Well, first, you're not dealing with open sets in my broad sense - containing a potentially unlimited number of different SPECIES of things.
[N.B. Extension to my definitions here - I should have added that all members of a set have fundamental SIMILARITIES or RELATIONSHIPS - and the set is constrained. An open set does not incl. "everything under the sun" (unless that is the title of the set). So a set may be "everything in that room" or "that street" or "text" but will not incl. "everything under the sun"] With respect to your example, a relevant broadly open-species set then might be "regular shapes" or "geometric shapes" incl. most shapes in geometry, (or if you prefer, more limited sections of geometry) - where "species" = different kinds of shapes - squares, triangles,fractals etc. I can't see how your work with squares will prepare you to deal with a broad range of geometric shapes - please explain. AFAICT you have take a very closed geometric space/set. More narrowly, you raise a v. interesting question. Let us take a set of just one or a v. few objects, as you seem to be doing - say one or two black squares. The relevant set then is something like "all the positionings [or movements] of two black squares within a given area [like a screen]". The set is principally one of square positions. You make the bold claim:"I can define an infinite number of ways in which a 0 to infinite number of black squares can move." - Are you then saying your program can deal with every positioning/configuration of two squares on a screen? [I'm making this simple as pos]. I would say;"no way. That is an open set of positions. And one can talk of different "species" of positions [tho I must say I haven't thought much about this]" And this is a subject IMO of central AGI importance - the predictability of object positions and movements. If you could solve this, your program would in fairly shortly order become a great inventor - for finding new ways to position and apply objects is central to a vast amount of invention. But it is absolutely,impossible to do what you're claiming - there are an infinity of non-formulaic, non-predictable - and therefore always new - ways to position objects - and that's why invention (and coming up with the idea of Chicken Kiev - putting the gravy inside instead of outside the food] is so hard. We're talking here about the fundamental nature of objects and space. From: David Jones Sent: Friday, July 02, 2010 1:53 PM To: agi Subject: Re: [agi] Open Sets vs Closed Sets narrow AI is a term that describes the solution to a problem, not the problem. It is a solution with a narrow scope. General AI on the other hand should have a much larger scope than narrow ai and be able to handle unforseen circumstances. What I don't think you realize is that open sets can be described by closed sets. Here is an example from my own research. The set of objects I'm allowing in the simplest case studies so far are black squares. This is a closed set. But, the number, movement and relative positions of these squares is an open set. I can define an infinite number of ways in which a 0 to infinite number of black squares can move. If I define a general AI algorithm, it should be able to handle the infinite subset of the open set that is representative of some aspect of the real world. We could also study case studies that are not representative of the environment though. The example I just gave is a completely open set, yet an algorithm could handle such an open set, and I am designing for it. So, your claim that no one is studying or handling such things is not right. Dave On Wed, Jun 30, 2010 at 8:58 AM, Mike Tintner <[email protected]> wrote: I'd like opinions on terminology here. IMO the opposition of closed sets vs open sets is fundamental to the difference between narrow AI and AGI. However I notice that these terms have different meanings to mine in maths. What I mean is: closed set: contains a definable number and *kinds/species* of objects open set: contains an undefinable number and *kinds/species* of objects (what we in casual, careless conversation describe as containing "all kinds of things"); the rules of an open set allow adding new kinds of things ad infinitum Narrow AI's operate in artificial environments containing closed sets of objects - all of wh. are definable. AGI's operate in real world environments containing open sets of objects - some of wh. will be definable, and some definitely not To engage in any real world activity, like "walking down a street" or "searching/tidying a room" or "reading a science book/text" is to operate with open sets of objects, because the next field of operations - the next street or room or text - may and almost certainly will have unpredictably different kinds of objects from the last. Any objections to my use of these terms, or suggestions that I should use others? agi | Archives | Modify Your Subscription agi | Archives | Modify Your Subscription ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
