Even if a computer simulated the universe, and even if it located earth, and even if it found a text titled “Finnegans Wake,” there a very large number of things that, throughout the universe, might be titled Finnegans Wake! So the computer would still need some algorithm to recognize the right Finnegans Wake.
So, universe-independent compression is where it’s at.
What do you think about the conditional K-complexity of everyday things? For example, does knowing Finnegans Wake help a lot with compressing War and Peace?
If I got to call substrings of Finnegans Wake when writing a computer program that generated War and Peace, I can see how that would make it shorter. Every time they shared a phrase longer than the call to Finnegans Wake, I could just call Finnegan’s wake, for example. But it wouldn’t save very much, I’d think.
On the other hand, a program that spat out both books could be much shorter than two programs for one book each, by some amount related to how much repetition there was.
Yes, definitely. A simple example: one tool that will be useful to compress FW is just a dictionary (or index) of English words. Instead of encoding the letters of a word, you encode the index of the word in the list, and save bits by doing so.
You have to pay an up-front cost to encode the dictionary itself, but it should still be worthwhile overall, even for a single novel. Now when you compress two novels together, you get the benefit of the dictionary for the second novel without having to repay the upfront cost.
Yes, of course. But I was thinking of a more substantial savings. The question is more like, does Finnegans Wake represent a sort of pointer to our branch of the multiverse, which you could use to compress War and Peace down to a couple kilobytes? How much “entanglement” is there?
Even if a computer simulated the universe, and even if it located earth, and even if it found a text titled “Finnegans Wake,” there a very large number of things that, throughout the universe, might be titled Finnegans Wake! So the computer would still need some algorithm to recognize the right Finnegans Wake.
So, universe-independent compression is where it’s at.
What do you think about the conditional K-complexity of everyday things? For example, does knowing Finnegans Wake help a lot with compressing War and Peace?
If I got to call substrings of Finnegans Wake when writing a computer program that generated War and Peace, I can see how that would make it shorter. Every time they shared a phrase longer than the call to Finnegans Wake, I could just call Finnegan’s wake, for example. But it wouldn’t save very much, I’d think.
On the other hand, a program that spat out both books could be much shorter than two programs for one book each, by some amount related to how much repetition there was.
Yes, definitely. A simple example: one tool that will be useful to compress FW is just a dictionary (or index) of English words. Instead of encoding the letters of a word, you encode the index of the word in the list, and save bits by doing so. You have to pay an up-front cost to encode the dictionary itself, but it should still be worthwhile overall, even for a single novel. Now when you compress two novels together, you get the benefit of the dictionary for the second novel without having to repay the upfront cost.
Yes, of course. But I was thinking of a more substantial savings. The question is more like, does Finnegans Wake represent a sort of pointer to our branch of the multiverse, which you could use to compress War and Peace down to a couple kilobytes? How much “entanglement” is there?
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