Interesting review of A New Kind of Science
Edwin Clark
P. Kadanoff, member of the National Academy of Sciences, in arXiv.org
e-Print archive and may be found at
http://xxx.lanl.gov/html/nlin.CG/0205068
I have just added this to my collection of such reviews at
http://www.math.usf.edu/~eclark/ANKOS_reviews.html
If you know of any substantive online review not in my collection
please send me the URL.
------------------------------------------------------------
W. Edwin Clark, Math Dept, University of South Florida,
http://www.math.usf.edu/~eclark/
------------------------------------------------------------
Michal Kvasnicka
review of ANKOS.
I am sure that similar and more, and more ... close up reviews will be tail
after this Kadanoff's review. In the end, I think at the latest next year,
will be ANKOS only one, more or less unknown, fragment of the Wolfram's
business approach to the scientific work.
Michal Kvasnicka
"Edwin Clark" <ecl...@math.usf.edu> píse v diskusním príspevku
news:Pine.GSO.4.21.02061...@tarski.math.usf.edu...
Nico Benschop
>
> In case you missed it, there is an interesting review of ANKOS by Leo
> P. Kadanoff, member of the National Academy of Sciences, in arXiv.org
> e-Print archive and may be found at
>
>
> I have just added this to my collection of such reviews at
>
> http://www.math.usf.edu/~eclark/ANKOS_reviews.html
>
> If you know of any substantive online review not in my collection
> please send me the URL.
>
> ------------------------------------------------------------
> W. Edwin Clark, Math Dept, University of South Florida,
> http://www.math.usf.edu/~eclark/
> ------------------------------------------------------------
Re[*]: Kadanoff's critique is, I find, justified -
at least as far as Wolfram's choice of title is concerned.
The basic concept here is a special kind of automata, of
deterministic type. So it's "science" should at least rest on some
kind of algebra - in order to obtain the compactness and predictive
power of mathematics/ dynamics we're used to, since Newton, Descartes.
In the digital domain, the past some 50 years, not that much has been
obtained in the algebraic sense, regarding general predictions of the
sequential behaviour of automata and state machines. However it
seems, since the fifties last century (Moore, Mealy) to have been agreed
upon that the finite state model of deterministic sequential behaviour
in general is necessary and sufficient, for all practical
(and theoretical) purposes.
The related algebra here is that of associative function composition,
in other words: (finite) semigroups. With an abstract formalization
/ generalization in the form of Category Theory (S.MacLane, in the
sixties). Not much, as far as I know, has been reached in a practical
sense, since the Krohn-Rhodes decomposition theorem (based on
Jordan-Hoelder's group decomposition Thm of the 19-th century,
adjoined to right-copy semigroups as model of set/reset memory
elements, viz. n-state 'flipflops'): the general structure theory
of finite semigroups is still out somewhere (after a promising start
by Shushkewitch's PhD thesis, Kiev, 1928 - on the structure of finite
simple semigroups).
So if S.Wolfram claims that cellular automata form a new kind of science
- *without* its algebra (finite semigroups) being developed
in some practical & general sense, then I'd say: how come?
-- NB - http://home.iae.nl/users/benschop/c-ranksm.dvi
"The structure of Constant-Rank State Machines"
http://arXiv.org/abs/math.GM/0103112 (on the 5 basic state machines)
W. Edwin Clark
>
> This is a first, from my point of view, concise, relevant and scientific
> review of ANKOS.
>
>
There is also the paper at
http://arXiv.org/PS_cache/quant-ph/pdf/0206/0206089.pdf
by Scott Aaronson which critiques two areas: computational
complexity and fundamental physics--especially quantum mechanics.
Ralph E. Frost
Nico Benschop <n.ben...@chello.nl> wrote in message
news:3D104425...@chello.nl...
> Edwin Clark wrote:
> >
> > In case you .....
...
> the general structure theory
> of finite semigroups is still out somewhere
...
>
> So if S.Wolfram claims that cellular automata form a new kind of science
> - *without* its algebra (finite semigroups) being developed
> in some practical & general sense, then I'd say: how come?
Imagine there are two plates stacked on one another. Have the top plate
represent all of abstract math. Have the bottom, supporting plate represent
the more fundamental, but less well known and often unappreciated analog
mathematics.
- - Ralph Frost
Use more robust symbols
Seek a thought worthy of speech.
Michal Kvasnicka
http://www.newscientist.com/opinion/opinterview.jsp?id=ns230516) common in
scientific community?
Michal Kvasnicka
Robert J. Kolker
Michal Kvasnicka wrote:
> Please tell me!!! Are these opinions (
> http://www.newscientist.com/opinion/opinterview.jsp?id=ns230516) common in
> scientific community?
I think Wolfram is a sincere lunatic. Kepler was that way, when he tried
to use the Platonic solids to model the orbits of the 5 known planets.
Someone ought to challange Wolfram to come up with a -feasible- scheme
of tessalated automata to model turbulence in a fluid or gas. If he
automata scheme can outdo a numerical solution to the Navier-Stokes
equation, he might just have something.
But playing toy games similar to Conway's -Game of Life- is bupkis as my
Grandmother of blessed memory, would say.
One place where synchronized automata arrays might actually be useful is
in solving the LaPlace equation on a finite mesh. The normal trick of
average the neighboring points synchronously fits right in with the
automata model.
When I was a sprightly lad I used automata arrays as a pattern
recognition device, but that is a far cry from a generalized schemata
for representing the Kosmos.
Bob Kolker
Nico Benschop
It is a matter of taste what the 'more fundamental' type of
mathematics
is (related to 'systems dynamics' cq. 'sequential behaviour'):
continuous (differential eqns / integerals / waves) [1]
or discrete (state machines / semigroups / particles) [2]
By the reviews of Wolfram's (and Ed Fredkin's) work neither have
concerned
themselves much with either [1] or [2] in a 'fundamental way'. Rather,
they
seem - as many people - enamored with the fascinating patterns
produced
by simple cellular automata in_the_plane, and/or by Mandelbrot's
fractals.
Neither of which appear to have predictable behaviour (yet generated
by
extremely simple rules). Rather than to study the *reasons* why this
is
so (e.g. using function composition, rather than polynomial
arithmetic,
re: the degree of the functional composition of two polynomes is the
*product* of the factor degrees vs. their sum for a product of
polynomes)
-- and bring insight to those areas that raise it to the level of what
we're used to in any 'science'. Their contributions are hardly more
than 'oh-and-ah' listings of behavioural patterns - almost as an
addiction;
not the kind of sharp analysis/synthesis of Newton/Maxwell/Einstein
type, would'nt you agree?
And (Jurjus): qua physics vs. computer science, the boundaries tend to
get more fuzzy, lately (say the past 50 years or so). The suggestion
of
space/time being discrete comes from the CS side, I presume, and may
be helpful to bring both PH & CS somewhat further by cross
vertilization:
at least don't keep them separate on purpose... Both the continuous
and
the discrete are useful for a model of our Universe (the latter
meaning
literally: One-way __ thus not-reversible: not groups but semigroups
;-)
-- http://home.iae.nl/users/benschop/math-use.htm
http://home.iae.nl/users/benschop/filosofy.htm -- NB
David Eppstein
"Michal Kvasnicka" <mkvas...@volny.cz> wrote:
> Please tell me!!! Are these opinions (
> http://www.newscientist.com/opinion/opinterview.jsp?id=ns230516) common in
> scientific community?
That's not opinion, that's an uncritical puff-piece.
--
David Eppstein UC Irvine Dept. of Information & Computer Science
epps...@ics.uci.edu http://www.ics.uci.edu/~eppstein/
Carl Devore
Edwin,
I love this review / parody of _A New Kind of Science_ that I found at
amazon.com. The author is anonymous. I don't know how to give an URL for
a single review from the 129 currently on Amazon, so I just cut and
pasted.
A New Kind of Review
by "a reader"
I can only imagine how fortunate you must feel to be reading my review.
This review is the product of my lifetime of experience in meeting
important people and thinking deep thoughts. This is a new kind of review,
and will no doubt influence the way you think about the world around you
and the way you think of yourself.
Bigger than infinity
Although my review deserves thousands of pages to articulate, I am
limiting many of my deeper thoughts to only single characters. I encourage
readers of my review to dedicate the many years required to fully absorb
the significance of what I am writing here. Fortunately, we live in
exactly the time when my review can be widely disseminated by "internet"
technology and stored on "digital media", allowing current and future
scholars to delve more deeply into my original and insightful use of
commas, numbers, and letters.
My place in history
My review allows, for the first time, a complete and total understanding
not only of this but *every single* book ever written. I call this "the
principle of book equivalence." Future generations will decide the
relative merits of this review compared with, for example, the works of
Shakespeare. This effort will open new realms of scholarship.
More about me
I first began writing reviews as a small child, where my talent was
clearly apparent to those around me, including my mother. She preserved my
early writings which, although simpler in structure, portend elements of
my current style. I include one of them below (which I call review 30) to
indicate the scholarly pedigree of the document now in your hands or on
your screen or committed to your memory:
"The guy who wrote the book is also the
publisher of the book. I guess he's the only
person smart enough to understand what's in it.
When I'm older I too will use a vanity press.
Then I can write all the pages I want."...
It is staggering to contemplate that all the great works of literature can
be derived from the letters I use in writing this review. I am pleased to
have shared them with you, and hereby grant you the liberty to use up to
twenty (20) of them consecutively without attribution. Any use of
additional characters in print must acknowledge this review as source
material since it contains, implicitly or explicitly, all future written
documents.
Dr Chaos
> By the reviews of Wolfram's (and Ed Fredkin's) work neither have
> concerned
> themselves much with either [1] or [2] in a 'fundamental way'. Rather,
> they
> seem - as many people - enamored with the fascinating patterns
> produced
> by simple cellular automata in_the_plane, and/or by Mandelbrot's
> fractals.
> Neither of which appear to have predictable behaviour (yet generated
> by
> extremely simple rules). Rather than to study the *reasons* why this
> is
> so (e.g. using function composition, rather than polynomial
> arithmetic,
> re: the degree of the functional composition of two polynomes is the
> *product* of the factor degrees vs. their sum for a product of
> polynomes)
> -- and bring insight to those areas that raise it to the level of what
> we're used to in any 'science'. Their contributions are hardly more
> than 'oh-and-ah' listings of behavioural patterns - almost as an
> addiction;
> not the kind of sharp analysis/synthesis of Newton/Maxwell/Einstein
> type, would'nt you agree?
Come on, that's unfair. Certainly people have looked at in say
statistical mechanics at the Perron-Frobenius operators for complicated
nonlinear dynamical systems. The answer is that quickly the distributions
that are solutions have very complicated and singular properties.
It's just really plain hard to get analysis types of bounds in "general"
though they do work very hard at things.
There is now an extensive literature of something somewhere between
mathematical analysis and experimental and simulational deductions
What are you trying to look for in a Newtonian type of synthesis?
Nico Benschop
> Nico Benschop <n.ben...@chello.nl> wrote:
> > By the reviews of Wolfram's (and Ed Fredkin's) work neither have
> > concerned themselves much with either [1] or [2] in a
> > automata in_the_plane, and/or by Mandelbrot's fractals.
> > Neither of which appear to have predictable behaviour (yet
> > generated by extremely simple rules). Rather than to study
> > the *reasons* why this is so (e.g. using function composition,
> > rather than polynomial arithmetic, re: the degree of the functional
> > those areas that raise it to the level of what we're used to in
> > any 'science'. Their contributions are hardly more than
> > 'oh-and-ah' listings of behavioural patterns - almost as
> > an addiction; not the kind of sharp analysis/synthesis of
> > Newton/Maxwell/Einstein type, would'nt you agree?
>
> Come on, that's unfair. Certainly people have looked at in say
> statistical mechanics at the Perron-Frobenius operators for complicated
> nonlinear dynamical systems. The answer is that quickly the distributions
> that are solutions have very complicated and singular properties.
> It's just really plain hard to get analysis types of bounds in
> "general" though they do work very hard at things.
>
> There is now an extensive literature of something somewhere between
> What are you trying to look for in a Newtonian type of synthesis?
What you refer to, it seems, is 'Chaos Theory' - which indeed is a
very complicated field - where classical analysis can bring one only
that far, although some interesting results are derived (e.g. turbulance
phenomena). But instead of nonlinear dynamics, I was thinking of the
Fredkin & Wolfram suggestion of 'quantized space & time' as a model for
physics, extending - as it were - the known computer science (CS) model
of a finite state machine (FSM) to an infinite state-domain: space/time
as an infinite 4-dimensional quantized 'grid'. Apparently in the hope
that such discrete dynamics (cellular automata) can benefit from CS and
disctrete maths - *without* clearly any drive to develop the underlying
associative algebra of (finite) function composition, namely: semigroup
structure theory. *Without* such improved insight, I think, the word
'science' does not apply to such discrete dynamics, and *with* such
developed algebra of discrete dynamics ('Digital Network Theory') it
_could_ yield a Nnew Kind of Science... What I'd suggest is:
to look upon FSM's and Semigroups in discrete dynamics, as
the DE's and Integrals of continuous dynamics (Newton/Maxwell).
> >
> > And (Jurjus): qua physics vs. computer science, the boundaries tend
> > to get more fuzzy, lately (say the past 50 years or so). Suggesting
> > space/time to be discrete comes - it seems - from the CS side, and
> > may be helpful to bring both PH & CS somewhat further by cross
> > vertilization: at least don't keep them separate on purpose...
> > Both the continuous and the discrete are useful for a model of
> > our Universe, meaning literally:
> > One-way --> thus not-reversible (not groups but semigroups;-)
> >
> > - http://home.iae.nl/users/benschop/math-use.htm
> > http://home.iae.nl/users/benschop/filosofy.htm -- NB
http://home.iae.nl/users/benschop/ism.htm (Integer State Machines)
ca314159
I suspect if Wolfram is saying anything, it's that that "the" natural theory
must emerge naturally, in parallel from a fundamental seed, growing as a crystal
within the supersaturated state of our current overloaded knowledge base.
Perhaps, this is why he does not elaborate further ?
Doing that would result in a multi-seeded, multi-faceted jumble of quantum rock candy,
rather than a pure small crystal seed being amplified into the macrocosm
unmodulated by conscious supranatural human influences.
Isn't that a "Science" in its most objective form ?
First an uncontrolled haiku observation.
Patience, wait, see what nature does.
Control and technology comes later.
This contrary to today's technology driven science,
where complete control is imposed at each and every femtoscopic step along the way,
and patience is considered uneconomical.
So he publishes his own guide book;
seemingly "a book about nothing" ala Seinfeld.
And now he sleeps, like Magrathea.
http://www.innerx.net/personal/tsmith/ficw.html
http://www.nd.edu/~qcahome/
http://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=growing+crystals
http://www.time.com/time/magazine/1998/dom/980112/box1.html
Tim Tyler
: I suspect if Wolfram is saying anything, it's that that
: "the" natural theory must emerge naturally, in parallel from a
: fundamental seed, growing as a crystal within the supersaturated
: state of our current overloaded knowledge base.
: Perhaps, this is why he does not elaborate further ?
: Doing that would result in a multi-seeded, multi-faceted jumble of
: quantum rock candy, rather than a pure small crystal seed being
: amplified into the macrocosm unmodulated by conscious supranatural
: human influences.
That sounds like a crystal of Wolframite ;-)
--
__________
|im |yler http://timtyler.org/ t...@tt1.org
W. Edwin Clark
ca314159 wrote:
> I suspect if Wolfram is saying anything, it's that that "the" natural theory
> must emerge naturally, in parallel from a fundamental seed, growing as a crystal
> within the supersaturated state of our current overloaded knowledge base.
>
> Perhaps, this is why he does not elaborate further ?
> Doing that would result in a multi-seeded, multi-faceted jumble of quantum rock candy,
> rather than a pure small crystal seed being amplified into the macrocosm
> unmodulated by conscious supranatural human influences.
>
> Isn't that a "Science" in its most objective form ?
> First an uncontrolled haiku observation.
> Patience, wait, see what nature does.
> Control and technology comes later.
A nice haiku, but isn't control and technology a part of "nature".
If not how do you separate it out?
Patience, wait, see what NATURE does.
Watch the Wolfram glider go by.
--Edwin Clark
ca314159
plonk:
Wolfram drops a single pebble into the pond, and the waves glide out.
The environment changes. The new environment may control me, but not my nature.
my nature:
that time-less subset of me that is unchangeable,
uninfluenced, and uncontrollable by the environment.
Pile any flavor on top of it: chocolate or neuroses;
it is the invisible skeleton of the observable me.
objective nature:
those time-invariant laws, the unchangeable, uncontrollable subset of
the observable phenomena of the environment. Pile anything on top of
them to pretty them up, or make them look as complex as one likes,
but still they don't change.
The environment may be controlled, but not nature; not in the sense of "Natural Laws";
which are used, but not controlled.
Time-invariant things are outside the rhelm of control.
If they were controllable, they wouldn't be time-invariant.
We also say: "It is in one's nature..." as if expecting that nature to never change.
For these reasons "nature" seems to be either some transcendent state of mind, or
a fundamental constant of the environment, to be elaborated upon by either humans or beasts.
We would have to be gods to control the gods: those truly natural time-invariant constants/laws.
At times we believe we can control them. But, then they turn out to be false gods.
Then these constellations soon get replaced by newer stars; new constants of nature, new laws of nature.
But how could they be "new" if they are supposed to be time-invariant ?
If it is "new", it probably isn't Nature.
Nature is old, a very old physics.
Older minds seem to like a data-compressed, relaxed and efficient metaphysics.
Younger minds seem to like do more more lucrative, expensive, obfuscatded, wordy,
control and technology.
"It's not the years, it's the mileage."
- Indiana Jones
I don't think nature controls itself,
which is probably why it seems so complex.
ca314159
:-))
A Freudian slip ? But was it yours, mine, or his ?
Perhaps he's thinking now (as we all seem to do eventually):
"Help me, help me !
I'm trapped in myself, and I can't get out !"
Dr Chaos
I think the problem there is not the lack of mathematical
maturity (that's a nice luxury) but of physics.
What physics does a 4-d finite-state-machine explain?
Why stick it in there at all?
By contrast, the continuous symmetries of conventional quantum
mechanics and dynamics explain a hell of a lot of important stuff.
>What I'd suggest is:
> to look upon FSM's and Semigroups in discrete dynamics, as
> the DE's and Integrals of continuous dynamics (Newton/Maxwell).
Well in the really simplest constructions the map induced on the
poincare section is the discrete (in time but not value)
correspondence.
You can define continous dynamical systems with "two times" and I
guess get poincare sections of those but I don't think that's going
to help.
I don't understand what else you are getting at.