Complexity theory studies non-linear emergent phenomena whereby networked interactions produce self-organization at ever higher levels. At certain threshold values of network interactivity certain “jumps” occur – called “saltations” – and the system changes behaviour. Despite the many advocates of complexity theory, the idea is facing many obstacles and often fails to inspire those that it should, people such as evolutionary biologists, neuroscientists, or political scientists. I believe that there are two main reasons for this. The first is cultural. Complexity theory is not being taught, at least not adequately enough, to young students of biology or political science. Their University departments are populated by professors who made their names and careers by following deterministic paths of thinking. As a systems engineer, I was surprised to discover the level of scepticism that complexity theory faces in scientific circles. The culture of engineering is of course different from the culture of science, which may also explain the second reason for the evident mistrust. Engineering is happy when things work. Science is only happy when there is an explanation of why things work. In this sense, complexity theory appears to be “mysterious”. It lacks a fundamental law. In the eyes of a scientist it may just be an alternative, clever mathematical way of describing something very trivial and adequately understood, for example the motion statistics of gas particles, or macroscopic quantum phenomena such as magnetization. And yet, a fundamental law may indeed exist behind saltations: a variant of the second law of thermodynamics, yet to be discovered. If this is proven to b e true, we may be able to explain, inter alia, evolution. Why did life “jump” from bacteria to uni-cellar eukaryotes, and then to multi-cellar organisms? What determined the threshold of biological complexity in order for new life forms, ever more complex, to emerge? The work of microbiologist Carl Woese is of particular importance here. Woese sees bacteria in terms of networked communities rather than individual cells, and interprets their evolutionary history as driven by non-linear self-organization. A worldview based on complexity opens an entirely novel interpretation of natural phenomena. By using computer models to simulate phenomena of emergence we may be doing something a lot more: introducing into the cosmos computations that create new levels of complexity, a genesis of numbers that may lead in the re-programming of life.