3 ms·

> Wouldn't that be amazing. We know that there's a lower limit to distillation that cannot be breached, "Kolmogorov Complexity", which extends Shannon entropy

> Wouldn't that be amazing. We know that there's a lower limit to distillation that cannot be breached, "Kolmogorov Complexity", which extends Shannon entropy significantly. Furthermore, though this limit is universal, it does (in a well defined way) depend on your prior knowledge. It may seem paradoxical but isn't - it's just too long for this space.... It is not proof in the mathematical sense, mostly because your statement cannot be qualified in such a sense, but it strongly hints that "it would be amazing" because it is impossible. Which is not to say we cannot do better than where we are today; but there is likely no solution that is, along all scenarios, better.

seg_lol 6y ago
You got me to chuckle at, "thought terminating thought experiment". I will file that in my cliché attaché. Are you saying that I am asking for a universal perfect compressor, like I am winning the Hutter Prize [1] ? I don't believe I said that. To add to the tooling, what if the forum itself "learned you", and took that into account when I respond. It would know everything you wrote, potentially everything you read (on this site), and you in turn would know me. It might help mediate a discussion or prevent folks from talking past each other. What if our systems, could allow us to contextualize communication so that it was grounded in the same basis of knowledge as the receiver? Might some of those signaling mechanisms be the norms and affectations of each branch of study? You have given me some things to think about [2] [1] http://prize.hutter1.net/ http://prize.hutter1.net/ [2] http://users.ics.aalto.fi/pkaski/kca/ http://users.ics.aalto.fi/pkaski/kca/ [3] Looks like they have some thought provoking books and interviews https://en.wikipedia.org/wiki/Gregory_Chaitin https://en.wikipedia.org/wiki/Gregory_Chaitin Is Mathematics Invented or Discovered? https://www.youtube.com/watch?v=1RLdSvQ-OF0 https://www.youtube.com/watch?v=1RLdSvQ-OF0 [4] A physicist looks at linguistics through a complexity lens http://www.its.caltech.edu/~matilde/LinguisticsToronto7.pdf http://www.its.caltech.edu/~matilde/LinguisticsToronto7.pdf http://www.its.caltech.edu/~matilde/MOL2019MathLinguisticsSlides.pdf http://www.its.caltech.edu/~matilde/MOL2019MathLinguisticsSl...
- beagle3 6y ago
  I'm not sure how I contributed to your cliche attache, but I'm happy to help :) (The quotes imply it's reference to my words - but I wonder which ones?) > Are you saying that I am asking for a universal perfect compressor, In many ways, I think you are, of the Kolmogorov/Chaitin kind, if you are talking about language (which I thought you were). If you are talking about tooling, that would expand the same text at different level to different readers, then -- I didn't understand that, and that wasn't my response; I'll have to ponder that for a while before I respond. I do think that algorithmic complexity is the right context to consider notation, if that wasn't clear -- not in that we can (or should) distill knowledge to the smallest representation, but in the implications of what different "interpretation machines" (that is, persons reading ...) need in order to understand a notation.

seg_lol 6y ago

You got me to chuckle at, "thought terminating thought experiment". I will file that in my cliché attaché. Are you saying that I am asking for a universal perfect compressor, like I am winning the Hutter Prize [1] ? I don't believe I said that. To add to the tooling, what if the forum itself "learned you", and took that into account when I respond. It would know everything you wrote, potentially everything you read (on this site), and you in turn would know me. It might help mediate a discussion or prevent folks from talking past each other. What if our systems, could allow us to contextualize communication so that it was grounded in the same basis of knowledge as the receiver? Might some of those signaling mechanisms be the norms and affectations of each branch of study? You have given me some things to think about [2] [1] http://prize.hutter1.net/ http://prize.hutter1.net/ [2] http://users.ics.aalto.fi/pkaski/kca/ http://users.ics.aalto.fi/pkaski/kca/ [3] Looks like they have some thought provoking books and interviews https://en.wikipedia.org/wiki/Gregory_Chaitin https://en.wikipedia.org/wiki/Gregory_Chaitin Is Mathematics Invented or Discovered? https://www.youtube.com/watch?v=1RLdSvQ-OF0 https://www.youtube.com/watch?v=1RLdSvQ-OF0 [4] A physicist looks at linguistics through a complexity lens http://www.its.caltech.edu/~matilde/LinguisticsToronto7.pdf http://www.its.caltech.edu/~matilde/LinguisticsToronto7.pdf http://www.its.caltech.edu/~matilde/MOL2019MathLinguisticsSlides.pdf http://www.its.caltech.edu/~matilde/MOL2019MathLinguisticsSl...

beagle3 6y ago
I'm not sure how I contributed to your cliche attache, but I'm happy to help :) (The quotes imply it's reference to my words - but I wonder which ones?) > Are you saying that I am asking for a universal perfect compressor, In many ways, I think you are, of the Kolmogorov/Chaitin kind, if you are talking about language (which I thought you were). If you are talking about tooling, that would expand the same text at different level to different readers, then -- I didn't understand that, and that wasn't my response; I'll have to ponder that for a while before I respond. I do think that algorithmic complexity is the right context to consider notation, if that wasn't clear -- not in that we can (or should) distill knowledge to the smallest representation, but in the implications of what different "interpretation machines" (that is, persons reading ...) need in order to understand a notation.