Yeah nice, thank you for thinking about this and writing this comment, Lorenzo.
an extension of this definition is enforcing a maximum effort E required to extract K
I think this is really spot on. Suppose that I compare the knowledge in (1) a Chemistry textbook, (2) a set of journal papers from which one could, in principle, work out everything from the textbook, (3) the raw experimental data from which one could, in principle, work out everything from the journal papers, (4) the physical apparatus and materials from which one could, in principle, extract all the raw experimental data by actually performing experiments. I think that the number of yes/no questions that one can answer given access to (4) is greater than the number of yes/no questions that one can answer given access to (3), and so on for (2) and (1) also. But answering questions based on (4) requires more effort than (3), which requires more effort than (2), which requires more effort than (1).
We must also somehow quantify the usefulness or generality of the questions that we are answering. There are many yes/no questions that we can answer easily with access to (4), such as “what is the distance between this particular object and this other particular object?”, or “how much does this particular object weigh?”. But if we are attempting to make decisions in service of a goal, the kind of questions we want to answer are more like “what series of chemical reactions must I perform to create this particular molecule?” and here the textbook can give answers with much lower effort than the raw experimental data or the raw materials.
Would be very interested in your thoughts on how to define effort, and how to define this generality/usefulness thing.
Yeah nice, thank you for thinking about this and writing this comment, Lorenzo.
I think this is really spot on. Suppose that I compare the knowledge in (1) a Chemistry textbook, (2) a set of journal papers from which one could, in principle, work out everything from the textbook, (3) the raw experimental data from which one could, in principle, work out everything from the journal papers, (4) the physical apparatus and materials from which one could, in principle, extract all the raw experimental data by actually performing experiments. I think that the number of yes/no questions that one can answer given access to (4) is greater than the number of yes/no questions that one can answer given access to (3), and so on for (2) and (1) also. But answering questions based on (4) requires more effort than (3), which requires more effort than (2), which requires more effort than (1).
We must also somehow quantify the usefulness or generality of the questions that we are answering. There are many yes/no questions that we can answer easily with access to (4), such as “what is the distance between this particular object and this other particular object?”, or “how much does this particular object weigh?”. But if we are attempting to make decisions in service of a goal, the kind of questions we want to answer are more like “what series of chemical reactions must I perform to create this particular molecule?” and here the textbook can give answers with much lower effort than the raw experimental data or the raw materials.
Would be very interested in your thoughts on how to define effort, and how to define this generality/usefulness thing.