters and convey their messages, producers basically make use of two kinds of language variations: foreign accented English and a range of English dialects. Linguistically, Julia R. Dubrow and Calvin L. Gidney define foreign accent as “the product of the interference of one linguistic system with another language system” while defining dialect as “simply, a variety -any variety- of a language.” Yet, the outcome of language variations is more significant than their actual meanings. Since these language variations are labeled as non-standard forms in a language system, they do not enjoy equal prestige and are associated with low quality. Upon their studies on evaluation of accented speech, Josiane F. Hamers, a professor of psycholinguistics, and Michel H. A. Blanc, who is an emeritus reader in applied linguistics, conclude that “any accent different from the accepted norm is less positively evaluated than the norm itself” (p.224). On the other hand, numerous researches have shown that standard-accented people are rated relatively highly for intelligence, education, wealth, and kindheartedness as opposed to people who speak with foreign accents and dialects. At this point, a question comes to mind; if there are standard-accented people, then what is a standard accent? In order to clarify what standard language is, it is practical to quote Dubrow and Gidney, as it is possible to find an answer to this question embedded within one of their sentences: “Generally, those dialects spoken by people who enjoy social prestige, power, and wealth are more favored than the dialects of people of more limited power, wealth, and social prestige; the former come to be known as the standard dialect.” It is noticeable that they do not define standard dialect in a linguistic manner. Instead, they point to a common acceptance of what constitutes norms of language variations in the society in relation to socioeconomic status. Regarding the power of pronunciation varieties, another authority in the area of sociophonology, Rosina Lippi-Green, even claims that accent is “a litmus test for exclusion,” supporting the argument that language variations are not just varieties of language but have more profound meanings concerning the identities of people (p.64). In our case, such linguistic characteristics, namely foreign accents and dialects, are used to representthe superiority, inferiority, amiability, and unfriendliness of characters.

A significant aspect of animated movies that should not be overlooked is studied by Harold Schiffman, a professor from University of Pennsylvania. He argues that the accents used in some animated movies are usually “non-authentic”-differing from the accent that would be used in real life- and that they are present to create an effect. That is, characters in the movies do not speak with a non-standard dialect or foreign-accented English because the characters in the movie have different origins. On the contrary, the linguistic variations are usually manipulated to build stereotypes or to indicate villain or hero status.

In order to illustrate the claim that producers use language varieties non-authentically to create an effect in its animated movies, we can provide some solid examples. For instance, racial stereotyping is evident in the movie Aladdin, which takes place in a mythical Arabian Kingdom. Throughout the film, evil characters are depicted with long beards, dark skins, and wicked laughs as well as with heavy Arab accents, whereas the lovable characters, Aladdin and Jasmine, are drawn light-skinned, and attractive, and, interestingly, Aladdin and Jasmine sound all-American. Noticing the non-authentic use of accents in the movie, Yousef Salem, a former spokesperson for the South Bay Islamic Association, accuses the film of being discriminatory against Arabs:

All of the bad guys have beards and large, bulbous noses, sinister eyes and heavy accents, and they’re wielding swords constantly. Aladdin doesn’t have a big nose; he has a small nose. He doesn’t have an accent. What makes him nice is they’ve given him this American character, [. . .] I have a daughter who says she’s ashamed to call herself an Arab, and it’s because of things like this. (in Giroux)

As in the movie Aladdin, negative portrayals of Arabs build stereotypes that affect child viewers. They learn that bad guys sound a certain way, look a certain way, and come from a certain part of the world. According to Lippi-Green, such depictions teach children “to assign values on the basis of variation in language linked to race, ethnicity, and homeland” (p.80). Undoubtedly, the accents of characters in the movie are not chosen randomly. On the contrary, they are present in their exact places to create a certain effect.

Another instance of stereotyping clearly shows itself in the movie The Lion King, which was the highest grossing film of the year in 1994. In the film, while the powerful and noble Lion King Mufasa speaks with a mainstream US English accent, his brother Scar, who is evil and plans the murder of his brother so as to be the king, has a heavy British accent. As the story takes place in Africa, authentically, both characters should have the same African dialect or they could both speak with mainstream US English without any implication as to the characters’ origins or characteristics. Conversely, the voiceover for Scar is provided by Jeremy Irons, who has a distinctive British accent, whereas the voice over for Mufasa is provided by James Earl Jones, who speaks with a mainstream US English accent. Scar’s British accent is there to draw audience attention, to help children distinguish his character as villainous in contrast to that of Mufasa, who has characteristics of a hero. Not only does such a portrayal reinforce ethnocentrism-imposing the idea that the one who speaks with standard American English, namely Americans, are superior to others-but also highlights the stereotype that the British are rather snobbish through Scar’s arrogant manners and feelings of superiority towards the rest of the animals in the movie. Another example from the same movie is that the malicious and sinister hyenas do not have standard American English accent although they live in the same jungle. Henry A. Giroux from Pennsylvania State University states that “racially coded language is evident in The Lion King where [. . .] Shenzi and Banzai, the despicable hyena stormtroopers speak through the voices of Whoopi Goldberg and Cheech Marin in racially coded accents that take on the nuances of the discourse of a decidedly urban, black and Latino youth.” It is an undeniable fact that these dialects are chosen on purpose in order to represent the villainous hyenas as racial and ethnic minorities speaking with an inner-city street dialect.

Yet another example of stereotypical depiction comes from Lady and the Tramp. In the movie, specific accents are manipulated in order to create an effect in the minds of the viewers. With chopsticks in their hands, cymbals on their heads and with their distinct accents, the Siamese cats represent Asians. Disgracefully, the cats are depicted as sinister, cunning, manipulative, and treacherous, creating stereotypes suggesting the Yellow Peril. Furthermore, it would be unjust to overlook the portrayal of Native Americans as savages in both Peter Pan and Pocahontas.

Although such stereotypical depictions are not confined solely to these animated movies, the abovementioned examples are more than adequate to support the argument that subtle ways of creating fear of “the other” and undermining dialogue and mutual acceptance is widespread in children’s animated movies. Consequently, children grow up with groundless stereotypes that seep into their conscious as well as their subconscious. But what exactly are the ramifications of stereotyping? Why should we be cautious about it? Stereotyping, which has detrimental outcomes, is defined by Stuart Price as making simplistic and usually negative social identifications of certain groups, in which the “supposed attributes of the group are applied to all those identified-rightly or wrongly-as group members” (in Barton). Moreover, According to Ron and Suzanne Wong Scollon, stereotyping also has social and political ends. In their book Intercultural Communication, they write:

Characteristics of the group are not only overgeneralized to apply to each member of the group but they are also taken to have some exaggerated negative or positive value. These values are then taken as arguments to support social or political relationships in regard to members of the groups. (p.168)

Unhappily, at a very young age, due to watching such movies and other social influences, children learn to stereotype, and the images constructed in their minds may affect their perspective throughout their lives. As a matter of fact, not only negative stereotyping but also positive stereotyping is harmful because although it seems to be innocent, categorizing people confines our perception of others and distorts reality. All in all, stereotypes “blind us to others” as well as limiting our understanding of intercultural dialogue through impeding communication and mutual understanding between groups of people (Scollon p.169).

In addition to producing prejudice against “the other” in the minds of children, another effect of non-authentic language variations is causing low self-esteem for young viewers with non-standard accents. It is very clear in certain animated movies that language variations are heavily used to determine hero versus villain status. That is, the bad guys are made distinctive through their non-standard accents while the friendly characters speak with standard American accents. Statistics show that of the characters who speak Standard English, 73.5 % are positive characters while only 19.9 % are negative. On the other hand, only 37 % of the representations of persons with foreign accents are positive (Lippi-Green p.92). Obviously, producers do not give specific accents to specific characters by accident. In contrast, this data conveys a message regarding the deliberateness of their preferences. There is also evidence that in animated movies mothers and fathers are most likely to have mainstream accents while foreign accents are usually assigned to “villains, servants, and silly characters,” and negatively portrayed characters in some way (Wynn). Such discriminatory representation may cause minority children to grow up with the idea that some positions are open to them in the world while some are not. They see heroes, lead characters, caring mothers, and good fathers all speak with mainstream US English accents in the movies, and observe that non-standard accented characters are negatively portrayed, which eventually affects their self-esteem. On the other hand, for American youth it produces prejudice against other racial and ethnic groups. It creates hard-to-forget stereotyped images of foreigners in their minds and teaches them to discriminate.

It is reasonable to claim that by indicating negative characters with foreign accents, another intention of producers’ is to create fear of “the other.” Interestingly enough, there is a strong correlation between the foreign policy of the US and the choice of foreign accents to indicate evilness. According to the article “The good, the bad, and the foreign: The use of dialect in children’s animated television”, during the late 1990s, villains were noticeably Russian, Eastern European, or German, reflecting the Cold War and World War II alliances. The Lady and the Tramp was released in 1955, soon after the Korean War and in the middle of a cold war fear with China. Accordingly, the negative representation of the aforementioned Siamese cats reflected the fear of the “Yellow Peril.” Nowadays, Arab characters are also having their share of a similar political and ideological stratagem under the impression of reality. James Monaco, the author of How to Read a Film: The World of Movies, Media, and Multimedia, discusses the relationship between movies and politics impressively. In his book, after emphasizing that there is no film that does not display a political nature even though it might seem trivial, Monaco points out to the power of film “to recreate reality” through producing “a fantasy of [its] own that eventually comes to be accepted as real” (p.262). Producers use this specific power of films to maintain the status quo and to create fear of the other through stereotypical representations of racial and ethnic groups. Lippi-Green is also in agreement with this claim as she states, “a study of accents in animated cartoons over time is likely to reveal the way linguistic stereotypes mirror the evolution of national fears” (85). Unfortunately, through animated movies, children are exposed to such ideological strategies and they fall prey to these ungrounded-but strongly established-fears.

In addition, while they are raised to be scared of “the other,” children who grow up with the idea that the others are “deviant, inferior, unintelligent, and a threat to be overcome” (Giroux) become increasingly ethnocentric. Under the influence of ethnocentrism, children think themselves superior to other cultures and cannot feel empathy for others. This in turn leads to a lack of intercultural communication and dialogue between nations as well as individuals. Yet again, Lippi-Green presents a concluding argument regarding the unfavorable effects of animated movies on children, “what children learn from the entertainment industry is to be comfortable with ‘same’ and to be wary about ‘other’, and that language is a prime and ready diagnostic for this division between what is approachable and what is best left alone”(p.103).

Since the stereotypical portrayal of characters construct a skewed view of foreign people, children learn to be suspicious about other groups of people.

The main risk of misrepresentation of “the others” in the animated movies lies in the fact that for a great number of children, the film industry is a key socializing agent. In real life, children usually do not have many opportunities to get to know people of other ethnic or national origins. Therefore, a great deal of information they have comes from what they see in the movies.

Besides, they do not watch them with skepticism; in other words, they trust what they see and their “tabula rasa” is filled with distorted and biased facts whose nature is determined by the producers. A quick glance at the statistics reveals how enormous and far-reaching the effect of animated movies is on the lives of children. According to the internet movie database, The Lion King and Aladdin as well as Beauty and the Beast ranked among the one hundred most profitable films ever made, by the number of movie tickets sold in the U.S. Adding to that the number of rentals and video interactive games leaves us with astonishing figures. However, behind the innocent fantasy world animated movies build up, there is a noteworthy reality that awaits young viewers.

As a result of stereotypical representations, children get positive or negative messages about the characters, and they apply them in real life to judge others on the basis of their accent, appearance, or national origin. Therefore, I suggest we be more mindful about the effects movies will have on young viewers and stay wide-awake while our younger siblings or children are watching their favorite animated movies. What we innocently believe to be a fantasy world might have serious effects for the young viewers and their worldviews later on. I believe we would be better to teach children to beware of stereotypical representations instead of teaching them to beware of “the others.”

Safiye Unal-Yigit is a sociologist living in Houston, Texas.

References

Barton, Geoff. Homepage. 11 Nov. 2004. 19 Nov. 2004. http://geoffbarton.co.uk/index.php

Dubrow, Julia R., and Calvin L. Gidney. “The Good, the Bad, and the Foreign: the Use of Dialect in Children’s Animated Television.” The Annals of the American Academy of Political and Social Science. May 1988: 105–120. General Reference Center Gold. Library, Houston Community College. 22 Oct. 2004. www.galegroup.com

Giroux, Henry A. Animating Youth: the Disnification of Children’s Culture. 1 Nov. 2004. www.neiu.edu/~ermeiner/girouxdis.htm

Hamers, Josiane F., and Michel H. A. Blanc. Bilinguality and Bilingualism. Cambridge: Cambridge UP, 2000.

Lippi-Green, Rosina. English with an Accent: Language, Ideology, and Discrimination in the United States. London: Routledge, 1997.

Monaco, James. How to Read a Film: The World of Movies, Media, and Multimedia. New York: Oxford UP, 2000.

Schiffman, Harold F. “Language and Authenticity.” Home Page. 10 Oct. 2004 http://ccat.sas.upenn.edu/~haroldfs/

Scollon, Ron, and Suzanne Wong Scollon. Language in Society 21: Intercultural Communication. Massachusetts: Blackwell, 1995.

Thomson, David S. Language. New York: Time-Life, 1975.

Wynn, Mary E. R. Linguistics. Course home page. 2003. Dept. of Linguistics. California State

U. 20 Nov. 2004. http://hss.fullerton.edu/linguistics/cln/spring01_articles/wynn-eng.htm

Halima was making her shopping list when the door bell started ringing wildly like there was a fire somewhere. She dropped the pen and went to the door. Yes, she guessed right! Her fist grader had returned from school. “What’s the matter, son? Is that the proper way to ring the bell? Your baby brother is sleeping. Your grandpa is performing the noon prayer. Do you want to disturb everybody?” she asked, frustrated that all the shopping items had fled her mind.

“Mom, Mom,” her son replied in great excitement as if he had not heard a word of her reproach, “Can you buy me a Change-former? Pleeeease?” he begged with urgency. “A what?” She was all ears now. “A change former is a robot machine. It flies like a plane, it floats like a boat and it goes like a car too. Gabriel has one and it’s so cool!” Halima could tell his fascination by his failure to take a breath.

“Oh, peer pressure and techno-mania,” complained Halima to herself. She took a deep breath knowing her words might throw her son into a fit. “Ahmed, listen dear. They are called transformers and you already have plenty of toys.” “But Mom,…” he tried to object. “No buts,” she insisted. “Now go to your room, change your clothes and sit with Grandpa until I come back from shopping.” “Can I come with you too?” He made one last attempt.

Perhaps he could sway her if only he could show her how cool the Change-formers were. “No,” Halima answered firmly. She knew better than to bring him along just to face a possible tantrum in public. She put on her beige jacket, adjusted her brown scarf in front of the mirror and turned toward him saying, “Now, be a good boy!” She kissed him on his cheek as she hurried to the door avoiding his angry eyes. The door slammed as if to reinforce the rejection. “Thank God,” she took a deep breath, “we didn’t face a storm this time.” The boy disappointedly went to his grandpa’s room.

Ahmed found him sitting in a crisscross position with his hands opened, palms up and his lips in gentle motion. Ahmed was immediately soothed by the serenity of the supplication, although he did not know what his grandpa was asking for. He sat in his lap and put his little pink hands over his grandfather’s large bony ones. He wished his grandpa would pray for his mom to miraculously change her mind and come home with a Changeformer in the shopping bag. Grandpa finished his supplication and rubbed the palms of his hands over his face, and then kissed Ahmed’s hands with great love. Ahmed turned toward his grandpa and poured out his heart, confident that Grandpa could fix any problem whatever it was. Grandpa listened carefully. “Ahmed, my dear, you already have many transformers.” “I do? Where?” he asked anxiously. “Look out of the window,” whispered Grandpa. Ahmed looked hard and in disappointment said, “There’s no transformer out there, just the apple tree.” “Exactly!” exclaimed Grandpa, challenging Ahmed to think harder. “I don’t understand.”

Ahmed was puzzled. “Don’t you remember? That tree in the winter was all naked and looked dead. Two weeks ago it was in full bloom; now it is covered with green leaves. Isn’t that a transformer?” Ahmed smiled at the analogy but he wasn’t ready to surrender. “Trees don’t move,” he replied. “Ok then, bring me the family album.” Ahmed got up and went to the bookshelf wishing he could read Grandpa’s mind. He got the big album and sat back in his Grandpa’s lap. They opened the album together. The first photo was a snapshot of Ahmed as a newborn in the hospital crib. “Who is this?” asked Grandpa, feigning surprise. “That’s me!” exclaimed Ahmed, thinking, “Grandpa looks so funny when he pretends he doesn’t know.”

“No way,” objected Grandpa, “He doesn’t look like you. He is too small. No hair, no teeth. Can’t walk. Can’t talk.” “Grandpa!” Ahmed was really amused. “That’s me as a baby. I grew up and changed a lot in six years.” “You did?! So you are a Change former! Or should I say a transformer?” Ahmed’s eyes brightened with the light of recognition. As he turned the pages of the album one by one, he understood what Grandpa meant. Everyone in the family had changed in those six years. Wow! Every human is a transformer! Yet, something still puzzled him. “Grandpa,” he objected one more time, “Humans can’t fly.” “Bring me that colorful book on the top shelf,” ordered Grandpa. Ahmed stood up swiftly to fetch it, filled with curiosity. “Look at this page. Can you read it?” challenged Grandpa.

“The life cy-cle of a but-ter-fly,” Ahmed read with the typical I–can–read–all–by–myself pride of a first-grader. He looked at the pictures and observed the eggs, the caterpillar, the cocoon and finally the pretty butterfly. He had studied butterflies earlier this year in school, but he had never looked at them this way. His grandpa smiled at him and caressed his head. “You know, Ahmed, every living being is an amazing transformer. In fact, nothing in creation is in perfect rest. But it’s important to see beyond the transformations.” “To see what?” asked Ahmed in excitement. “To see the Ultimate Artist behind every piece of artwork. The Qur’an tells us that God is Al-Musawwir. That’s an Arabic word meaning “the Perfect Giver of forms or colors.” “Al-Mu-saw-wir,” repeated Ahmed as if trying to make a mental note. “Come, let’s take your little brother and go outside,” Grandpa proposed all of a sudden. “I have one more exciting transformer to introduce to you who is fun and cool.” They could tell his seven-month-old baby brother had awakened because of the loud giggle coming from his room. Grandpa lifted the baby out of the crib. Ahmed tickled the baby’s chubby tummy, asking, “How is big brother’s cute transformer?” He received a big toothless smile as a reply. Grandpa dressed the baby and helped Ahmed fasten his shoes. Outside everything spoke of spring and powerful transformation. They started walking toward the lake. “This is the perfect time to hunt for transformers,” commented his grandpa while pushing the stroller. He had put a big jar and a small net in the stroller’s basket. Ahmed was very impatient to meet the mysterious creature. Meanwhile, Halima turned the key and opened the door. She had forgotten to take her purse on her way to the market and needed to come back home in rush hour traffic.

“Well, I will go tomorrow, God willing,” she con soled herself. “Maybe it’s better this way. At least I will have time to finish my shopping list before then.” The house was silent. “Where has everybody gone?” she wondered. “They must have gone for a walk around the lake,” she thought when she saw the stroller was missing. “Good thinking, Father. You are priceless!” Halima started preparing dinner. She was almost done when the doorbell rang again, this time gently. She hurried to open the door.

Ahmed stood there as happy as can be, holding a big jar half full of water with something swimming in it. “Welcome,” she greeted them, smiling at Grandpa with a look that said “Father, you are a gem.”

“What’s this?” she asked Ahmed. “Prepare to meet my transformers,” he said solemnly. Halima bent a little and through the glass she saw two little tadpoles swimming frenziedly. “They look like fish but they are not, and they will turn into frogs in six weeks. Mom, can we please keep them till then?” Halima didn’t want to break his heart a second time so she consented, “Ok, my son, but promise to take good care of them. They have a right to live and we don’t own them.” Ahmed put the jar on the kitchen counter and went to wash his hands. Dinner was ready and Daddy would be home soon. In fact, they could hear his car pulling up in the driveway. Halima set the table. At dinner her husband listened with great interest to his son talk about what he had learned during the day. “Daddy, you know, these creatures are the best, better than any robot. They are perfect and don’t need batteries to work. Besides, Grandpa told me that engineers use living creatures as models when they design robots. God surely is the best of designers. He is Al-….” He paused trying to remember.

“Al Musawwir,” Grandpa jumped in to help. Everyone around the table seemed to enjoy this conversation even more than the delicious food. Two hours later, after she had finished washing the dishes, Halima took the unfinished shopping list out of her bag. She added a couple of items. Ahmed was sitting close by looking at the tadpoles. “Ahmed,” she called.” I am finishing my shopping list. Is there anything you want me to buy for you?” “No, Mom, thanks,” he replied without looking at her.

“Are you sure?” she asked in a reminding tone. He turned his head this time, winked at her and replied, “Maybe I don’t need a transformer after all….”

]]> https://fountainmagazine.com/all-issues/2008/issue-61-january-february-2008/halwat-and-uzlat-privacy-and-seclusion/ Tue, 01 Jan 2008 00:00:00 +0000 http://107.21.79.195/all-issues/2008/issue-61-january-february-2008/halwat-and-uzlat-privacy-and-seclusion/ Literally meaning solitude and living alone, halwat and ‘uzlat (privacy and seclusion) within the context of Sufism denote an initiate’s going into retreat to dedicate all of his or her time to worshipping God under the guidance and supervision of a spiritual master. He or she seeks purification from all false beliefs, dark thoughts and feelings, and conceptions and imaginations that separate him or her from the Truth, closing the doors of his or her heart to all that is not God, and conversing with Him through the tongue of his or her inner faculties.

Seclusion is one dimension of privacy; austerity is another. The first step in privacy is completed in forty days, therefore known as the forty-day period of austerity. When the spiritual master takes the initiate into privacy, he takes him or her to a quiet room, where he prays for the initiate’s success, and then leaves. In that room, the initiate lives an austere life, utterly alone. He or she eats and drinks little in that room of seclusion, which is regarded as a door opening on nearness to God. Bodily needs decrease and are disciplined, carnal desires are forgotten, and all time is dedicated to worshipping God, meditation, reflection, prayer, and supplication.

In its aspect of the avoidance of people and austerity, privacy dates back to the early days of Sufism, even to the great Prophets. Numerous Prophets and saints, most particularly the glory of humankind, upon him be peace and blessings, spent portions of their lives in seclusion. However, their original system of privacy and seclusion has undergone undesirable change over time. The seclusion of Prophet Abraham, the forty-day periods of Prophet Moses, the austerity of Prophet Jesus, and the privacy of the prince of the Prophets have been practiced in different ways by many people, and have therefore undergone certain alterations.

Such changes can be regarded as natural to some extent, for in as much as seclusion is related to an individual’s moods, temperament, and spiritual capacity, only perfect spiritual masters can know and decide how long and under what conditions an initiate must be kept in seclusion. In the early days of his initiation, Rumi underwent many forty-day periods of austerity in seclusion. However, when he found a true, perfect master, he left seclusion for the company of people (jalwat). Many others before and after him have preferred being with people, rather than avoiding them.

Austerity, one of the two dimensions of privacy, means keeping a tight rein on carnal gratification and urging the spirit to rise to human perfection, with which it is enamored.1 Only through austerity can the carnal self be restrained, forced to renounce evil impulses and passions and submit to the commandments of God, forced to adopt humility and be the soil of a flowerbed:

Be like earth so that roses may grow in you

For nothing other than soil can be a medium for the growth of roses.

One can receive a certain Divine grace through austerity. Some can adorn their knowledge with high morals and their religious acts with sincerity and pure intention, thereby gaining mannerliness in their relations with both God and people. Others find themselves tossed this way and that in their relationship with their Lord, and continuously search for ways to get nearer to Him. There are still others who, like a moth just out of its cocoon, spend their lives among spiritual beings who may be regarded as the butterflies of the celestial worlds they have just reached.

What is essential to privacy is that the initiate must seek nothing other than God’s pleasure, and must constantly wait in expectation of that Divine favor. The initiate must not be idle while waiting for this favor, but rather wait with the eye of his or her heart open, in the utmost care and excitement, so that no Divine inspiration or gift that may flow into his or her heart will be missed. They must wait with the courtesy and decorum appropriate to being in the presence of God. The following words of La Makani Husain Efendi express this meaning very aptly:

Clean the fountain of your soul until it becomes perfectly pure.

Fix your eyes on your heart until your heart becomes an eye.

Give up doubts and put the pitcher of your heart to that fountain.

When that pitcher is filled with the water which gives delight,

Withdraw yourself and submit to its Owner His home.2

When you leave it, God doubtless comes to His home.

Never let the devil-robber enter the home of your heart,

For once he has entered, it is very difficult to throw him out.

It is true that God is absolutely free of all time and space constraints, and that His relationship with the believer occurs on the “slopes” of the believer’s heart. For this reason, the heart’s “emerald hills” or “slopes” must always be ready to receive the waves of His manifestations so that, in the words of Ibrahim Haqqi of Erzurum, the King may descend to His palace at night.

God Almighty decreed to Prophet David: Keep that home empty for Me so that I will be in it.3 Some have interpreted “keeping the heart empty” as purifying the heart of all that is not God, and as not having relations with others without first considering God’s pleasure. The following words of Rumi express this most appropriately:

One wise and sensible prefers the bottom of the well,

For the soul finds delight in privacy (to be with God).

The darkness of the well is preferable to the darkness people cause.

One holding on to the legs of people has never been able to arrive with a head.4

One must seclude oneself from others, not from the Beloved.

Fur is worn in winter, not in spring.

Since the purpose of seclusion is to purify the heart of the love which is not directed toward God and to be always with the Beloved, those who always feel the presence of God while living among people and who continuously discern the Divine Unity amidst multiplicity are regarded as always being with God in seclusion. In contrast, however, the seclusion of others who, although they spend their lives in seclusion, have not purified their hearts from attachment to whatever is other than God, is a deception.

Those who always feel themselves in the presence of God do not need to seclude themselves from people. Such people, in the words of Rumi, are like those who keep one foot in the sphere of Divine commandments and turn the other, like a compass needle, round the world. They experience ascent and descent at every moment. This is the seclusion recognized and preferred by the Prophets and saints.

God Almighty once said to Prophet David: O David, why do you seclude yourself from people and choose to remain alone? David, upon him be peace, answered: Lord, I renounce the company of people for Your sake. The Almighty warned him: Always keep vigil, but do not keep aloof from your brethren. However, seclude yourself from those whose company is of no benefit to you.

Notes

1.As the spirit is from God, it innately longs for Him and is enamored with perfection. The carnal soul or self, on the other hand, is enamored with animal desires.

2.“Home” signifies the heart, whose Owner is God.

3. Al-Qushayri, Al-Risala, 327.

4. That is, one who relies on people to attain his or her goal will fail.

]]> https://fountainmagazine.com/all-issues/2008/issue-61-january-february-2008/peer-instruction-a-better-way-to-learn/ Tue, 01 Jan 2008 00:00:00 +0000 http://107.21.79.195/all-issues/2008/issue-61-january-february-2008/peer-instruction-a-better-way-to-learn/ Teaching and learning are two common human activities. If we need to name a great difference between humans and animals, this is the one. As Nursi points out1 almost from the very moment of birth an animal seems to have been trained and perfected elsewhere, whereas people are born knowing nothing of life and their environment and so must learn everything. Learning more and the correct things improves one’s life. So, we are all concerned with how we can learn more efficiently, and, in turn, how we can teach more efficiently.

Education becomes more formal at school. There are a great many different teaching styles inspired by different educational philosophies. Likewise, there are very many learning styles based on different personalities. Every person is created differently and every person may have a slightly different learning style. However, at schools where mass teaching is done, teachers need to decide on a certain method. There are some traditional methods and some novel ones. Here we will focus on peer instruction,2 a non-traditional teaching method developed over the last decade based on physics education research, and later applied in other science teaching as well. We will also try to extract lessons from the peer instruction experience to guide us not only in learning in the classroom but also in everyday informal learning practices.

Eric Mazur is a professor of physics at Harvard University. About a decade ago, Mazur discovered that his students could not correctly answer seemingly simple qualitative questions, despite being able to work through much more difficult quantitative problems. He was shocked as he was considered to be one of the best instructors in the physics department. Mazur began to document the disparity between student performance on the two types of questions, by including on his exams paired qualitative and quantitative questions on a single physical concept. He soon confirmed that for his students, success in solving traditional physics problems did not imply that they understood the underlying physics. Many physics instructors across the United States shared Professor Mazur’s experience. Mazur started developing what is now known as peer instruction.

As the name suggests, peer instruction promotes learning through interaction with one’s peers in the classroom, in addition to listening to the instructor. This is very new, considering that many remember science classes in the form of a plain lecture, where the only player is the instructor, and the students are the audience, except for a few outgoing students who are not always appreciated by their peers. Peer instruction transforms the students into active players during the class. This is actually common sense in all our education experiences. If you just listen to an idea, you will understand very little, and retain very little. If you think about the subject matter, try to apply it in different circumstances, and finally teach it to someone else then your chance of comprehension and retention greatly improves. This is what the instructor achieves through peer instruction. The students are gently pushed toward thinking, discussing, and finally teaching each other, and so they learn more and better.

Every class in peer instruction includes three or four short mini-lectures followed by (or sometimes preceded by) a conceptual question. Students are assigned prior reading so as to come to the class prepared and to have at least some familiarity with the new concepts and terminology. Each mini-lecture’s goal is to highlight certain concepts and give the students further insight. Very different from traditional physics lectures, the instructor does not feel obligated to solve many example problems where a lot of math is needed. That is done through homework and during the problem sessions, which are usually administered by teaching assistants. Between mini-lectures three to five conceptual questions are distributed. Each conceptual question is a qualitative multiple-choice question that gives students and the instructor a means to assess what students have learned. Most questions are asked twice. In the first stage, the instructor shows the question on a projector screen and reads it aloud. Each student is asked to think individually about the answer. No talking is allowed. At the end of this first one- or two-minute period, the instructor asks the students to show their responses. This can be done with flashcards, or electronic transmitters (clickers). A flashcard may have the choices (A, B, C, …), or the instructor may prefer to use color flashcards. Some schools provide students with clickers (or students buy them), and the instructor has the receiver that is connected to a computer.

After receiving the answers from the students, the instructor assesses the situation. If there are only a few correct answers, then the question was asked prematurely. If there are only a few incorrect answers, then the question was too easy, no more time is devoted to that concept. However, in most cases the instructor selects a question to which 30–70% of the answers will be correct. Then, in the second stage, without giving the correct answer, the instructor asks the students to turn to their peers sitting next to them, and discuss the answer and its reasoning. This is peer instruction. These interactions between students have proven very useful. At the end of the second stage, which typically lasts two to three minutes, the instructor asks the students to show their responses to the same question once again. It has been shown that most of the time the number of correct answers goes up. Clearly, success is conditional on the pre-class reading, a mini-lecture that highlights the concepts, and selection of the carefully designed conceptual questions. Based on the responses, the instructor can decide whether to elaborate on the topic or proceed to something new.

Here is a conceptual question3 that may be asked while studying the law of gravitation:

The Moon does not fall to Earth because…

1. it is in the Earth’s gravitational field.

2. the net force on it is zero.

3. it is beyond the main pull of the Earth’s gravity.

4. it is being pulled by the Sun and planets as well as by the Earth.

5. All of the above.

6. None of the above.

At this point we suggest that the reader should think about this question before reading the next paragraph, which includes the correct answer at the end. If possible, ask someone near you and discuss your reasoning.

This question is carefully designed with choices representing various misconceptions. For example, any student with some introductory knowledge of physics will accept that if the net force on an object is zero, then the object will not move, so it is tempting for some students to say, “Oh, yes. The Moon does not fall to Earth. This means that the net force on it is zero!” Or, everybody has a direct experience of the gravitational pull of the Earth. You jump and you fall to Earth. You cannot escape. Again, it is tempting to say that the Moon is beyond the main pull of the Earth’s gravity, but that is not true because if there were not enough gravitational force on the Moon, it would escape the Earth’s orbit. Option 4, for example, is correct as a statement. By virtue of having a mass, the moon is pulled by the Sun and other planets. One might tend to think that there is a balance between the gravitational forces applied by the Earth and other heavenly objects. But, no, that is not the actual reason for the Moon not to fall to Earth. None of the options alone gives the correct answer. Since two of the options (2 and 3) are incorrect, the correct answer to this question is option 6, “None of the above.” The correct answer is that the Moon orbits the Earth as well as being pulled by its gravitational force. The reason the Moon keeps changing its direction is the gravitational pull of the Earth. The Moon was given an initial speed so that it does not fall. If the Moon should stop at any instant, it would fall to Earth.

To reiterate our main point, peer instruction causes students to think through and apply a general principle to different cases through conceptual questions and teach each other what they have just learned. That is, our brain becomes much more active, and it is forced to synthesize difference pieces of information, rather than keeping busy with factual information only.

Research has shown that peer instruction improves the learning gains of the students greatly.4,5,6,7 Peer instruction has been used in astronomy, chemistry, biology, and mathematics as well. How can we benefit from the peer instruction experience to improve our everyday teaching and learning practices? Before trying to answer this question, let us remember occasions when we learn and teach in our daily lives. We teach and learn when we talk to our friends. When we browse through a newspaper, listen to the radio, or watch a TV program, we are bombarded with information. We read books hoping to learn something from them.

The first message we should receive from the success of peer instruction is that passive listening and watching only injects a lot of information in a short time into our memories. Because such information is not processed with an active mind, or we do not try to apply it in different situations, we should be aware that such information might not be so reliable in general. The irony is that many people in the twenty-first century look to the TV, movies, and radios for information. On the TV screen we see twenty-four pictures every second, that is, about a quarter million pictures daily, if we watch TV for three hours per day. In order for TV and radio to be useful, as peer instruction shows, viewers and listeners need to stop and think about what they have just seen and listened to. If possible, then turn to a friend, discuss what you have just watched and get their opinion. Try to teach what you have just learned and see the reaction of people around you.

When we read we have more time to think. We should gently push our brains to make connections with what we know, and what we have just read. What is the purpose? What is the message? Why is this significant? Then again, try to teach it to a friend, enter into a short discussion. This can really help minimize misconceptions and refine our understanding. It will help us assimilate the information, and make it our own. As Nursi puts it, “A learned guide should be a sheep not a bird. A sheep gives its lamb milk, while a bird gives its chick regurgitated food.”8 Yes, we should try to digest information, and our chances of digesting it improves with continuous thought, meaningful discussions, and when we try to teach someone else, just like what happens in peer instruction.

Notes:

1.Bediuzzaman Said Nursi, The Words, The Twenty-Third Word, Fourth point, NJ, The Light: 2005, pp 331–32.

2.http://mazur-www.harvard.edu/research/detailspage.php?ed=1&rowid=8.

3.Eric Mazur, Peer Instruction: A User’s Manual. Prentice-Hall, Upper Saddle River, NJ, 1997.

4.D. Meltzer, and K. Manivannan, Am. J. Phys. 70, June 2002.

5.Mark C. James, Am. J. Phys. 74, August 2006.

6.Catherine H. Crouch and Eric Mazur, Am. J. Phys. 69, September 2001.

7.T. J. Bensky, Am. J. Phys. 71, November 2003.

8.Bediuzzaman Said Nursi, The Letters, Seeds of Truths, NJ, The Light: 2007, pp 445-458.

Rainbows in all directions across the horizon,

Touched by all these dazzling colors, humankind.

Angels look on them with praise.

Their faces to the ground, their hearts God’s abode,

A heavenly invitation is their belief.

Humankind is an exalted ore made of dust and mud,

An incomparable mirror deep and brilliant,

Reflecting the infinite, facing the beyond.

Strive, and you can attain your essence!

Be one with your soul, boil with your spirit!

Wail a bit more, shedding tears.

Sprout slowly like a bud,

Follow the light until you are there,

Roots in the soil, eyes fixed on the light.

This mysterious struggle broke out in the heavens

And will go on until Doomsday.

Never stop! Stretch and run, for victory is on the horizon!

]]> https://fountainmagazine.com/all-issues/2008/issue-61-january-february-2008/citadel-of-the-self-incompleteness-theorem/ Tue, 01 Jan 2008 00:00:00 +0000 http://107.21.79.195/all-issues/2008/issue-61-january-february-2008/citadel-of-the-self-incompleteness-theorem/ What is consciousness? Is it established in the brain, or distributed throughout the whole body? Is it physical? Can I jump out of my own consciousness? These are the questions that have occupied the minds of thinkers for centuries. This article does not promise answers but more questions.

Thinking about thought and understanding our own understanding encapsulates an inherent difficulty: self reference. Self reference is the ability of a complex system to reflect upon its own existence. No matter how it might be the basis of our consciousness, it brings inconsistencies. With self reference we are able to build sentences like “This sentence is wrong.” This very well known paradoxical statement is the point in our immense potential that makes us different from all other creatures, and it is the point where we start to perceive our weakness at comprehending our own selves. Self reference is the means of knowing our own reality, but it only gives a blurry glimpse of it. A mathematical theorem shows that we will never be able to capture our own reality in a clear picture, there will always be inconsistencies. The theorem is known as Gödel’s Incompleteness Theorem after the famous mathematician Kurt Gödel (1906–1978). Gödel used mathematical reasoning in exploring mathematical reasoning itself. In this article the implications of this theorem for self consciousness will be investigated.

The scientific study of mathematical reasoning begins with the concept of formal systems. In formal systems there are axioms and rules. The axioms are the very basic statements that are accepted as true by default (e.g. any two points in space can be joined by a straight line). The rules are common notions that are consistent with the rules of the nature (e.g. things that equal the same thing also equal one another). Formals systems apply the rules to axioms in order to reach true mathematical propositions (valid theorems).

New valid theorems are built on the existing ones and the formal system is iterated for exploring mathematical reality; hence, the formal system learns the mathematical truth with formal iteration. The structure and the development of formal systems are similar to that of human beings: babiesare born with some built-in knowledge of the environment (axioms), and new knowledge is acquired through learning in the guidance of physical laws (rules). Just like human beings, a formal system that is rich and complex enough can make reference to its theorems, as in “This theorem is right” or to its own self as in “This formal system is consistent.” Gödel’s theorem universally states that the formal systems that can make self reference suffer from an inherent incapability to comprehend the “self.” A formal system cannot be sure that it is consistent because the theorem “This formal system is consistent” cannot be proven inside the system, which makes the system incomplete. In fact, the existence of such a theorem is the sole source of inconsistency. Consistency and completeness are required in a formal system to reach reality. Therefore, with the ability to reflect upon itself, a formal system cannot decide on the true nature of its own reality and lacks a complete understanding of itself. The Gödelian argument applies only to systems that are rich enough to have self reference, and interestingly richness of the systems brings about its downfall. It is analogous to the concept of “critical mass” in nuclear physics. A radioactive substance will blow up only beyond a critical mass; otherwise it will stay stable.

Though the system is intrinsically incapable of having a complete understanding of its own self, intelligence outside of the system can decide on the system’s consistency and can fully comprehend it. The need for an outside agent to comprehend reality is exemplified by the analogy of an ant walking on a Mobius strip (Fig. 1). A Mobius strip is a two-dimensional surface with only one side, unlike a regular strip which has two sides. It can be easily made by taking a paper strip and giving it a half-twist, and then merging the ends of the strip together to form a single strip.

If you start drawing a line from a point on the Mobius strip, you will reach the point you started. This is a characteristic of a round three dimensional shape, like cylinder (Fig. 2). When an ant walks on a Mobius strip, it will cross the location that it started at (Fig. 3). The same will happen when it walks on the surface of a cylinder. An ant on these geometric shapes will not be able to differentiate between the two-dimensional Mobius strip and three-dimensional cylinder, and hence will not comprehend the true natural geometry of the system that it is in. Only an agent outside of these shapes can understand the true geometry of the shapes, just like an intelligent agent outside the formal system fully comprehending the system. The question is, can an ant ever get out of the geometry that it is in? Sure, it can step outside of the Mobius strip, but yet again it will be on another geometric shape that it cannot comprehend. Similarly, new theorems can be added to the formal system that patch the existing holes and make the system step outside itself, but this improved formal system still suffers from the same problems caused by self reference.

The futile struggle to jump outside of the system is beautifully illustrated in another painting by Escher (Fig. 4). Escher explains his painting Dragon (1952): “However much this dragon tries to be spatial, he remains completely flat.Two incisions are made in the paper on which he is printed. Then it is folded in such a way as to leave two square openings. But this dragon is an obstinate beast, and in spite of his two dimensions he persists in assuming that he has three; so he sticks his head through one of the holes and his tail through the other.” Hofstadter adds in his seminal book Gödel, Escher, Bach: An Eternal Golden Braid, “No matter how cleverly you try to simulate three dimensions in two, you are always missing some ‘essence of three-dimensionality.’ The dragon tries very hard to fight his two-dimensionality. He defies the two-dimensionality of the paper on which he thinks he is drawn, by sticking his head through it; and yet all the while, we outside the drawing can see the pathetic futility of it all, for the dragon and the holes and the folds are merely two-dimensional simulations of those concepts, and not a one of them is real. But the dragon cannot step out of his two-dimensional space, cannot know it as we do.”

Consider an intelligent creature living on a two-dimensional plane, and we are observing its world from above, but it can not see us since there is no such thing as “above” in its world. In his free time, the creature wanders on the plane to seek new realities (theorems) of its world and learn them. We accidentally touch the plane that he is living in with one of our fingers; obviously the creature will only see the two-dimensional projection of the adjacent finger surface. I am sure it will be surprised to experience an object appearing out of nowhere, and even more surprised to see the shape suddenly disappear when we withdraw our finger. It will question the consistency of the system that it is living in and ask, “Is my world inconsistent?” Then, it might go crazy while figuring out what has happened or simply patch the informational hole in its world by saying, “Sometimes things of the shape that I saw might suddenly appear and disappear in my world.” Our creature will be happy again after resolving the unfortunate inconsistency, but can it be sure that the system of knowledge (theorems) is complete? We will not let our unlucky creature rest and we will put a cup on him; since the two dimensional projection of the touching surface of the cup draws a circle, the creature will be surrounded by a circular prison again appearing out of nowhere. It will be surprised but this time devastated also. Then, there will come another patch to its knowledge about the system: “Sometimes, a circular prison can suddenly appear and enslave me.” As you can imagine, there are infinitely many operations that we can apply to the two-dimensional world of our poor creature, and each one of them will lead to a patch in the system of knowledge of its world. However, it will never be able to generalize the newly added theorems (due to anomalies) since neither the rules nor the existing two-dimensional theorems are well suited to grasping the three-dimensional operations that are applied. The two-dimensional world of the creature will never be complete: there will always be phenomena that it cannot explain with existing theorems. Let us put our creature to the hardest test of all time: pick it up from its plane, take it to our three-dimensional world, let it experience the extraordinary “third dimension” and then let us put it back on the plane where it belongs.1 I cannot imagine the struggle of the creature to tell its fellows what it experienced “out there.” Could its folks ever understand? The reader might have pitied the two-dimensional creatures with their inability to understand the “real” world. Well, it might be that we are, as human beings, just one more dimension better than them: what if there is a fourth dimension?2

Mathematical reasoning suggests that a formal system can talk about itself but it cannot jump out of itself. Even it speciously achieves that by adding new theorems, it becomes an improved formal system with a new boundary but the same inability. Can we jump out of ourselves and self-transcend? If we could do it, we would be able to comprehend our own physical reality, but even then we are inside another reality beyond the usual that we can’t fully comprehend. We are always limited by a boundary that is set by the “self.”

The exploration of the “self” is tightly related to the query of the soul or the spirit. The Qur’an addresses this issue in Isra 85: “They ask you about the spirit. Say: ‘The spirit is of my Lord’s Command, and of knowledge, you have been granted only a little.’” The verse is a declaration of the inability of human beings to comprehend their own spirit. More importantly, it indicates that the reality of us as human beings will be communicated to us through information sources that can jump out of the system3. Can we ever be able to fully comprehend the true nature of humanity and of our reality without knowledge from the divine?

Notes

1.This allegory might be compared with the concept of ascension. See the verses on the Ascension of the Prophet (Qur’an 4:14) and angels (Qur’an 70:4).

2.See the verses about the higher dimensional operations on our 3D world (Qur’an 21:82 and 27:38–39).

3.Messengers of the Creator. See Qur’an 2: 136, 213.

Reference

Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid, 1999, Basic Books.

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