The opposite of altruism is the stinginess and selfishness that arise from avarice and attachment to this world. Both stinginess and selfishness are regarded as reasons for becoming distanced from the Creator, the created, and Paradise.^[1] While stinginess arises from avarice and attachment to the world, generosity, benevolence, and perfect goodness arise from altruism.

Generosity means that believers give some of their belongings to others without feeling any unease in the heart. Benevolence means considering one’s own happiness as dependent on the happiness of others and, more than that, putting the welfare of others ahead of one’s own happiness. As for perfect goodness or excellence (ihsan), it means preferring others, even when one is in need oneself. The Qur’an points to such excellence or the highest degree of altruism in this verse (59:9): They feel in their hearts no displeasure because of whatever the others are given, but rather give them preference over themselves, even though poverty be their own lot.

Altruism is valuable when one attains and follows it freely; it has no value if one is forced or if one performs such an act not out of one’s own free will.

The generosity and benevolence that arise from and are dimensions of altruism have degrees, as follows:

• Sacrificing one’s soul in God’s way (for God’s cause), therefore for the sake of belief and for the good of the believers, is considered the highest degree of nobility.
• Being able, when it is necessary, to renounce a (rightful) claim to leadership or similar high position for the well-being and unity of society, is seen as altruism one step below the first degree.
• Preferring the (economic) welfare of others over one’s own, is a third degree of nobility.
• Allowing others to benefit from one’s knowledge and ideas without expecting anything in return, is a virtue not quite as noble as the previous ones.
• Giving to others out of one’s income – this includes responsibilities for the giving of the prescribed and voluntary alms (zakah and sadaqa).
• Showing warmth, speaking soft and kind words, being of use to others, and being the means of various instances of good – these are examples of altruism that almost anyone can strive for in any situation.

The first of these degrees of generosity and benevolence is a profound and fundamental dimension of altruism that not everyone can achieve. Mawlana Jami’,^[2] the author of Baharistan (The Land of Spring), expresses it most memorably:

It is easy to show generosity with gold and silver
Worthy of respect is he who shows generosity with his soul.

Among the characteristics and degrees of those who practice altruism are:

• Offering food and feeding others at the cost of one’s own hunger and thirst, and neglecting oneself in the provision of others. Provided that no one’s rights are violated, this is a virtue characteristic of truly pious, saintly people.
• Despite all adversities, spending whatever one has as a favor from God in God’s way and purely for His good pleasure, and in such a disinterested manner that one forgets what good one has done. This virtue is particular to those with considerable nearness to God, who take far greater pleasure in giving than receiving.
• Attributing to God exclusively all the accomplishments with which one is favored without seeing oneself as the agent of any good and, without expecting any return, even in the form of spiritual pleasures, for all that one does for God’s sake, always being aware of Him and experiencing oneself as the shadow of the light of His existence.

This last one is the attitude and practice of those nearest to God, including primarily the noblest of humankind and the greatest of all times and places, upon him be peace and God’s blessings. His Ascension is a demonstration of his being accorded the highest honor and being sought after (by all the angels and many among human beings and jinn) as a reward for his incessant efforts for perfect knowledge of God. His return from the realms beyond the heavens to be among people in this world is such a great degree of altruism that nobody else has ever been able to achieve it. His emerging from Paradise and letting his profuse tears fall into the pits of Hell for the salvation of humankind expresses the greatest possible altruism.

O God! For the sake of your chosen Prophet, Muhammad, make us of those who do not begrudge what has been given to their brothers-in-religion, but prefer them to themselves, even though poverty be their lot, and may Your blessings and peace be on our master Muhammad and on His family and Companions.

^[1] Sunan al-Tirmidhi, “Birr,” 40.

^[2] Mawlana Nur al-Din ‘Abd al-Rahman ibn Ahmad al-Jami’ (1414-1492), commonly called the last great classical poet of Persia, and saint, composed numerous lyrics and idylls, as well as many works in prose. His Salaman and Absal is an allegory of profane and sacred love. Some of his other works include Haft Awrang, Tuhfat al-Ahrar, Layla wu Majnun, Fatihat al-Shabab, Lawa’ih, al-Durrah. (Trans.)

New developments in scientific thought and hypotheses testing are changing the ways we think about truth and certainty.

Not only do scientific decisions rely heavily on tools and procedures of quantitative analysis, but also on social life and daily decisions. I want to start with a story from the judiciary system about the misuse of an important quantitative tool of the scientific community, Hypothesis Testing. It’s about the overturned Amanda Knox case in Italy. In 2007, she was accused of killing her roommate and sent to jail. The odds of DNA matching in the case of accidental death were reported as incredibly rare by a forensic data analyst, who examined data with regard to incidents of crime, concluding that the accident is not statistically an accident. The judges then made their decision based on this rareness, a single value, named p-value. Later, this was overturned (New York Times, March 27, 2013), because of a misinterpretation by the judges and lawyers, of the rare probability. What factors forced the judiciary system to make this decision based on a single value alone? Honestly, this is the story of the century and a story of Hypothesis Testing. This article introduces the logic behind their decision, draws attention to the misuse of data, and mentions alternative logics to this traditional approach on the matter (in March 2013, Italy’s Supreme Court ordered a retrial and found the two suspects guilty on January 30, 2014).

What is Hypothesis Testing?

We live in a data-driven world. Statistical inference is the process of drawing conclusions or decisions from data. The Hypothesis Testing procedure in the Neyman-Pearson paradigm is one of the procedures of this process, widely used in the scientific community for over a century. In this mindset, two complementary hypotheses are first defined: one is the conventional thesis (the null hypothesis) accepted to be true by default; the other is the alternative thesis (the alternative hypothesis) that needs evidence from data to falsify the null hypothesis. It results in a single value, called p-value, which is calculated from the data using theoretical model assumptions. A p-value is a measure – in probability sense, ranging from 0% to 100% – of how much evidence you have against the null hypothesis. The smaller the p-value, the more evidence you have against the null hypothesis. One may combine the p-value with the significance level to make decisions on a given hypothesis. This is also called significance testing. It has an accept-reject mindset (dichotomous decision or binary logic); in such a case, if the p-value is less than some threshold (usually .05) then the null hypothesis is rejected. Basically, it is a black or white decision, without considering the contrasts between them. This interpretation has been widely accepted in the twentieth century of scientific research, and many scientific journals routinely publish papers using this interpretation for the results of hypothesis tests, even though there are current tendencies not to use this. Let’s take a look at the history of this black-white logic.

History

The history of the process of hypothesis testing starts with Fisher (1890-1962), around the early twentieth century. Later, the contributions of Pearson (1857-1936) and Neyman (1894-1981), who were early fathers of statistics, about the interpretation of the hypothesis tests were integrated into present-day applications. Fisher’s approach focuses on inductive inference about a single hypothesis, whereas the Neyman-Pearson approach informs future behavior based on a test using two complementary hypotheses (Newman 2007).

These approaches are strongly influenced by Popper’s logic of falsification. Falsification can be defined as the act of disproving a proposition, hypothesis, or theory. This logic asserts that sufficiently improbable events can be considered impossible. A p-value suggests whether a null hypothesis is sufficiently improbable to be considered practically falsified in the sense of a logical refutation (Newman 2007). When we come back to the Amanda Knox case, the decision the judges made and justified is followed from this falsification logic in hypothesis testing. Another criticism with this mindset is: how fair it is to rely on a single value that yields a rare result? Are we going to generalize one lucky drawing of raffle tickets to believe all tickets are winners?

Logics and proofs

We use logical flaws and biases in our daily life. Finding the logical flaw in scientific papers is something most readers aren’t interested in. Instead, the results are believed as a fact. One of the widely used flaws/biases is in seeking or interpreting evidence in ways that are partial to existing beliefs or a hypothesis in hand (Mercie and Sperber, 2011). We tend to prove or show the accessibility or superiority of arguments by bringing evidence. Failure to prove that a treatment – say, a low fat diet – is effective is not the same as proving it is ineffective.

Let me give another example to clarify this: The New York Times editorial news reported on February 9, 2006, “Millions of Americans have tried to reduce the fat in their diets, and the food industry has obligingly served up low-fat products. Yet now comes strong evidence that the war against all fats was mostly in vain.” Actually, in the hypothesis testing mindset, the evidence collected from research should either reject the null hypothesis which is “diet is ineffective,” or fail to reject it. The mindset in testing is not about finding evidence to support the null statement. It is also not about proving the alternative hypothesis, “diet is effective.” Rather, it is basically looking for evidences to falsify the null statement. In the report, the “evidence” the reporter meant should be against the null hypothesis, not against the alternative hypothesis. Data is collected to falsify the null hypothesis, not to prove its truthiness, because the null is already accepted to be true unless convincing evidence is collected against it.

Let me give another example of this paradigm. As Newfoundland (2013) described, a person is innocent until proven guilty by bringing convincing evidence. The jury can’t say “he is innocent,” instead, the jury uses evidence that produces reasonable doubt to reject his innocence.

Developments in inferential paradigms

The accept-reject paradigm in inference represents a conventional wisdom. There are other, or currently developing, paradigms in inference, too. One of the dominating paradigms is the Bayesian-likelihood approach. After enjoying much wider acceptance in social and natural sciences, the Bayesian method suggests different views of hypothesis testing. The Bayesian approach is a method of data analysis in which subjectivity, conditionality, or past information is used to update the hypothesis as additional evidence is acquired. This approach in hypothesis testing offers a dynamic structure in probability calculation so hypotheses, and decisions, are not seen as a static truth; instead, they are updated with current data and the decision is stated in the sense of likelihood.

In our court room example, the Bayesian inference is applied to all evidence presented, with the past information being combined with the current evidence. The benefit of a Bayesian approach is that it gives all historical information so the decision is unbiased all along as the past data (prior knowledge) is used correctly. This paradigm changes the way statistics are calculated and how the result and inference are interpreted. Currently it is widely appreciated in quantitative data analysis, especially after convenient software exists for its implementation. However, the criticism to this approach, made by many, is found in its subjectivity. Objectivity and handling prior knowledge is a concern here so that different people, having different opinions, may arrive at different results.

Another developing paradigm: Fuzzy Logic

Fuzzy logic is another method in quantitative decision making. In contrast to binary logic (yes-no, or accept-reject), fuzzy logic can be thought of as gray logic, which allows a way to express in-between data values. It emerged in the development of the theory of fuzzy sets, by Lotfi Zadeh (1965). Fuzzy logic is mostly seen as a branch of artificial intelligence that deals with reasoning algorithms used to emulate human thinking and decision making. It handles the concept of partial truth using linguistic variables, where the truth value may range between completely true and completely false. The concept of partial truth would be subjective and would depend on the observer. For example, for the temperature of the weather, we want to determine when to say cold, warm, and hot. The meaning of each of these concepts can be represented by a certain membership (called a fuzzy set). The concept of each would be subjective. One might consider cold for all values up to 40 0F. In Figure 1, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale to “truth values” ranging from 0 to 1. A point on that scale has three truth degrees, one for each of the three functions (expressions). The vertical line in the figure represents a particular temperature that the truth values (see three arrows) are measured. Since the red arrow points to zero, this temperature may be interpreted as “not hot.” The orange arrow (pointing at 0.2) may describe it as “slightly warm,” and the blue arrow (pointing at 0.8) “fairly cold” (Fuzzy Logic, 2013, para. 6). A rule could then be adopted, like for example, if “slightly warm” then stop the fan.

Picture was obtained from

Fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon, and it summarizes data analysis in facts with truth degrees, and leaves the decision to the observer. Its advantage is its ability to deal with vague situations with respect to linguistic variables. While the significance testing for a hypothesis declares one accept or reject, fuzzy logic allows for degrees of acceptance or rejection. However, in fuzzy logic, the notion of truth doesn’t fall by the wayside, but it is expressed in degrees and offers possibilities for different situations. Regarding inference, fuzzy logic uses the mindset ‘everything is a matter of degree and open to interpretation,’ and this mindset is also adopted to machine learning, which is considered a more suitable mindset with human reasoning instead of binary logic. The constraints in fuzzy logic are found in its tools and interpretations when complex inputs are considered.

The developments of paradigms in statistical inference have similar fates as in the developments of mathematics, geometry, and physics. According to the Euclidean parallel postulate, in space, there exist no two parallel lines that intersect each other. However, after Non-Euclidean geometry was developed in the nineteenth century, a wider geometrical and mathematical reasoning stemmed from it; accordingly, the geometry of the physical universe and particles came to be understood better. The development of Riemannian geometry, offering that distance properties might vary, resulted in the synthesis of diverse results concerning the geometry of higher dimensional surfaces and the behavior of geodesics on them. It also made Einstein’s theory of general relativity justifiable. Likewise, as time passes, we witness wider paradigms or logics that abandon or correct former approaches in scientific decision making tools. This is a good reason why teachers and professors should update their current teachings as to be consistent with convincing trends, as well as to train students to be ready for wider paradigms in the future.

Conclusion

In today’s scientific community, the way decisions are made and fallacies proved, are changing as new paradigms emerge. In order to make better decisions or to validate claims, many aspects and methodologies should be considered. One way to avoid mistakes as much as we can would be to expect fallacy points to exist in human mental processing during decision making, and improving and seeking better alternatives with well-established wisdoms.

(Thanks Ugur Sahin for reviewing the preliminary copy of this article.)

References

• Fuzzy Logic. In Wikipedia. Retrieved August 1, 2013, from http://en.wikipedia.org/wiki/Fuzzy_logic
• Kass, Robert E. 2011. Statistical Inference: The Big Picture 1. Statistical Science, 2011, Vol. 26, No. 1, 1-9, DOI: 10.1214/10-STS337, Institute of Mathematical Statistics.
• Mercier, Hugo, Dan Sperber. 2011. “Why do humans reason? Arguments for an argumentative theory.” Behavioral and Brain Sciences. 34, 57-111.
• Newfoundland, Jason. 2013. “The Cell Phone-Brain Cancer Controversy.” The Fountain Magazine, Jan-Feb, Issue 91.
• Newman, Michael C. 2008. “‘What exactly are you inferring?’ A closer look at hypothesis testing.” Environmental Toxicology and Chemistry, Vol. 27, No. 5, pp. 1013-1019, 2008.

We photons are the envoys of the sun. Our duty is to carry the energy that was stored in the sun during the creation of the universe to the earth. In the sun’s center, during the nuclear reaction called fusion, four hydrogen nuclei form one helium nucleus. The mass of four hydrogen nuclei is 4 x 1,6726 x 10 ^-24 grams (i.e. 6,6904 x 10 ^-24 grams); the mass of one helium nucleus is 6,6447 x 10 ^-24 grams. It is clear that the mass of one helium nucleus is a little smaller than the mass of four hydrogen nuclei. If we calculate the difference: 6,6904 x 10 ^-24 g – 6,6447 x 10 ^-24 g = 0,0457 x 10 ^-24 g. This small mass difference is transformed into great energy by order of the Creator, and in this way we and our relatives, neutrinos, are created.

Our Lord has created us as the fastest particles in the universe. We cover 300,000 kilometers in a second. Although we move so fast, the sun’s center is very dense. The density is about 150 times greater than the density of water (1 g/cm3). Thus, as soon as we move, we crash into the hydrogen and helium nucleuses around us. They swallow us, but then they immediately set us free; then yet another strike waits for us immediately. In every collision, our energy is reduced a little, and we divide into several light particles with lower energy levels. Most of our lives-perhaps 100 thousand years-is spent in these collisions.

If we left the center of the sun without any collisions, the earth would be blasted to pieces in a moment when we hit it. As a result of the collisions, we, who have a high energy level in the beginning, are converted into low energy level light particles.

So many of us are created in the sun that at every second a four-million-ton mass is converted into energy. In the sun, which is 5 billion years old, approximately a hundred times the mass of the earth has been converted into energy up to today.

While we are created in the center of the sun, we reach the outer layer of the sun, the photosphere, by passing slowly through the layers from the center to the surface of the sun. On leaving the surface, our energy decreases, our number increases, and our temperature goes down to 5,800 degrees C. You may consider this temperature very high, but you should not forget that our temperature in the beginning was 15 million degrees C.

We pass the 700,000 kilometers from the center of the sun to the photosphere layer in 100,000 years. The photosphere’s density is so low that it is only one percent of the atmosphere’s density at sea level. We leave this layer fast without any collisions. To reach the earth, there is 150 million kilometers of space ahead of us. Here we show our speed, which we did not have a chance to display earlier because of the collisions we have inside the sun. We travel the 150-million-kilometer distance in 8.5 minutes and reach the earth. There are some of us with extremely high energy levels who can cause damage on earth. The ozone layer is responsible for picking them off. The non-dangerous ones among us reach the face of the earth by traveling through the 100-kilometer-deep atmosphere in 1/10000 of a second. Finally, it is time to deliver the energy we have carried to you.

Every photon has a duty. Some of us heat the earth; some of us vaporize the water in the seas to bring the merciful rains. We have many other duties as well as these. Perhaps our most important duty is to be swallowed by the chlorophyll in plant leaves, so as to provide the energy in the food you eat and in the oxygen you breathe.

Possibly the energy that you have used while reading this essay was obtained from a bean you ate in your lunch. Do not forget that we brought from the sun’s center both the energy in the bean you ate and the energy in any plant that was food for any animal whose meat you have eaten.

We also carried the energy that was in the gas of the truck that brought these pages to you. If our brothers that came to the earth a million years ago had not brought energy to the plants at that time, could those plants have been transformed into oil or coal by decaying underground?

Our Lord gave us light particles a mission to carry the energy that is stored in substances so that the energy will be a source of life for you. We fulfill our duties without any error so that you might think and learn a lesson from these facts.

In your next meal, consider looking at the blessings on your plate from the following perspective: “I am about to eat energy that was heated approximately 100,000 years ago at 15 million degrees C in an oven in the sun’s center and later cooled and made appropriate for the bodies of human beings.”

The sun radiates an enormous amount of energy-at a rate of 3.9×1026 Joule per second. This is roughly equivalent to the energy of a 10 billion megaton TNT bomb every second. This huge amount of energy has been maintained for several billion years and will continue for several more. The fusion reaction of the Sun is a process in which hydrogen burns, transforming into helium, which is then followed by thermonuclear explosions. Isotopes of hydrogen, such as deuterium and tritium, are fused to form heavier helium. During this process the released energy can be as high as 17.6 MeV. The energy released from a 17 lbs deuterium fusion is equal to 1,000 kilotons of TNT. Every second the Sun fuses 675,000,000 tons of hydrogen into 653,000,000 tons of helium.

Scientists have attempted to make fusion work on the earth to make larger amounts of energy, thus solving our energy problems for the future. The first nuclear fusion trials were carried out for nuclear weapons. The released energy from the fusion trials was 500 times higher than that from the fission reactions of nuclear weapons¹. The energy released was equal to that of approximately 12 million tons of TNT. The civilian applications for energy production began in the early 1950s, and we are still trying to solve how to control this amount of energy in reactors.

In nuclear fusion, the negative and positive ions of hydrogen, called plasma, reach temperatures of 100 million degrees. To achieve the plasma parameters of the Sun, for example, the same temperature and density, the plasma must be heated to 100 million degrees Celsius and be kept dense and confined for at least 1 second.

Plasmas are mostly heated by Ohmic (resistive) heating, beam injection, or radio frequency heating. Ohmic heating is the result of an induced current being passed through the plasmas. This mechanism is also used to make electric bulbs and heaters work. Ohmic heating cannot attain plasma temperatures; such heating does not rise above 20-30 million degrees Celsius. When the temperature increases, the resistivity of the plasma decreases. Natural beam injection is one of the mechanisms used to obtain higher energy temperatures. Injecting a high-energy beam of neutral atoms into the plasma causes more collisions and increases the plasma temperature by transferring the atoms’ energy to the plasma. Radio frequency heating is another collision mechanism that increases the plasma temperature. Radio waves generated by oscillators transfer their energy at appropriate frequencies to ions or electrons, thus increasing the plasma temperature. Scientists have managed to get to high enough temperatures; however, these plasmas cannot be contained by the reactor walls easily and the reactions cannot be sustained. To prevent a loss of reaction control and to make the plasmas denser, magnetic confinement mechanisms have been developed such as TOKAMAK, Z-PINCH and ICF.

The TOKAMAK (Toroidal Chamber) device was invented in the late 1950s by the Russian physicists Igor Tam and Andrei Sakharov. In this system, mixtures of deuterium and tritium plasmas, confined by doughnut-shaped magnetic fields, are produced by the toroidal coils, which are then heated to very high temperatures. The temperature achieved by the Princeton Labs is 510 million degrees-almost 30 times greater than the temperature of the Sun. One of the major problems in TOKAMAK is that superconducting magnetic coils are needed for the electricity demand, but the superconducting magnets only operate at cold temperatures. So, a space between the plasma and coils must be maintained to avoid the plasma reaching the coils and damaging them. This mechanism is still assumed to be the best for the confinement of plasmas².

Another confinement system is the Z-pinch (Zeta-Pinch) pulse power device. The current flow of experimental devices is in the Z-axis, so the device was called the Z-pinch by the British scientists in the late 1950s. In this mechanism, very tiny wires, thinner than a human hair, are positioned in different configurations, such as cylindrical or nested geometries, and are then placed in an anode cathode gap.

Applying high voltage on the system causes the energetic plasmas to compress and heat the deuterium or tritium fuel in small pellets. The current flows through these wires axially, generating magnetic fields that confine the plasma. The temperature achieved is about 1.6 billion degrees; this result, reported by the Sandia National Labs, is almost 250 times higher than the interior of the Sun. Z-pinches produce the most powerful plasmas, but the generated plasmas are very unstable³.

Lasers were invented in 1962, and have been applied in many areas. Lasers were used in infusion research to confine the plasma in the late 1960s by scientists at Lawrence Livermore. This laser-based process is called ICF (Inertial Confinement Fusion). In this mechanism, laser light is used to compress and heat the pellet. The temperature achieved is about 100 million degrees Celsius and the plasma is compressed almost 1,000 times its liquid density. However, this confinement occurs in less than in a microsecond, which is not enough time to allow the ions to build on the energy of their own inertia.

Today, many countries have invested millions of dollars in confinement and ignition systems to create fusion power. ITER is an International TOKAMAK fusion project that will be built in France (for more information: http://www.iter.org/). Its participants have agreed to provide funding of $13.1 billion. When it is completed, the ITER will be one of the most expensive scientific projects in the world. However, despite the high cost, there are good reasons why scientists insist on the use of fusion. One of these is that no CO2 is produced during the process. Everyone is aware that CO2 has negative effects; for example, it leads to increased pollution and global warming. Another reason is the abundance of hydrogen available for fusion in seawater and on the earth’s crust. Another important reason is that fusion is safer than fission or other energy sources: There are no nuclear accidents, and in case of malfunction, the plasma is absorbed and cooled by the reactor walls. Also, the generated amount of radioactive particles is fewer than those generated by fission.

If everything goes well, scientists expect that fusion will be used as a source of energy in a couple of decades. If fusion is successful, it can provide clean, safe, reliable, sustainable, and widely applicable energy.

M. Fatih Yilmaz is a graduate researcher at Physics Department, University of Nevada.

Notes

1. Frisch O. R.: “The Discovery of Fission – How It All Began.” Physics Today 20 (1967), 11, pp. 43-48; http://en.wikipedia.org/wiki/Nuclear_fission.

2. http://en.wikipedia.org/wiki/Tokamak; http://www.ppdl.gov.

3. James Glanz, Science 18 July 1997:Vol. 277. no. 5324, p. 306 DOI: 10.1126/science.277.5324.306.

The appeal of the Golden Ratio to the human eye and brain has been scientifically tested. When subjects are presented with a range of rectangles, people invariably pick out as most pleasing ones those whose sides are of the Golden Ratio. This golden number is the basic number at work in aesthetics; there are even claims that the Golden Ratio was used by Leonardo da Vinci when painting the Mona Lisa, and by the Greeks in building the Parthenon. But the surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. In a newly published article in Physical Review B, it is stated that the Golden Ratio appears in the structures of some metals. The Golden Ratio is seen in the arrangement of seeds on flower heads, in the spirals of sea shells and galaxies, even in black holes. This ratio can be found almost everywhere in the universe.

Although the Greek mathematician Euclid first defined the Golden Ratio in around 300 BC, the followers of Pythagoras probably knew of it two centuries earlier. Euclid defined it as a line that can be divided into two unequal parts (Figure 1), where the ratio of the smaller part of the line to the longer part is the same as the ratio of the longer part to the whole. This ratio is 1.6180339887…, the Golden Number.

What makes the Golden Ratio special is the number of mathematical properties it possesses. The Golden Ratio is the only number whose square can be produced simply by adding 1 and the reciprocal of which can be arrived at by subtracting 1. If you take a Golden Rectangle – that is a rectangle where the length-to-breadth ratio is equal to the Golden Ratio, and take out a square, what remains is another, smaller Golden Rectangle. Also, think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. If you start with 7 and 11, then what you have is:

7, 11, 18, 29, 47, 76… When you have written down approximately 20 numbers, calculate the ratio of the last to the penultimate: the answer should approximate the Golden Number.

In mathematical terminology it is (an/an-1) equals to the Golden Ratio.

Another example of the Golden Ratio is the Fibonacci Numbers, that is a number series where each number is simply the sum of the previous two numbers. These numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… The ratio between any two successive Fibonacci numbers approaches the Golden Ratio as the numbers get larger. We can find the Fibonacci series particularly in the spirals of sea shells and in the arrangement of seeds on sunflower heads.

It was the elusive nature of the Golden Ratio that led the Italian friar and mathematician Luca Pacioli to equate it with the incomprehensibility of God. In the 15th century, he wrote a three-volume treatise, Divina Proportione (Divine Proportion), that was crucial in the dissemination of the Golden Ratio beyond the world of mathematics. After him, many artists, architects, and musicians used the Golden Ratio in their works; for example, musicians such as Debussy and Bartok and the architect Le Corbusier.

Let’s examine the arrangement of leaves on the stem of the plant Phyllotaxis. As each new leaf grows, it does so at an angle offset from the leaf below. The most common angle between successive leaves is 137.5 degrees – the Golden Angle; 137.5=3d 360-360/G, where G is the Golden Ratio. Why does the Golden Ratio play a role in the arrangement of leaves? It is all down to the irrationality of the number. A new leaf must collect sunlight without throwing too much of a shadow on the leaves below. A plant must arrange its leaves in such a way that the greatest number can spiral around the stem before a new leaf can sprout immediately above a lower one – that is at 360 degrees. If the leaves were arranged at an angle of 120 degrees, then the leaves would grow as 3 separate columns with large gaps between them. This would effectively block out the sunlight to the lower leaves. If the angle were 50 degrees, then there would be spaces between the leaves. But, with an angle of 137.5, the maximum amount of leaves can be arranged with a minimum of space being left between the leaves.

The Golden Ratio also crops up in hard sciences. Let’s take a look at the growth of “quasi-crystals.” These maintain a five-fold symmetry, which means that they make a pattern that looks the same when rotated by multiples of one-fifth of 360 degrees. Since the time when these crystals were discovered in 1984, many physicists have been researching their properties. In Brookhaven National Lab in New York State, Tanhong Cai imaged the microscopic terrain of the surface of such crystals made from alloys of aluminum-copper-iron and aluminum-palladium-manganese. It is found that flat terraces are punctuated by abrupt vertical steps. The steps come in two predominant sizes, with the ratio of the heights of these two steps being the Golden Ratio. This fact was discovered in 2002.

The most surprising place where the Golden Ratio appears is in black holes, a discovery made by Paul Davies of the University of Adelaide in 1989. Black holes and other self-gravitating bodies, such as the sun, have a negative specific heat. This means that they get hotter as they lose heat. In a spinning black hole there is an outward centrifugal force acting to prevent any shrinkage of the hole. The force depends on how fast the black hole is spinning. It turns out that at a critical value of the spin (when the ratio between the square root of the mass value and the square root of the spinning parameter is equal to the golden ratio), a black hole flips from having negative to positive specific heat. In other words, the Golden Ratio determines the character of the black hole.

Figure 2 shows the finger bones of a hand. The ratio of each bone at the top of the hand to the bones at the bottom of the fingers is the Golden Ratio. Pine-cones show the Golden Ratio spiral clearly (Figure 3). If one looks carefully at an ordinary cauliflower, one can see a center point where the florets are smallest, and the florets are organized in spirals around this center in both directions (Figure 4). The flower, Echinacea Purpura, has the same spirals (Figure 5).

With the help of developing science, new examples of the Golden Ratio are waiting to be discovered in the universe. The latest discoveries demonstrate that by using this ratio in technology, new products which make our lives easier will soon be available to all. This mystery that is spread throughout the universe may be an opportunity to renew and change our points of view on life.

Reference

• Chown, Marcus, “Why Should Nature Have a Favorite Number,” New Scientist, 21-28 December 2002, 55-56.

In his Models of My Life, social scientist Herbert Simon stated that science’s purpose is to find meaningful simplicity in the midst of disorderly complexity. Although the systems in nature and society seem to be very complex, we need simple theories to understand them. The key to finding these simple rules or principles, which Plato called perfect form and thing-in-itself and Kant described as a kind of untouchable essence behind physical things or systems, is mathematics.

Mathematics and social science

One of mathematics’ main challenges is its uses in social sciences. But does mathematics, which is considered rigid and restrictive and the best tool for explaining matter, have laws for human life? The latest studies in sociology, biology, and epidemiology show that such laws and meaningful patterns do exist and can be discovered. One of the great achievements of mathematics and physics in sociology is explaining the six degrees of separation (i.e., the small world) phenomenon.(1)

Almost everyone has met someone far from our home who is a friend of a friend. This is so common that it has become a clich: It’s a small world “ even though there are now more than 6 billion people. Even more surprising is the structure of social networks, the map of who knows whom, which shows that all people are closely connected.(2)

A social network is a collection of people, each of whom is acquainted with some subset of others. This can be represented as a set of points (nodes) denoting people, joined in pairs by lines (edges) denoting acquaintance, in a company, university, or even a global community. Social scientists have studied such networks, both empirically and theoretically, for at least 50 years.

A revealing experiment

One of the first and famous empirical studies was conducted in 1967 by Stanley Milgram, a Harvard psychology professor: the small world phenomenon. He asked: Starting with any two people in the world, what is the probability that they will know one another? In a large social network, although X and Z might not know each other, they might have a mutual acquaintance. Moreover, X might be linked to Z by a series of links. In other words, X knows a, who knows b, who knows c … who knows y, who knows Z. But how many intermediate acquaintance links are needed, on the average, to connect X and Z?

According to Milgram (3), this phenomenon raises the issue of a certain mathematical structure in society, one that often plays a part in discussions about history, sociology, and other disciplines. For example, during western Europe’s Dark Age, cities became isolated because inter-city communications broke down and thus severely limited the network of individual acquaintances. Thus, social disintegration was expressed in the communities’ growing isolation and people’s infrequent contact with non-local people.

Milgram asked his test subjects, chosen at random from Nebraskan and Kansan telephone directories, to get a letter to one of his Boston stockbroker friends. The letters were to be sent passing them from one person to another, but only if both parties were on a first-name basis. Since it was unlikely that the letter’s initial recipient and a Boston stockbroker would be on a first-name basis, their best strategy was to pass the letter to someone whom they felt would be socially or geographically closer to the stockbroker.

A moderate number of the letters eventually reached their destination. Milgram discovered that the average number of steps in this process was about six. This is usually considered evidence of the small world hypothesis: Most pairs of people, even in a very large population, can be connected by a short chain of intermediate acquaintances.

Milgram’s work passed into folklore and was immortalized in John Guare’s 1990 play Six Degrees of Separation, where Ouisa claims: Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice…. It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people. It’s a profound thought…. How every person is a new door, opening to other worlds.(4)

Watts and Strogatz used this model to explain the six degrees of separation in society- and nature-based networks.(5) Their model employs mathematical graph theory, which consists of nodes (people) and links (acquaintance). They modified the regular network, in which every node has short-range fixed number of connections, by adding long-range connections to the regular network to simulate the short path length between nodes. This model is now used in such areas as networks connected with biological metabolism, genomes, proteins, the Internet backbone, power grids, companies, and the stock market.

Research on social networks has helped health professionals understand how epidemics spread. Epidemiological models help them to predict how fast a disease will spread and to develop small world theory strategies to combat them, for scientists now realize that this social network property is a main cause for the outbreak of epidemics. This network offers a super-connected web of stepping stones for infectious diseases. After analyzing the social network’s structure, public health specialists can devise new vaccination strategies to slow or stop the epidemic. The small world theory also explains the rapid spread of news, rumors, fashions, and gossip.

Other types of systems show similar properties: networks of actors involved in the same movie, scientific collaboration networks of scientists who coauthor an article, and even the Internet, where millions of web pages are connected via mutual links. Recent research shows that in all of these networks, there are only a few steps between one node and any other node. The average shortest path between a network’s nodes, is 3.5 for the actor network and 9.5 for the scientific collaboration network. Despite the Internet’s more than 800 million nodes, there are, on average, only 19 steps between one web page and any other.(6)

Conclusion

The small world theory is a great success of the theory of complexity in nature and social life. It reveals an underlying dynamic of interconnectedness that expresses itself indelibly in who we are and how we think, behave, and communicate. Such close interconnectedness reveals one important fact for constructing a peaceful and beneficial world: There are no strangers, for everyone is one of our friends’ or neighbors’ friend or relative. The key element in understanding people is communication. Mutual love and good relations continue as long as we understand each other. We are loyal and faithful to the extent that we share our friends’ troubles, because ignorance only builds an impenetrable wall between us.(7)

Hasan Guclu is a doctoral student in the field of very large complex systems, such as computer networks, social networks, epidemics, and surface growth.

Footnotes

1. See, respectively, A. L. Barabasi, Linked (Perseus Publishing: 2002); D. J. Watts, Small Worlds (Princeton University Press: 1999); and M. Buchanan, Nexus (W. W. Norton: 2002).
2. D. J. Watts and S. H. Strogatz, Collective Dynamics of Small World Networks, Nature 393 (1998):440-42.
3. S. Milgram, The Individual In A Social World (Addison-Wesley: 1977).
4. J. Guare, Six Degrees of Separation: A Play (Vintage: 1990).
5. Watts and Strogatz, Collective Dynamics.
6. A. L. Barabasi, Linked.
7. F. Gulen, Pearls of Wisdom (The Fountain: 2001).

As we approach the new millennium, satellite-based communication systems will be the next frontier for this industry. They will assume a vital role in infrastructure, securing telecommunication links during disasters and supporting humanity’s space-based efforts.

A new epoch in space-based wireless communications has already begun with the deployment of two low-Earth-orbiting (LEO) communication satellite systems: Iridium and Globalstar. The Motorola-led Iridium consortium successfully launched the last five satellites in its strong network during the last year. The entire Iridium network integrates terrestrial phone systems and satellites.

Several other satellite systems having global or broad geographical coverage will join this new arena within the next 3 to 4 years, thereby complementing and extending existing terrestrial wireless services. Users of conventional terrestrial cellular services, business people, travelers, maritime vessels, aeronautical and industrial facilities, journalists, government agencies, the Coast Guard and emergency-related organizations, others on the go, and people living in sparsely populated areas will be able to communicate with each other via these services.

Satellite-based mobile communication systems are characterized by the distance of their satellites from Earth. LEO satellites are typically located 310 miles (500 kms) to 932 miles (1,500 kms) above the planet, whereas medium-Earth-orbit (MEO) versions are located from 3,100 miles (5,000 kms) to 7,456 miles (12,000 kms) above the planet. Geosynchronous Earth-orbit satellites, located 22,245 miles (35,800 kms) above the equator, move in synchronism with Earth’s rotation. While GEO satellites seem to be stationary to an Earthbound observer, LEO and MEO satellites appear to be in constant movement.

GEO SYSTEMS

GEO satellites have been used in such commercial communication services as television broadcasting and long-distance telephone trunking, and for maritime communication services since 1965. With the exception of the polar regions, global coverage can be provided by three GEO satellites equally spaced above the equator. In the past, GEO satellites were not viable for hand-held phone communications due to the lengthy signal propagation delay and large power loss. Advances in space technology, however, allow satellites equipped with large-aperture phased array antennas to increase their transmitting power, thereby making the GEO approach viable for delivering telephony to hand-held phones in vast areas of the world.

Several operators have opted for regional GEO systems, which typically require a single satellite. The Asia Cellular Satellite System (ACeS), which is being developed by a three-company consortium from Indonesia, Thailand, and the Philippines, will provide services in 26 Southeast Asian countries, including Japan, China, India, and Pakistan. ACeS’s satellite, positioned over the equator at 118 degrees east longitude above the island of Borneo, offers mobile phone, facsimile, data, and paging services. Hence, many people in this region who have no access to terrestrial communication links will one day be able to roam anywhere they wish and still keep in touch with each other.

Another regional GEO satellite, Thuraya, will furnish mobile satellite services to 1.8 billion people in 58 countries ranging from the Middle East and North Africa to eastern Europe, Turkey, the Indian subcontinent, and Central Asia. Thuraya will be positioned over the equator at 44 degrees east above the Somali coast. The program, a consortium of 14 telecommunications organizations in various Arab countries, is run out if its headquarters in the Thuraya Satellite Communications Co., located in Abu Dhabi, United Arab Emirates.

The Thuraya system will use a time-division-multiple-access (TDMA) scheme and support 13,750 voice channels. Hughes Network Systems will supply the dual-mode handsets. The satellite will connect calls from users to other users through its 256 reconfigurable spot beams. The company presently envisions an air-time price of US $0.50 per minute for system users.

LEO SYSTEMS

LEO satellites at very low altitudes differ from GEO satellites in two main ways: they are close enough to receive hand-held device signals with a very small propagation delay, and they form cellular towers in the sky. The major disadvantage of LEO systems, when compared with GEO systems, is that they require more satellites with a smaller size and lighter weights to provide global coverage. Complicated ground-based tracking systems are needed to control LEO satellites.

The Iridium system operated by the Motorola-led international consortium of 20 telecommunications and industrial companies is the first LEO system to turn the promise of global wireless service into a reality. By integrating ground-based cellular infrastructures with 66 LEO satellites and thus forming a cross-linked grid 485 miles (780 kms) above the Earth, Iridium provides such global telecommunications as telephony, data, and pager services.

Each satellite in the Iridium constellation rotates around the Earth within a period of approximately 100 minutes at one of the six orbital planes of 86.4 degrees inclination. With one global telephone number and an Iridium satellite phone, you can contact anyone on the planet. The satellite’s on-board processor processes calls placed by hand-held subscribers or forwarded by gateways and routes to other Iridium satellites in the constellation or to gateways on the ground. This inter-satellite networking capability and direct access of hand-held subscribers to the satellite is a significant distinguishing feature of the Iridium system.

The system operates at four different links and in four different frequency bands. Each satellite in the constellation is connected by radio transmission to four others at frequencies between 23.18-23.38 GHz. Hand-held users can communicate directly with the satellite in the 1.616-1.626 GHz band. Links between the satellite and ground gateways also operate in 19.4-19.6 GHz (downlink) and 29.1-29.3 GHz (uplink) frequency range. Iridium handsets are dual-mode, working both as a typical cellular telephone and as a satellite telephone. Both TDMA and frequency-division-multiple-access (FDMA) technologies are embedded in the handsets, as in cellular GSM handsets. The satellites are controlled by a master control center located in Lansdowne, Virginia, USA.

Iridium launched its final satellites in early May 1998. The system is now operational and offers a wide variety of services to travelers, aeronautical industries, and military and governmental organizations. It provides voice, facsimile, and data communications for the cockpit and at passenger seats across all aviation segments. According to a recent press release by Stratos, an Iridium service provider, the American government had a contract with it and Hughes Global Services to obtain access to multi-network Iridium satellite services.

Another LEO satellite system that will provide global voice and data services is Globalstar. This system is global in nature, except for the polar regions. It is a constellation of 48 satellites orbiting with a period of 113 minutes in eight circular planes, and is inclined at 52 degrees at an altitude of 879 miles (1,414 kms). Global-star’s satellites are less complicated and cheaper than their Iridium counterparts. They have no on-board processor or intersatellite links (Iridium does), and thus act like well-established reflectors in the sky relaying signals directly to ground gateways. Rather than directly connecting one caller to another by satellite, calls are first routed to gateways and then uplinked to the satellite. The satellite then downlinks this received call to another gateway.

The primary owners of Globalstar are Loral Space and Communications Ltd., and Qualcomm Inc. The system is operated and serviced by 12 telecommunications companies. In order to avoid communication linkage drops, three or four 16-foot to 20-foot (5-meter to 6- meter) dish antennas are installed at Globalstar gateways. Unlike Iridium, Globalstar handsets utilize code-division-multiple-access (CDMA) technology. Globalstar’s unique capability is that signals from three or four visible satellites are combined at the gateways, and the strongest one is chosen to maximize power efficiency and eliminate call interruption. Therefore, satellites will be seamlessly added to and removed from calls in progress, as they are constantly moving in and out of view. So far, Globalstar has put 24 satellites in orbit. “With only two more successful launches of four satellites each, Globalstar will have the coverage required to initiate a regional roll-out of service in September,” says Bernard L. Schwartz, chairman and chief executive officer of Globalstar.

OTHER LITTLE LEOs and MEOs

Other LEOs, notbly Orbcomm and Teledesic, provide such telecommunication services as broadband Internet access, videoconferencing, and multimedia; however, they do not allow phone calls. These satellites are relatively small compared with those of Iridium and Globalstar, and were designed for two-way data communications. Orbcomm is a consortium of Orbital Science Corp., Canada’s Teleglobe Inc., and Malaysia’s Technology Resources Industries Bhd. Orbcomm’s total of 36 little LEOs will travel in two different circular orbits: one is located 460 miles (740 kms) above the Earth with 70 degrees inclination in pair, and the other is located at 523 miles (825 kms) in planes of eight with 45 degrees inclination. The Teledesic system will consist of 288 little LEO satellites in 12 polar orbital planes. It will provide data rates of 64 Mb/s, data rates 2,000 times faster than standard telephone modems. The system’s operation frequency will be 27.5 GHz in the uplink (from user to satellite), and 28.5 GHz in the downlink (from satellite to user). The company plans to start commercial service in 2002. Its investors are Microsoft founder Bill Gates, cellular phone pioneer Craig McCaw, Boeing, and the AT&T Corp.

ICO Global Communications will feature 10 operational MEO satellites located at an altitude of 6,434 miles (10,355 kms) in 45 degrees and 135 degrees inclined orbits. ICO’s ground network will consist of 12 ground stations with multiple antennas distributed strategically around the globe. Its gateways will function in ways similar to those of Global- star. The ICO system will launch its full service in 2000. ICO satellites are derived from an existing Hughes GEO satellite, and are four times heavier than Iridium satellites: 6,063 pounds (2,750 kgs) in orbit. ICO satellites travel more slowly than LEO satellites, thereby reducing the need for frequent handovers from one satellite to another.

Ellipso, an MEO system owned by Mobile Communications Holding Inc., Lockheed Martin Corp., Harris Corp., and three others from Australia and South Africa, will become fully operational in 2001. With 17 satellites in three orbital planes, it can provide almost complete global coverage. Seven equally spaced satellites located above the equator at an altitude of 5,008 miles (8,060 kms) will serve a 25 degrees north and a 55 degrees south latitude region. Another 10 satellites will orbit in two elliptical orbits inclined at 116 degrees. Each satellite will be able to handle 3,000 simultaneous phone calls.

REFERENCES

• Big LEO/MEO/GEO Market and Financial Review (1998).
• Glenister, Simon. “Iridium to Offer Aeronautical Service.” Integrating Global Air Traffic Management, ICAO/ISC (June 1998). (See also: www.
• iridium.com/english/industry/wero/medialarticle_index.html.)
• http://www.globalstar.com.
• http://www.iridium.com.
• Miller, Barry. “Satellites Free the Mobile Phone.” IEEE Spectrum Magazine (March 1998): 26-35.