> > I believe that the precision with which digital computers can do things, > > will allow intelligence to be implemented more simply on them > than in the > > brain. This precision allows entirely different structures and > dynamics to > > be utilized, in digital AGI systems as opposed to brains. For > example, it > > allows correct probabilistic inference calculations (which > humans, at least > > on the conscious level) are miserable at making; it allows compact > > expression of complex procedures as higher-order functions (a > representation > > that is really profoundly unbrainlike); etc. > > > I'd be curious to hear more about what you mean by this last > statement. You are referring to the nature of nesting complex > function calls within one another? > > Brad
No, "higher-order functions" is a technical term from the theory of functional programming. It refers to the use of functions that have functions as arguments. For instance, the derivative operator in calculus is a higher-order function: it maps functions into functions. So, the type of the real function x^2 is R-->R, but the type of the derivative operator is [R-->R]-->[R-->R] so the derivative is a second-order function... Programming languages like Haskell (www.haskell.org) use higher-order functions to achieve remarkably compact programs doing very complex things. These programs are not terribly intuitive to most humans, mainly because our limited "stack size" runs into trouble when dealing with functions deeper than maybe third-order... "Combinatory Logic", invented by Haskell Curry in the 50's, is a foundation for mathematics based on higher-order functions, see e.g. http://www.cwi.nl/~tromp/cl/cl.html The Novamente design involves using higher-order functions to represent complex procedures and patterns. There are a lot of technical advantages to this. For one thing, it allows one to express extremely complex "mathematical" patterns without using any variables.... Having complex patterns expressed with no variables is good for Novamente's reasoning algorithms; variables as used in ordinary non-combinator math would complicate things TERRIBLY (as we discovered in Webmind). Anyway, this is a very deep and technical topic; I introduced it as an example of the kind of direction you can get led in when you think NOT about the human brain but rather about the FUNCTIONS carried out by the brain and how to most effectively carry them out in a digital computer context. Higher-order function representations are not robust in the sense that neural representations probably are: they aren't redundant at all, one error will totally change the meaning. They're not brainlike in any sense. But maybe (if my hypothesis is right) they provide a great foundation for complex procedure learning and pattern recognition in a digital computer context. They seem to integrate very nicely with the other parts of Novamente, anyhow. -- Ben G ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
