I'm not sure that I get this. Perhaps I understand the maths, but not the point of it. Here are two optimization problems:

1) You have to output 10 million bits. The goal is to output them so that no two consecutive bits are different.

2) You have to output 10 million bits. The goal is to output them so that when interpreted as an MP3 file, they would make a nice sounding song.

Now, the solution space for (1) consists of two possibilities (all 1s, all 0s) out of 2^10000000, for a total of 9,999,999 bits. The solution space for (2) is millions of times wider, leading to fewer bits. However, intuitively, (2) is a much harder problem and things that optimized (2) are actually doing more of the work of intelligence, after all (1) can be achieved in a few lines of code and very little time or space, while (2) takes much more of these resources.