On a cold winter day in a small Anatolian city, in a narrow street of an old neighborhood, in a small apartment, the mother of Mehmet, who was not yet one year old, looked anxiously at her son's pale face. It was discovered that Mehmet had blood poisoning. Mehmet was hospitalized in a larger city, but as days passed, hopes were fading. Mehmet's blood type was rare, and the conditions of the time made it difficult to find the blood he needed.
On the fifth day of his hospitalization, a middle-aged woman appeared. She wore an old coat, with traces of fatigue on her face. She said she wanted to donate blood. When the nurse learned the woman's blood type, her eyes lit up. It matched Mehmet's group. At that moment, cries of joy echoing through the hospital corridors spread in waves throughout the hospital.
Years flowed like water. Mehmet was now a university student in Istanbul. Life was flowing in another city. One day, an urgent announcement was heard on campus. A very rare blood type was being sought. When Mehmet heard his own blood type, he shuddered as if a hand from the past had touched his shoulder. He immediately rushed to the hospital.
After giving blood, he made eye contact with an elderly woman waiting in the corridor. The woman was there due to her grandchild's illness. When Mehmet learned that the blood he donated would be used for the woman's granddaughter who was waiting there, he wanted to meet the woman and offer her encouragement.
The concern in the woman's eyes reminded Mehmet of something. They began to talk. The woman told him that years ago she had donated blood and saved a little boy's life. Mehmet's heart raced. As they talked, they realized that the blood the woman had given years ago had saved Mehmet's life.
At that moment, the hospital corridor transformed into a bridge that seemed to contain all the times of Istanbul. Past and future had met on this bridge. The help the woman had given had come back to her years later. Just like the waters of the Bosphorus, life was flowing within itself and seemingly returning to where it had flowed before.
This event, which seemed like a coincidence, was actually a small-scale example of a complex social dynamic.
So, how can we understand these types of social interactions? Here, we will try to interpret this social event using the language of mathematics, especially Topology and Game Theory.
What is Topology and What Does It Have to Do with Helping Others?
Topology is a field of mathematics that studies the fundamental properties of shapes. It is a branch of geometry that examines the features of surfaces and general shapes, but does not concern itself with lengths and angles. It studies the properties of geometric shapes that do not change under continuous deformations such as stretching, bending, or twisting. For example, a cup and a donut are considered topologically the same because one can be continuously deformed into the other (both have one hole). Also, in both objects, it is possible to return to the starting point regardless of the shape when starting from a point. Every object with a topology has a group of points, or a connection, that starts from a point on it, passes through other points, and returns to the point where it started. We can call it a connection when an ant starts walking on a teacup and returns to the point where it started by walking. As can be understood, the ant can return to the point where it started by walking not only on a single path, but on many paths.
In the context of helping others, if we define the life we are in as an object with topological space, we can think of social relationships and interactions as a kind of "social field". In this space, we can represent each of the points in the object we call life as a person or an individual, and the relationships between them as "connections". This approach can help us understand how helping behavior spreads and takes shape within society.
In our story, the decision of the woman who donated blood to Mehmet created a new connection in this topological space, "social field" which we can define, and with this connection, Mehmet also had the opportunity to donate blood. The blood donation made to Mehmet years ago, the connection formed by the woman benefiting from it, returned to the woman herself, just like an ant reaching the point where it started by walking on a cup.
This connection can affect other people and lead to more connections over time. In other words, it could have been someone else, not Mehmet, who donated blood to the woman's grandchild, just as the ant can return to the point where it started not only from one path, but from different points.
Game Theory and Altruism
It is possible to explain the phenomenon of altruism with another mathematical approach, Game Theory. Game theory is a branch of mathematics that studies strategic decision-making processes. We can think of "blood donation" behavior as a game. Each individual decides whether to donate blood or not. So, why do some people choose to donate blood?
Here, the concept of "reciprocal altruism"[1] comes into play. This concept suggests that individuals cooperate to provide mutual benefits in the long term. In other words, Mehmet and the woman who donated blood to him believe and act on the idea that by donating blood, they are contributing to a system that they or their loved ones might need in the future.
This awareness and consciousness of blood donation also leads to the development of a "dominant strategy" among people, and society develops a dominant strategy around this awareness. Subsequently, an "equilibrium" forms. In game theory, this is called Nash equilibrium. In social life, we can also call this equilibrium as "culture of living".
From an Islamic perspective, Allah's promise to reward those who help others more abundantly [2] can be interpreted as changing the rules of this game. This promise makes the strategy of helping more attractive and encourages the spread of altruism in society. Consequently, individuals organize themselves for the act of helping, and thus society forms a dominant strategy. This creates a Nash equilibrium towards more altruism.
Mathematical Model
We can explain this process in a simpler way [3]. The spread of helping behavior in a society can be thought of like a ripple created by a stone thrown into a calm lake. Initially, the helping behavior spreads slowly because few people exhibit this behavior. However, over time, as more people start to help, this behavior spreads faster and reaches distant points.
This spreading process continues up to a point. Eventually, when a large portion of society adopts the helping behavior, the rate of spread slows down and reaches an equilibrium point. At this equilibrium point, the number of new people starting to help is approximately equal to the number of those who stop helping for various reasons.
This process can be thought of as Mehmet's decision to donate blood and its consequences being observed by other people and influencing them to donate as well. Thus, the helping behavior continues to spread in society.
A Real-Life Example
According to research, Finland is known as one of the happiest countries in the world [4]. The high rankings of Nordic countries in happiness indices are closely related to concepts of social cohesion and trust. In these countries, a culture of mutual aid and reciprocal trust forms strong connections in a topological space which we called "social field". Just as in Mehmet's blood donation story, the network of mutual assistance between individuals in these societies increases the overall welfare of the community.
In the case of Finland, social cohesion and trust have been supported by an egalitarian social structure formed through historical processes, a widespread education system, and transparent institutional structures. When considered topologically, this structure creates a system where every point in society is interconnected, and a movement of mutual aid starting from any point can spread to the entire society. Consequently, this sense of trust and cohesion can be seen as fundamental factors that enable the formation of policies and social structures that support happiness, just as in our blood donation example where individual decisions lead to positive effects at the societal level.
This environment of trust, when viewed from a game theory perspective, leads to society adopting a "win-win" strategy. Individuals become more inclined to forgo personal interests for the general welfare of society. This situation increases the speed at which helping behavior spreads, as mentioned in our mathematical model, while reducing the rate of abandoning mutual aid.
Conclusion
The mathematical interpretations in this article are an attempt to demonstrate the social benefits and importance of altruism using the language of mathematics. According to our approach, we can accept that the social life we are in is like an object with topological characteristics, and it demonstrates that the understanding of "the help an individual gives returns to the individual" is true. With this interpretation, we can reach the idea that helping others is not only a moral and Islamic behavior, but also a natural consequence of social dynamics. Mathematics, topology, and game theory can help us understand and even predict such social phenomena. However, it should be remembered that these models are simplified representations of real life. They may not always fully reflect all the complex aspects of life. The real world has "frictions", and is often more complex and variable than these models.
In conclusion, seemingly simple individual decisions like Mehmet's decision to donate blood are actually part and result of complex social processes. The spread of helping behavior in society can contribute to the formation of happier and more environmentally conscious social structures, like those in Finland and Scandinavian societies.
References
- Trivers, R. L. (1971). The Evolution of Reciprocal Altruism. The Quarterly Review of Biology, 46(1), 35-57.
- "...Whatever you spend for others (in the way of good), Allah will replace it with better. He is the best of providers." (Surah Saba, verse 39)
- Sterman, J. D. (2000). Business dynamics: Systems thinking and modeling for a complex world. McGraw-Hill.
- Helliwell, J. F., Layard, R., & Sachs, J. D. (2020). World Happiness Report 2020. New York: Sustainable Development Solutions Network.