Lesson plan
Logical depth
Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can recreate a given piece of information. It differs from Kolmogorov complexity in that it considers the computation time of the algorithm with nearly minimal length, rather than the length of the minimal algorithm. Informally, the logical depth of a string x to a significance level s is the time required to compute x by a program no more than s bits longer than the shortest program that computes x . Formally, let p^* be the shortest program that computes a string x on some universal computer U . Then the logical depth of x to the significance level s is given by \text{min}\{T(p): (|p| - |p^*| where T(p) is the number of computation steps that p made on U to produce x and halt.
Article summary
Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can recreate a given piece of information. It differs from Kolmogorov complexity in that it considers the computation time of the algorithm with nearly minimal length, rather than the length of the minimal algorithm. Informally, the logical depth of a string x to a significance level s is the time required to compute x by a program no more than s bits longer than the shortest program that computes x . Formally, let p^* be the shortest program that computes a string x on some universal computer U . Then the logical depth of x to the significance level s is given by \text{min}\{T(p): (|p| - |p^*| where T(p) is the number of computation steps that p made on U to produce x and halt.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.