Thoughts on sub-Turing interactive computability

The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new approach would see such resources as external rather than internal to computing devices. They could or should be accounted for explicitly in the antecedents of logical formulas expressing computational problems.