In Chapter 26 of the book Artificial Intelligence: A Modern Approach (3rd edition), the textbook discusses "technological singularity". It quotes I.J. Good, who wrote in 1965:
Let an ultra-intelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultra-intelligent machine could design even better machines; there would then unquestionably be an "intelligence explosion," and the intelligence of man would be left far behind. Thus the first ultra-intelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control.
Later on in the textbook, you have this question:
26.7 - I. J. Good claims that intelligence is the most important quality, and that building ultr- intelligent machines will change everything. A sentient cheetah counters that "Actually speed is more important; if we could build ultrafast machines, that would change everything" and a sentient elephant claims "You're both wrong; what we need is ultrastrong machines," What do you think of these arguments?
It seems that the textbook question is an implicit argument against I.J. Good. Good may be treating intelligence as valuable, simply because man's strengths lies in that trait called "intelligence". But other traits could be equally valued instead (speed or strength) and sentient beings may speculate wildly about their preferred traits being "maximized" by some machine or another.
This makes me wonder whether a singularity could occur if we had built machines that were not maximizing intelligence, but instead maximizing some other trait (a machine that is always increasing its strength, or a machine that is always increasing its speed). These types of machines can be just as transformative - ultrafast machines may solve problems quickly due to "brute force", and ultrastrong machines can use its raw power for a variety of physical tasks. Perhaps a ultra-X machine can't build another ultra-X machine (as I.J. Good treated the design of machines as an intellectual activity), but a continually self-improving machine would still leave its creators far behind and force its creators to be dependent on it.
Are technological singularities limited to ultra-intelligences? Or technological singularities be caused by machines that are not "strong AI" but are still "ultra"-optimizers?