Warning: This question takes us into VALIS territory, but I wouldn't underestimate the profundity of that particular philosopher.
There is a non-AI definition of intelligence which is simply "information" (see definition 2.3). If that information is active, in terms of utilization, I have to wonder if it might qualify as a form of algorithmic intelligence, regardless of the qualities of the information.
What I'm getting at is that fields such as recreational mathematics often produce techniques and solutions that don't have immediate, real world applications. But there's an adage that pure math tends to find uses.
So you might have algorithms applied to a problems that outside of the problems from which it originated, or that couldn't initially be implemented in a computing context. (Minimax in 1928 might be an example.)
Goal orientation has been widely understood as a fundamental aspect of AI, but in the case of an algorithm designed for one problem, that it subsequently applied to a different problem, the goal may simply be a function of the algorithm's structure. (To understand the goal of minimax precisely, you read the algorithm.)
If you regard this form of information as intelligence, then intelligence can be general, regardless of strength in relation to a given problem.
- Can we consider this form of codification of information to be algorithmic intelligence?
And, just for fun, if a string that encodes a cutting-edge AI is not being processed, does it still qualify as artificial intelligence?