After seeing the success of the integer sequence and the ability of systems to "guess" the function, I would propose a new system that would analogously "guess" one or more "models" of how to produce that sequence, given a "noisy" set of data points. [If this has already been done before, then I'd be interested in links/pointers/references.] Take the following example. A particular human has the capability to run fast for a short while, run further if he/she slows down some, and run even further if he/she slows down a lot. For example, a human might be able to run a 9 second 100 yard dash, or a 3:40 mile, or a 2:10:00 marathon (26 miles). (I apologize for the use of English units -- we're only using units of the "willing", right now!) There might be a variety of physiologic reasons why longer distances require slowing down -- e.g., a variety of energy storage and release mechanisms, where the fastest methods get depleted quickly. One might conceive of a mathematical system that was given various datapoints such as the ones given above, and the system would hypothesize a family of models that "fit" those data points, and might then ask for additional datapoints in order to distinguish the models. Thus, for example, the system might be given one datapoint -- a 9 second 100 yard point. The system would hypothesize that the person runs at a constant speed. You then tell the system that the person runs a 3:40 mile, which is 8 yds/sec versus 11.11 yds/sec for the 100 yard dash. The system then posits some two-level component (smooth) system wherein there are two energy-releasing mechanisms, one fast and one slow, and the fast one "runs out of gas" before the distance of a mile is reached. The system then might ask one or more questions regarding datapoints shorter than 100 yards, intermediate points, or points for distances longer than one mile. If the system is given the marathon datapoint (46,145 yards in 7800 seconds, or 5.92 yards/sec), this point might not introduce more complexity into the system in terms of additional energy systems, but might simply bound the various coefficients more tightly. The idea of this system is not merely to interpolate values, for which there are thousands of different methods, but to come up with one or more "natural" models, which could eventually be used (with much additional research) to start to propose hypotheses about how the human system might actually work, at least in terms of the most important factors for these distances and times. Obvious interpolation schemes would include polynomial and rational functions, sums of exponentials, sums of exponentials times polynomials, etc. I would imagine that such a system ought to be smart enough to "rediscover" a significant number of the simpler "laws of nature" -- e.g., Ohm's law, Colomb's law, etc. Henry