Operative definition of knowledge K about X in a localised region R of spacetime:
Number N of yes/no questions (information) which a blank observer O can confidently answer about X, by having access to R.
Notes:
-Blank observer = no prior exposure to X. Obvious extension to observers which know something already about X.
-Knowledge makes sense only with respect to some entity X, and for a given observer O.
-Access to K in a given R may be very difficult, so an extension of this definition is enforcing a maximum effort E required to extract K. Max N obtained in this way is K.
-Equivalently, this can be defined in terms of probability distributions which are updated after every interaction of O with R.
-This definition requires having access to X, to verify that the content of R is sufficient to unambiguous to answer N questions. As such, it’s not useful to quantify accumulation of knowledge about things we don’t know entirely. But this has to be expected, I’m pretty sure one can map this to the halting problem.
Anyway, in the future it may be handy for instance to quantify if a computer vision system (and which part of it) has knowledge of objects it is classifying, say an apple.
-To make the definition more usable, one can limit the pool of questions and see which fraction of those can be answered by having access to R.
-The number N of questions should be pruned into classes of questions, to avoid infinities. (e.g. does an apple weighs less than 10kg? Less than 10.1kg? Less than 10.2kg? …)
-Mutual information between region and environment: Enforcing a max effort E implies that rocks have small amount of knowledge, since it’s very hard to reverse engineer them.
-Mutual information over digital abstraction layers: The camera cannot answer yes/no questions, so no knowledge. But a human with access to that camera certainly has more knowledge than one without.
-Precipitation of action: Knowledge is with respect to an observer. So no knowledge for the map alone.
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.
I will briefly give it a shot:
Operative definition of knowledge K about X in a localised region R of spacetime:
Number N of yes/no questions (information) which a blank observer O can confidently answer about X, by having access to R.
Notes:
-Blank observer = no prior exposure to X. Obvious extension to observers which know something already about X.
-Knowledge makes sense only with respect to some entity X, and for a given observer O.
-Access to K in a given R may be very difficult, so an extension of this definition is enforcing a maximum effort E required to extract K. Max N obtained in this way is K.
-Equivalently, this can be defined in terms of probability distributions which are updated after every interaction of O with R.
-This definition requires having access to X, to verify that the content of R is sufficient to unambiguous to answer N questions. As such, it’s not useful to quantify accumulation of knowledge about things we don’t know entirely. But this has to be expected, I’m pretty sure one can map this to the halting problem.
Anyway, in the future it may be handy for instance to quantify if a computer vision system (and which part of it) has knowledge of objects it is classifying, say an apple.
-To make the definition more usable, one can limit the pool of questions and see which fraction of those can be answered by having access to R.
-The number N of questions should be pruned into classes of questions, to avoid infinities. (e.g. does an apple weighs less than 10kg? Less than 10.1kg? Less than 10.2kg? …)
Regarding, your attempts at: https://www.lesswrong.com/s/H6kiZXJwYgxZubtmD/p/YdxG2D3bvG5YsuHpG
-Mutual information between region and environment: Enforcing a max effort E implies that rocks have small amount of knowledge, since it’s very hard to reverse engineer them.
-Mutual information over digital abstraction layers: The camera cannot answer yes/no questions, so no knowledge. But a human with access to that camera certainly has more knowledge than one without.
-Precipitation of action: Knowledge is with respect to an observer. So no knowledge for the map alone.
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.