Robots continue to advance and develop every year, and these consistent improvements continue to amaze us with how much they physically resemble humans. Even though these robots lack spiritual qualities and function way below the human brain, we still admire these developments, for they lead to even more discoveries and help us understand the miraculous human body even more.

Notwithstanding our medical knowledge that continues to build upon nearly 3,000 years of shared human experience and research, new discoveries about the human body, the magnificent work of God Almighty, continue to increase our admiration.

The discovery of the “Interstitium” and the “Subcapsular Proliferative Foci” in 2018 allow us to develop an even greater appreciation for the complexity of our bodies. They are called the “macro organ” and “micro organ” according to the amount of space that they occupy in our bodies, along with the nicknames “buffer organ” and “control center organ” according to their function. These newly discovered biological structures did not attract much attention earlier because, in accordance with our current understanding, organs are more easily visible structures such as the hands, arms, eyes, nose, kidneys, and lungs that have a certain shape and a set of clearly-defined functions. It is interesting that although these complex structures are so widespread in our bodies, they were not known until recently; they are now considered as organs [1].

The Macro Organ: Interstitium

According to an article published in Scientific Reports on March 27, 2018, the “interstitium” was discovered rather serendipitously by David Corr-Loce and Petros Benias of Mount Sinai Beth Medical Center along with Neil Theise, a pathologist from New York University. The discovery came when these physicians were analyzing a cancer patient’s bile duct. Although they had been conducting the same routine over the years, it was the first time they had the sight of slots between examined tissues. They realized that the interstitium was unnoticed earlier due to the disappearance of interstitial fluid after they had examined the tissue with their usual histological methods. Subsequently, the researchers found that this structure was found not only in the bile duct but also in many other organs.

Specifically located under our skin, these micro-compartments were also found in almost all organ membranes except the intestines, lungs, veins, and muscles in order to form a network around the organs with malleable but sturdy proteins. The interstitium, the entirety of the intercellular spaces filled with liquid, has been defined as the largest organ in the body. Actually, examining cells and tissues has been the subject of histology and cytology science for the last 150 years, and the fluid that fills the tissues and forms a basis for supporting these cells was not new to the medical world. However, its definition as a new organ was a first.

The researchers froze the biopsy tissues obtained from the bile ducts of 12 patients in order to preserve and examine the anatomy of the discovered structure. One of the reasons that this organ exists is because it protects the surrounding organs by acting as a shock-absorber and has an effect similar to that of a car’s bumper. Damage to tissues and internal organs remains minimal when one falls, hits something or is impacted Using a micro-endoscopic camera, the volume of this whole organ was revealed to be about ten liters in an adult human [2].

It was later discovered that the interstitium is also present in the structure of lymph nodes, the most important part of the body’s immune system, and that cancer cells enter the lymphatic system through the interstitium. In this case, the interstitium play a significant role as a passageway, or conduction interface, for spreading cancer cells across the body. In an analogy, this organ is akin to the water in which fish swim, the air that surrounds us, and the soil that borders the roots of trees. In this liquid that rotates the cells and spans on the base where they are positioned, any exchange of substances of body biochemistry is regulated within the required amount and size to provide a good setting to the cells, and the hard mechanical effects that may impact the cells are alleviated and absorbed by this liquid pad.

Each discovery of the interstitium’s features, including its significant contributions in the fight against cancer, reveals more and more about how this great organ aids in intercellular communication.

The Micro Organ: Subcapsular Proliferative Foci

One of the most important features of the immune system is that it has its own “memory.” The cells of the immune system can remember the infections a person has contracted before, and can fight infections before they spread. How quickly the immune system reacts based on memory may vary, for instance depending on the type of infection, but is usually quite rapid. Considering how many bacteria multiply in a matter of seconds, a quick response must be launched to prevent infections from spreading across the body.

Professor Tri Phan of the Garvan Medical Research Institute led the team of researchers that discovered the subcapsular proliferative foci (SPF), a “micro-organ” that appeared in the lymph nodes during an infection. Lymph nodes and lymphoid organs such as tonsils, thymus, and spleen are surrounded by a protective capsule made of connective tissue. This capsule was considered to serve the purpose of a mechanical support only to enclose and protect the lymph nodes. However, recent research has shown that in some areas under this capsule, cells that had been alerted to previous encounters with harmful invasive organisms are gathered. These main subcapsular cells are memory B cells that carry information on how to counter the invasive organisms. Memory B cells also proliferate into plasma cells, which are highly important for producing antibodies. Therefore, when an infection reoccurs in our body the subcapsular proliferative foci act quickly to form the first defensive front to prevent the possible spread of infection.

The purpose of vaccines is to activate the attenuated form of a harmful organism to be stored in the body’s memory as an immune response. If the body comes back into contact with similar bacteria in the future, the immune system will remember how to fight it. The discovery of the sub-capsule foci also revealed that these centers are the home for the memory B cells. If they can unveil the development and training processes of the memory B cells in these slots, scientists can produce vaccines that enhance the memory of the immune system even more quickly and efficiently.

The reason why these structures have not been noticed earlier is due to their emaciation, brief emergence, and disappearance. The sub-capsule proliferation centers presented in the article “Memory B Cells Are Reactivated in Subcapsular Proliferative Foci of Lymph Nodes” published in Nature Communications on August 22, 2018 are defined by some authoritative scientists as the “micro-organ.” According to the findings about this new organ, if our infection-fighting immune system would have activated longer than it currently does, we would easily die. Every minute is very crucial in this struggle. These excellent centers that produce memory cells under the lymph node [3] capsules fight bacteria which can replicate in multitudes every 20–30 minutes during an infection.

Although the world of science has been working with the microscope for about 400 years, these centers that have been embedded in our body since its creation could only be noticed today when the microscope design has reached its technological peak.

There are trillions of bacteria living in the intestinal cavity, skin, and orifices of our body. Some of these are already protective and beneficial, yet others are pathogenic. But they do not make us sick because of B cell production centers. When our immune system is weakened for any reason (such as stress, insomnia, or malnutrition) these bacteria can cause illnesses and meet little resistance. These sub-capsular micro-organisms surrounding the lymph nodes were placed in the most strategic places across the human body to fight infections in the fastest way, while the lymph nodes were placed at locations that are most vulnerable to microbial attack.

Consequently, these discoveries increase our admiration for the palace and magnificent realm called our body. It is likely in the light of this information that the anatomy and histology books may be rewritten and the definitions of organs and tissues may be redefined.

References

• Claire Maldarelli, “Scientists found a new organ, but it might not be what you’re expecting,” Popular Science, 3 April 2018.
• iflscience.com/health-and-medicine/newly-discovered-microorgan-helps-explain-how-vaccine.
• nature.com/articles/s41598-018-23062-6

I, the protective system that you call the “immune system,” am divided into different groups and sections, each of which has its own area of expertise. Just like a military unit, each of my groups has to be partially or fully trained before it begins life in my system so that it can properly fulfill its defensive function. “Soldiers” in this protective troop work according to what expertise they have and the type of “enemy” (alien microorganisms) they encounter. Some are equipped with heavy weapons against tough enemies; some produce a special poison with which they kill their enemies by injecting it into their bodies, some work like a waste disposal, smashing up the dead bodies of the enemies, and some of them eat the alien intruders alive when they attack your body. Others produce raw material to arm your body, some turn that material into weapons, some work as defenders, some are signalers, some are rangers and some are equipped with a special intelligence which allows them to recognize the previous invaders and destroy them more easily at their future encounter. In this intelligence system, which works like an information center, the soldiers check the dangerous invaders and remember their previous experience with them. Then, they develop a strategy to fight against those invaders. If the enemy is known well, the defense against it will be easier.

Now, using this analogy, I will talk about your enemies and the features of my soldiers that are placed in your body to fight against them. However, I have to remind you of something first: as you know, every army has to have a top commander. Similarly, there is someone who has placed such a perfect system like me in your body, someone who has boundless knowledge and power, and has no one else superior to Him or has no one to receive orders and instructions. That is our Lord God Almighty. Since He knows very well what kinds of enemies you will face, He has created me with all my troops so that you can be defended against those enemies.

The enemies of your body are germs, which enter your body through different passage ways, including digestion, respiration, excretion and the skin. “Germ” is a general term referring to many kinds of micro-organisms. Some of them are bacteria, some are fungi and some are viruses. Your body needs different special tactics to defend against each group of germs and my soldiers are quite talented in those tactics. I have to be always watchful against germs coming from outside. Not only that, but I also have to be careful about inner enemies, that is, the cells in your body which suddenly turn into “terrorists” becoming harmful and spoiling the system. You call those cells “cancerous.” It is a great challenge for me to cope with those cells because they originate from among your very own cells and they know our tactics very well. Nevertheless, with God’s help, we can defeat them. However, when too much stress and anxiety weaken me I might miss some of those cancerous cells, which will grow and become tumors. In fact, cancerous cells develop much more in number than is commonly known. But my soldiers constantly check every single cell that is formed in your body and try to see whether it is normal or not. As soon as they discover a cancerous “terrorist” cell, they try to quickly destroy it. However, some cancerous cells are disguised like a wolf wearing a sheepskin so that they can avoid detection. My soldiers make rounds and check the cells from outside by only looking at their skin. Thus, they can be manipulated. All of your cells, including those with germs or cancer, contain protein with a special code which identifies the cells as being yours. When my soldiers encounter our fellow cells carrying those coded proteins, they release them. But the enemies who do not carry this code (or password) are immediately caught and destroyed. When we have diseases like cancer, however, the cancerous cells may evade our “rounds man” because they know this password. Sometimes the opposite may happen: my soldiers get confused and cannot identify their fellow cells despite carrying the right password, assume that they are enemies and start to attack them. These types of diseases, called Autoimmune diseases, emerge with a quite complicated mechanism which is a puzzle even for me! For example, during rheumatoid arthritis, which is among the many long-lasting and unrecoverable diseases, my soldiers attack and gradually destroy the tissues like cartilage, cardiac muscle, eye lenses, and the tubes of the kidneys with which they share a body. In fact, when we are created as a whole system (when you are only an embryo in your mother’s womb), some of my soldiers make an agreement with the other cells of your body, announcing that they will forever stay friends with them, will show tolerance to them and will only attack the enemies. But, somehow this agreement is broken later; my soldiers do not obey me anymore.

Now it is time for my group of soldiers to introduce themselves:

The most general term by which we are identified with is white blood cells or leukocyte. We appear approximately 6,000 to 7,000 times in each cubic millimeter of human blood. The other blood cells, which are called red blood cells (erythrocyte) are red in color; it is for this reason that we are called white. Since blood vessels can reach to the remotest edges of the body, we roam around the body through those vessels and look for work to do. Of course, not everyone can do everything. So, we are first divided into two sections. The cells in the first section contain microscopic granules, so they are called granular leukocyte. The cells in the second section do not contain such granules, so they are called agranular leukocyte. Those sections are divided into groups among themselves. The first section has three groups: neutrophils, eosinophils and basophils. The second section has two groups named monocyte and lymphocyte.

Eosinophills: You may not know much about these soldiers that make up 12% of the whole protective body. However, during allergic reactions and diseases caused by parasites, the number of these soldiers increases. They complete the effect of the antibodies produced against the antigens. Some chemical substances like histamine appear as a reaction to antigens, such as itchiness, rash, and swelling. Eosinophils reduce the effects of those substances and the symptoms.

Basophils, which are the least in number, make up the 0.5% of the body. Those soldiers are present mostly in the scars that are healing or in highly infected areas. The granules inside basophils contain two very important substances called heparin and histamine. Histamine helps expand the blood vessels and accelerates the release of active substances within me from the blood vessel walls, enabling them to reach to the affected area. Heparin also prevents the blockage of blood vessels because of blood clot.

Lymphocytes of the second section are the group of soldiers which goes through special training and has expertise in many subjects. They make up 20-25% of the soldiers in my system. Those soldiers detect antigens and germs and remove them from the body. Every soldier has a detector which identifies a certain antigen. Therefore, in your blood, there are millions of lymphocyte soldiers, which are different from each other and do not have a pair. For any antigen of a germ, you will definitely find a lymphocyte that finds and kills it. Those soldiers can be grouped according to their appearances, as small, medium, and large lymphocytes. Each group has different special features. We can also divide them according to their maturation and training process as B-lymphocytes and T-lymphocytes. Although both of them originate from stem cells in the bone marrow, T-lymphocytes mature in the thymus before they move to the other lymph tissues such as the spleen, liver, and tonsils (Thymus is a gland in the chest that talked about itself in the previous issue). B-lymphocytes, however, mature in the bone marrow, and go directly to the tonsils, appendicitis, spleen and other lymph tissues. When the T lymphocytes mature in the bone marrow, they acquire different new features. Some of them work as T helper cell, some work as natural killer T-cells and some work as suppressor T-cell. A helper T-cell, which is triggered by an antigen that is specific to it, secretes lymphokines, which makes B-cells produce antibodies. Among those lymphokines, interleukin-2 activates the natural killer T-cells, which kill the infected cells. The killer T-cells do not bind directly to an antigen. Rather, they secrete a substance that kills the infected cell after joining with the antibodies that were previously bound to the infected cells. On average, T-cells live 2-4 years; some, however, live more than 10 years. Today, the defense mechanism of the T-lymphocytes creates an issue in terms of organ transplantation. If, for some reason, a foreign organ (a kidney or heart, for example) is transplanted into the body, the T-lymphocytes attack that organ immediately. Those “headless” soldiers do not know that the body really needs that organ and try to eliminate it, therefore, leading to transplant rejection or tissue incompatibility. The T-lymphocytes treat the foreign organ the same way as they do to the cancerous cells: they attack and try to destroy it. For this reason, the immunologists are trying to discover medicines that will help them control the soldier T-lymphocytes whenever they need to be stopped.

Dear Peter, have you ever thought about how all this happens? While you have no idea about a germ that might enter your body, those memory cells, which are placed in your blood with a boundless compassion by our Creator, remember an enemy that they saw years ago, and begin to make weapons right away. Since those cells are devoid of reason and consciousness, to operate them there has to be Someone with a great knowledge and will.

The lymph nodes are production centers for the lymphocytes found at some particular places in the body. They resemble variously sized military headquarters. The lymphocytes are produced mostly at infection sites, which are the little lymph tissue groups located under the epithelium that lines along the walls of the digestive tube, respiratory track, and the bladder. When fighting with bacterial infections the lymph nodes swell and enlarge as much as 1–2 cm. In addition to the lymph nodes that extend through the lymph vessels, the areas such as nape, groin and the axilla (underarm) also contain lymph nodes. If you get an upper respiratory tract infection, the lymph nodes at your tonsils and neck areas become swollen. If you get a urinary track infection the nodes in your groin area become swollen. As for digestive track infections, it is the responsibility of the lymphocytes in your appendix to fight against germs. Some scientists view this organ, which is an extension of the cecum (the blind gut), as a “dead” piece of intestine. Both the appendix and tonsils are quite useful organs that produce lymphocytes in normal circumstances; they are not some useless remnants. For that reason, it is not right to remove them when it is not really necessary. However, we have to remember the proverb that says, “We salt the food so that it does not smell bad; but, what do we do if the salt itself smells bad? Then, we have to get rid of the salt.” Similarly, in some bodies where my system is weak and so is lymphocyte production, those areas become home to germs and you have to remove them.

Other than the soldiers of the immune system, several organs in your body have their own ways of protecting your body. Those organs do not have soldiers like in my system; theirs are like a “civil defense.” Chief among those are your skin which works as a natural barricade against the entrance of the germs, the mucous membrane that lines along the walls of your mouth and inner nose, interferon which is a substance produced by your cells against viruses, and an antibacterial substance called lysozyme which exists in your tears and sweat. Therefore, sweating, crying, and runny nose are not things to be ashamed of; they are only the protective systems that have been naturally placed in your body by our Lord God.

Dear Peter, I think I should stop here although there are still so many features of me that you have to discover. After all, beneath all diseases and deaths you will find disorders related to me. The biochemical processes in which many of my soldiers operate are not exactly known yet. If those are revealed, doctors will likely succeed in healing many other diseases. However, sooner or later you will reach the destined end: death. No creation can be immortal; there will definitely be a problem and you will have to leave this world, wherein you are only a guest. If you carefully contemplate the works of art in your body, in the hereafter you will have solved the riddle of the delicacies of those works. Of course, everyone’s time of death is unknown. Therefore, in this limited time, give your organs their due and give thanks to the God Almighty who gave you those gifts. Live according to His will, and always remember to glorify Him. Goodbye, Peter! May you and your troop be healthy!

Irfan Yilmaz is a professor of biology at Dokuz Eylul University, Izmir, Turkey

This time, with your permission, I won’t be talking about the last two weeks that I have spent in this alien city, as I usually do. Instead, I feel obliged to reflect on your anger at the fact that your father did not use the opportunity he had during his youth to become a medical doctor. What I’m going to tell you has been said by many great thinkers in the past, but I want to bring their words up-to-date and relate them to my studies here. I hope to give you an alternative understanding of tolerance by using the idea of networks.

As commonly defined, networks are web-like maps of nodes that represent entities and links that connect the nodes and represent their interactions. Networks have become very popular these days, and are used to analyze everything from ecology and biochemistry to social infrastructures.

Try to visualize your father 30 years ago in a large network that consisted of his two brothers and three sisters, his fiance of 2 years standing, maybe a very close friend who had recently died, maybe another friend who already had had a child, along with the fear of leaving his hometown for the first time, and so on. All of us, including your father, are surrounded by such factors all the time. Perhaps your father could have overcome some of them, like his fear of loneliness or impatience, but he certainly could not have overcome all of them, because his family, surrounding events, and many other factors existed on their own and didn’t develop according to your father’s will.

Upon further reflection, however, maybe none of these factors, even the trivial ones, were ever in his grasp and thus were never under his control. Let’s think back even further. When your father was in the womb, he had only one obvious link with the world: his mother. But wait a minute, you might ask, didn’t he have other links, such as his genes, family, and birthplace? Of course, you would agree that your father had no choice in any of these crucial factors. Moreover, I don’t think that it’s hard to accept that, for example, his impatience was probably the result of his cultural make-up, genes, interactions with his family members, and other things. As you know, all of these were independent of your father’s will. Thus, your father, and indeed every person, was born into a predetermined world, one in which most choices had already been made for him. Moreover, these initial determinations had an undeniable impact upon the rest of his life and decisions.

Imagine a circle in the center of a big picture. The circle is you, and the picture represents your life, or else all of the interactions that you make during your life. As mentioned above, even in the very beginning, that circle is not unique. Now imagine a few more circles which represent your family members and hometown, and draw a line from each circle to yourself. This is you in the beginning. Without a doubt, soon some circles will fade away and other circles will appear in a continuously regenerating network. Let this little human being live in this world (morph his network, as we say) for some years and, in the end, you’ll obtain a dreadfully complex picture that is almost impossible to understand.

Nevertheless, let’s consider for a moment the evolution of this self-network. At each decision point, we make a choice that is influenced by our personal self-network, defined as a collection of those choices over which we had no control and those which we made due to our personal network at that time. This recursive definition of self, which is entirely reasonable, makes it impossible for us to judge other people’s behavior, for we can never know if such behavior is the result of free will or of the previous self-network. We find it easy to criticize students who drop out of school, or behave anti-socially, or sleep all day. But maybe they had no other option in the context of their self-network. If this is the case, criticizing them is almost like criticizing a fish because it cannot fly. It is quite possible that no alternative choices were within their reach.

The key observation lies in this: When we see a person do something that we don’t like, we don’t know and can never know how much his or her self-network has influenced that specific act. Therefore, my friend, who are we to judge other people’s acts unless we have this kind of knowledge? Given this, if we want to be true to ourselves, what other alternative do we have but to exercise complete tolerance toward others?

Before going on, however, I should stress that I am talking about tolerance for acts that don’t violate other people’s rights and freedoms. In addition, I’m talking about personal tolerance only, for obviously everyone must follow the law for the sake of society. For example, a thief should be punished according to the law. Therefore, given that there are many underlying reasons for a person’s act, we should hesitate before passing judgment, for it benefits both of us if we are tolerant. As shown above, this is not only a more pragmatic, but also a more rational approach.

The world’s great religions and great minds have said such things many times. For example, we read in the Bible: Judge not, that ye be not judged (Matthew 7:1) and Therefore thou art inexcusable, O man, whoseoever thou art that judgest… (Romans 2:1). The great Hellenistic philosopher Epictetus says: If a man drinks much wine, do not say that he drinks badly, but that he drinks much. For till you have decided what judgment prompts him, how do you know that he acts badly? 1 Even more, another Biblical verse states: Therefore judge nothing before the time, until the Lord come, who both will bring to light the hidden things of darkness, and will make manifest the counsels of the hearts: and then shall every man have praise of God. (I Corinthians 4:5). This verse supports tolerance, for it tells us that we should have comprehensive knowledge of a person before judging their acts. Such knowledge, as we all know, is possessed only by God.

An interesting result of considering individuals as nodes located in the center of a complex network occurs when we try to influence a person’s views, acts, and beliefs. In order to appreciate how difficult (if not impossible) this is, imagine the self-network of the person you want to influence, with all of his or her beliefs, memories, friends, as well as all of the nodes acquired while morphing his or her self-network.

Now imagine the fraction of nodes in that self-network that are directly related to you. I don’t think that you’ll claim to be a big part of that person’s life, unless both of you have been on intimate terms for quite a while. The proportion of the nodes that you represent in his or her self-network can be quite an accurate measure of how much influence you will have. For example, you can alter a lonely or a simple person’s beliefs in a shorter time, since in a short time you can become a large proportion of his or her self-network.

By the way, you might be amazed to hear that the English mathematician Thomas Bayes (1702-61) tried to formulate quantitatively how a person’s beliefs would change upon receiving new information that contradicts his or her previous beliefs. In a Bayesian analysis, a set of experiences (in our case, links) are seen as something that influences opinion and decision. I won’t discuss this further, however, since it’s beyond both my and this letter’s scope.

In my opinion, the reason why we almost always criticize and blame others, and constantly see faults in everybody else is because we refuse to make an honest self-criticism; that is to consider our own responsibilities, not those of other people.

Forgive me for saying this, but you want to achieve a better quality of life now; this is something for which you have to work really hard. Yet, if your father had become a doctor, you probably would already be living this better life, and so you wouldn’t have to push yourself. Hence, we can find a convenient scapegoat in your father, who, for whatever reason, didn’t set you up with such a life!

Another example, one in the future, might be that a person explains his/her beliefs in the hope of influencing someone else. Unable to convince this person, he/she blames that person for not opening their heart and really listening. Easy, isn’t it? However, remember that you can’t really influence a person if you are not a large part of his or her life.

Do you see what’s missing in this picture? Reality and, more than that, a solution. It lacks reality, for we can never hold someone absolutely responsible for anything. And why not? Because we have no way of knowing which actions were based upon free-will and which ones were the result of his or her prior self-network. By blaming others, regardless of whether we are correct in doing so or not, we not only contradict reality, we also ignore our own mistakes, closing the roads to a solution that could come from ourselves, and taking a passive position of stagnancy that, I think, won’t make a better world for ourselves or anybody else.

Before ending, I’d like to apologize if some of my words sound harsh. However, I consider you a true friend who will appreciate my openness. Even if some of my words have upset you, perhaps you’ll be patient with me. For this to be, before blaming me, stop for a moment and try to look at this situation from another perspective. Try to find some truth in my words, and try to be hard on yourself. Below are some extraordinarily beautiful lines from Nietzsche, which I think are appropriate to our discussion. He writes:

Why so hard? the kitchen coal once said to the diamond. After all, are we not close kin?

Why so soft? O my brothers, thus I ask you: are you not after all my brothers?

Why so soft, so pliant and yielding? Why is there so much denial, self-denial, in your hearts? So little destiny in your eyes?

And if you do not want to be the destined inexorable ones, how can you one day triumph with me?

And if your hardness does not wish to flash and cut through, how can you one day create with me?

For all creators are hard. And it must seem bliss to you to impress your hand on millennia as on wax, bliss to write on the will of millennia as on bronze harder than bronze, nobler than bronze. Only the noblest is altogether hard.

This new tablet, O my brothers, I place over you: become hard!2

Yes my friend, become hard, very hard on yourself; and soft, very soft towards others.

Footnotes

1 Epictetus, The Discourses of Epictetus, tr. P. E. Matheson (New York: Heritage Press, [1968]).

2 Friedrich W. Nietzsche, Thus Spoke Zarathustra, tr. Walter Kaufmann (USA: Viking Penguin, 1966), 214.

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).