In other words, every entry in the lookup can be mapped to a 0.8 KiB string. That means for any sequence longer than 0.8 KiB, there MUST be a permutation you can make which has no answer (pigeonhole principle). Because so many entries answers long structured sentences, short random ones must mostly be filtered out.
This text itself is past halfway to that limit. If I doubled the length then lookup-only is no longer possible and a logic parser is an absolute must. Applying compression to the query only increases what can be answered by a fixed factor.
I think you’re off by 2 bits (round up and don’t forget to always add 1 at the end), but regardless I think the comparison doesn’t work.
True that it would be comparable in size to a 0.8 KiB string but not necessarily in complexity. If his lookup table didn’t do it by character but by word or sound it could have a ton more information stored there.
Your comment stored as a string isn’t nearly maximally information dense, like you’ve made god’s info
Log2(10^2000) = 6643 bits
In other words, every entry in the lookup can be mapped to a 0.8 KiB string. That means for any sequence longer than 0.8 KiB, there MUST be a permutation you can make which has no answer (pigeonhole principle). Because so many entries answers long structured sentences, short random ones must mostly be filtered out.
This text itself is past halfway to that limit. If I doubled the length then lookup-only is no longer possible and a logic parser is an absolute must. Applying compression to the query only increases what can be answered by a fixed factor.
I think you’re off by 2 bits (round up and don’t forget to always add 1 at the end), but regardless I think the comparison doesn’t work.
True that it would be comparable in size to a 0.8 KiB string but not necessarily in complexity. If his lookup table didn’t do it by character but by word or sound it could have a ton more information stored there.
Your comment stored as a string isn’t nearly maximally information dense, like you’ve made god’s info
Even if you compress it by 99.9% losslessly, it will only make it ≈ 0.8MB, which is big but not that big