Funny though, sometimes while walking in the enchantment of the awakening nature around me, I run into a tree, and I hug it as if I met a friend. You can imagine how entertaining I am to the passers-by.

It was one of those days when I felt the presence of a second person near me. Strange enough, though, he wasn’t laughing at my hugging the tree.

“Hi fellow, what is wrong with you? Why aren’t you laughing at this lunatic who is in love with trees instead of people?” I asked.

I was shocked upon hearing his answer:

“The sight of people is of no value to me because I cannot see the light coming from them. But you are certainly shining through your voice.
“For me, people shine through their presence; they change my heart beat.”

I exhaled the air that was hiding in my lungs with anxiety, and teased: “So, I should be careful when I am talking to you since I cannot hide my true feelings from you!”

“You bet. But don’t worry; your voice is giving me positive signals.”

Then, I quickly returned: “I am happy to hear that. So, shall we play a game together?”

“Like what?”

“Alright. Only by listening, we are going to try to predict the coming of the next person.”

“I’ll take your challenge,” he said.

And, we kept silent in order not to miss the clues of an approaching person. Believe it or not, we waited for minutes and not a single person passed by. We could hear voices of kids running in the distance, wind rubbing the leaves, trunks of the trees squeaking as they swing, flies, birds flying or landing, etc., but not a single person passing by. Suddenly he said:

“Maybe we should play something else.”

“You know what? You are the ever first person with whom I can play the game of solitude. We are together but not like cans on a shelf. We are together like two flowers smiling at each other although we cannot see or hear one another. Outsiders may think we are lonely. But in essence, we are hand in hand in the depths of our hearts.”

“It is strange that you say this. Why should you enjoy solitude?” he asked.

I did not answer that question. Actually my silence was the answer; and I think, or hope, he got my answer. I didn’t want my discovery of a solitude-mate to disappear so abrupt.

“Here comes one!” he exclaimed. I could feel his joy of catching the first person. I smiled; and he felt it because I give out a warm and vibrating breath when I smile.

“It is so alive,” he said.

“What? The person?” I was startled. Why was he using “it” for a person?

“No, your smile. I don’t feel many smiles like yours. I usually hear frozen laughs and smiles of mass-production, which carry no sincerity.”

I was embarrassed by his compliment. Again I kept silent, but my face was burning up, and he felt that as well.

“Now you are as flushed as I was when we started talking.”

“Yeah, what had happened to you? Why were you so flushed earlier?” I inquired.

“I climb this tree often. I actually do this whenever there is nice weather. Sometimes, I feel the footsteps of someone, whom I want to catch. I rush down to the ground hoping not to miss the encounter. But always, I miss the person. Now, that spirit is standing before me.”

Once more, I was embarrassed. I didn’t know what to say. We both kept silent for a while. Then, I heard my daughter calling: “Dad, it’s time.”

She was the one predicted by my solitude-mate.

“Forgive me for disturbing your conversation,” she added.

“A conversation by presence cannot be disturbed by words,” replied my friend. We all chuckled.

I felt my daughter pulling my arm – an authoritative sign meaning “let’s go.” I grasped her hand firmly, turned back to my solitude-mate, and gave a goodbye silence, and he did the same to me. Then I gave him that lively smile, and he went through that shower of heat. I picked up my cane and started knocking on his ears again as I returned home with my daughter as my guide.

“The human brain, then, is the most complicated organization of matter that we know.”
Isaac Asimov

If someone asks what you recall when you look at the following pictures, I can hear you say ‘President Obama’ and ‘Statue of Liberty’. You just see a fragment of the pictures and remember them.

So, how does it happen? This is just a simple task for the brain. It stores an image and retrieves it whenever a part of it is seen. Amazing features of the brain, especially its power to learn and make decisions, inspires computer scientists in the field of artificial intelligence.

In computer science, an artificial neuron is a simple computational model of a neuron in the brain that excludes biological properties. Artificial neural networks (ANNs) are composed of artificial neurons, and they are utilized to solve specific problems, especially those that require learning and decision-making. ANNs may not be the best solutions in various machine learning problems; however, they are accepted as strong alternatives. Although ANNs don’t claim to be so, currently they are not even close to producing a simple model of the brain. Let’s take a short journey into the world of ANNs to experience the extreme difficulty of modeling the brain.

Some Applications of ANNs

Figure 1: Overview of ALVINN structure. Images obtained from the camera installed on the vehicle are provided to the ANN, and ANN decides the steering angle.

(adapted from: http://virtuallab.kar.fei.stuba.sk/robowiki/images/e/e8/Lecture_ALVINN.pdf).

ANNs have various applications in very large spectrum of problems that require learning, such as the Autonomous Land Vehicle in a Neural Network (ALVINN). The structure of ALVINN is shown in Figure 1. The ALVINN project by Carnegie Mellon University started in 1986 and aims to make a vehicle without a driver (Mitchell, 1997). In this project, ANN learns the steering habits of a driver. A camera is mounted on the vehicle to capture the images of the road. With respect to the continuous images provided, ALVINN determines the steering level with 45 different angle positions from sharp left to sharp right. Steering is updated 15 times per second so that it allows real-time control while driving at 55 mph. The system is trained by the data obtained from a human driver in a simulator and a real vehicle. ALVINN was able to speed up to 70 mph and successfully drive at 55 mph for 90 miles.

Figure 2: Handwritten zip codes (LeCun, et al., 1989)

Another example is handwritten zip code recognition (LeCun, et al., 1989). Zip codes from US Mail written by various people with large variety of styles and sizes were used in the experiments. Figure 2 presents some examples of zip codes in the experiment database. After the ANN was trained with more than 7,000 digits in the zip codes, it was 99% successful in recognizing around 2,000 digits in new zip codes.

Learning and Decision-making in ANNs

In order to understand the challenges better, we will first examine learning and decision-making in neurons and ANNs on simple examples.

Figure 3: (a) A typical neuron (adopted from http://commons.wikimedia.org/wiki/File:Neuron_-_annotated.svg), (b) artificial neuron in computer

Figure 3(a) illustrates a typical neuron which is the constituent of brain’s complicated network structure. Each neuron receives information as signals via dendrites, then evaluates it and generates a signal that is transmitted through its axon. A neuron has many connections between its dendrites and the axons of various other neurons. Figure (b) demonstrates an artificial neuron in computer science. It is considered a function: dendrites as the inputs of the function and generated signal via the axon as the output of the function.

Let’s see an example of an artificial neuron that understands if a given produce is a red apple or not. Think about how you understand whether a produce is a red apple or not. You see the shape and the color. However, it might be an artificial one for decoration. Then you can taste it and you get the sweetness of the apple. Similarly, our neuron receives three pieces of information as the input; ‘has circular shape?’, ‘is sweet?’, and ‘has red color?’. If the output is ‘yes’, that means the neuron recognizes the produce as a red apple. Otherwise, it will be ‘no’, which means the produce is not a red apple (Figure 4). Here, the neuron’s function is defined in such a way that it only generates ‘yes’ when all the inputs are ‘yes’.

Figure 4: Example inputs and outputs for the artificial neuron.

In an artificial neuron, some of the information can be more important than the others. For instance, to have red color may be more valuable in determining the price of produce. Assume that round shape and sweetness has equal value of $1; however, having red color is $2 – twice as valuable as the other features (Figure 5).

Figure 5: Artificial neuron with different input weights. Arrow thickness indicates the importance.

So, what is the big fuss about artificial neurons if they are only functions? In fact, the main feature of artificial neurons is learning. Considering the last example above, the neuron initially does not know the importance of the dendrites, i.e. the weights of inputs are all the same. If not trained, the neuron will generate the following answers which are sometimes wrong as indicated in Table 1.

Table 1: Artificial neuron before training; highlighted answers are wrong.

In real life, a teacher trains students. For instance, the teacher asks a question and if the received answer is not correct, she provides the right answer. Students learn the right answer and use this correct information in their lives. It is similar in artificial neurons as depicted in Figure 6. When the response of the neuron is incorrect, it adjusts the importance of the dendrites with respect to the correct answer hence it answers the same question correctly next time. During the training session, the neurons will be continuously asked the values of all the produce until it learns them all.

Figure 6: The learning process of the artificial neuron.

What if the problem gets complicated? Then one artificial neuron will not be sufficient, and we will need a network of neurons; ANNs. A more complex problem, ‘learning the digits’ is indicated in Figure 7.

Figure 7: (a) Digit learning problem, (b) ANN structure that learns digits. Due to the difficulty, only the connections between the input layer and first / last neurons in the middle layer are shown.

ANN has 3 x 5 = 15 input units like receptors of an eye retina. Each input unit corresponds to one square in the digits; either filled or blank. Each input unit is connected to the dendrites of all neurons in the middle layer. The output of each cell in the middle is connected to the dendrites of all neurons in the output layer. There are 10 output neurons corresponding to the digits from 0 to 9. After the ANN is trained, it provides a correct answer to the given digit as input. When digit ‘3’ is provided to the network, the neuron labeled with number ‘3’ in Figure 7(b) is triggered and outputs ‘yes’ whereas the rest of the neurons output ‘no’.

Figure 8: Faulty digit ‘3’ with a missing black square on the top right side.

Initially, all neurons in the network have equally weighted dendrites. After a reasonable amount of training, neurons adjust their weights, and ANN is able to identify digits. Here, we have some major challenges: what does ‘reasonable amount of training’ mean? When the ANN is undertrained, it will not always answer correctly to the digits given in Figure (a). In the other case, when the ANN is overtrained, it will memorize the digits provided during the training and will not recognize the faulty ones such as the one in Figure 8.

Challenges of ANNs

Beyond the mentioned the overtraining / undertraining problems, ANNs have a bigger challenge – how to determine the structure of ANN that fits the problem? In the digit learning example, we’re lucky because the structure is provided in Figure 7(b). However, the outcome of the solution may drastically depend on the number of neurons and the connections among them which is indeed a hard problem for ANNs.

The huge capability of the brain in learning and decision making comes from the huge number of neurons – around 100 billion – and the enormous amount of connections among them – from 100 to 500 trillion. The challenge to design such a huge network requires huge computation power. With the increasing number of neurons, ANN dramatically slows down especially during the learning process. Here, our example is a simple learning task of 3×5 pixel digits compared to the brain’s acquisition capacity of hundreds of images in our daily life. 

When the number of neurons gets larger, the reliability of network also reduces. Small adjustments in weights may change the entire behavior of the network hence it is easy to lose control of ANN. In contrast, the brain has a robust system, and its fault tolerance is admirable. Although neurons die every day, this doesn’t affect its performance significantly. The training method and how to update the weights are other hard problems leading to many different approaches in the neural computation field.

We have presented some simple tasks that can be solved using a few neurons and their challenges. On the other hand, consider the thousands of problems, various and incredible amount of information we have learned, and the thousands of decisions we make. The brain is truly amazing from the computer science perspective.

Bibliography

• Hertz, J. A., Krogh, A. S., & Palmer, R. G. (1991). Introduction To The Theory Of Neural Computation. Reading, MA: Addison-Wesley.
• Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational properties. Proceedings of the National Academy of Sciences of the USA , 79, 2554-2588.
• LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., et al. (1989). Backpropagation applied to handwritten zip code recognition. 1 (4), 541-551.
• Mitchell, T. M. (1997). Machine Learning. McGraw-Hill.

A mysterious program
Far beyond our reasoning,
The ones open to mysteries
Never fall on their knees.
Do have the faith, then,
Never be felled by confusion!

Close not your eyes to the beauty
Do not be stuck in the ugly!
Behold Him as mountains do the sun!
Watch ever for His Holy Light,
Put the darkness aside!

Keep whirling within the phenomena
As the sage do!
Glimpse the good sides of both
pleasure and grief

Relinquish gloom and worry
If your willpower is bustling
Become the spring of hope for all,
If you can!

Till the seekers of a tranquil corner
Shall run to you;
And those joining your aura
Shall overflow with fervent happiness.

According to the British writer Raymond Williams, culture is one of the two or three most complicated words in English. It has many definitions but here is the crux to remember: Culture is the way of life of a given society. Our culture is what we are as a group; it is learnt from birth and is passed down from one generation to another.¹

Culture is to the person as water is to the fish. It influences the way we perceive the world, tells us how to behave, and tells scholars how to think about the causes of behavior. It even shapes the moods and opinions of public about what to eat, what to wear, what to think is right or wrong, and much more. However, people are generally unaware of their cultural conditioning and do not realize that the way they recognize the world is not necessarily same as the way other groups do.²

An array of traditions, norms and values observed in a society raise its cultural character which distinguish societies from one another. These cultural variations influence the course of communications, may cause (the escalation of) conflict when it leads to miscommunication or misinterpretation, and can be problematic in cross-cultural encounters when one acts as if differences did not exist.³ The deeper one interacts with a different cultural group, the more he/she understands its the norms and priorities. This awareness of the ways cultures operate in communication and conflict will yield to the ability to respond effectively to these differences and prevent misunderstandings in intercultural settings.

One can list many dimensions or their sublevels that cause variations both between and within cultures.  Below, we will discuss some major aspects along which cultures vary. Although it seems that there are no direct linkages between each topic, it is interesting to see how they actually relate to one another.

Senses of Self:

From the outside, a tree grown in California would probably look just like a tree grown in Japan. However, the growth of each tree is largely dependent on the soil that roots of the trees have to interact with in order to grow. The strength of the roots is also dependent on the environment the tree is exposed to, from sunshine to thunderstorms. Imagine the values of a particular culture represented as the roots of a tree. These roots (values) are the source of strength needed by the tree to survive in the surrounding environment (society). Of course, we don’t really see the roots, but we are constantly exposed to the tree nevertheless. The type of fertilizer and water fed to the tree contributes significantly to the growth of it. In addition, you can not transplant a tree into other soil unless you prepare the roots for the new soil.

The roots of each tree may have a different form, much like the cultures they represent. The Japanese roots are twisted together because they may have rockier soil and need the combined strength of the roots to support the tree during rough weather. The American roots, however, are individual, separate, straight, and deep, responding to their soil condition. ⁴

Societies that value individual uniqueness and self-determination are referred to as individualistic cultures in which people make up their own mind and show initiative independently. In this way of life, people deem themselves as the masters of their lives which they think they can control by themselves. On the contrary, cultures in which people identify themselves with groups are categorized as collectivistic societies. These societies consider many external parameters outside one’s control that affect the course of their lives, and there is more emphasis on the role of destiny in daily life. Many of the Asian cultures are collectivist, while Anglo cultures tend to be individualist.

A “self-determining” individual tries to preserve his/her image and interests by taking a competitive stance in interpersonal encounters. However, for those in collectivistic cultures, direct confrontation may reflect poorly on the group or disturb overall harmony; then open criticisms of others are generally avoided. When there is conflict, a third party is utilized for resolution. Since no direct confrontation takes place, potential damage to the relationships is minimized.

The value placed on individual freedom in individualist societies leads to the idea that everybody is equal regardless of age, social status, or authority, which calls for a tendency to be informal when addressing one another. In the US, for instance, superiors and subordinates often interact socially as equals, and an outsider typically cannot tell them apart. However, collectivistic societies place more value on seniority and hierarchy and, therefore, are more formal. They also put more emphasis on the role of power/status: Is the boss, a) always right because he is the boss, or b) only when he gets it right?

Someone devoted to freewill and someone with a more philosophical orientation may face miscommunication. The first would expect immediate action and responsibility and, failing to see it, may conclude that the latter is lagging, hindering, or dishonest. The second person would expect respect for the natural order of things and, failing to see it, may conclude that the former is pushy or impolite.

Communication styles:

Japanese can find Westerners to be offensively blunt. Westerners can find Japanese to be secretive, devious and bafflingly unforthcoming with information. French can feel that Germans insult their intelligence by explaining the obvious, while Germans can feel that French managers provide no direction. ⁵

In some cultures, people presume ample commonality of understanding and attitude in their counterparts hence they feel that it is unnecessary to be “over-explicit”; information is communicated in indirect ways embedded in the existing context or internalized in the person per se. Whereas in other cultures, information is part of, and conveyed through, the verbal content of the communication; things are made explicit, and there is considerable dependence on what is actually said. The first types of cultures are known as high-context, and the latter low-context respectively. Due to the significance of social information networks, collectivistic cultures tend to be high context.

Since the focus is the message itself rather than the context, low context cultures are open to communication errors when they assume more shared knowledge than there actually is. This direct approach may help to avoid communication errors when used properly (in a good timing and context). However, communicators may fail to “feel the emotional state” of the other party, or may hurt feelings while trying to be “direct.”

Though, low context cultures expect thorough explanations, high context cultures take them as redundant discussions on details, and even somewhat hesitate to make mistakes with too much talk.  These cultures are more cautious about the potential implications of the message delivered. Silence and other indirect/non-confrontational methods are frequently applied and patience is promoted for the sake of overall harmony. On one side, silence is viewed as a communication breakdown, whereas on the other it is utilized as an actual communication component at times.

Perception of time:

I was once told that one of the South American groups in the U.S. used to send to different invitations for the same occasion. One was truly showing the ceremony time, yet the other was for an hour before the actual kickoff. The first was for the American friends and the latter one was for their own community to offset possible delays.

Time is beyond what a clock reads: “There are two blessings in which most people are in great loss:  Good health and free time.” ⁶ In addition to being a major blessing, it is one of the most central differences that separate cultures and cultural ways of doing things.

In the West, time has a present focus moving toward the future at an acknowledged swiftness. Events are explained via specific causes, and there is an appropriate time and place for everything. This notion of time is actually a product of the Industrial Revolution which requires certain tasks to be achieved at a predetermined hour. Concentration is on one event at a time, schedules and deadlines take priority, and interruptions are not very welcome, which ultimately seals people off from one another, as limited time allows some people in and leaves some others out.

In Western cultures, time is considered as a limited reserve which is continually being used up. It’s like having a bathtub full of water that is running down the drain, and can never be replaced. It has to be used as it runs down the drain or it is wasted.⁵ Time is perceived quantitatively; it is measured and almost tangible. Many expressions such as Boucicault’s following words highlight its importance and urge its awareness in these societies: “Men talk of killing time, while time quietly kills them.” “Time is money” is a household expression, and people often talk about “saving,” “spending,” “wasting,” “finding,” or “losing” time. Time orders life and priorities: “I don’t have time to do that.” Since time is prioritized, so is accomplishing a task as quickly as possible; thus taking risks are expected to bring the future closer.

As time is limited, punctuality becomes a desirable quality and wasting someone’s time is regarded as an insult. Lest communication takes more time, individual-oriented cultures promote direct and competitive communication, whereas group-oriented cultures prefer indirect and harmonious approaches to communicate and avoid direct confrontation. Individualistic cultures may view this communication avoidance as passive, unwilling, or even ignorant. On the other hand, collectivistic cultures may view the direct approach to communication as being rude.

In the East, time is circular, spiral, even repetitive, and has unlimited continuity; in old agricultural societies which depend on the months/seasons of the year, it renews itself annually (traditional Chinese calendar has a period of 12 years). Other unrelated events or mystical reasons may be used to explain a given event, “as time is viewed an unfolding of stories already written, or a play in which much of the set is invisible.” ³ This idea of time also goes along with fate and destiny, and is connected to other people as well as periods of history. People may handle many things at once in this approach. A manager’s office in such a culture typically has an open door, a ringing phone and a meeting all going on at the same time. Within all these intermingling events, punctuality is nice, but not essential.

In Eastern cultures, time is more plentiful and people tend to be more patient. It is quite acceptable to make people wait all day, and then tell them to come back later. Time-abundant cultures tend to rely on trust to do business, whereas time-limited cultures don’t have time to develop trust and have other mechanisms to substitute trust (such as judiciary mechanisms).⁵ This time pressure may also account for segmented relationships in Anglo cultures, while time-abundant societies tend to establish lifetime relationships. Furthermore, societies that have a more flexible sense of time are more comfortable with uncertainties and accommodate changes in verbal plans, whereas time-limited cultures prefer everything to be expressed in written details and abide by these binding plans.

In one viewpoint, past and future are both present in this stretching time that loops back and forth. In the other, time starts with the very current instant and extends into the future. In a negotiation setting of parties with these two different notions of time, one of the parties may take time to provide extensive information regarding their stories and their relationships to the issue; weaving themes, feelings, ideas, and experiences together as they remember the past and project the future. When it is the other party’s chance to speak, they may promptly project flow charts showing processes for decision-making and speak about their intentions for entering the negotiation process right away. Neither side would feel satisfied with this meeting, but everyone would feel that they were not “on the same page.” ³

Therefore, as people from different cultural backgrounds work together, they should ask questions about their values and needs, and how these may affect their progress. Both cultures would be comfortable with meeting face to face in a mediation setting to frankly discuss differences of any sort.

Figure 1, serves as a summary of the dimensions we have mentioned so far. While the generalizations listed do not apply uniformly to all cultures, they will help convey a pattern:

Figure 1. Comparison of various cultural dimensions

Most North European and North American cultures fall into Group A.

Most Latin American, Asian, South European, and some African cultures overall fall into Group B.

Each of the variables discussed here shows only a glimpse of various dimensions across cultures, which do not apply to all individuals within a culture. One should not generalize by ignoring individual differences; e.g., “he is like that because he is Asian – all Asians are nonverbal.” An individual’s behavior may well vary depending on the situation, individual personality, mood, etc. as well. Cultural differences discussed here are general guidelines and there will always be exceptions. Anyone is unique in a sense and must be approached accordingly. It is important to remember this uniqueness at times of negotiations or unease, and not rush to make decisions before clearly understanding the situation. Keep in mind that different cultures see the world through diverse filtering lenses; there may not be a disagreement but just a different interpretation of what is going on.

As a result of globalization, the world is becoming smaller and people of various cultures are able to communicate freely. Ideas and perspectives can span across cultures through different forms of media like the television, the newspapers and the Internet; thus, cultures are blending more and more every day, which makes dialogue and mutual understanding essential. Only by learning about, respecting, and celebrating these differences, we can build mutuality and co-operative relationships, rather than breeding enmities.

Osman Senkaya has a Master’s Degree in Nonprofit Leadership.

Notes

¹ http://www.celt.iastate.edu/international/culture-extras/CultureResources.pdf

² Kim, Min-Sun. 2002. Non-Western Perspectives on Human Communication: Implications for Theory and Practice. Thousand Oaks, Cal.: Sage Publications.

³ LeBaron, Michelle. “Cross-Cultural Communication.” http://www.beyondintractability.org/essay/cross-cultural_communication

⁴ Elashmawi, Farid, and Philip R. Harris. 1993. Multicultural Management: New Skills for Global Success. 3rd ed.: Gulf Publishing Company.

⁵ “Differences in Cultures.” http://www.analytictech.com/mb021/cultural.htm

⁶ Sahih Bukhari: Vol. 8, Book 76, Number 421.

⁷ Foster, Dean A. 1992. Bargaining Across Borders: How to negotiate business successfully anywhere in the world: McGraw-Hill.

Every human being asks the question “why,” though at different levels, to explain the unexplained. It follows a pattern of questions, like “Why did the financial crisis in the U.S. happen in August 2008?” “Why did the space shuttle Challenger explode?” “Why did the terrorists commit the September 11 attacks?” In statistical terms, such unexpected events are named “outliers,” however, they are part of the system and among the components constituting the overall system’s complex behavior. Thus, they need to be part of the explanation in order for the explanation to be complete. We are naturally tempted to come up with universal explanations of the complexity behind these major events so that we can be ready when a similar thing happens again. Though simple mathematical equations or relationships relate to us better and provide a universal explanation, they are typically practical only when the outliers are excluded from the system behavior. Statistics help us greatly in quantifying and characterizing the outliers, especially in the form of probabilistic expressions, such as “there is a 30% chance of a hurricane next week.”

Understanding the complexity around us involves the development of a model that is simple enough for us to comprehend but yet universal enough to capture most of the dynamics of the complexity. The simpler and the more universal the model, the more powerful it is. The universality of a model, however, is hindered by the potential inability to capture something unexpected. The tradeoff between simplicity and universality exists in all modeling efforts; and the models finding the delicate balance in this tradeoff are the most effective ones. A simple mathematical relationship known as “the power law” has been used extensively to characterize and model various natural and social phenomena.

What is the Power Law?

The “power law” does not refer to a misconception that “whoever has power will rule,” but rather it refers to a particular way of characterizing dependency between two quantities. When the number or frequency of an object or event varies as a power of some attribute of that object (e.g., its size), the number or frequency is said to follow a power law. In more general terms, there exists a power law relationship between x and y if y is growing or reducing polynomially when x is growing linearly (y  _͌ x^–α). Mathematically speaking, this means that the relationship between y and x is mainly characterized by the exponent -a. An exponent is simply shorthand for multiplying that number of identical factors. So, 4³ is the same as 4x4x4; that is three identical factors of 4. As shown in Figure 1, a quantity with an exponent has three components: the base, the exponent, and the coefficient. So, for 4³, the base is 4, the exponent is 3, and the coefficient is an implicit 1.

Figure 1: Description of an exponent in a power law relationship.

Figure 2: Sample power law relationships between x and y, where y = x^–α.

The power law relationships are traditionally expressed with a negative exponent, which simply means the inverse of the quantity. That is, y  _͌ x^–α is equivalent to y  _͌ 1/x^α. For example, when a is 2, y will reduce from 1/4 (i.e. 0.25) to 1/9 (i.e. ~0.11) if x grows from 2 to 3. Likewise, when a is 0.5, y will reduce from 1/2 (i.e. 0.5) to 1/3 (i.e. 0.33) if x grows from 4 to 9. For those who enjoy graphs, Figure 2 illustrates these mathematical relationships in linear and logarithmic scales.

Power law on different scales: Atoms to planets

To start with, gravitation, acoustics, electrostatics, and light and electromagnetic radiation, all exhibit a form of power law in that physical quantity or strength that is inversely proportional to the square of the distance, which corresponds to a power exponent of 2. [1] Gravitational force between two particles, the electrostatic force of attraction between two electrically charged particles, the intensity of sound signals coming from a source, and finally the intensity of light or electromagnetic field coming from a source all follow a power law with respect to the distance.

What makes the power law relationships more interesting is their independence from scale or size of the measures being related to each other. This is why we sometimes call power law relationships as “scale-free” relationships or “scale-invariance.” For example, the gravitational force between two spherical particles decays with a power exponent of 2 regardless of the sizes of the particles though the actual force is certainly dependent on the particle sizes. So, the particles can be at nano scales (e.g. a group of atoms) or macro scales (e.g. a planet), but the relationship stays the same!

Power law in frequency: Wealth, terror, and earthquakes

A common usage of power law relationships has been to model and understand frequency of a varying measure. A power law typically very well represents the distribution of wealth in a society. [2] According to a recent study, the distribution of wealth in China during the years 2003–2005 follows a power law with an exponent ranging from 1.758 to 2.285. If we consider an average exponent of 2 for Chinese wealth distribution, this means that if there are 1 million Chinese people who owned $1000 there were 1000 that owned $1M. Thus, the power law essentially expresses how skewed the distribution of a frequency is (see Figure 2). The larger the power exponent, the more skewed the distribution. In this case, a larger power exponent means a more imbalanced wealth distribution while a power exponent of 1 refers to an evenly distributed wealth.

Many other social patterns exhibit power law. A recent study showed that it exists even in terror events! The number of casualties per insurgent event and the number of insurgent events per day follow a power law. [3] Historical data for the last two centuries show further that the number of casualties per war or a terror attack follows a power law distribution. What is even more interesting is that the number of casualties and the number of attacks within an insurgent conflict both follow power law. That is, when only a particular conflict between two countries or ethnic groups is considered, the number of casualties per insurgent event and the number of insurgent events per day follow the power law. This suggests a “self-similar” pattern. Likewise, traffic measurements for many systems show power law distributions of size. For instance, if one observes the data traffic on an Internet connection and counts the number of bytes being transmitted per hour over that connection, a power law distribution of the count of bytes will emerge. Further, if this counting is done per minute instead of per hour, a similar distribution will still emerge – again showing a self-similar pattern. [4]

The power law has been observed in several natural phenomena as well. The frequency of earthquake magnitudes follows a power law. [5] This refers to the intuitive notion that the number of earthquakes with small magnitudes (which humans do not even feel) is much larger than the number of earthquakes with large magnitudes, (which can kill many humans). Small earthquakes are the norm while large ones the outliers. However, without the outliers, there is no power law distribution! Thus, the power law distribution of a quantity comes with an interesting observation: If a quantity is indeed following a power law distribution, then the likelihood of an outlier event increases as the time goes by without an outlier event. This is why geoscientists would make comments like “The region X is due for a major earthquake!” indicating that the region X has not been receiving a major earthquake (i.e. an outlier) for several years. The issue, though, is determining the threshold for an outlier is typically ambiguous and may require many years of measurements and data, which may be impractical.

Power law in growth: Rich get richer

Growth of systems also exhibit power law in various ways. Social growth follows power law due to the well-known “rich get richer” rule, which refers to the intuition that “important” people in the society attract more of the attention of newcomers. This dynamic situation is observed, for example, in the growth of the Internet. Several studies [6] showed that the connections between Internet Service Providers (ISPs) (e.g., AOL, Yahoo!, AT&T, Sprint) follow a power law distribution in that the number of connections per ISP (which shows how well an ISP is connected to the rest of the world) is represented by power law. In other words, there are few ISPs with many connections to other ISPs while most ISPs have a few connections to the others. This is believed to be due to the “rich get richer” rule since an existing ISP with many connections is more likely to gain the business of a new ISP who is joining to the Internet. So, it is somewhat an economic pattern too.

If economics (or the money) is taken out of the picture, social growth still exhibits power law. Online social networks such as Facebook, LinkedIn, and Flickr are clearly following a power law distribution. It is found that the power exponents are in the range of 2.5 to 3.7, indicating a highly imbalanced social growth pattern where few people are at the “center” of the social network with hundreds or thousands of friends, and many people have only one or two friends. [7] Again, the typical explanation for this growth pattern has been the “rich get richer” rule, but “richness” refers to the number of existing friends in this context rather than money.

Physical growth shows power law too in many ways. For instance, roughness of a growing surface as time goes by follows a power law distribution with an exponent ranging between 0 and 1 where an exponent of 0 refers to a smooth growth and 1 refers to a stiff growth. The surface roughness is measured by the variance of heights of surface locations. [8]

Does it really exist? Why does it exist?

Verifying existence of a power law distribution is not easy and requires enough number of samples to show the “tail” of the distribution. The tail of the distribution refers to the samples with large (or rare) values. For example, for the power law distributions in Figure 2, the portion of the distribution when x is greater than 10 (i.e. x>10) roughly corresponds to the “tail.” The tail corresponds to the rare samples. Though statistical theory calls those rare samples “outliers,” the distribution will not be a power law distribution without them. They are strictly parts of pieces that constitute a power law relationship, and observing them typically requires long periods or large numbers of measurements. Due to this difficulty, the existence of the power law is questioned for many real systems. Most of the time, claims of the existence of the power law typically come with an error factor indicating the confidence of the claim. The bottom-line is to observe trends in the samples and thus establish sufficient confidence (e.g., more than 95%) that the power law distribution does exist in the samples.

For those systems with clear exhibition of power law, the root causes of it have been of high interest. The “rich get richer” rule is intuitively one of the root causes, and it is intuitively a natural dynamic to get attracted by a rich member rather than a poor one. Growth certainly naturally follows the “rich get richer” rule, but we have system components slowing their growth, flattening, and then deteriorating. So, not everything is growing, and actually, we have as many things deteriorating as growing. For instance, participants join or leave the Internet or the social networks, and likewise, people join (i.e. birth) or leave (i.e. death) society. How does the power law stay in such systems then?

Due to the “rich get richer” intuition, the power law is considered to be the signature of “self-organization.” The fact that so many natural or synthetic systems are exhibiting this signature deserves the question: “Is it really self-organization?” Maintaining a global power law distribution for a system requires either (i) every member joining or leaving the system according to the “rich get richer” rule and having global knowledge of the whole system or (ii) somebody who knows everything about the system and gives explicit direct orders to each member when they are joining or leaving. Which one is more likely?

Murat Yuksel is an Assistant Professor at the CSE Department of The University of Nevada – Reno (UNR), Reno, NV.

References

[1] Wikipedia, “Inverse-square law,” http://en.wikipedia.org/wiki/Inverse-square_law

[2] M. A. Santos, R. Coelho, G. Hegyi, Z. Néda, and J. Ramasco. 2007. “Wealth distribution in modern and medieval societies,” The European Physical Journal, Volume 143, Number 1, pages 81-85.

[3] J. C. Bohorquez, S. Gourley, A. R. Dixon, M. Spagat, and N. F. Johnson. 2009. “Common ecology quantifies human insurgency,” Nature, Volume 462, December, pages 911-914.

[4] T. Karagiannis, M. Molle, and M. Faloutsos. 2004. “Long-Range Dependence: Ten Years of Internet Traffic Modeling,” IEEE Internet Computing, September/October, pages 57-64.

[5] T. Lay and T. Wallace. 1995. Modern Global Seismology, Academic Press, San Diego, CA.

[6] M. Faloutsos, P. Faloutsos, and C. Faloutsos. 1999. “On power-law relationships of the Internet topology,” ACM Computer Communication Review, Volume 29, Issue 4.

[7] R. Kumar, J. Novak, and A. Tomkins. 2006. “Structure and evolution of online social networks,” Proceedings of ACM SIGKDD, pages 611-617.

[8] A. L. Barabasi and H. E. Stanley. 1995. Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, England.

This article is mostly based on the book of the Spanish historian and paleontologist, Ignacio Olagüe, La Revolución Islámica en Occidente (The Islamic Revolution in the West), also translated into French as Les arabes n’ont jamais envahi l’Espagne (The Arabs Never Invaded Spain), which portrays some of the ideas of the historian and philologist Americo Castro, especially known for his writings about convivencia.

According to the way that history is taught in most Spanish schools, the Moors invaded the Iberian Peninsula in 711 AD. Here, the following question can be asked: Who did the Moors invade? In order to understand this, it is important to give a background of the inhabitants of Hispania at the time. The Iberian Peninsula was populated by Celts, Iberians, Sephardic Jews, Romans and Visigoths. The majority of Visigoths were Unitarian, meaning that they believed in only one God and were waiting the coming of the Messiah. They also saw Jesus as a Prophet. The rulers of Hispania in 711 AD were Visigoths as well. However, it was a civilization that constantly used force as a means of controlling the citizens of the peninsula, which resulted incessant instability. It was at this time that the Arabs, according to many historians, invaded Hispania.

De la Guardia² states that “in no way were the newcomers all Arabs.”³ The leaders came from Damascus, but they were only a few, and the majority that arrived in Hispania were Muslim Berbers. She later added, as well as Dr. Francisco Layna, author and professor of Harvard University: “Everybody that studies history at any university is aware that there was not an Arab invasion in 711 AD. The Gibraltar Canal that separates Morocco from Spain has always been known as a tool for merchants to trade on both the Spanish and Moroccan Coast. Hence, this was not the first time that the Berbers had visited Spain.”4

We can also ask if the Arabs were in a condition to invade Spain in 711 AD or not. In the middle of the eighth century the Berbers brought the Arabs’ progress to a halt twice and this suspended the conquest of Northern Africa for another fifty years. Hence, the Arabs that came to Northern Africa were weak and few and therefore could never have invaded Hispania.

Olagüe adds that people never take the time to think how the “invaders” of North Africa crossed the Gibraltar Canal in a blink of an eye. In other words, how were they able to conquer 544,192 km2, the most mountainous region in Europe, in three years? Even more astonishing is how the 7,000 men of General Tariq, were enough in number, to defeat Rodrigo and his people in the Battle of Guadalete. Olagüe continues: “If our math is right, each of the 25,000 Arabs was responsible for 23 km2. Since this was too easy for them, they ran to traverse the Pyrenees to dominate France.”⁵ How could a person cover 23 km2 especially in those harsh and mountainous conditions? Olagüe writes that “even if these soldiers conquered Hispania in these conditions, they would each have had 23 km2 of land and therefore would be like a needle in a haystack, compared to the other populations.”⁶ Due to these reasons, we can conclude that an Arab invasion never took place. Furthermore, if natives of the Iberian Peninsula would have resented these newcomers, Hispania would have never been Muslim, would have never planted the seeds for the Renaissance in Europe, and would have not had scientific and artistic advancements that later influenced Europe and the American continent. If it were an invasion, the natives would have forced them to leave Hispania as it occurred when Napoleon in 1807 tried to seize Spain and asked permission of the Catholic Spanish Monarchy for his French troops to pass through Spain in order to invade Portugal. However, once in Spanish territory, Napoleon declared himself Emperor of Spain. It was at this point that the Spanish population resisted and with the help of sticks and stones drove the French out of the country. This was never the case when the Muslims arrived in Spain. Actually, the natives from the Iberian Peninsula welcomed them and were happy to see someone that respected their faith and their traditions and had similar beliefs as the majority of the natives of Hispania were Unitarian Christians. They believed in only one God, saw Jesus as a Prophet and awaited the Messiah, exactly as Muslims. The following treaty was signed in 713 CE-within two years after the first organized entry of Muslims into Spain from the south under the command of Tariq ibn Ziyad-between the Arab commander Abdal-Aziz and Theodomir, the Visigothic prince of Murcia, is a proof of the freedoms the natives of Hispania enjoyed after the Arab conquests.

In the Name of God, the Most Merciful, the Most Compassionate. This is the text that Abd al Aziz ibn Musa presented to Teodomiro ibn Gandaris, in virtue in which it is agreed that in the territory will be in peace by the promising it to God, His Prophets and His Messengers that this territory will be protected by God y the protection of His Messenger Muhammad- peace be upon him. Nobody will be forced, nothing will be taken away from you; Nobody will be slaves; you will not be separated from your wife or children; you lives will be respected; you will not be killed and your churches will not be burned down. You will be free to practice your own religion. (Text of the Treaty of the Visigoth Ruler of Murcia, Teodomiro and Abd Al Aziz).⁷

“In the name of God, the merciful and compassionate. This is a document [granted] by ‘Abd al-‘Aziz ibn Musá ibn Nusair to Tudmir, son of Ghabdush, establishing a treaty of peace and the promise and protection of God and his Prophet) may God bless him and grant him peace). We [‘Abd al-‘Aziz] will not set special conditions for him or for any among his men, nor harass him, nor remove him from power. His followers will not be killed or taken prisoner, nor will they be separated from their women and children. They will not be coerced in matters of religion, their churches will not be burned, nor will sacred objects be taken from the realm, [so long as] he [Tudmir] remains sincere and fulfills the [following] conditions that we have set for him. He has reached a settlement concerning seven towns: Orihuela, Valentilla, Alicante, Mula, Bigastro, Ello, and Lorca. He will not give shelter to fugitives, nor to our enemies, nor encourage any protected person to fear us, nor conceal news of our enemies. He and [each of] his men shall [also] pay one dinar every year, together with four measures of wheat, four measures of barley, four liquid measures of concentrated fruit juice, four liquid meastures of vinegar, four of honey, and four of olive oil. Slaves must each pay half of this amount. {Names of four witnesses follow, and the document is dated from the Muslim month of Rajab, in the year 94 of the Hijra (April 713).} “The Treaty of Tudmir” in Reading the Middle Ages: Sources from Europe, Byzantium, and the Islamic World. ed. Barbara H. Rosenwein. Peterborough, Ont.: Broadview, 2006, p. 92.

Although there were other capitulation agreements with the same nature dating from 711, this one signed on the surrender of the city of Orihuela has survived to this date. The inhabitants of the conquered territories of Spain were suitably impressed by the tolerance which the Muslims offered them once active resistance had ceased. It is these earlier agreements and their successful implementation that prompted Theodomir and the population of Orihuela to agree to sign the treaty.⁸

If the people that arrived were not Arabs in majority, why are they referred to Arabs in Spain and why was Arabic spoken and even carved in some of their architectural beauties such as the Al-hambra in Granada? Guardia clearly states “they were not Arabs, even when the majority of Spain was Muslim. However, they adopted Arabic as their language.”? Arabic was the language of scholars and Latin was the language of soldiers. Little by little, the natives of the Iberian Peninsula adopted Arabic as their own language, even people from other faiths. In the ninth century, a Bishop of Cordoba wrote: “Many of my colleagues read poems and stories; they study their philosophies as well as the Muslim theologians in Arabic, not to refute them, but to learn how to express themselves in Arabic more correctly and elegantly.”¹⁰

Olagüe states that it took 300 years for the natives of the Iberian Peninsula to adopt and utilize the Arabic language. We can see a wonderful fusion of the jarchas, or poetry from Al-Andalus or Muslim Spain, where it can easily be seen how Arabic and Latin fused. These were love poems that were written in Arabic, and ended in Latin.

Poetry is only one of the many examples of the advances Spain experienced during this era. When in many cities of Europe people walked in streets of mud, people in Hispania walked on pavement, had a drainage and sewage system. Cordoba, once the capital of Al-Andalus, was famous for its scientific advances in medicine. Andalusians had stomach operations and very specialized cataract operations. Some specific instruments that were used at that time in medicine are still used today in the same field.

The first university in the West was founded in Cordoba, Spain. Scholars from all over the world came to gain knowledge in all the natural and social sciences such as medicine, technology for agriculture, astronomy, literature, and jurisprudence to name a few. The city of Toledo is another example of intercultural exchange, where the School of Translation efficiently contributed to the culture of mutual understanding.

Among many inventions Andalusians developed was the astrolabe which was used to determine the latitude of a ship at sea by measuring the noon altitude of the Sun or the meridian altitude of a star of known declination.¹¹ It was with the help of this astrolabe that Christopher Columbus was able to travel to the American continent in 1492.

This intercultural and multicultural convivencia between Jews, Christians and Muslims in Al-Andalus was key to the development of different sciences that later contributed to give birth to the Renaissance in Italy. When the inhabitants of Al-Andalus put emphasis on their spirituality, this was also the time when their scientific and technological advances were strongest, also influencing Catholics in later times.

Towards the last century of Muslim Spain, the Christians had adopted the majority of Muslim traditions as well as the scientific discoveries and advances that they had accomplished during more than 800 years in the Iberian Peninsula.

In conclusion, the Arab invasion is only a myth and Al Andalus was in its majority composed of natives of the Iberian Peninsula and not Arabs. This civilization that spanned across eight centuries was a unique model of respect for other cultures and religions, a model that we can learn a lot from in our times.
Islamic Caligraphy at the Alhambra Palace in Granada,Spain.

Karin de Villa is a Spanish Professor at St. Mary’s University, San Antonio, TX.

Notes

1. The Spanish Word for coexistence, also referred sometimes by Americo Castro as Las Tres Culturas or The Three Cultures: Jews, Christians and Muslims living together in peace during the Muslim rule.
2. One of the contemporary famous Historians and Chair of the University Autónoma de Madrid.
3. De La Guardia, Carmen. Lecture: Jews, Christians and Muslims in Spain and Latin America. Middlebury College: Spain, Madrid, 2006.
4. Lecture: Don Quijote, Spain: Madrid, 2006.
5. Olagüe, Ignacio. La Revolucion Islamica en Occidente. Espana: Cordoba, 2004. 36.
6. Ibid.
7. Historia de Espana, vol. 3. Historia 16 extra XV Madrid, 1980.
8. The Treaty of Orihuela. The Surrender of Orihuela, Spain, 713 C.E. http://cyberistan.org/islamic/treaty713.html.
9. De La Guardia, Carmen. Lecture: Jews, Jews, Christians and Muslims in Spain and Latin America. Middlebury College: Spain, Madrid, 2006.
10. Alvarez, Fe Bajo & Pecharroman, Julio Gil. Historia de Espana. Sociedad General Espanola de Libreria. S.A. de Alcobendas: Madrid, 1998. 48.
11. Morrison, J. The Mariner’s Astrolabe. http://www.astrolabes.org/mariner.htm. 2002.

Expansion can be dealt with in two categories: Our relationship with the created, and our relationship with the Creator.

With respect to our relationship with the created, expansion means that we are careful of our connection with God and the Truth; that we live in our communities as one of its inhabitants, being open with and showing respect to everyone; and that we treat people according to their level of understanding.

The noble Prophet, upon him be peace and blessings, was sincere and frank with those around him, and avoided ceremony or formality. He spoke according to his listeners’ level of understanding, and sometimes made wise and meaningful jokes. Although he suffered inwardly from the unbelief, injustice, and sins he witnessed, and was anxious about everyone’s end and afterlife, he always smiled and behaved pleasantly. As said in al-Minhaj: “A heart is like a mirror: too much and too frequent solemnity may cause it to steam up, and the only way to remove that steam is to tell pleasant jokes.”

With respect to our relationship with God Almighty, expansion signifies the simultaneous experiencing of fear and hope in our souls. Being states of the soul, fear and hope are usually found in those who have just started to advance on the path to God. Expansion, on the other hand, is a state of those with knowledge of God and, moreover, is a dimension of the heart’s life. The state resembling the expansion of those still striving to reach this level of expansion is an exhilaration coming from knowledge of God. This may lead them to become relaxed in their relationship with God, and thus lose their self-control and self-possession.

Expansion appears when a traveler on the path of God is completely freed from carnal desire and passion, and becomes a bright “mirror” to reflect God’s Names and Attributes. This station, whether called the Station of Combination (where the traveler experiences God’s Existence and Unity) or Annihilation (where the traveler’s annihilation of self causes forgetfulness of self when in the throes of ecstatic love of God and perception of God’s Existence and Unity), is a mysterious point where the traveler directs himself or herself according to the Divine inspirations received and assumes “colors” unknown to everybody else. It is impossible for such people to conceal their expansion, while it is insolent of those who have not attained it to talk about it. How aptly Rumi expresses it:

If the king’s courtier behaves in an affected manner to attract the king’s attention, you must not attempt to do so, for you do not have the document (to justify your doing so). O one who cannot be freed from the restrictions of this transient life, how can you know what (the stations of) annihilation, drunkenness, and expansion mean?

Indeed, servants of the body cannot be aware of the states of the spirit. It is impossible for those imprisoned in the body to be aware of spirituality. We should ask those souls who have burned and been “roasted” many times in the fire of the love of God about the pains of a heart that has been cleft open, and their expansion and contraction.

O God! Endear belief to us and make it appealing to our hearts, and make unbelief, transgression, and rebellion hateful to us; and include us among those with right conduct and sound thinking. And bestow blessings and peace on our Master Muhammad and his Companions, all of them.

The existence of antimatter was suggested in 1928 by Paul Dirac and was confirmed experimentally in 1932 by Carl D. Anderson. They state that every elementary particle (matter) has its own anti-particle (antimatter): electrons have anti-electrons (positrons) and protons have anti-protons and so on. Antimatters have the same mass as matter, but they carry an opposite electrical charge [1]. For that reason, if matter and antimatter collide they cancel each other out, resulting in annihilation. This collision produces a tremendous amount of energy. For instance, a collision of 1 kg of matter and antimatter releases the energy equivalent to the explosion of 43 megatons of TNT [2].

However, producing antimatter is not an easy process and requires very energetic collisions in giant accelerators such as CERN, located near Switzerland, and Fermilab, located near Chicago, US. The annual amount produced in these laboratories is 1^-10 nanograms. The typical process is to accelerate protons to almost the speed of light, and then send them into a metal target, which is usually tungsten. Because of the collision, the protons are slowed or stopped by the nuclei of the tungsten atoms. The protons’ kinetic energy is converted into matter that contains subatomic particles, and some of these particles are antiprotons [3].

To avoid annihilation, antimatter must be separated from other subatomic particles. One way to do that is to use the Penning trap in which charged particles of antimatter are confined radially by homogenous magnetic fields and axially by quadropole electric fields. Penn State and NASA scientists have already built such a device capable of holding 10 million antiprotons for a week. Now they are developing a Penning trap with a capacity 100 times greater [3].

Figure 1: Schematic of Penning Trap: Electric fields are blue, Magnetic fields are red, a: end cap, b: ring electrode, c; magnets (www.en.wikipedia.org)

Many of us remember the antimatter engine from the Star Trek series. Interplanetary travel has been humankind’s dream for centuries. Now, scientists are designing a spacecraft propulsion system that will work by expelling the products from the annihilation of protons and antiprotons. Such a propulsion system requires antimatter the size of an aspirin (10 grams) for hundreds of light years of travel. However, this amount of antimatter is not available yet, and with current technologies, it would cost around 100 trillion dollars to produce 1 milligram of antimatter.

One of the discoveries made by scientist at Penn State was that a space propulsion system would need only a small fraction of the antimatter consumed by a beamed core engine. It would work with an antiproton induced micro-fission (ACMF). In this process, Deuterium-Tritium (D-T) pellet and Uranium-238 (U-238) are compressed with a proton beam [1 in Figure 2]. After two nanoseconds, the pellet is subject to antiproton beams [2 in Figure 2]. Uranium U-238 absorbs the antiprotons and the result is a hyper neutronic fission that transfers the heat energy from the uranium core to D-T pellet and ignites it [3 in Figure 2]. Propellant inside the pellet is expanded to produce a pulsed thrust [4 in Figure 2].

Figure 2: Illustration of ACMF reaction chain, in four steps (www.ffden-2.phys.uaf.edu)

Another concept is called Antimatter-initiated micro-fusion (AIM), which was also designed by Penn State scientists. In this mechanism, electromagnetic fields continuously compress a small concentration of antiproton plasma [1 in Figure 3] Than the Deuterium-Tritium droplet injected into the plasma [2 in Figure 3]. Also a small amount of U-238 is allowed to annihilate with the antiprotons, which fully ionizes and heats the plasma. The resulting product is expelled out of a magnetic nozzle to produce thrust [3 in Figure 3]. Finally potential well is relaxed to its original state [4 in Figure 3] 

Figure 3: Illustration of AIM reaction chain, in four steps (www.ffden-2.phys.uaf.edu)

Scientists also believe that antimatter has the potential to be applied in medical sciences and one of them is fighting cancer. Currently, scientists at CERN are investigating the antiproton beam therapy as an alternative treatment. Experiments have compared the damage of proton and antiproton beams on hamster cells. The results show that the damage inflicted by antiprotons to cells at the end of the beam path was four times greater than that of proton beams. This means that one antiproton is enough to achieve the same damage as four protons, and moreover, antiprotons have unsurpassed ability to preserve healthy tissue [4].

Image of antimatter cell interaction experiment (www.rsc.com)

It seems that producing large quantities of antimatter is difficult and expensive today, but as long as we are on the right track with the right developments, one day, it could become a reality. If a significant amount of antimatter can be produced and controlled, this could help us obtain more information about nature, and it might become one of the world’s primary energy sources. It can also bring innovative solutions with medical benefits such as cancer therapy. Last but not least, antimatter also offers implications of existence beyond what we can see, thus an infinitely vast area of research to conduct via not only with our minds but also with our hearts.

Mehmet Fatih Yýlmaz is Assistant Professor at the engineering faculty of Mevlana University, Konya, Turkey.

Note: Author would like to thank Margaret Johnson for her useful comments on this article.

References

1. Dirac, Paul. 1928. “The Quantum Theory of the Electron,” from Proceedings of the Royal Society of London: Series A 117 (778): 610–624.

2. www.wikipedia.com

3. www.engr.psu.edu/antimatter

4. www.press.web.cern.ch

To date, many have spoken for Islam: experts, apologists, extremists, politicians, religious leaders, even fiction writers. In this cacophony of voices everyday Muslims have remained silent. Many have speculated on their silence, promoting causes and foreseeing the clash of civilizations and the end of world.

The silenced majority of Muslims have spoken for Who Speaks for Islam? written by John L. Esposito, professor of Islamic Studies at Georgetown University and Dalia Mogahed, a senior Analyst and Executive Director of the Gallup Center for Muslim Studies, provides a comprehensive analysis on a multiyear, mammoth, Gallup poll data – “the largest study of its kind” – which attempts to answer popular questions such as: Is Islam to blame for extremism? Why is there so much anti-Americanism in the Muslim world? Who are the extremists? What do Muslim women really want?

The Gallup Institution surveyed over 55,000 Muslims in over 35 Muslim populated countries. When we ponder on the role this data may play in the betterment of relations with 1.3 billion inhabitants of the world, we can’t help, but appreciate in depth the painstaking efforts shown in this project. Readers can also read about the challenges and method of the survey at the end of the book.

Most of the answers of the surveyed go against the popular perceptions and shed light on the level of misinformation and distortion we all are exposed to, reminding us one more time of Einstein’s advice that a man should look for what is and not for what he believes should be. Constructed in a comprehensive design and plain language, the data can easily be grasped by say, even the statistics illiterate. Every effort is made to ensure a wider readership. The book is organized in five chapters under five crucial questions:

Who are Muslims?

After exploring the five pillars of Islam (i.e. profession of faith, prayer, fasting during Ramadan, almsgiving, and pilgrimage to Mecca), the books touches upon sensitive issues such as the meaning of jihad, the role of family and culture in Islam, nostalgia for a glorious past, and politics.

Democracy or theocracy?

Many important questions are tackled in this chapter such as: Why is democracy absent in so much of the Muslim world? Is Islam the problem? How do Muslims view democracy? Should support for Sharia make the West panic? What do Muslims believe the chances are of improving relations with the West? Many Muslims view democracy as necessary for progress but skeptical about America and Europe’s intentions in promoting democracy in Muslim countries.

What makes a radical?

Extremists and terrorists were thought to be uneducated, poor, religious fanatics who reject modernization and technology, yet within weeks of 9/11, the media reported the “stunning discovery” that many of the attackers were, like Bin Laden and Dr. Ayman al- Zawahiri, well educated (some of them in western universities), middle to upper class, and from stable family backgrounds. Investigating diagnosis and misdiagnosis, this chapter explores the causes of extremism based on poll data.

What do women want?

When asked by the Gallup Poll of American households, “What do you admire least about Muslims or Islamic world?” American women answer “gender inequality” as among the top responses. Many have engaged in struggle to liberate the Muslim woman, yet her voice rarely makes its way in the discourse. Interesting answers are given by Muslim women to questions, like: How do Muslim women feel about Islam and the Sacred Law (Sharia)? Do they want to be liberated by the West? How do they view gender equality?

Clash or coexistence?

Confronting myths vs. realities, this chapter offers insights into what can be done to end global terrorism. The ability to move beyond presuppositions and stereotypes in our attitudes and policies and to form partnerships that transcend an “us” and “them” view of the world is critical to this cause. According to data findings, public diplomacy, defined as winning minds and hearts, is required. Finally, here is a trial size bite from the book without spoiling it. There is a prevalent assumption about Islam and democracy being incompatible. Yet that the majority of the respondents declared democracy as one of the things they admired most about West. Another impressive finding of this book was the answer Muslims gave to the open ended question: What can the West do to improve relations with Muslims? The answer was: Show respect. Respect comes with better understanding and reading Who Speaks for Islam? may be an important step toward it.

What do you think?

A small-scale blueprint of the universe, the human body is a miraculous work of art that manifests the beautiful divine names and attributes of God Almighty. A human body is made up of a set of hierarchically organized components: an organ system, organs, tissues, cells, organelles, macromolecules, molecules, atoms, neutrons, protons, electrons, and subatomic particles. In this biological organization, it is striking to observe a proportionately allocated space between components on each level for their efficient functioning. The size of human body would be reduced if these spaces between organs, tissues, cells, and atoms could be removed, and the entire human body would not be bigger than a small ball.

The structure of an atom explains a lot concerning the real size of our body, which is filled with space. An atom is comprised of protons and neutrons in its nucleus, around which electrons continuously orbit. The mass of neutrons is almost equal to the mass of protons. Electrons, however, are 1,837 times smaller in mass than neutrons and protons. That is, almost 99.95% of the atom’s mass is in its nucleus. The mass of electrons is almost non-existent compared to the nucleus.

Both the universe and our body are filled with more hydrogen than any other atom. In each one billion atom in our body, six hundred thirty million are hydrogen atoms. In a hydrogen atom, electrons rotate only 0.53 nm (one billionth of a meter) away from the nucleus, which makes the atom’s volume to be around 6.10^-28m³, whereas the volume of the proton is 7.10^-45m³, i.e., the nucleus is only as big as one hundred quadrillionth (100.10¹⁵) of the atom’s total volume. In other words, while the nucleus comprises almost the entire mass of the atom, its volume is of no considerable size. The density of protons in the nucleus is 2,3.10¹⁷ kg/m^{3 (where does the period go here??)}, which means that there is around a hundred trillion tons of matter in only one cubic meter. If we could gather all neutrons and protons in one spot, a man who is 69 kg would be only 3.10^-7 mm³ in volume. That is, the volume the total substance of our body takes up is around one ten millionth of a cubic millimeter. The human body, which is constructed of atoms with electrons rotating on an orbit quite far away from the nucleus, is in a way no different than an “inflated space.” For a comparison, the space between the earth and the sun can be filled with as many as 107 suns, whereas 450 thousand protons are needed to fill up the distance between the proton and electron in a hydrogen atom.

The subatomic world is even more amazing. In subatomic particles are found six types of quarks. A quark is considered a fundamental constituent of matter. Combinations of quarks in different shapes and numbers result in subatomic particles, the further combinations of which produce atoms, molecules, and so on. Quarks are considered to be without mass; that is to say, they are nothing else but energy. Humans have mass, but this mass consists of quarks that are without mass.

This incredibly vast space between atoms that make up matter teaches us that our true value does not lie in our physical structure, but in the artworks of no comparison designed by the Divine as manifestations of His most beautiful names. Thus, we, who are so little in material substance, should seek other gateways in the depth of our souls and attain some value with proximity to the Divine.

We may never have revolted against God Almighty in our entire life; yet still our material minority should free us from all kinds of pride and conceit. Our physical structure is very much like the number “zero,” for 0 is also nothing, and it is drawn by inflating.