The crazy scientist Zhang Kuai built a device that would automatically activate upon his death. Once triggered, the machine would kill someone every second: in the first second, anyone who personally knew Zhang Kuai; in the following seconds, anyone who knew someone who had already been killed. If humanity were completely wiped out, the machine would then self-destruct.
Now, by the seventh second, the machine would blow itself up. Why? This is actually due to the “Six Degrees of Separation” theory.
In real life, humanity is connected through a massive social network. On average, a person may directly know around 200 people, but there’s often overlap — for example, one friend might know 100 of those same 200. To simplify things, let’s use a very conservative estimate: 45. Suppose each person knows 45 people, and each of those 45 knows another 45 unique individuals, and so on. By the sixth step of this chain (not counting the starting point, or “degree zero”), the network already spans nearly the entire human population.
That’s why, by the seventh second, the machine would have no one left to kill — and would self-destruct.
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The crazy scientist Zhang Kuai built a deadly machine that activates upon his death. In the first second, it kills anyone who personally knew him. In following seconds, it kills anyone connected through the social network. By the seventh second, the machine self-destructs because no one is left alive.
A social network is a structure of relationships between people. Each person is represented as a node, and their relationships are shown as edges connecting the nodes. When we look at one person, we can see all their direct connections, forming a web of relationships that extends throughout the entire network.
The Six Degrees of Separation theory suggests that any two people on Earth are connected by at most six intermediate relationships. This means you can reach anyone through a chain of no more than six connections. The theory demonstrates how surprisingly small our world really is when viewed through the lens of social networks.
Let's examine the mathematics of network growth using a conservative estimate of 45 connections per person. Starting with one person, we reach 45 people in the first step. In the second step, we reach 45 squared, which equals 2,025 people. The third step gives us 45 cubed, or 91,125 people. This exponential growth pattern shows how quickly networks expand at each step.
Now let's walk through each second of the machine's operation with precise calculations. In the first second, 45 people die. In the second second, each of those 45 people's connections die, totaling 2,025 deaths. By the third second, we reach 91,125 deaths. The geometric progression continues, with each step multiplying by 45, creating an unstoppable cascade of destruction.