Azamat and Paola, (01)
Stephen Wolfram earned a PhD in physics, he was a professor of physics,
and his Mathematica system supports the major branches of applied
mathematics that are used in physics, engineering, and finance.
So Wolfram is well versed in both the continuous methods of math
used in physics and the discrete methods used in digital computers. (02)
AA> The NKS is mostly about digital ontology, going also as digital
> philosophy, digital physics, or digital metaphysics. Its main
> assumption is as follows... (03)
That talk addressed just a tiny part of what he wrote in the very
large NKS book. Don't assume that he limited his thinking to just
the digital representations. (04)
PDM> I like the idea of a simple underlying approach to complexity. (05)
As a physicist, he had studied the continuous mathematics of
differential equations. But those are very complex, and it is
not easy to see where the complexity arises. (06)
That is why he wanted to demonstrate the immense complexity that
arises from the repetition of just very simple digital patterns.
His rule #30 was the simplest example that could lead to very
complex, nearly random looking patterns. (07)
AA> So the universe is a gigantic digital computer, a sort of
> Turing's discrete state machines, where entities are digital
> beings, and real processes are computational state transitions. (08)
No. That is not what he said. Wolfram knows very well that the
world is much more complex than those digital automata. But he
wanted to start with something very simple to see how complexity
could be generated from something simple. (09)
AA> But nothing is new under the sun (or moon). And this hypothetical
> proposal also comes from an old legacy controversy: Discrete or
> Continuous (as discrete particles and continuous waves), now
> Digital or Analogue. (010)
Wolfram knows that. He was not trying to replace a continuous world
with a discrete model. He was trying to see how an extremely simple
model could generate complexity. (011)
One of the issues he was trying to study is the origin of the
kind of complexity that arises in turbulent fluid flow (which
arises in continuous fluids, both liquids and gases). He was
also trying to study the origin of the kinds of phenomena that
arise in a chaotic breakdown. (012)
Wolfram made the point that the continuous differential equations
are much more complicated than the very simple digital automata.
But even our ordinary digital computers are so complex that it is
hard to find the origin of complexity. (He was talking very fast,
so some of the points were easy to miss.) (013)
Therefore, he wanted to study the extremely simple cellular automata,
which can be completely described by just a few patterns. His point
was that if such complexity could arise from a simple digital pattern
in rule #30, the kinds of complexity that could arise from continuous
differential equations (or the real world) could be far more complex. (014)
AA> The latter one is all about studying the hypothetical digital
> computational nature of the world, where the NKS is aimed to. (015)
In the NKS book, he's trying to address the full complexity of the
continuous world. But he's trying to study it through a variety
of different kinds of approximations. In his short lecture, he
started with digital examples because they are easier to explain. (016)
I suggest that you listen to the lecture once again in order to
see how he related the digital and continuous representations. (017)
http://www.youtube.com/watch?v=_eC14GonZnU&feature=related (018)
By the way, I have not studied Wolfram's work in full detail,
and I don't want to defend or explain everything he's doing.
But I do want to point out that he wasn't making the mistake
of claiming that the real world is as simple as a digital
automaton. (019)
John (020)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (021)
|