We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor. When you send a piece of mail by cargo, you pay according to the weight of your cargo. Or imagine using an hourly Internet service in a library or airplane; the more hours you use the Internet, the more you pay.

A group of people want to rent a bus. The number of people does not affect the cost of rent for a bus. However, the cost per person could change depending on of the number of people. The more passengers, the less fee they pay for each passenger. Conversely, if the number of passengers is less, the cost of the bus fee could be more.

The examples are given above help to understand the mathematical function more easily. We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor.

Consider shipping by mail. There are actually two situations here; the weight of the cargo sent and the amount of money paid based upon the cargo’s weight. This gives us a hint for the payable amount. For example, we may know how many pounds of cargo can be sent for $10. We also may calculate how much money is needed to ship 5 pounds of cargo. We can formulate this shipping problem:  Let x be the weight of the cargo and let y be the amount to be paid. In addition, for each parcel sent, including taxes, let us assume that it costs $3. In this case, we get an equation such as y = 2x + 3. Here, the number 2 given in front of the variable x is the money paid per pound. We calculate how many dollars we will pay for a 4-pound cargo: (2×4) + 3 = $11. If 2 dollars per pound is received, a 4-pound package shipping fee is 11 dollars.

Another example would be the use of the Internet. If 40 cents is requested per hour, $1.2 will be given for 3 hours of internet usage. Thus, the equation can be written as y=40x, where x is internet usage time per hour, y is amount to be paid.

The bus rental example is slightly different from the above two examples. Although this example specifies the function, this time there is a reverse situation. In the first two examples, like (x or) input increases, (y or) output will increase. In the case of bus rental, the bus rental fee is fixed and as the number of passengers increases, the payment per person will decrease. Let’s say $400 is required for the daily rental of a bus. 40 people pay $10 per person while 8 people pay $50 per each person.  This equation would be; y=400/x, where x is the number of people, y is the amount of money paid per person. Functions are important in understanding the relationship between two variables.

Life is a function. In mathematics first, what is the function in its simplest form? Let us give the known definition in schools.

Function: Let A and B be two sets different from the empty set and there is a relation f from set A to set B. If the relation f associates each element of the set A to one and only one element of the set B, this relation is called the function from set A to set B. It is shown as f: A→B or A→B. A is called the definition set of the function and B is called the set of values. A set of elements that match the elements of set A in set B is called the set of images of the function and is denoted by f (A).

In this case, if we clarify the definition a little, a relationship from A to B to be defined in order to function f; the following conditions must be met:

1. There should be no elements in the definition set that do not have an image. However, the element can remain exposed in the value set.
2. Each element in the definition set must not have more than one image.

Let us try to find the reflections of the definition in our lives. We assume that A is the world in which we live. If we say “World” for Set A (Definition Set), we would call Group B “the Afterlife” (Value Set). Because there is a connection from this world to the other world. We will see our values in the afterlife against what we do in this world. As someone who fits the definition of a “good” person will be of high value, the definition of a “bad” person will consequently result in a lower value. So, set A considers the world and its elements as ‘living people’. We can think of all the people in the world and include them in this group since life is finite for all of us. The mathematical meaning of this reality is the following:  all elements will be moved from set A to set B (Let A and B be two sets different from an empty set and a relation f from set A to set B.). There is such a connection (or relation) that one who leaves the world cannot go to two places at the same time. Destinations are clear: abode of reward or abode of punishment. We will all be eventually placed into one of these two groups. In some cases, the last stop of the people will be paradise, even if there are those who go to hell first and purify their sins. Consequently, in the last case, no one will be in two places at the same time (If the relation f associates each element of the set A to one and only one of the set B, this relation is called the function from the set A to the set B).

Just because everyone has one final destination does not mean that that destination can only hold one person. If the levels of Heaven and Hell are considered correctly, it is possible that there is more than one person for each level or that no one has come to that level. It is possible that there are those who have sinners at the same level. We can speculate that there may even be such a level that is inaccessible to all people. The Creator creates such places in order to show His grace, mercy, and power. (In the definition set, there should not be any elements without an image. But in the value set, there may be exposed elements.)

Life itself is a function. God created life according to certain rules. We should do our best to explore, find, and use these rules. Seeing the beauties of life and being amazed by the astonishment and capturing happiness in both worlds is achieved by seeing the manifestations of God everywhere.

The basic freedoms of humanity that range from personal rights to political and general ones – such as the freedom of belief, worship, thought, the freedom to have a family, to work, to own personal property, the right of freedom of expression and association, of electing, and being elected, etc. – are not among the subjects to be discussed in “Emerald Hills of the Heart.” However, they have always been regarded as among the most important matters in human history.

Being the most fundamental and vital dimension and the most important human faculty, namely free-will, which is considered an important pillar of conscience, freedom (hurriya) is one of the most valuable gifts of God to humanity. This great gift has been defined in Islamic literature as an individual’s assertion and enjoyment of his/her basic rights. However, in order to fully perceive freedom one must be able, to some extent, to perceive its opposite. This opposite is the individual’s dependence on others for the enjoyment of those rights, which is a form of servanthood. It is God Almighty Who grants these rights to humanity, so a person has no right to change or sell them or transfer them to others. Those who commit such a sin, that is, change or sell their fundamental rights or transfer them to another, have lost their humanity to a certain extent and will be held accountable before God for that loss. Such an action shows, first of all, disrespect for human values, and those who commit such disrespect cannot be conscious of their existence, and those who are not conscious of one’s existence have no relationship with the truth and no share in the love of and servanthood to God.

In short, it cannot be asserted that those who do not recognize God, Who is the Truth and the source of human rights, are free in the sense that they are conscious of human rights, nor can those who have not been able to free themselves from slavery to others than God be free in the real sense of the term.

What we have so far said about freedom is only by way of introduction to the freedom that is one of the emerald hills of the heart.

The freedom inherent in Islamic Sufism, being one of the most significant fruits of austerity, is that a person does not submit or bow to any power other than God, indicating thereby that the heart of that person has become a clear mirror receiving and reflecting the manifestations of God. The person who has reached this point on the way to God through austerity and by God’s special help, severs inward relation with all things and beings other than God, and with emotions pulsing with freedom, heart beating joyfully with a yearning for freedom, and having broken all the restrictions around the selfhood, that person sets for him or herself this single goal and, in the philosophy of the respected saint Harith al-Muhasibi, weaves the tissue of his or her thought with the threads of the hereafter.

True freedom is attainable only by freeing one’s heart from worldly worries and anxieties about the things of this world, and so being able to turn to God with one’s whole being. In order to express this reality, the leaders of the Sufi way say: “Child, undo the bonds of servanthood and be free; how much longer will you remain enslaved to gold and silver?” The answer of Junayd al-Baghdadi to those who asked him what freedom was, “You can taste freedom when you are free from all bonds other than slavery to God” also expresses the essence of freedom.

If freedom is directly proportional to sincere devotion and servanthood to God Almighty, and it is, then it is not possible to assert that those who live their lives under the direction of others are really free. In this respect, the following anonymous couplet speaks significantly:

If you would like to beat the drum of honor,
Go beyond the wheel of the stars;
As this circle filled with rings is a drum of humiliation.

True freedom is necessary in order to be a perfect servant of God. The measure of a person’s true freedom is servanthood to God. Those who cannot realize servanthood to God can neither be free nor attain human values in their full reach and meaning. Such people can never be saved from corporeality and sensuality so as to reach the achievable horizon of spiritual life with a “sound heart,” nor can they feel the essence of human existence in the depths particular and special to it.

People who spend their life in the captivity of worldly considerations grow in arrogance in the face of the blessings granted to them. Instead of becoming more thankful to God, they attribute to themselves whatever achievement God has enabled them to realize, and are disappointed time after time when they fail, and shiver with the fear of losing whatever advantages they have accrued-such unfortunate people have no share in freedom, even if they are as kings in the world.

As long as the heart sets itself upon various goals, loved ones, and ambitions, it can never taste freedom. How can those be free who are constantly worrying about how to hold onto or pay back the goods they expect from others, who have mortgaged most of their life’s energy to others in return for worldly interests and bodily pleasures?

It is a great trial, one that leads to perdition if one wanders in the whirl of physical considerations and is confined to worldly aims with a heart attuned to worthless, fleeting objects. By contrast, it is a great favor from God upon those whose inner world He has sealed off from the many attributes of the ephemeral world that attract the carnal self; it is a great favor from God that He cuts away the relation of the heart with the world. For that relation is a form of bondage, and that cutting away is a bridge by which humanity is able to reach true freedom.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

References

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

One recent example of such phenomena is the Schrödinger equation that explains the behavior of matter at the atomic level. This relation just happens to work, and its derivation is intuitive rather than rational. It also has the simplest mathematical form among its possible competitors in terms of expressing nature.

We will now look at another example of such axiom-like relations that we usually ignore, although it is frequently encountered in our everyday life. Before revealing it as fully as we can, let us relate one situation where this effect is very apparent.

We usually move objects by pushing or pulling them. Suppose now we are on a motorboat and we have run out of gas in a place very close to the shore. We (the strong crew members) surely do not want to be carried away from the shore by the backwash from the waves. One of us has the brilliant idea to push on the sides of the boat until we reach harbor. What would you suggest? Some of us think that it is not a good idea because the boat is very heavy and our pushing will be negligible. It is true that the boat will not move. However, the failure has nothing to do with the weight of the boat. On the other hand, some other crew members suggest using oars, which will obviously work, but why? (Personally, with all my respect to other opinions, I would suggest using the phone to call the beach police to get some help; but this would distract us from our subject matter.)

Impulse, direction, and momentum

If you think about the “why” question above, you will guess that we are talking about impulse in the loose meaning of the word. In physics, impulse has a more precise definition. This definition arose from the need to describe an object’s ability to have an impact on other objects, but the idea is still vague: How do we quantify this ability in order to put some flesh on this notion? Let us try to figure out an answer to this question.

Now, let us consider a few possible ways of defining impulse that look reasonable. We may decide intuitively that an impact should be related to an object’s speed: the higher the speed the greater the impact. If you ever played marbles in your childhood, you will recall that the easiest way to dislodge the marbles in the targeted row is to cast your own marble as fast as you can. Impulse should also have a relation to mass. Certainly, the impact of as many as a thousand bullets aimed at a train will not move the train even a meter. These are some simple observations anyone can experience or have a feeling of from their daily life.

We also expect that this strange quantity should somehow be transferred by the interaction of two objects. One object colliding with another stationary object transfers something that causes the latter to travel in a direction. With this example, another important feature of our impulse idea emerges: direction. Those who like to play the game of American pool or billiards know this very well. (I am sure everyone does it for the noble reason to experiment the laws of physics.) It makes a significant difference in a collision of two masses if they hit each other at an angle.

Wait a minute! We have been talking about the effect of an object’s impact, but the object has something that it is carrying even before the impact, and this “something” is the reason why we have an impact in the first place. So, what is this “something”? Let us call it momentum so as not to violate the traditions of physics.

All this stuff so far is good, but we are not done yet: how should these ideas appear in our equations? Now, let us bring together all our findings. We know momentum manifests itself as the impact (P) of one object on another. From its effect (impulse), we understand that momentum is related to the mass (M) of the object and its velocity (V). We also know that momentum has a directionality, which is termed vectorial. Then, perhaps momentum is something like:

P = a x M + b x V

where a and b are constants. This seems acceptable since it satisfies our observation: the more the mass, the more the momentum. But for a stationary object (V=0), there is no point in talking about impulse; so the axM terms looks unnecessary. If there is no good reason for a physical quantity to appear in a physical equation, then the simplicity principle says it should be removed. Therefore, we look for a simpler alternative relation with only one term like below:

P = c x M2 x V5

where c is a constant. But this one is a highly non-linear relation with exponential terms, so it is really not looking good. Another problem with this equation is that it does not fit our daily experience very well. If we reconsider our train example, with a high velocity power term like this, even the very small bullets can have a considerable effect on a train, enough to move it in fact. As a simple example, let c be equal to 1, take 0.1 kg as the mass of a bullet and 105 kg (100 tons) as the mass of the train, and give 400 m/s velocity to the bullet. Assuming that the impulse of the bullet is transferred to the train (conservation of momentum), we roughly get:

Pbullet = c x m2 x Vb5 = 1011

Ptrain = c x M2 x Vt5 = 1010 Vt5

By equating both sides we roughly get, 1.6 m/s (5.7 km/h) for the train velocity.

A single bullet moving a big train at such speed? This is a very counter-intuitive result. However, we will not give up easily. How about if we try an expression which is more familiar?

P = d x MV2

where d is a constant. This relation also agrees with our intuition (i.e. it has mass and velocity terms proportional to P.) I can already hear some objections from those who are acquainted with physics saying “No! This is the energy formula of a body with mass M and velocity V.” Indeed, this equation is reserved for energy which is a non-vectorial quantity. As a matter of fact, none of the above is a correct description for momentum. The actual expression is, interestingly, the simplest of all possibilities:

P = MxV

So, why not the more complex ones but this, the simplest one? The rigorous answer is subtle and requires a thorough analysis of linearity and homogeneity of space, which could be the subject of another essay. But we repeat the remark that we made in the beginning: if there is a simpler and more beautiful way of describing a natural law, then that description often turns out to be the correct one in the end. In fact, for some giants of physics like Paul Dirac, the beauty of a theory is more important than its results and is a better indication of the theory’s correctness. There is more to it than that. There are whole theories like Dimensional Analysis which are implicitly based on the idea of writing down the equations in the simplest (and most beautiful) form.

So, the final point is that, like other fundamental relations in physics, the idea of impact or momentum is best described in the simplest and most intuitive way: P= MxV. And behold! This gives us exactly the relation that has passed all the scientific tests in the range of classical physics. This result implies that the beauties we see in nature can be explained in terms of the simplest possible physical relation. Pondering all these, one cannot help but ask how in the world a mindless, blind natural law could exhibit beauty based on simplicity.

A: Before discussing the equality of men and women, we should first look more closely at the meaning of “equal” and “equality.”

“Equal” means that there is no difference between things, that they have the same nature, quality, value and dimension. On the other hand, “equality” means that there is no discrimination between people in terms of rights.

Having established these definitions of “equal and “equality,” then how are we to view women in relation to men?

a) Difference in Nature

God has created everything in the universe in pairs. It is impossible to say that one of these pairs is equal to the other in all respects. “And of everything we have created pairs that you may reflect.” (Az-Zariyat, 51/49).

From atoms to plants, and from these to the male and female of animals and human beings, everything has been created in pairs and each member of the pair is in need of the other. Positives are in need of negatives, electrons are in need of protons, night is in need of day, summer is in need of winter, the surface of the earth is in need of the sky, men are in need of women and vice versa. In addition, there are probably other pairs that we may not know of yet, but we will learn about these with the development of science and technology.

Just as God has created the electron in relation to the proton, the negative in relation to the positive, and the female seed in relation to the male seed, God has created women and men, and He has formed a unity between these couples. But just as positive and negative are not equal, nor are the electron and proton equal, women are not equal to men. This is an unchanging rule of the nature of creation. Moreover, other than God, Who is One, everything else is deficient and insignificant and cannot continue its existence by itself. So, men and women, who are imcomplete by themselves, will come together to form a union, and it is this union that is the essence of the whole.

Therefore, women and men are not equal, but they complete each other. Prophet Muhammad (pbuh), in one of his hadith says: “Women are (the other) half of men.”

The word for “other half”-sakik-in this hadith means a piece of a whole divided into two through the middle. This means that each piece that is forming the whole is the sakik of the other. Thus, according to this hadith, women and men are equal halves as human beings. But they are never the same as the other; that is, their natural, spiritual and psychological structures are different. As a woman can never be equal to a man according to his physical and spiritual structure, a man can never be equal to a women according to the same aspects. Neither are men biologically superior, nor are women inferior to men. As human beings cannot really change the difference between the sexes, both believers and nonbelievers should give up their dreams of bein equal and should accept women and men as they are.

In addition, we cannot even claim that individuals of the same sex are totally equal to one another. Trying to verify this would be to attempt to change the rules of creation; such efforts are useless. Here we should mention that the difference in the creation of women should not lead men to feel superior. On the contrary, God states, “And Who made (things) according to a measure, then guided rightly” (Al-Ala 87/3). He is the One who creates women and men in the best pattern of creation and He is the One Who teaches them how to improve themselves. He is the One Who makes them complementary to one another and the protector and guardian for one another.

b) Differences in Duty

As is clear from the above explanations, just as women and men cannot be equal in their nature, nor can they be equal in duty. If you expect a woman to perform the same duties as a man, you will in fact be oppressing her. It is obvious that women are different from men physically, biologically and spiritually. It is therefore only normal that, arising from this difference in their natures, that there should be a difference in duties. For instance, men are stronger than women. In this respect, it is very difficult for a woman to do some of the work that a man does. This is not to be seen as an inadequacy of women. Women are generally more merciful, compassionate, intuitive and emotional when compared to men. In this respect, men cannot be compared to women in any way. Both sexes are equipped according to the necessities of their duties; this is the true justice. Therefore, instead of studying men and women as if they were on equal terms, we should evaluate women and men separately and according to their own particular natures.

Women have certain rights and duties based on the nature of their creation, and if women make use of these qualities they will then be able to obtain better results.

New generations are brought into this world by women and are brought up by them. Humanity gains good individuals through their efforts. It is a great kindness and wisdom of God that women have been equipped with such compassion when we consider that they are in charge of bringing up children. In this respect, among all the members of the family, women deserve the greatest respect. They are the educators, teachers, and the source of the family’s endurance and the peace of the home. Men are reassured by them. Children grow up under their compassionate wing, and are raised with healthy emotions, compassion, and strong values. If the mother lives a chaste life, then the children will be saved from degeneration, and a community formed of these children will be saved from oppression.

When we compare all the things that humans provide women with in the name of equality with those favors that God the Almighty provides, the former will be very small in comparison. Moreover, all the rights granted to women and all the effort expended on behalf of their gaining “equal rights” is as ridiculous as if we were to give a copper medal to someone whose chest was already covered in gold medals.

God has given everyone their own nature. With the granting of this nature he did not make anyone coarse or foolish. If he had granted any superflurous duties to people, then this would have been no more than an injustice or an act of oppression.

The tasks or duties that women do should be suited to their physical, psychological and spiritual nature. Offering a woman a job that she cannot handle, or employing her in a job that is not in her nature to accomplish, has nothing to do with equality or treating a woman as an equal; this is not a humanitarian approach. On the contrary, such behavior is little more than the forceful seizure of the majority of her rights.

A hadith of Prophet Muhammad (pbuh), expresses the subject in a beautiful and elegant manner: “They had put a cow to yoke. It turned and said to its master: I have not been created for such jobs.” Rather, it is the ox that was created for such jobs.

In conclusion, everything has been created for a reason. For true justice to prevail, every creature should be employed according to its capabilities and according to the reason for its creation.

As was pointed out earlier (in previous issues), God is beyond all comparison and whatever we conceive of Him, He is different from it. We can only acquire some knowledge of Him, not of His Divine Essence, but His Attributes and Names, by meditating on His acts and creatures and studying them. However, in order to understand His acts, sometimes we have to resort to comparisons, as is allowed in the Qur’anic verse, God’s is the highest comparison. Thus, in order to get some glimpse of the relation between Divine Knowledge and Destiny and Decree, we may ponder the following comparison:

Suppose there is an extremely skilful man, who is an engineer as well as an architect and a builder. He wants to build a magnificent house. First, he must have conceived of what kind of a house he wants to build. This is the existence of the house in the builder’s mind. Then, the skilful man draws a detailed plan of the house. This is the existence of the house as an actual design or plan. Afterwards, he puts this design into practice and builds the house according to it. This is the material existence of the house. The house is recorded in numerous memories, and even if it is destroyed completely, it continues to live in these memories and in the mind and plan of its builder. This is the final form of the house’s existence and has acquired some sort of perpetuity.

Another, similar comparison.

Before starting to write a book, an author must have the full content or knowledge of the full meaning of the book in his mind. This is the existence of the book as knowledge or as meaning. The existence of something (as in the examples for the book or house) as knowledge or meaning, is its essential existence. Even if this knowledge or meaning is not put into words or into practice, it exists in the mind. Therefore, although it needs ‘matter’ to be visible in the material world and known by others, knowledge or meaning is the essence in existence, upon which material existence depends.

In order to make his knowledge on a subject or the meaning in his mind visible and known by others in the material world, the author must express it in words. So, before putting it in words, he arranges it in chapters, sections and paragraphs, that is, he makes a detailed plan. Then, he writes it out and gives it material existence. Even if the book is completely destroyed and removed from the earth, it continues to live in numerous memories and in the mind of its author.

Likewise, God has full and exact knowledge of the universe as a whole and with all its parts down to the minutest particles. In order to have a glimpse of the infinite extent of His Knowledge, we can ponder the verses whose literal translations are as follows:

It may be that you dislike a thing although it is good for you, and love a thing although it is bad for you. God knows, but you know not. (al-Baqara, 2.216)

Say: ‘Whether you hide what is in your breasts or reveal it, God knows it. He knows all that the heavens and the earth contain; and He has power over all things.’ (Al ‘Imran, 3.29)

With Him are the keys of the Unseen. None but He knows them. And He knows what is in the land and the sea. Not a leaf falls but He knows it; not a grain amid the darkness of the earth, nothing of wet or dry, but (it is) in a Manifest Book. (al-An’am, 6.59)

Say: ‘If the ocean were ink for the words of my Lord, assuredly the ocean would be used up before the words of my Lord were finished, even if We brought another (ocean) like it, for its aid.’ (al-Kahf, 18.109)

Even if He had not created the universe, the universe would still exist in His Knowledge. Since God Himself is beyond all time and space and all time and space is united in His Knowledge in a single point, and since His Knowledge does not depend on time and space, in relation to Him and His eternal, all-encompassing Knowledge, there cannot be things like precedence or posteriority or sequence or division of time. Time and space are only two dimensions of creation.

Everything eternally exists in God’s Knowledge. God knows all things with the exact peculiarities of each, and Divine Power clothes a thing in material existence according to Divine Will. This transference from Knowledge to the realm of material existence takes place within the limits of time and space. Knowledge and Will are two essential Attributes of Divine Being: God knows things; things exist in Knowledge, Will determines them with all their peculiarities according to a certain measure, and Power gives them material existence. The relation which we are trying to explain between Divine Knowledge and Destiny, is best expressed in the verse, the literal translation of which is as follows:

There is not a thing but with us are the stores thereof. We send it not down save in appointed measure. (al-Hijr, 15.21)

Divine Decree and Destiny in relation to registry and duplication

Everything which exists in Divine Knowledge in individualized form according to a certain measure or, if we may say so, as a plan or project, is in a Record which the Qur’an calls ‘the Supreme Preserved Tablet’ (al-Buruj, 85.21) or the Manifest Record (Ya Sin, 36.12). The Qur’an explicitly states that nothing befalls us save that which God has decreed or preordained for us (al-Tawba, 9.51) and there is not a moving creature on the earth, nor a flying creature flying on two wings, but they are communities like mankind, and that God has neglected nothing in the Record (al-An‘am, 6.38). This Record or the Supreme Preserved Tablet is a title for Divine Knowledge in relation to creation. We can also call it the original Register. In the ‘process’ of creation, this Register is duplicated. Its first, most comprehensive copy or duplication which comprises the whole of creation is called in the Qur’an the ‘Tablet of Effacement and Confirmation’ or the ‘Manifest Book’. While the Supreme Preserved Tablet or the Manifest Record relates to the originals of creatures in Divine Knowledge and the principles and laws of creation, the Manifest Book or the Tablet of Effacement and Confirmation is the reality and, metaphorically, a page of the stream of time. Divine Power transfers things from the Supreme Preserved Tablet onto the Tablet of Effacement and Confirmation. In other words, Divine Power arranges things on the page of time or attaches them in turn to the string of time. Nothing changes on the Supreme Preserved Tablet; everything is fixed there, but in the ‘process’ of creation, God effaces what He wills, and confirms and establishes what He wills. (al-Ra‘d, 13.39).

The second kind of duplication is like this:

After birth, everyone is registered in a registry of births. Then, according to the information in this state register of persons, everyone is given an identity document. Similarly, everyone is registered on the Supreme Preserved Tablet with all his personal characteristics, particularities, and future life-history down to the smallest details. This original register of everyone is copied out by angels, and the part of it which relates to the life of the body is encoded in cells as information or laws. However, for this information to be used or for the body to work and come to life, the spirit has to be breathed into the body. The other part of the copy of the original register which relates to man’s life as a conscious, intelligent being is fastened around his neck as an invisible book (al-Isra’, 17.13). During his whole life, man enacts whatever is in that book. However, that does not at all mean that Destiny or the pre-determination of a man’s life history compels him to behave in a certain way. As we are trying to explain, Destiny is some sort of knowledge. It is like this: for example, you send someone to a place to do some job. You have previously procured whatever he will need during that journey and given him necessary instructions to do the job. Since you knew in advance how he would behave in every step of his journey, you have recorded all the details of that future journey in a notebook and placed it in a secret pocket in the jacket of that man. He starts out unaware of the notebook in the pocket and behaves however he wills during the whole of his journey. Together with him, you dispatch two of your most reliable men to follow him wherever he goes, observe all his acts and record on a videotape secretly whatever he does and says and however he acts. On his return, you compare the video-tape recordings with the content of the notebook in his secret pocket and see that there is not the slightest difference between them. Afterwards, you call him to account for whether he did the job in accordance with your instructions and either reward him or punish him or forgive him.

As in the example above, God, Who knows everything in advance and is beyond all time and space, pre-recorded in registers the life-histories of all people to come to the world. Angels copy out the registers and fasten around each person his own record or register, which is what we call destiny or fate. God’s fore-knowledge and recording of whatever a man will do in his whole life never compels the man to do that. He acts of his own free will and does of his free will whatever he does. All his life is recorded by two angels, whom we call Kiramun Katibun (noble scribes). On the Judgement Day, the recordings of his life by these angels will be presented to him and he will be told to read his Book:

Every man’s book of life-history (fate) have We fastened around his neck, and We shall bring forth for him on the Day of Resurrection a book which he will find wide open. (It will be said unto him): ‘Read your book. Your own self suffices as a reckoner against you this day. (17.13-4)

Divine Decree and Destiny in relation to Divine Will

As pointed out above, God registers everything in His Knowledge in a record and gives it its own particular characteristics, appointing for it its life-span and provision. He also (pre-)records when and where one will be born and die and what one will do during one’s whole lifetime. All this takes place by Divine Will.

It is through Divine Will that everything and every event, whether in the realm of Divine Knowledge or in the realm of material existence, including man’s life, is (pre-)determined and given a certain course or direction. Nothing occurs beyond the scope of the Divine Will.

Consider that, for example, there are innumerable alternatives before an embryo in the female womb: whether it will grow as an animate being or come to the world or not, when and where it will be born, how long it will live, when and where it will die, etc. All beings are different from one another in complexion and countenance, down to the fingerprints, in character, in likes and dislikes, and so on, although they are all formed from the same basic elements. Again, for a particle of food which enters a body either in the stage of embryo or full development, there are countless alternatives where it will go and be settled. If, for example, a single particle which must go to the pupil of the right eye and be settled there, were to go to the right ear, this might result in an anomaly. Thus, it is by the all-encompassing Divine Will that everything occurs according to a miraculously calculated plan, and it is again by the Divine Will that there is a miraculous order and harmony in the universe. No leaf falls, nor a single seed germinates under earth, but God wills it to do so.

Man’s free will is also included in the Divine Will. Nevertheless, the relation between the Divine Will and man’s free will is not the same as that between the Divine Will and the lives of other things or beings. God Almighty has endowed man with the power of choice-free will-and, taking into account his future choices in life, (pre-)determined his life down to its smallest details. As explained above, God’s (pre)determination of man’s life and actions is like knowing them in advance. We should, however, add that the theistic conception of God is not correct. That is, God did not leave the universe to itself after He had created it. We are contained by time and space and therefore cannot draw exactly true conclusions about the relation between the Creator and the creation. Also, we are unable to perceive eternity; we have little true information about the material domain of existence. God is beyond all time and space; He is infinite and eternal. He holds the universe in His ‘hand’ and controls and manages it however He wills. However, in order that we might catch some glimpse of His actions and acquire some knowledge of Him and His Attributes, He places on His manifestations the limits of time and space. Other-wise, life would not be, nor could we have any knowledge of Him and the universe. Therefore, all the explanations we have made so far about His Will and Destiny, should be considered in the light of the fact that we can approach the subject only from within the bounds of this life, which is limited by time, space and matter, and also from within the bounds of our very existence.

In sum, the Divine Will dominates over the whole of creation, and nothing is or occurs beyond Its scope. It is by the Divine Will that there is a miraculous order and harmony in the universe, and everything and every event is given a certain direction and certain characteristics of its own. However, the Divine Will does not exclude man from having a free will.

Divine Decree and Destiny in relation to creation

There are two aspects of the relation between Divine Decree and Destiny and creation:

1. As a determining and compelling factor, except for the realm where man’s free will has a part, Destiny is absolutely dominant. Everything occurs, all events take place, according to the measure, determination, judgement and direction of Destiny. God is the absolute owner of sovereignty in the whole universe and He acts and disposes however He wills in His Kingdom. He does whatever He wills and no one can call Him to account for His acts. He is absolutely Just and Wise and also absolutely Merciful and Compassionate. Therefore, whatever He does is good and He never wrongs any of His creatures.

We cannot interfere with the operation of the universe: the sun always sends us heat and light completely independent of us, the earth rotates around itself and the sun; days, months, seasons and years come and go one after the other and we cannot do anything with respect to whatever happens in ‘nature’. There are innumerable instances of wisdom in all such acts of God, and they are all to the use and benefit of man, so what falls on man is to study and reflect on His acts and try to find the instances of wisdom in them:

In the creation of the heavens and the earth, and in the alternation of night and day, there are signs for men of understanding. Those that remember and mention God standing, sitting, and lying down, and reflect upon the creation of the heavens and the earth. ‘Our Lord! You have not created this vain. Glory be to You! Protect us from the punishment of the Fire.’ (Al ‘Imran, 3.190-91)

Man should also reflect on whatever befalls him in his life. God never wills evil for His creatures, so, as the Qur’an explicitly states, whatever of evil befalls a man is from himself (al-Nisa’, 4.79); it is because of his sins. God allows misfortunes to strike man in order to either forgive his sins or promote him to higher ranks. But this does not mean that He always punishes a man with some misfortunes because of every sin of his; He overlooks many of his sins without punishing him.

2. The second aspect of the relation between Divine Destiny and creation concerns the religious injunctions and prohibitions, which relate to human free will.

While Divine Destiny is absolutely dominant and compelling in the part of existence where man’s free will has no part, such as the creation and control of all things and beings or animate and inanimate bodies, and the movement of planets and all ‘natural’ events or phenomena, in the human realm, It takes man’s free will into consideration. However, as God creates all things and events in ‘nature’, He also creates whatever man wills and does. This is so because God has honoured man with free will and prepared for him an eternal abode. Although He desires His servants to always will and do good and insistently invites them to it, He does not refrain from giving external, physical existence to their bad choices and evil acts, however displeased with them He is.