Re: [agi] Open Sets vs Closed Sets

[Mike Tintner]

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  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 opera

Re: [agi] Open Sets vs Closed Sets

[David Jones]

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 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 
>  | 
> ModifyYour Subscription
> 
>



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Re: [agi] Open Sets vs Closed Sets

[Mike Tintner]

PS Come to think of it, one can also talk of

open spaces vs closed spaces
open fields vs closed fields (of operation)

a space contains a set, wh. is its contents -  so the conceptual space of 
"chairs" contains a/the set of chairs 

I would go on to talk of every program, machine or agent working and solving 
problems in a "field of operations", wh. always has a physical character , 
whereas spaces are cognitive, abstract entities.

Even if an agent is just thinking about an abstract cognitive space, (like 
"chairs" or "politics"), it is located in a physical field, and its cognitive 
operations take place in a physical medium/field like the brain/computer.

Again, I maintain, nothing in rationality, incl robotics to date AFAIK is 
designed for open sets, spaces or fields. (Of course many will *suggest* they 
are in one way or another, but won't begin to be able to demonstrate it).


From: Jim Bromer 
Sent: Wednesday, June 30, 2010 3:13 PM
To: agi 
Subject: Re: [agi] Open Sets vs Closed Sets


The use of the terminology of mathematics is counter intuitive, if, what you 
want to say is that mathematical methods are inadequate to describe AGI systems 
(or something like that.)
That is what I meant when I said that people don't always mean exactly what 
they seem to be saying.  You are not really defining a mathematical system, and 
you are not trying to conclude that a specific presumption is illogical are 
you?  Or are you?
There is another problem.  We can define sets so we can define things like a 
closed set of sets each containing infinities of objects.

However by qualifying your use of concepts like this and then appealing to a 
reasonable right to be understood as you intended, you can certainly use this 
kind of metaphor.
That's my opinion.
Jim Bromer


 
On Wed, Jun 30, 2010 at 8:58 AM, Mike Tintner  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?

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Re: [agi] Open Sets vs Closed Sets

[Mike Tintner]

Thanks for comment. I intend no comment on any other use of the terms, merely 
to ensure that my use is reasonable and not confusing. And I hope that you & 
others will agree that the conceptual distinction I am making is a fundamental 
and essential one in itself.

Whether you agree that it is fundamental to narrow AI vs AGI is another but 
also v. fundamental matter.I would maintain that there is no method of any kind 
in the whole of rationality - i.e. esp. logic, maths, and computer programming 
- that is designed for, or can deal with open sets (per my term) - and that is 
of extreme importance.


From: Jim Bromer 
Sent: Wednesday, June 30, 2010 3:13 PM
To: agi 
Subject: Re: [agi] Open Sets vs Closed Sets


The use of the terminology of mathematics is counter intuitive, if, what you 
want to say is that mathematical methods are inadequate to describe AGI systems 
(or something like that.)
That is what I meant when I said that people don't always mean exactly what 
they seem to be saying.  You are not really defining a mathematical system, and 
you are not trying to conclude that a specific presumption is illogical are 
you?  Or are you?
There is another problem.  We can define sets so we can define things like a 
closed set of sets each containing infinities of objects.

However by qualifying your use of concepts like this and then appealing to a 
reasonable right to be understood as you intended, you can certainly use this 
kind of metaphor.
That's my opinion.
Jim Bromer


 
On Wed, Jun 30, 2010 at 8:58 AM, Mike Tintner  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   



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Re: [agi] Open Sets vs Closed Sets

[Jim Bromer]

The use of the terminology of mathematics is counter intuitive, if, what you
want to say is that mathematical methods are inadequate to describe AGI
systems (or something like that.)
That is what I meant when I said that people don't always mean exactly what
they seem to be saying.  You are not really defining a mathematical system,
and you are not trying to conclude that a specific presumption is illogical
are you?  Or are you?
There is another problem.  We can define sets so we can define things like a
closed set of sets each containing infinities of objects.

However by qualifying your use of concepts like this and then appealing to a
reasonable right to be understood *as you intended*, you can certainly use
this kind of metaphor.
That's my opinion.
Jim Bromer



On Wed, Jun 30, 2010 at 8:58 AM, Mike Tintner 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 
>  | 
> ModifyYour Subscription
> 
>



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[agi] Open Sets vs Closed Sets

[Mike Tintner]

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
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