Regards intellectual tasks, things like puzzle solving, algorithm development, general problem solving, etc that's kind of what it is, things requiring mental effort. As for asi it could go from weak asi which is better than the best human genius and prodigy at all tasks but not by much, to the possibility of a qualitative leap in the same manner that evolution produced a qualitative leap over our primate ancestors in humans. In animals with a cortex, it is observed that the greater the neuron count in the cortex the greater the measured level of general intelligence, this is tested with a wide variety of puzzles and tests of varying degrees of complexity. The higher the general intelligence the more complex a problem or puzzle that can be solved by the animal culminating in humans which exhibit a qualitative leap after the scaling that gave rise to the human brain.
To give a hypothetical example of what could be a qualitative leap, it has been seen that people with certain forms of synesthesia exhibit great advantages at certain tasks. A hypothetical superintelligence might be able to control the qualia it experiences, such as we control words, it might control flavors, colors, smells, etc perhaps with elements and even sensations beyond what any of our senses can perceive. It might also be able to communicate using these sensations, not just smells, colors, shapes, tastes, etc but sensations that we can't even imagine or comprehend. Such a language of qualia I've previously called qualiange. Thinking and communicating in qualiange, might allow for unknown benefits we can't currently conceive.
An asi doesn't need to predict the outcome of many complex adaptive systems to any high degree. That might be intractable if Wolfram's irreducible computational complexity idea which affects much of the real world turns out impossible to bypass in principle. There could exist underlying patterns even within pure perfect randomness, but that is doubtful and would be too much to hope for. Asi only needs to be able to develop radical new technologies of unmatched power, to provide a vast advantage. The geniuses of the Manhattan project did not need to predict anything about Germany or Japan during the war to provide the USA with a decisive advantage that lasted decades with their innovation.
My suspicion is given vast similarity is observed across animal cortical tissues, and cortical columns, it is likely that nature came up with what is possibly a theoretically optimal algorithm and has been scaling it up as neuron count increases in an animal's cortex. This algorithm can lead to qualitative leaps with increasing scale as happened in humans. If scaled beyond it may very well lead to additional qualitative leaps and superintelligence. This would need the discovery of the algorithm.
