Knowledge, Information, Compression. Useful?

Knowledge is having a simple representation for complex data. "If you can't explain it simply, you don't understand it well enough." Knowledge is having a lot of data to work with in the first place.

Sometimes, knowledge is only knowledge within a specific domain. I "know" that the sun is hot. Is this fact useful in an elementary school classroom? Yes! Is this fact useful when calculating orbital trajectories and I want to know if my spaceship will burn up? Less so. Nominally, if we consider knowledge to be a justified, true belief, should we expand it to be justified, true, and relevant to the problem at hand? Can you gain new knowledge simply by inspecting what you already know and performing no additional observations?

What is information? Is information simply new knowledge? Is information data that we lack a simple representation for? If so, does information become knowledge through this simplification or is the raw information knowledge enough? Is intelligence the varying levels of ability to simplify?

What is compression? Is compression the difference in complexity between your data and your representation? How do you measure this complexity? Length when written down? Kolmogorov complexity? Are there different types of compression? Is compression in space fundamentally different from compression in time?

How do these things apply to our life? If knowledge is a virtue, getting more will be a combination of information collection and compression. I can find more interesting information by talking to interesting people. I can compress information by having a broad set of potential analogies to make - stemming from a well-rounded background. In short, talk to people and read new books.