- Puzzles are problems with a definite answer the only thing that makes them difficult is missing information. The more information, the clearer the solution. These types of problems can generally be solved by consistent and patient hard work. They do not require any particular intellect to solve. Cryptography might be said to be the science of puzzles. Generally I think algorithms can solve puzzles.
- Mysteries are problems whose solution is generally not apparent and may not exist, certainly not a simple solution. Mysteries differ from puzzles in that more information is not always helpful. Solving mysteries usually necesitates skill and experience, and perhaps some genius. Often, mysteries require a narrowing down of available information to find the relevant pieces. I think mysteries may also never have a final completely satisfactory answer. Answers to mysteries are generally phrased in probabilities. Science itself (or perhaps statistical analysis) might be said to be the science of mysteries. I'm not sure if algorithms can so easily be applied to myseries.
[here's the key: I was going to hold off on my analysis for a bit. This is one of those problems my subconscious is so much better at solving than my conscious mind. I guess because it's a mystery and not a puzzle, and my subconscious is exceedingly good at mystery resolution, unlike my conscious mind which always tries to treat a problem like a puzzle.]
But I don't need to hold off, because that's the solution to the mystery. Let's discuss it a little. Mysteries usually are driven by a need, whereas Puzzles are driven by a lack of information. (or inconsistent information structure) The biological systems in our lower-brain are similarly need-driven and so they are fine-tuned to solve mysteries. It is the essence of what our senses do. Contextualize and filter a large amount of information. Puzzles are cortex-issues.
This is actually the answer to Ze Frank's question yesterday: What is consciousness good for? Consciousness solves puzzles. Consciousness cares about why. Subconsciousness cares about what and how--mainly how.
Mysteries require animal-thinking. Puzzles require human-thinking. (surprised that this is at the heart of the science vs. religion debate? it's a puzzle vs. mystery debate at its core.)