Re: [agi] The Math Behind Creativity

[rob levy]

That's interesting, and I think I agree mostly, at least abstractly.  So
this is really just a high-level comment on how to approach creativity,
correct?  I guess the title "Mathematics of Creativity" is what confused
me.  None of this suggests any real mathematical or computational
perspective that will tell us something new or useful (or creative?) about
creativity, right?  Or am I missing something?

On Sun, Jul 25, 2010 at 9:42 PM, Mike Tintner wrote:

>  I wasn't trying for a detailed model of creative thinking with
> explanatory power -  merely one dimension (and indeed a foundation) of it.
>
> In contrast to rational, deterministically programmed computers and robots
> wh. can only operate in closed spaces externally, (artificial environments)
> and only think in closed spaces internally,  human (real AGI) agents are
> designed to operate in the open world externally, (real world environments)
> and to think in open worlds internally.
>
> IOW when you think about any creative problem, like "what am I going to do
> tonight?" or "let me write a post in reply to MT" - you *don't* have a nice
> neat space/frame of options lined up as per a computer program, which your
> brain systematically checks through. You have an open world of associations
> - associated with varying degrees of power - wh. you have to search, or
> since AI has corrupted that word, perhaps we should say "quest" through in
> haphazard, nonsystematic fashion. You have to *explore* your brain for ideas
> - and it is a risky business, wh. (with more difficult problems) may "draw a
> blank".
>
> (Nor BTW does your brain "set up a space" for solving creative problems -
> as was vaguely mooted in a recent discussion with Ben. Closed spaces are
> strictly for rational problems).
>
> IMO though this contrast of narrow AI/rationality as "thinking in closed
> spaces" vs AGI/creativity as "thinking in open worlds" is a very powerful
> one.
>
> Re your examples, I don't think Koestler or Fauconnier are talking of
> "defined" or "closed" spaces.  The latter is v. vague about the nature of
> his spaces. I think they're rather like the "formulae" for creativity that
> our folk culture often talks about. V. loosely. They aren't used in the
> strict senses the terms have in rationality - logic/maths/programming.
>
> Note that Calvin's/Piaget's idea of consciousness as designed for "when you
> don't know what to do" accords with my idea of creative thinking as
> effectively starting from a "blank page" rather than than a ready space of
> options, and going on to explore a world of associations for ideas.
>
> P.S. I should have stressed that the "open world" of the brain is
> **multidomain**, indeed **open-domain" by contrast with the spaces of
> programs wh. are closed, uni-domain. When you search for "what am I going to
> do..?"  your brain can go through an endless world of domains -  movies,call
> a friend, watch TV, browse the net, meal, go for walk, play a sport, ask
> s.o. for novel ideas, spend time with my kid ... and on and on.
>
> The "space thinking" of rationality is superefficient but rigid and useless
> for AGI. The "open world" of the human, creative mind is highly inefficient
> by comparison but superflexible and the only way to do AGI.
>
>
>
>
>  *From:* rob levy 
> *Sent:* Monday, July 26, 2010 1:06 AM
> *To:* agi 
> *Subject:* Re: [agi] The Math Behind Creativity
>
> On Sun, Jul 25, 2010 at 5:05 PM, Mike Tintner wrote:
>
>>  I think it's v. useful - although I was really extending his idea.
>>
>> Correct me - but almost no matter what you guys do, (or anyone in AI does)
>> , you think in terms of spaces, or frames. Spaces of options. Whether you're
>> doing logic, maths, or programs, spaces in one form or other are
>> fundamental.
>>
>> But you won't find anyone - or show me to the contrary - applying spaces
>> to creative problems (or AGI problems). T
>>
>
>
> I guess we may somehow be familiar with different and non-overlapping
> literature, but it seems to me that most or at least many approaches to
> modeling creativity involve a notion of spaces of some kind.  I won't make a
> case to back that up but I will list a few examples: Koestler's bisociation
> is spacial, D. T. Campbell, the Fogels, Finke et al, and William Calvin's
> evolutionary notion of creativity involve a behavioral or conceptual fitness
> landscape, Gilles Fauconnier & Mark Turner's theory of conceptual blending
> on mental space, etc. etc.
>

Re: [agi] The Math Behind Creativity

[Mike Tintner]

I wasn't trying for a detailed model of creative thinking with explanatory 
power -  merely one dimension (and indeed a foundation) of it.

In contrast to rational, deterministically programmed computers and robots wh. 
can only operate in closed spaces externally, (artificial environments) and 
only think in closed spaces internally,  human (real AGI) agents are designed 
to operate in the open world externally, (real world environments) and to think 
in open worlds internally.

IOW when you think about any creative problem, like "what am I going to do 
tonight?" or "let me write a post in reply to MT" - you *don't* have a nice 
neat space/frame of options lined up as per a computer program, which your 
brain systematically checks through. You have an open world of associations - 
associated with varying degrees of power - wh. you have to search, or since AI 
has corrupted that word, perhaps we should say "quest" through in haphazard, 
nonsystematic fashion. You have to *explore* your brain for ideas - and it is a 
risky business, wh. (with more difficult problems) may "draw a blank".

(Nor BTW does your brain "set up a space" for solving creative problems - as 
was vaguely mooted in a recent discussion with Ben. Closed spaces are strictly 
for rational problems).

IMO though this contrast of narrow AI/rationality as "thinking in closed 
spaces" vs AGI/creativity as "thinking in open worlds" is a very powerful one.

Re your examples, I don't think Koestler or Fauconnier are talking of "defined" 
or "closed" spaces.  The latter is v. vague about the nature of his spaces. I 
think they're rather like the "formulae" for creativity that our folk culture 
often talks about. V. loosely. They aren't used in the strict senses the terms 
have in rationality - logic/maths/programming.

Note that Calvin's/Piaget's idea of consciousness as designed for "when you 
don't know what to do" accords with my idea of creative thinking as effectively 
starting from a "blank page" rather than than a ready space of options, and 
going on to explore a world of associations for ideas.

P.S. I should have stressed that the "open world" of the brain is 
**multidomain**, indeed **open-domain" by contrast with the spaces of programs 
wh. are closed, uni-domain. When you search for "what am I going to do..?"  
your brain can go through an endless world of domains -  movies,call a friend, 
watch TV, browse the net, meal, go for walk, play a sport, ask s.o. for novel 
ideas, spend time with my kid ... and on and on.

The "space thinking" of rationality is superefficient but rigid and useless for 
AGI. The "open world" of the human, creative mind is highly inefficient by 
comparison but superflexible and the only way to do AGI.





From: rob levy 
Sent: Monday, July 26, 2010 1:06 AM
To: agi 
Subject: Re: [agi] The Math Behind Creativity


On Sun, Jul 25, 2010 at 5:05 PM, Mike Tintner  wrote:

  I think it's v. useful - although I was really extending his idea.

  Correct me - but almost no matter what you guys do, (or anyone in AI does) , 
you think in terms of spaces, or frames. Spaces of options. Whether you're 
doing logic, maths, or programs, spaces in one form or other are fundamental.

  But you won't find anyone - or show me to the contrary - applying spaces to 
creative problems (or AGI problems). T




I guess we may somehow be familiar with different and non-overlapping 
literature, but it seems to me that most or at least many approaches to 
modeling creativity involve a notion of spaces of some kind.  I won't make a 
case to back that up but I will list a few examples: Koestler's bisociation is 
spacial, D. T. Campbell, the Fogels, Finke et al, and William Calvin's 
evolutionary notion of creativity involve a behavioral or conceptual fitness 
landscape, Gilles Fauconnier & Mark Turner's theory of conceptual blending on 
mental space, etc. etc.


The idea of the website you posted is very lacking in any kind of explanatory 
power in my opinion.  To me any theory of creativity should be able to show how 
a system is able to generate "novel and good" results.  Creativity is more than 
just outside what is known, created, or working.  That is a description of 
novelty, and with no suggestions for the why or how of generating novelty.  
Creativity also requires the semantic potential to reflect on and direct the 
focusing in on the stream of playful novelty to that which is desired or 
considered good.  


I would disagree that creativity is outside the established/known.  A better 
characterization would be that it resides on the complex boundary of the novel 
and the established, which is what make it interesting instead just a copy, or 
just total gobbledygook randomnes

Re: [agi] The Math Behind Creativity

[rob levy]

On Sun, Jul 25, 2010 at 5:05 PM, Mike Tintner wrote:

>  I think it's v. useful - although I was really extending his idea.
>
> Correct me - but almost no matter what you guys do, (or anyone in AI does)
> , you think in terms of spaces, or frames. Spaces of options. Whether you're
> doing logic, maths, or programs, spaces in one form or other are
> fundamental.
>
> But you won't find anyone - or show me to the contrary - applying spaces to
> creative problems (or AGI problems). T
>


I guess we may somehow be familiar with different and non-overlapping
literature, but it seems to me that most or at least many approaches to
modeling creativity involve a notion of spaces of some kind.  I won't make a
case to back that up but I will list a few examples: Koestler's bisociation
is spacial, D. T. Campbell, the Fogels, Finke et al, and William Calvin's
evolutionary notion of creativity involve a behavioral or conceptual fitness
landscape, Gilles Fauconnier & Mark Turner's theory of conceptual blending
on mental space, etc. etc.

The idea of the website you posted is very lacking in any kind of
explanatory power in my opinion.  To me any theory of creativity should be
able to show how a system is able to generate "novel and good" results.
 Creativity is more than just outside what is known, created, or working.
 That is a description of novelty, and with no suggestions for the why or
how of generating novelty.  Creativity also requires the semantic potential
to reflect on and direct the focusing in on the stream of playful novelty to
that which is desired or considered good.

I would disagree that creativity is outside the established/known.  A better
characterization would be that it resides on the complex boundary of the
novel and the established, which is what make it interesting instead just a
copy, or just total gobbledygook randomness.



---
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

Re: [agi] The Math Behind Creativity

[Mike Tintner]

I think it's v. useful - although I was really extending his idea.

Correct me - but almost no matter what you guys do, (or anyone in AI does) , 
you think in terms of spaces, or frames. Spaces of options. Whether you're 
doing logic, maths, or programs, spaces in one form or other are fundamental.

But you won't find anyone - or show me to the contrary - applying spaces to 
creative problems (or AGI problems). T

And what's useful IMO is the idea of **trying** to encompass "the space of 
creative options" - the options for any creative problem [wh can be as simple 
or complex as "what shall we have to eat tonight?" or "how do we reform the 
banks?" or  "what do you think of the state of AGI?" ]. 

It's only when you **try** to formalise creativity , that you realise it can't 
be done in any practical, programmable way - or formal way. You can only do it 
conceptually. Informally. 

The options are infinite, or, at any rate, "practically endless." - and 
infinite not just in number, but in *diversity*, in endlessly proliferating 
*domains* and categories extending right across the world.

**And this is the case for every creative problem - every AGI problem**   (one 
reason why you won't find anyone in the field of AGI, actually doing AGI, only 
narrow AI gestures at the goal).  

It's only when you attempt - and fail - to formalise the space of creativity, 
that the meaning of "there are infinite creative options" really comes home. 
And you should be able to start to see why narrow AI and AGI are fundamentally 
opposite affairs - thinking in "closed spaces" vs thinking in "open worlds".

{It is fundamental BTW to the method of rationality - and rationalisation - 
epitomised in current programming - to create and think in a closed space of 
options, wh. is always artificial in nature].




From: rob levy 
Sent: Sunday, July 25, 2010 9:16 PM
To: agi 
Subject: Re: [agi] The Math Behind Creativity


Not sure how that is useful, or even how it relates to creativity if considered 
as an informal description?


On Sun, Jul 25, 2010 at 10:15 AM, Mike Tintner  wrote:

  I came across this, thinking it was going to be an example of maths fantasy, 
but actually it has a rather nice idea about the mathematics of creativity.

  
  The Math Behind Creativity
  By Chuck Scott on June 15, 2010

  The Science of Creativity is based on the following mathematical formula for 
Creativity:



  In other words, Creativity is equal to infinity minus the area of a defined 
circle of what’s working. 

  Note:  is the geometric formula for calculating the area of a circle; where  
is 3.142 rounded to the nearest thousandth, and R is a circle’s radius (the 
length from a circle’s center to edge).



  **

  Simply, it's saying - that for every problem, and ultimately that's not just 
creative but rational problems, there's a definable space of options - the 
spaces you guys work with in your programs - wh. may work, if the problem is 
rational, but normally don't if it's creative. And beyond that space is the 
undefined space of creativity, wh. encompasses the entire world in an infinity 
of combinations. (Or all the fabulous multiverse[s] of Ben's mind).  Creative 
ideas - and that can be small everyday ideas as well as large cultural ones - 
can come from anywhere in, and any combinations of, the entire world (incl 
butterflies in Brazil and caterpillars in Katmandu -  QED I just drew that last 
phrase off the cuff from that vast world). Creative thinking - and that incl. 
the thinking of all humans from children on - is "what in the world ?" 
thinking - that can and does draw upon the infinite resources of the world. 
"What in the world is he on about?" "Where in the world will I find s.o. 
who..?" "What in the world could be of help here?"

  And that is another way of highlighting the absurdity of current approaches 
to AGI - that would seek to encompass the entire world of creative 
ideas/options in the infinitesimal spaces/options of programs.





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

Re: [agi] The Math Behind Creativity

[rob levy]

Not sure how that is useful, or even how it relates to creativity if
considered as an informal description?

On Sun, Jul 25, 2010 at 10:15 AM, Mike Tintner wrote:

>  I came across this, thinking it was going to be an example of maths
> fantasy, but actually it has a rather nice idea about the mathematics of
> creativity.
>
> 
> The Math Behind Creativity 
>
> By Chuck Scott  on June 15,
> 2010
>
> The Science of Creativity is based on the following mathematical formula
> for Creativity:
>
> [image: C = {infty} - {pi}R^2]
>
> In other words, Creativity is equal to infinity minus the area of a defined
> circle of what’s working.
>
> Note: [image: {pi}R^2] is the geometric formula for calculating the area
> of a circle; where [image: pi] is 3.142 rounded to the nearest thousandth,
> and R is a circle’s radius (the length from a circle’s center to edge).
>
>
>
> **
>
> Simply, it's saying - that for every problem, and ultimately that's not
> just creative but rational problems, there's a definable space of options -
> the spaces you guys work with in your programs - wh. may work, if the
> problem is rational, but normally don't if it's creative. And beyond that
> space is the undefined space of creativity, wh. encompasses the entire world
> in an infinity of combinations. (Or all the fabulous multiverse[s] of Ben's
> mind).  Creative ideas - and that can be small everyday ideas as well as
> large cultural ones - can come from anywhere in, and any combinations of,
> the entire world (incl butterflies in Brazil and caterpillars in Katmandu -
> QED I just drew that last phrase off the cuff from that vast world).
> Creative thinking - and that incl. the thinking of all humans from children
> on - is "what in the world ?" thinking - that can and does draw upon the
> infinite resources of the world. "What in the world is he on about?" "Where
> in the world will I find s.o. who..?" "What in the world could be of help
> here?"
>
> And that is another way of highlighting the absurdity of current approaches
> to AGI - that would seek to encompass the entire world of creative
> ideas/options in the infinitesimal spaces/options of programs.
>
>
>
>
>*agi* | Archives 
>  | 
> ModifyYour 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
<><><>

[agi] The Math Behind Creativity

[Mike Tintner]

I came across this, thinking it was going to be an example of maths fantasy, 
but actually it has a rather nice idea about the mathematics of creativity.


The Math Behind Creativity
By Chuck Scott on June 15, 2010

The Science of Creativity is based on the following mathematical formula for 
Creativity:



In other words, Creativity is equal to infinity minus the area of a defined 
circle of what's working. 

Note:  is the geometric formula for calculating the area of a circle; where  is 
3.142 rounded to the nearest thousandth, and R is a circle's radius (the length 
from a circle's center to edge).



**

Simply, it's saying - that for every problem, and ultimately that's not just 
creative but rational problems, there's a definable space of options - the 
spaces you guys work with in your programs - wh. may work, if the problem is 
rational, but normally don't if it's creative. And beyond that space is the 
undefined space of creativity, wh. encompasses the entire world in an infinity 
of combinations. (Or all the fabulous multiverse[s] of Ben's mind).  Creative 
ideas - and that can be small everyday ideas as well as large cultural ones - 
can come from anywhere in, and any combinations of, the entire world (incl 
butterflies in Brazil and caterpillars in Katmandu -  QED I just drew that last 
phrase off the cuff from that vast world). Creative thinking - and that incl. 
the thinking of all humans from children on - is "what in the world ?" 
thinking - that can and does draw upon the infinite resources of the world. 
"What in the world is he on about?" "Where in the world will I find s.o. 
who..?" "What in the world could be of help here?"

And that is another way of highlighting the absurdity of current approaches to 
AGI - that would seek to encompass the entire world of creative ideas/options 
in the infinitesimal spaces/options of programs.







---
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
<><><>