Thus spake Owen Densmore circa 09-11-03 09:02 AM:
> On Nov 2, 2009, at 5:54 PM, Nicholas Thompson wrote:
>
>> <snip>
>> Despite our best efforts, I still think Crutchfield, for instance, is
>> ambiguous.
>
> Nonsense!
Cool! This will be an easy challenge. All I need to do is find a
_single_ statement of his that's even a little bit ambiguous and I win. ;-)
>> Note for instance how the different respondents to my question
>> understood him.
>
> Then consider the fault theirs.
Of course the fault is the receiver's. That's the definition of
"ambiguous"! Sorry... I couldn't resist. "Ambiguous" means
"multi-valued". If the reader is the co-domain and the author is the
domain, then it is entirely up to the reader to determine whether or not
Crutchfield's expressions have more than one value in the reader's mind.
> Anyone who really wants to reduce the ambiguity has but to read Ref[1]
> or any of Crutchfield/Shalizi papers on the topic. Shalizi's thesis for
> example.
Uh-oh... Now you're saying _reduce_ the ambiguity, which is different
from denying the claim that there is NO ambiguity... Curses, foiled
again. [grin]
" ... innovation is associated with a change in model class. One
would expect this change to correspond to an increase in computational
sophistication of the model class, but it need not be. Roughly,
innovation is the computational equivalent of speciation ? recall that
the partial ordering of a computational hierarchy indicates that there
is no single way ?up? in general. In concrete terms, innovation is the
improvement in an agent?s notion of environmental (causal) state."
We have the first inklings of the fundamental ambiguity within the above
quote... what with the denial that innovation go "upward" and the
immediate requirement for "improvement". If that ain't equivocation, I
don't know what is.
Moving on. It's not clear whether Crutchfield proposes that hopping
from infinite descriptions to finite descriptions is the only
categorization of models he uses to define innovation. On the one hand,
he says things like:
"At each level in a hierarchy there are a number of elements that can be
identified, such as the following."
And this is an indicator that he might be willing to spread his
definition of innovation over categorizations other than whether they
can finitely represent something that other classes can only represent
infinitely. But everything he talks about with any unambiguous
specificity is based on the epsilon machines and finite representations.
(Note that the class boundaries he cites: "... from determinism to
indeterminism, from finitary support to finitary measure, from
predictability to chaos, from undifferentiated patterns to domains and
particles, and from observed states to hidden internal states" were all
crossed in the service of finite representations... So, even though they
may be considered innovative by Crutchfield even if the infinite-finite
boundary were NOT crossed, it is not explicitly stated in this paper.)
That's ambiguity. Does innovation _require_ a move from a class of
models where a data stream is infinitely represented to a class of
models where it is finitely represented? Or could we, perhaps, develop
some other computational mechanics and categorize models based on some
other property? And then still label class hopping as innovation?
So, we can see that even down there at the core of the rhetoric in these
two papers, there are fundamental ambiguities. We, as the co-domains
for the paper, are at liberty to interpret him in many different ways.
Of course, we're always able to add more detail to the rhetoric, perhaps
even asking Jim himself some direct questions. And those additions to
the rhetoric may well disambiguate it. But Nick's original assertion
wasn't really about Crutchfield the person, it was about the original
paper we read and it even extends to this other cited paper.
P.s. Note that it's not bad to be ambiguous. Ambiguity is the spice of
life! In fact, some people even think it's necessary for life. ;-)
--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
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