Mike, yes, I am sure you are right: there is a large overlap
between Holland's Complex Adaptive Systems picture and the themes in
Wolfram's NKS. But Wolfram does add a number of features which seem
to me unique (even if what seems to me his major motivation, digital
physics, is not so unique: I know of at least Konrad Zuse, Ed
Fredkin, even Richard Feynman, plus one other, for example, who
worked on it before him). (01)
The largest and most general of those uniquenesses is the Principle
of Computational Equivalence. He goes on at some length, in the
main text and in the notes, to describe it while also distinguishing
it from Church's thesis. In the end, however, it seems to my
formally-untrained eye that that is to slip in the "strong
suspicion" and "guess" (NKS p730) that it extends to continuous
systems too, with the obvious motive, namely to justify his attempts
to pursue digital models for fundamental physics (hence my "heart
and mind" speculation in my earlier email below). Conventional
physicists and mathematicians often seem driven to insist that only
continuous mathematics could possibly do justice to the complexities
of the real physical world (in addition to invoking the spectacular
successes of the mathematics of continuous spaces). Wolfram even
notes (p1136) that "Turing at least seems to have thought that
[Church's thesis] might not apply to continuous processes in
physics." So he is responding to the evident need to address a
serious though perhaps merely intuitive philosophical obstacle to
acceptance of his approach. He then even goes on to use the
thus-widened Principle of Computational Equivalence to argue (p736)
that even "the particular methods of perception and analysis that we
as humans happen to use" cannot be more sophisticated
computationally. So perhaps we are not as complex as we think we
are. (Though he doesn't dare spell it out quite as crudely!) That
then leads to the next point: (02)
There is another philosophical obstacle, even larger, namely the
deterministic nature of the CA-like approach. Partly in answer (in
my interpretation of him), Wolfram adds (p738) "a very fundamental
phenomenon that follows from the Principle of Computational
Equivalence and that I call computational irreducibility." (The
phenomenon is labelled without the upper-case, in contrast to the
Principle, but he doesn't explain.) In essence, plainly stated,
most natural phenomena are so complex that we cannot predict
outcomes, we can only simulate possible cases. But he does take
that rather banale position into new fields, most instructively. (03)
That then leads naturally to a section (p750ff) entitled "The
Phenomenon of Free Will", where his conclusions seems somewhat
ambivalent. On the one hand the inscrutability of our behaviour
that we take as freedom is merely a function of its apparent
complexity, which as we know from the Principle of Computational
Equivalence is not necessarily so complex. But on the other hand we
are free because computational irreducibility means we cannot fully
predict our behaviours. (I can't say that conclusion is as
satisfying as we might like, but I suspect many of us tend to
subscribe to something rather like it (excepting, of course, the
diehard physical reductionists).) (04)
So he certainly is not saying that the universe is a big computer,
because that could mean nothing practical, as underlined by his
'computational irreducibility'. But I am sure in my own mind (until
corrected...) that he is nonetheless still trying to find that
"final and correct one [rule] for the whole universe." (05)
However, I cannot leave you with the rather negative tone of much of
the above! To cut a long story short let me just add that I agree
with Wolfram in most points I have tried to represent above, as I
sketched a very similar picture - and faith - on pp82-88 of my 1986
book, with significant correspondences in our arguments addressing
the exact same philosophical objections. But I would differ on this
point: I do not agree that the rule we have been seeking for so
long (he since the 1980s, me since 1964) will be the final or most
fundamental one. I would however say that our ontological positions
coincide inasmuch as we do not confuse model with reality. (06)
Then of course Wolfram has advanced far further than I have! His
Mathematica is a hugely better tool than the APL I got into in about
1981 for that same purpose, attracted by its array-handling and
reflective capabilities. I even bought an APL terminal and arranged
the APL software on our HP3000 so that I could undertake the
experimentation and, as I had envisaged, program the genetic
processes for automated selection of promising candidate rules. But
other priorities had intervened and later HP3000s did not support
APL. (Hence my 1986 disclosure, though I had also presented the
concept at the University of Cape Town in the late 1970s.) (07)
Wolfram has of course displayed far greater inventiveness with CA
definitions. I am most impressed by how he has stretched their
topologies and worked towards the requirements of General
Relativity. I liked the small step in NKS (pp429-432) towards human
social systems, and wished for more. I can certainly see how that
technique could extend naturally into a world which has adopted The
Mainstream Architecture for Common Knowledge. But that is a
subject - with vast vistas! - for another time... (08)
Christopher (09)
----- Original Message -----
From: "Mike Bennett" <mbennett@xxxxxxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Saturday, April 25, 2009 3:38 PM
Subject: Re: [ontolog-forum] Digital Ontology and digital ontology (010)
>I thought that the idea that the complexity of the real world can
>arise from very simple patterns had been well explored by Holland
>and others in the "complexity" world. Surely that's no longer a
>contentious point, though I don't know how Wolfram treats it.
>
> Mike
>
> Christopher Spottiswoode wrote:
>> Paola, many many thanks for your pointer to that Wolfram lecture!
>> His entire work teems with deep questions that are certainly
>> relevant to ontology, and you were very right to draw our
>> attention to that amazing performance.
>>
>> John, thanks too for the usual balance in your response.
>> However, I'm not sure that on the face of it this is correct:
>>
>>> [...] he wasn't making the mistake of claiming that the real
>>> world is as simple as a digital automaton.
>>>
>> Whether or not that would be a mistake (which is a whole other
>> question...), I think he does in fact claim that the real world
>> has a certain underlying simplicity.
>>
>> He does indeed propose and investigate many kinds of digital
>> automata that are far from the simple cellular automata we've all
>> seen. But his work is about how apparently real-enough
>> complexity can be produced by simple automata. And on NKS p469
>> he does say this:
>>
>> "But it does mean that if one once discovers a rule that
>> reproduces sufficiently many features of the universe, then it
>> becomes extremely likely that this rule is indeed the final and
>> correct one for the whole universe."
>>
>> where the "it" clearly refers to a long line of reasoning to
>> which he appears to subscribe. And while NKS does cover many
>> other areas of application of his complexity-out-of-simplicity
>> theme, and his "computational irreducibility" does have a great
>> generality, his heart and mind do appear set on discovering that
>> one rule!
>>
>> That is my impression, anyway, after having studied much of his
>> NKS (as best I could...) and tried to follow his doings since.
>> But I would be keen to learn of any counter-arguments.
>>
>> Christopher (011)
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