Truly nontrivial predictions are those that most will not believe until they come true. We will mostly restrict ourselves to trivial predictions like those above and refrain from too much speculation in form of nontrivial ones. However, we may have a look at previous unexpected scientific breakthroughs and try to discern a pattern, a pattern that may not allow us to precisely predict the details of the next revolution but at least its timing.

## 3.1 A Pattern In The History Of Revolutions?

Let us put the AI-oriented developments [27] discussed above in a broader context, and look at the history of major scientific revolutions and essential historic developments (that is, the subjects of the major chapters in history books) since the beginnings of modern man over 40,000 years ago [30, 31]. Amazingly, they seem to match a binary logarithmic scale marking exponentially declining temporal intervals [31], each half the size of the previous one, and measurable in terms of powers of 2 multiplied by a human lifetime (roughly 80 years—throughout recorded history many individuals have reached this age, although the average lifetime often was shorter, mostly due to high children mortality). It looks as if history itself will *converge* in a historic singularity or Omega point Ω around 2040 (the term *historic singularity* is apparently due to Stanislaw Ulam (1950s) and was popularized by Vernor Vinge [39] in the 1990s). To convince yourself of history's convergence, associate an error bar of not much more than 10 percent with each date below:
1. Ω − 2 9lifetimes: modern humans start colonizing the world from Africa 2. Ω − 2 8lifetimes: bow and arrow invented; hunting revolution 3. Ω−2 7lifetimes: invention of agriculture; first permanent settlements; beginnings of civilization

4. Ω − 2 6lifetimes: first high civilizations (Sumeria, Egypt), and the most important invention of recorded history, namely, the one that made recorded history possible: writing 5. Ω−2 5lifetimes: the ancient Greeks invent democracy and lay the foundations of Western science and art and philosophy, from algorithmic procedures and formal proofs to anatomically perfect sculptures, harmonic music, and organized sports.

Old Testament written (basis of Judaism, Christianity, Islam); major Asian religions founded. High civilizations in China, origin of the first calculation tools, and India, origin of alphabets and the zero 6. Ω − 2 4lifetimes: bookprint (often called the most important invention of the past 2000 years) invented in China. Islamic science and culture start spreading across large parts of the known world (this has sometimes been called the most important event between Antiquity and the age of discoveries)
7. Ω − 2 3lifetimes: the Mongolian Empire, the largest and most dominant empire ever (possibly including most of humanity and the world economy), stretches