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[Does] information content scale linearly with length, regardless of topic? Information content pretty clearly doesn't scale linearly with length. I used to joke that The Scarlet Letter author...
Answer
#1: Initial revision
by
Michael
·
2024-03-06T21:05:07Z (2 months ago)
> ### [Does] information content scale linearly with length, regardless of topic? Information content pretty clearly doesn't scale linearly with length. I used to joke that The Scarlet Letter author wrote everything at least three times, so you only needed to read 30% of the words to understand what was happening.[^hawthorne] Consider this extremely contrived "information:" ``` AAAAAAAAAAAAAAAAAAAA ``` Rewriting it as "20 As" loses no information, and it's lots shorter. But only the context determines what the effect of shortening it further to "As" might be. > ### Can you summarize any explanation? No. At some point, there will be a case "where the information loss is catastrophic" as you put it. Determining the catastrophic case is the tricky part. Catastrophic for what? If you're making a tire for a wheel that is 1 meter in diameter, the tire's inner edge needs to be π meters, or 3.14159… meters. How important the extra digits are depends on your tools, the stretchiness of your tire material, and so on. > “…the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” _Albert Einstein, 1933_ [^hawthorne]: Literature fans: Please don't hate me. Instead, suggest a Unicode character to wear in penance.