Richard Loosemore <[EMAIL PROTECTED]> wrote: >"Understanding" 10^9 bits of information is not the same as storing 10^9 >bits of information.
That is true. "Understanding" n bits is the same as compressing some larger training set that has an algorithmic complexity of n bits. Once you have done this, you can use your probability model to make predictions about unseen data generated by the same (unknown) Turing machine as the training data. The closer to n you can compress, the better your predictions will be. I am not sure what it means to "understand" a painting, but let's say that you understand art if you can identify the artists of paintings you haven't seen before with better accuracy than random guessing. The relevant quantity of information is not the number of pixels and resolution, which depend on the limits of the eye, but the (much smaller) number of features that the high level perceptual centers of the brain are capable of distinguishing and storing in memory. (Experiments by Standing and Landauer suggest it is a few bits per second for long term memory, the same rate as language). Then you guess the shortest program that generates a list of feature-artist pairs consistent with your knowledge of art and use it to predict artists given new features. My estimate of 10^9 bits for a language model is based on 4 lines of evidence, one of which is the amount of language you process in a lifetime. This is a rough estimate of course. I estimate 1 GB (8 x 10^9 bits) compressed to 1 bpc (Shannon) and assume you remember a significant fraction of that. Landauer, Tom (1986), “How much do people remember? Some estimates of the quantity of learned information in long term memory”, Cognitive Science (10) pp. 477-493 Shannon, Cluade E. (1950), “Prediction and Entropy of Printed English”, Bell Sys. Tech. J (3) p. 50-64. Standing, L. (1973), “Learning 10,000 Pictures”, Quarterly Journal of Experimental Psychology (25) pp. 207-222. -- Matt Mahoney, [EMAIL PROTECTED] ----- Original Message ---- From: Richard Loosemore <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Wednesday, November 15, 2006 9:33:04 AM Subject: Re: [agi] A question on the symbol-system hypothesis Matt Mahoney wrote: > I will try to answer several posts here. I said that the knowledge > base of an AGI must be opaque because it has 10^9 bits of information, > which is more than a person can comprehend. By opaque, I mean that you > can't do any better by examining or modifying the internal > representation than you could by examining or modifying the training > data. For a text based AI with natural language ability, the 10^9 bits > of training data would be about a gigabyte of text, about 1000 books. Of > course you can sample it, add to it, edit it, search it, run various > tests on it, and so on. What you can't do is read, write, or know all of > it. There is no internal representation that you could convert it to > that would allow you to do these things, because you still have 10^9 > bits of information. It is a limitation of the human brain that it can't > store more information than this. "Understanding" 10^9 bits of information is not the same as storing 10^9 bits of information. A typical painting in the Louvre might be 1 meter on a side. At roughly 16 pixels per millimeter, and a perceivable color depth of about 20 bits that would be about 10^8 bits. If an art specialist knew all about, say, 1000 paintings in the Louvre, that specialist would "understand" a total of about 10^11 bits. You might be inclined to say that not all of those bits count, that many are redundant to "understanding". Exactly. People can easily comprehend 10^9 bits. It makes no sense to argue about degree of comprehension by quoting numbers of bits. Richard Loosemore ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
