So, you’re disagreeing that an algorithm that is optimal, on average, over a set of randomly-selected computable environments, will perform worse in any specific environment than an algorithm optimized specifically for that environment?
Because if not, that’s all I need to make my point, no matter what subtlety of NFL I’m missing. (Actually, I can probably make it with an even weaker premise, and could have gone without NFL altogether, but it grants some insight on the issue I’m trying to illuminate.)
The NFL deals with a space of all possible problems—while the universe typically presents embedded agents with a subset of those problems that are produced by short programs or small mechanisms. So: the NFL theorems rarely apply to the real world. In the real world, there are useful general-purpose compression algorithms.
The NFL deals with a space of all possible problems—while the universe typically presents embedded agents with a subset of those problems that are produced by short programs or small mechanisms.
Okay. I stated the NFL-free version of the premise I need. If you agree with that, this point is moot.
In the real world, there are useful general-purpose compression algorithms.
Now I know I’m definitely not using NFL, because I agree with this and it’s consistent with the point in my initial post.
Yes, there are useful general-purpose programs: because researchers recognize regularities that generally appear across all types of files, which there must be because the raw data is rarely purely random. But they identify this regularity before writing the compressor, which then exploits that regularity by (basically) reserving shorter codes for the kinds of data consistent with that regularity.
Likewise, people have identified regularities specific to video files: each frame is very similar to the last. And regularities specific to picture files: each column or row is very similar to the neighboring.
But what they did not do was write an unbiased, Occamian prior program that went through various files and told them what regularities existed, because finding the shortest compression is uncomputable. Rather, they imported prior knowledge of the distribution of data in certain types of files, gained through some other method (type 2 intelligence in my convention), and tailored the compression algorithm to that distribution.
No “universal, all purpose” algorithm found that knowledge.
So, you’re disagreeing that an algorithm that is optimal, on average, over a set of randomly-selected computable environments, will perform worse in any specific environment than an algorithm optimized specifically for that environment?
Because if not, that’s all I need to make my point, no matter what subtlety of NFL I’m missing. (Actually, I can probably make it with an even weaker premise, and could have gone without NFL altogether, but it grants some insight on the issue I’m trying to illuminate.)
The NFL deals with a space of all possible problems—while the universe typically presents embedded agents with a subset of those problems that are produced by short programs or small mechanisms. So: the NFL theorems rarely apply to the real world. In the real world, there are useful general-purpose compression algorithms.
Okay. I stated the NFL-free version of the premise I need. If you agree with that, this point is moot.
Now I know I’m definitely not using NFL, because I agree with this and it’s consistent with the point in my initial post.
Yes, there are useful general-purpose programs: because researchers recognize regularities that generally appear across all types of files, which there must be because the raw data is rarely purely random. But they identify this regularity before writing the compressor, which then exploits that regularity by (basically) reserving shorter codes for the kinds of data consistent with that regularity.
Likewise, people have identified regularities specific to video files: each frame is very similar to the last. And regularities specific to picture files: each column or row is very similar to the neighboring.
But what they did not do was write an unbiased, Occamian prior program that went through various files and told them what regularities existed, because finding the shortest compression is uncomputable. Rather, they imported prior knowledge of the distribution of data in certain types of files, gained through some other method (type 2 intelligence in my convention), and tailored the compression algorithm to that distribution.
No “universal, all purpose” algorithm found that knowledge.