Kinds of complexity

[Pamela McCorduck]

As a followup to an on-line discussion, the face-to-face FRIAM group  
last week spoke some more about kinds of complexity.  I mentioned a  
paper of Seth Lloyd's, which is called "Measures of Complexity: A non-
exhaustive list."  I have a hard copy, undated, and retrieved from  
Joe Traub's files,.  I have no idea if this brief note has been  
published elsewhere.  (Joe remembers its first appearance as "31  
Flavors of Complexity" with a jokey little nod to Baskin-Robbins.)

Anyway, it begins:

        "Recently, measures of complexity have multiplied rapidly.  Some  
take this proliferation as a sign that no one knows what complexity  
really is.  In fact, asking for the true mathematical definition of  
complexity today is like asking for the true mathematical definition  
of electricity in 1800: to understand electricity, it turned out to  
be much more productive to define several quantities, such as charge,  
current, voltage, inductance, etc., that could be related by simple  
formulas, than to define a single mathematical definition of  
electricity.  In addition, like  H  and B , a number of quantities  
that originally were thought to describe different effects, later  
were discovered to be closely related, and in many circumstances,  
identical.  The many definitions of complexity stand in similarly  
close relations to each other.  This list groups measures that are in  
some situations closely related to each other, or identical."

He then lists 5 groupings of kinds of complexity which seem related  
to each other, along with subgroups.  The large groupings are  
information, mutual and conditional information, computational  
complexity, distinguishability, and definitions without precise  
mathematical expression.

In short, the field is in its infancy.  We force it into premature  
adulthood at our own cost.

Pamela




                I sit in one of the dives
                On Fifty-second Street
                Uncertain and afraid
                As the clever hopes expire
                Of a low dishonest decade


                                W. H. Auden




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[Robert Holmes]

On 8/9/06, Pamela McCorduck <pamela at well.com> wrote:
>
> <snip>...In fact, asking for the true mathematical definition of
> complexity today is like asking for the true mathematical definition of
> electricity in 1800: to understand electricity, it turned out to be much
> more productive to define several quantities, such as charge, current,
> voltage, inductance, etc.
>

At least those scientists had the good sense to give these quantities
different names. We just call each of our disparate quantites 'complexity'
and then wonder why we can't get any equations to work.

Robert
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[Stephen Guerin]

Robert writes:
> At least those scientists had the good sense to give these
> quantities different names. We just call each of our
> disparate quantites 'complexity' and then wonder why we can't
> get any equations to work.

The history of thermodynamics was interesting when folks had many defintions for
the concept of "heat" and later "work". Early definitions struggled when these
terms were defined as things that flow instead of defined as processes. I
speculate that Complexity, if it is ever defined, will also be a closely-related
process definition.

-Steve

> -----Original Message-----
> From: Robert Holmes [mailto:robert at holmesacosta.com]
> Sent: Wednesday, August 09, 2006 2:14 PM
> To: The Friday Morning Applied Complexity Coffee Group
> Subject: Re: [FRIAM] Kinds of complexity
>
>
>
> On 8/9/06, Pamela McCorduck <pamela at well.com> wrote:
>
> <snip>
> ...In fact, asking for the true mathematical definition
> of complexity today is like asking for the true mathematical
> definition of electricity in 1800: to understand electricity,
> it turned out to be much more productive to define several
> quantities, such as charge, current, voltage, inductance, etc.
>
>
> At least those scientists had the good sense to give these
> quantities different names. We just call each of our
> disparate quantites 'complexity' and then wonder why we can't
> get any equations to work.
>
> Robert
>
>
>

[Louis Macovsky, Dynamic BioSystems]

How would you differentiate between complicated and complex?

Lou



----- Original Message -----
From: "Stephen Guerin" <[hidden email]>
To: "'The Friday Morning Applied Complexity Coffee Group'"
<friam at redfish.com>
Sent: Wednesday, August 09, 2006 6:47 PM
Subject: Re: [FRIAM] Kinds of complexity


> Robert writes:
> > At least those scientists had the good sense to give these
> > quantities different names. We just call each of our
> > disparate quantites 'complexity' and then wonder why we can't
> > get any equations to work.
>
> The history of thermodynamics was interesting when folks had many
defintions for
> the concept of "heat" and later "work". Early definitions struggled when
these
> terms were defined as things that flow instead of defined as processes. I
> speculate that Complexity, if it is ever defined, will also be a
closely-related

> process definition.
>
> -Steve
>
>
>
>
>
> > -----Original Message-----
> > From: Robert Holmes [mailto:robert at holmesacosta.com]
> > Sent: Wednesday, August 09, 2006 2:14 PM
> > To: The Friday Morning Applied Complexity Coffee Group
> > Subject: Re: [FRIAM] Kinds of complexity
> >
> >
> >
> > On 8/9/06, Pamela McCorduck <pamela at well.com> wrote:
> >
> > <snip>
> > ...In fact, asking for the true mathematical definition
> > of complexity today is like asking for the true mathematical
> > definition of electricity in 1800: to understand electricity,
> > it turned out to be much more productive to define several
> > quantities, such as charge, current, voltage, inductance, etc.
> >
> >
> > At least those scientists had the good sense to give these
> > quantities different names. We just call each of our
> > disparate quantites 'complexity' and then wonder why we can't
> > get any equations to work.
> >
> > Robert
> >
> >
> >
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

[Russell Standish]

I think the distinction is along the same lines as the distinction
between "resultant" emergence, and the general case. Complicated
systems have no non-resultant emergence.

On Wed, Aug 09, 2006 at 07:30:19PM -0700, Louis Macovsky, Dynamic BioSystems wrote:
> How would you differentiate between complicated and complex?
>
> Lou
>

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