System theorists know that it's easy to couple simple-to-understand systems into a "super system" that's capable of displaying behavioral modes that cannot be seen in any of its constituent parts. This is the process called "emergence."

In fact, the very nature of an X-event is that it is both rare and surprising. So I would not say that any specific X-event is likely. What I would say, though, is that some X-event is not only plausible, but very likely in a time scale of a few years.

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.

From the 1990s onward, the financial sector created a vast array of instruments designed to separate investors from their money, financial derivatives of an ever-increasing level of complexity. At some point, this complexity reached a point where even the creators of the derivatives themselves didn't understand them.

My own guess is that quite quickly the machine intelligence will start dreaming machine dreams and thinking machine thoughts, both of which would totally incomprehensible to us. This would then lead to each species, we and the machines, moving off on to its own separate life trajectory.

I think that in the immediate aftermath of a superhuman machine intelligence revealing itself, most people would feel very threatened but take solace in the thought that we can always pull the plug.

To function effectively, the system scientist must know a considerable amount about the natural world AND about mathematics, without being an expert in either field. This is clearly a prescription for career disaster in today's world of ultra-high specialization.