I suspect that it’s even worse: that even the concept of correlation of difficulty is irrelevant and misleading. Your illustrations show a range of values for “difficulty for humans” and “difficulty for computers” of around the same scale.
My thesis is that this is completely illusory. I suspect that problems are not 1-dimensional, that their (computational) difficulties can be measured on multiple scales. I further expect that these scales cover many orders of magnitude, and that the range of difficulty that humans find “easy” to “very difficult” covers in most cases one order of magnitude or less. On a logarithmic scale from 0 to 10 for “visual object recognition” capability for example, humans might find 8 easy and 9 difficult, while on a scale of 0 to 10 for “symbolic manipulation” humans might find 0.5 easy (3 items) and 1.5 (30 items) very difficult.
At any given time in our computing technology development, the same narrow range effect occurs, but unlike human ranges they change substantially over time. We build generally faster computers, and all the points move down. We build GPUs, and problems in the “embarrassingly parallel” scales move down even more. We invent better algorithms, and some other set of graphs has its points move down.
Note that the problems (points) in each scale can still have a near-perfect correlation between difficulty for computers and difficulty for humans. In any one scale, problems may lie on a nearly perfectly straight line. Unlike the diagrams in the post though, at any given time there is essentially nothing in the middle. For any given scale, virtually all the data points are off the charts in three of the four quadrants.
The bottom left off-the-scale quadrant is the Boring quadrant, trivial for both humans and computers and of interest to nobody. The top right is the Impossible quadrant, of interest only to science fiction writers. The other two are the Moravec quadrants, trivial for one and essentially impossible for the other.
Over time, the downward motion of points due to technological progress means that now and then the line for some small subclass class of problems briefly overlaps the “human capability” range. Then we get some Interesting problems that are not Moravec! But even in this class, the vast majority of problems are still Boring or Impossible and so invisible. The other classes still have lots of Moravec problems so the “paradox” still holds.
I suspect that it’s even worse: that even the concept of correlation of difficulty is irrelevant and misleading. Your illustrations show a range of values for “difficulty for humans” and “difficulty for computers” of around the same scale.
My thesis is that this is completely illusory. I suspect that problems are not 1-dimensional, that their (computational) difficulties can be measured on multiple scales. I further expect that these scales cover many orders of magnitude, and that the range of difficulty that humans find “easy” to “very difficult” covers in most cases one order of magnitude or less. On a logarithmic scale from 0 to 10 for “visual object recognition” capability for example, humans might find 8 easy and 9 difficult, while on a scale of 0 to 10 for “symbolic manipulation” humans might find 0.5 easy (3 items) and 1.5 (30 items) very difficult.
At any given time in our computing technology development, the same narrow range effect occurs, but unlike human ranges they change substantially over time. We build generally faster computers, and all the points move down. We build GPUs, and problems in the “embarrassingly parallel” scales move down even more. We invent better algorithms, and some other set of graphs has its points move down.
Note that the problems (points) in each scale can still have a near-perfect correlation between difficulty for computers and difficulty for humans. In any one scale, problems may lie on a nearly perfectly straight line. Unlike the diagrams in the post though, at any given time there is essentially nothing in the middle. For any given scale, virtually all the data points are off the charts in three of the four quadrants.
The bottom left off-the-scale quadrant is the Boring quadrant, trivial for both humans and computers and of interest to nobody. The top right is the Impossible quadrant, of interest only to science fiction writers. The other two are the Moravec quadrants, trivial for one and essentially impossible for the other.
Over time, the downward motion of points due to technological progress means that now and then the line for some small subclass class of problems briefly overlaps the “human capability” range. Then we get some Interesting problems that are not Moravec! But even in this class, the vast majority of problems are still Boring or Impossible and so invisible. The other classes still have lots of Moravec problems so the “paradox” still holds.