tephen Harris < XXXX@XXXXX.COM > wrote or quoted:
The claim was that an increase in the complexity of the primitives
is *necessary* for higher-order emergent properties to emerge:
``Ansatz. Given an appropriate simulation framework, an appropriate
increase of the object complexity of the primitives is necessary and
sufficient for generation of successively higher-order emergent
properties through aggregation.
Once a particular dynamical systems framework has been chosen, our
ansatz states that additional object complexity is necessary for
producing additional levels in a dynamical hierarchy.''
- http://mitpress.mit.edu/journals/pdf/alife_7_4_329_0.pdf
The paper was cited as claiming:
``(Rasmussen et al. 2001a) propose that it may be impossible to
extend the levels in a hierarchy, without adding to the complexity
of the base units.''
Note use of the term "impossible". That claim *does* seem to be
what the paper is saying in the section quoted above.
IMO, Turing completeness of simple systems like the GOL illustrates
that the idea not correct - and I can't see how the paragraph above
rescues the thesis - except by contradicting it :-(
--
__________
|im |yler http://timtyler.org/ XXXX@XXXXX.COM Remove lock to reply.
state of the art on dynamical hierarchies Turing
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Re: state of the art on dynamical hierarchies Turing
by Tim Tyler » Sat, 23 Apr 2005 18:59:24 GMT
Re: state of the art on dynamical hierarchies Turing
by Stephen Harris » Sun, 24 Apr 2005 04:08:19 GMT
"Tim Tyler" < XXXX@XXXXX.COM > wrote in message news: XXXX@XXXXX.COM ...
Your quote of the word "impossible" does not come from alife*pdf.
It comes from
http://www.csse.monash.edu.au/~aland/PAPERS/dynHier_ALIFE8_WWW.pdf
where the authors are summarizing their interpretation of Rasmussen, not
quoting him.
I did not find the word "impossible" in Rasmussen's Ansatz paper.
Rasmussen writes in the early part of that paper:
and in the same paper:
I think Rasmussen views this as a clarification, not a contradiction. It
seems
to me Rasmussen is saying that prediction is not available to the simple
cellular automata rules, but if the primitives are orignally formulated in a
more complex form, then some element of prediction can be extracted.
abstract:
"Second, we demonstrate how the framework for dynamical hierarchies
can be used for realistic (predictive) physicochemical simulation
of molecular self-assembly and self-organization processes."
SH: Rasmussen is not making any claim that his complex primitive
approach transcends the potential production range of simple CA rules
or with denying Turing equivalence. Rasmussen is saying his method
permits some degree of prediction which is not available to *humans*
using the simpler primitives that require more *human* extrapolation.
Human ability to predict new states is not the same as creating new states
and does not constrain simple rules from achieving more complex states.
Rasmussen's idea has nothing to do with Turing equivalence which is
why he calls it an "apparent contradiction". His idea is vulnerable to
contesting that more complex primitives enable prediction. How does
one know how to suitably complexify the primitives? I haven't seen
any consensus that his idea won't work. Mainly the paper by McMullin.
I've often seen it claimed that Nature has a natural hierarchy. Going back
to Wolfram's hunch that a simple CA rule could have evolved the universe.
First one needed the temp{*filter*}evolution of stars before those stars could
supernova and create the elements necessary for life and life seems a more
complex aspect in the scheme of things by human reckoning. This statement
that you chose to quote seems just about obviously true to me. I think the
keyword in the quote is "additional".
S. Rasmussen et al. Ansatz for Dynamical Hierarchies:
2.1 Physico-Chemical Examples
"The dynamical hierarchies we are going to discuss have the following
properties. We start by identifying a collection of objects (perhaps
heterogeneous) and a set of dyamical rules for how those objects interact
as a ?rst "level" of phenomena. In reality, the ?rst-order objects may well
have internal structure and their interactions might well be explainable in
terms of more fundamental interactions among the components of these
objects. But we have to start our analysis somewhere, so when we identify a
dynamical hierarchy we treat the ?rst-order objects and their interactions
asif axomatically given. Now, the dynamics of the ?rst-order objects
creates various kinds of new, second-order objects, typically formed as
certain kinds of aggregates of ?rst-order objects. These second-order
objects have new kinds of properties, not present in the ?rst-order objects,
including new kinds of interactions with other second-order objects and/or
?rst-order objects. Intuitively speaking, second-order objects have emergent
second-order
Your quote of the word "impossible" does not come from alife*pdf.
It comes from
http://www.csse.monash.edu.au/~aland/PAPERS/dynHier_ALIFE8_WWW.pdf
where the authors are summarizing their interpretation of Rasmussen, not
quoting him.
I did not find the word "impossible" in Rasmussen's Ansatz paper.
Rasmussen writes in the early part of that paper:
and in the same paper:
I think Rasmussen views this as a clarification, not a contradiction. It
seems
to me Rasmussen is saying that prediction is not available to the simple
cellular automata rules, but if the primitives are orignally formulated in a
more complex form, then some element of prediction can be extracted.
abstract:
"Second, we demonstrate how the framework for dynamical hierarchies
can be used for realistic (predictive) physicochemical simulation
of molecular self-assembly and self-organization processes."
SH: Rasmussen is not making any claim that his complex primitive
approach transcends the potential production range of simple CA rules
or with denying Turing equivalence. Rasmussen is saying his method
permits some degree of prediction which is not available to *humans*
using the simpler primitives that require more *human* extrapolation.
Human ability to predict new states is not the same as creating new states
and does not constrain simple rules from achieving more complex states.
Rasmussen's idea has nothing to do with Turing equivalence which is
why he calls it an "apparent contradiction". His idea is vulnerable to
contesting that more complex primitives enable prediction. How does
one know how to suitably complexify the primitives? I haven't seen
any consensus that his idea won't work. Mainly the paper by McMullin.
I've often seen it claimed that Nature has a natural hierarchy. Going back
to Wolfram's hunch that a simple CA rule could have evolved the universe.
First one needed the temp{*filter*}evolution of stars before those stars could
supernova and create the elements necessary for life and life seems a more
complex aspect in the scheme of things by human reckoning. This statement
that you chose to quote seems just about obviously true to me. I think the
keyword in the quote is "additional".
S. Rasmussen et al. Ansatz for Dynamical Hierarchies:
2.1 Physico-Chemical Examples
"The dynamical hierarchies we are going to discuss have the following
properties. We start by identifying a collection of objects (perhaps
heterogeneous) and a set of dyamical rules for how those objects interact
as a ?rst "level" of phenomena. In reality, the ?rst-order objects may well
have internal structure and their interactions might well be explainable in
terms of more fundamental interactions among the components of these
objects. But we have to start our analysis somewhere, so when we identify a
dynamical hierarchy we treat the ?rst-order objects and their interactions
asif axomatically given. Now, the dynamics of the ?rst-order objects
creates various kinds of new, second-order objects, typically formed as
certain kinds of aggregates of ?rst-order objects. These second-order
objects have new kinds of properties, not present in the ?rst-order objects,
including new kinds of interactions with other second-order objects and/or
?rst-order objects. Intuitively speaking, second-order objects have emergent
second-order
Re: state of the art on dynamical hierarchies Turing
by Stephen Harris » Sun, 24 Apr 2005 08:57:18 GMT
Well, Dorin interprets Rasmussen's paper as claiming "impossible". That is not what Rasmussen says. My impression is that he (R) is saying something similar to a high-level description like in C++ is easier for programmers to understand and work with/predict than machine language, not that C++ and machine language have a different range of possible programs. But this analogy is not exactly on target. Nor do I think Rasmussen means that discussing the gold standard, paper money and economics, doesn't require understanding photosyntheis to make trees to make paper or understanding the atomic weight of gold. His idea seems more concrete than making an abstraction level distinction. I meant to give links to my research in this topic for other people to follow in case they were interested. I notice I made a typo: "I became intrigued with this topic and *proved my notes, for those interested, below." I meant provide, not *proved. I didn't attempt to prove that the ideas presented by the various authors were consistent when I included those various urls in an early post. Regards, Stephen
Re: state of the art on dynamical hierarchies Turing
by Stephen Harris » Mon, 25 Apr 2005 04:08:30 GMT
http://www.**--****.com/ (1994) "The essential idea of moving up the hierarchy is that the symmetries assumed by the agent are broken by the data when reconstruction leads to an infinite model at some level of representation ... The key step to innovating a new model class is the discovery of new equivalence relationship. This interpretation provides a more elaborate definition of emergence: A process undergoes emergence if at some point the architecture of information processing has changed in such a way that a distinct and more powerful level of intrinsic computation has appeared that was not present in earlier conditions." SH: This definition by Crutchfield does not apparently violate Turing equivalence. So when Rasmussen advances the idea of designing a CA with more complex primitives it no more repudiates Turing equivalence than Crutchfields' description does. Regards, Stephen
Re: state of the art on dynamical hierarchies Turing
by Tim Tyler » Mon, 25 Apr 2005 20:03:59 GMT
Stephen Harris < XXXX@XXXXX.COM > wrote or quoted: A lot of words - do they mean anything? Conventionally, emergence is about the appearance of qualitatively new sorts of behaviour - and does not require that there's anything "more powerful" about them. -- __________ |im |yler http://www.**--****.com/ @XXXXX.COM Remove lock to reply.
Re: state of the art on dynamical hierarchies Turing
by Tim Tyler » Mon, 25 Apr 2005 20:21:16 GMT
Stephen Harris < XXXX@XXXXX.COM > wrote or quoted: [An Alan Dorin & Jon McCormack paper says:] [...] [...] Well, that was where I came in, wasn't it? The top of this post has the "impossible" quote. I noticed it was bogus, tracked down the reference - and found that it's thesis was: ``Ansatz. Given an appropriate simulation framework, an appropriate increase of the object complexity of the primitives is necessary and sufficient for generation of successively higher-order emergent properties through aggregation.'' If that paper doen't *actually* mean that an increase in the complexity of the base units is necessary for the generation of successively higher-order emergent structures, it is /extremely/ easy for me to understand how those citing the paper /thought/ that it was making that claim. Anyway, the idea under discussion: ``that it may be impossible to extend the levels in a hierarchy, without adding to the complexity of the base units'' ...has turned out to be a bogus one - as I think you agree. Whether the Rasmussen paper cited as the source of the notion is being deliberately obtuse, has suffered in translation, was misleading by accident, or was simply misinterpreted, I'll avoid going into further. -- __________ |im |yler http://www.**--****.com/ @XXXXX.COM Remove lock to reply.
Re: state of the art on dynamical hierarchies Turing
by Stephen Harris » Mon, 25 Apr 2005 21:54:54 GMT
"Tim Tyler" < XXXX@XXXXX.COM > wrote in message news: XXXX@XXXXX.COM ...
What you call conventionally, Crutchfield describes as the intuitive
definition of emergence, which along with pattern formation doesn't fit
the requirements for defining what he calls intrinsic/operational emergence.
http://www.calresco.org/offline.htm
Is Anything Ever New ? : Considering Emergence
Jim Crutchfield (64k ps.z) Abstract:
"A synthesis of tools from dynamical systems, computation and
inductive inference is used to outline how we can discover
'novelty in our world, ideas that go beyond our current
understanding. Extrinsic emergence (with respect to an
external observer) is contrasted with Intrinsic emergence
(meaningful in terms of the system itself)".
Is Anything Ever New ? : Considering Emergence, page 10
"The arguments to this point can be recapitulated by an
operational definition of emergence. A process undergoes
emergence if at some time the architecture of information
processing has changed in such a way that a distinct and
more powerful level of intrinsic computation has appeared
that was not present in earlier conditions. It seems, upon
reflection, that our intuitive notion of emergence is not
captured by the "intuitive definition" given in the first
section. Nor is it captured by the somewhat refined notion
of pattern formation. "Emergence" is meaningless unless it
is defined within the context of processes themselves; the
only wellefined notion of emergence would seem to be
intrinsic emergence. Why? Simply because emergence defined
without this closure leads to an infinite regress of observers
detecting patterns of observers detecting patterns .... This
is not a satisfactory definition, since it is not finite. The
regress must be folded into the system, it must be immanent
in the dynamics. When this happens complexity and structure
are no longer referred outside, no longer relative and
arbitrary; they take on internal meaning and functionality."
SH: I think he uses "more powerful" in the same sense that
a more complex logic* is considered more powerful. I think
that founders in the CA field who have garnered enough
respect to head their own departments have earned the
right to have their views listened to carefully. Normally,
they will have thought about issues which have not occurred
to their less educated, less philosophically precise readers.
*"We will then move on to take a preliminary look at the
language of first-order predicate logic ("quantification theory").
This is the logically richer language that results from the
augmentation of sentential logic by incorporating into our
logical formalism the means to express structure of two
additional sorts:
(i) that associated with quantity (as is accomplished, e.g.,
with such English locutions as at least one, every, some, all,
at most three, none, etc.); and
(ii) that associated with predicates and relations (as is done,
e.g., in ascribing particular properties to things or in
asserting that one thing is larger than another)."
"Logical depth is the computational resources (chiefly time)
taken to calculate the results of a program of minimal length.
It is thus a combination of computational complexity and
Kolmogorov complexity. Bennett uses it to formalise the level
of organisation in systems. All present-day organisms can be
viewed as the result of a very long computation from an
incompressible program and are t
What you call conventionally, Crutchfield describes as the intuitive
definition of emergence, which along with pattern formation doesn't fit
the requirements for defining what he calls intrinsic/operational emergence.
http://www.calresco.org/offline.htm
Is Anything Ever New ? : Considering Emergence
Jim Crutchfield (64k ps.z) Abstract:
"A synthesis of tools from dynamical systems, computation and
inductive inference is used to outline how we can discover
'novelty in our world, ideas that go beyond our current
understanding. Extrinsic emergence (with respect to an
external observer) is contrasted with Intrinsic emergence
(meaningful in terms of the system itself)".
Is Anything Ever New ? : Considering Emergence, page 10
"The arguments to this point can be recapitulated by an
operational definition of emergence. A process undergoes
emergence if at some time the architecture of information
processing has changed in such a way that a distinct and
more powerful level of intrinsic computation has appeared
that was not present in earlier conditions. It seems, upon
reflection, that our intuitive notion of emergence is not
captured by the "intuitive definition" given in the first
section. Nor is it captured by the somewhat refined notion
of pattern formation. "Emergence" is meaningless unless it
is defined within the context of processes themselves; the
only wellefined notion of emergence would seem to be
intrinsic emergence. Why? Simply because emergence defined
without this closure leads to an infinite regress of observers
detecting patterns of observers detecting patterns .... This
is not a satisfactory definition, since it is not finite. The
regress must be folded into the system, it must be immanent
in the dynamics. When this happens complexity and structure
are no longer referred outside, no longer relative and
arbitrary; they take on internal meaning and functionality."
SH: I think he uses "more powerful" in the same sense that
a more complex logic* is considered more powerful. I think
that founders in the CA field who have garnered enough
respect to head their own departments have earned the
right to have their views listened to carefully. Normally,
they will have thought about issues which have not occurred
to their less educated, less philosophically precise readers.
*"We will then move on to take a preliminary look at the
language of first-order predicate logic ("quantification theory").
This is the logically richer language that results from the
augmentation of sentential logic by incorporating into our
logical formalism the means to express structure of two
additional sorts:
(i) that associated with quantity (as is accomplished, e.g.,
with such English locutions as at least one, every, some, all,
at most three, none, etc.); and
(ii) that associated with predicates and relations (as is done,
e.g., in ascribing particular properties to things or in
asserting that one thing is larger than another)."
"Logical depth is the computational resources (chiefly time)
taken to calculate the results of a program of minimal length.
It is thus a combination of computational complexity and
Kolmogorov complexity. Bennett uses it to formalise the level
of organisation in systems. All present-day organisms can be
viewed as the result of a very long computation from an
incompressible program and are t
Re: state of the art on dynamical hierarchies Turing
by Stephen Harris » Tue, 26 Apr 2005 07:14:10 GMT
"Tim Tyler" < XXXX@XXXXX.COM > wrote in message news: XXXX@XXXXX.COM ...
About "through aggregation" at the end of the quote above.
http://www.stephenwolfram.com/publications/articles/ca/83-statistical/7/text.html
"Cellular automata have been developed in this paper as general
mathematical models. One may anticipate their application as simple
models for a wide variety of natural processes. Their nontrivial
features are typically evident only when some form of growth
inhibition is present. Examples are found in aggregation processes
in which aggregation at a particular point prevents further
aggregation at the same point on the next time step."
SH: To me Rasmussen is stating that "nontrivial features" can be
guided with "an appropriate increase of the object complexity of
the primitives ..."; so then selected iterative rules provide
"growth inhibition".
I think it is true that the same functional emergence can be achieved
by various CAs and I don't think they all achieve the emergence
with the same number of cycles. Doesn't that indicate that alternate
initial configurtions and iterative rules have more efficiency?
Maybe I don't understand this correctly and I am under misimpression?
So I'm thinking this is not a matter of Turing equivalence, but the
issue of prediction without a full simulation. The process of an
evolving CA which demonstrates emergence would have a sequence
of structural changes.
http://cscs.umich.edu/~crshalizi/notebooks/cellular-automata.html
"The growing interest in CA is, incidentally, a good example of what
the late Heinz Pagels meant when he talked about "the computer and
the rise of the sciences of complexity." It is extraordinarily
difficult to predict, a priori, how a CA will evolve from an
arbitrary starting-point; usually the only way to do it is to work
the calculation through explicitly."
I do agree. But I never thought that Rasmussen was careless/stupid
enough to make a statement which refuted Turing equivalence, and
I think he distanced himself from this intepretation when he explained
that his statement was only an "apparent contradiction" to Turing
equivalence. So I have been looking for what he really meant.
Regards,
Stephen
About "through aggregation" at the end of the quote above.
http://www.stephenwolfram.com/publications/articles/ca/83-statistical/7/text.html
"Cellular automata have been developed in this paper as general
mathematical models. One may anticipate their application as simple
models for a wide variety of natural processes. Their nontrivial
features are typically evident only when some form of growth
inhibition is present. Examples are found in aggregation processes
in which aggregation at a particular point prevents further
aggregation at the same point on the next time step."
SH: To me Rasmussen is stating that "nontrivial features" can be
guided with "an appropriate increase of the object complexity of
the primitives ..."; so then selected iterative rules provide
"growth inhibition".
I think it is true that the same functional emergence can be achieved
by various CAs and I don't think they all achieve the emergence
with the same number of cycles. Doesn't that indicate that alternate
initial configurtions and iterative rules have more efficiency?
Maybe I don't understand this correctly and I am under misimpression?
So I'm thinking this is not a matter of Turing equivalence, but the
issue of prediction without a full simulation. The process of an
evolving CA which demonstrates emergence would have a sequence
of structural changes.
http://cscs.umich.edu/~crshalizi/notebooks/cellular-automata.html
"The growing interest in CA is, incidentally, a good example of what
the late Heinz Pagels meant when he talked about "the computer and
the rise of the sciences of complexity." It is extraordinarily
difficult to predict, a priori, how a CA will evolve from an
arbitrary starting-point; usually the only way to do it is to work
the calculation through explicitly."
I do agree. But I never thought that Rasmussen was careless/stupid
enough to make a statement which refuted Turing equivalence, and
I think he distanced himself from this intepretation when he explained
that his statement was only an "apparent contradiction" to Turing
equivalence. So I have been looking for what he really meant.
Regards,
Stephen
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