Richard, what is your definition of "understanding"? How would you test whether a person understands art?
Turing offered a behavioral test for intelligence. My understanding of "understanding" is that it is something that requires intelligence. The connection between intelligence and compression is not obvious. I have summarized the arguments here. http://cs.fit.edu/~mmahoney/compression/rationale.html -- Matt Mahoney, [EMAIL PROTECTED] ----- Original Message ---- From: Richard Loosemore <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Wednesday, November 15, 2006 2:38:49 PM Subject: Re: [agi] A question on the symbol-system hypothesis Matt Mahoney wrote: > 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. Matt, So long as you keep redefining "understand" to mean whatever something trivial (or at least, something different in different circumstances), all you do is reinforce the point I was trying to make. In your definition of "understanding" in the context of art, above, you specifically choose an interpretation that enables you to pick a particular bit rate. But if I chose a different interpretation (and I certainly would - an art historian would never say they understood a painting just because they could tell the artist's style better than a random guess!), I might come up with a different bit rate. And if I chose a sufficiently subtle concept of "understand", I would be unable to come up with *any* bit rate, because that concept of "understand" would not lend itself to any easy bit rate analysis. The lesson? Talking about bits and bit rates is completely pointless .... which was my point. You mainly identify the meaning of "understand" as a variant of the meaning of "compress". I completely reject this - this is the most idiotic development in AI research since the early attempts to do natural language translation using word-by-word lookup tables - and I challenge you to say why anyone could justify reducing the term in such an extreme way. Why have you thrown out the real meaning of "understand" and substituted another meaning? What have we gained by dumbing the concept down? As I said in previously, this is as crazy as redefining the complex concept of "happiness" to be "a warm puppy". Richard Loosemore > 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 > > ----- 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
