The Threshold of Fragility

Certain architectures are, quite literally, doomed to collapse. And the tendency to collapse is usually displayed precisely by the most dynamic, fast, and complex structures. One could say that if the rate of growth in complexity exceeds a certain threshold, the collapse of the system becomes inevitable.

What threatens our contemporary civilization, first and foremost, is not ecological or resource problems, not epidemics and genetic degeneration—though all of this threatens it too. The most inescapable danger lies in the intrinsic, form-defining properties of the civilizational machine itself.

The arrow of our current civilization's development points straight toward the swiftest possible attainment of that level of complexity beyond which inevitable ruin lies.

Here I am reminded of Arthur Clarke's story "The Nine Billion Names of God." In this text, a certain monastic community spends millennia trying to write out all the combinations of a certain number of characters, in order to assemble every possible combination of the name of God. After which, according to their beliefs, the inevitable end of all things must come.

One day the monks hire a group of programmers, and those programmers, quick as anything, in ten lines of code, print out all nine billion of those character combinations on a screen. As the programmers, pleased with the work they have done, are riding home, they watch the stars going out in the sky.

The technicians sped up the monks' work decisively and efficiently. Something similar is happening today with the evolution of our current civilizational space. The more efficiently and impressively our modern specialists work, the closer the world we are used to draws to its natural end.

To designate the threshold beyond which further growth in complexity makes the collapse of a structure unavoidable, I have coined the term "the systems-engineering threshold of fragility."

Imagine a system composed of a multitude of elements. Each of the elements contains a certain amount of uncertainty.

The elements work in concert. They carry out a certain branching tree of interconnected tasks. Each of the elements will perform its task as required of it only in a certain, albeit high, percentage of cases. This is precisely what the uncertainty contained within the element consists of.

If you dispatch a truck full of nails to your client, it may, for one reason or another, fail to reach him. The probability that the truck will not arrive is comparatively small—otherwise no one would order nails from you. But that probability is not zero. And everyone in the world understands this. You, and the client, and the criminal underworld, and the arbitration court. To denote the property of the world under discussion, vulgar people say, "our world isn't perfect."

Imagine that the complexity of the system grows continuously and very rapidly. It is not only the number of elements in the system that grows. Their diversity and connectivity grow as well.

The growth of connectivity leads to objects increasingly conditioning one another's behavior. At the same time, new complex quasi-objects form, possessing an enormous number of external and internal connections. Parallel processes appear, aimed at a single result. The speed of such multitasking processes is very high, but the result depends on the success of each individual process. In general, what occurs is what in our contemporary world is called "the drive for efficiency."
The large gains that come from increased efficiency are immediately spent on raising the scale, variability, and connectivity of the system.

At every cycle of its operation, in each of its new states, such a system has a certain probability of collapse. It is intuitively clear that the higher the connectivity, scale, and variability of such a system, the higher its probability of collapse as well.
The probability of this machine's crash depends, quite literally and directly, on a certain composite index of its complexity. There exists a complexity of the system at which the probability of its collapse will equal one. At such a complexity, the system will begin to crumble of its own accord, without additional external causes. This place in the evolution of the system is what I call "the systems-engineering threshold of fragility."