Kadanoff on A New Kind of Science
W. Edwin Clark
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
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.
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W. Edwin Clark, Math Dept, University of South Florida,
http://www.math.usf.edu/~eclark/
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Robin Chapman
news:3D0FCD9D...@math.usf.edu
>
> In case you missed it, there is an interesting review of ANKOS
Interesting acronym. It stands for "A New Kind Of Science".
Just as well you didn't abbreviate "Wolfram's A New Kind Of Science".
Robin Chapman
--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
Nico Benschop
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.
Since the fifties last century (Moore, Mealy) it seems 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)
Herman Jurjus
"Nico Benschop" <n.ben...@chello.nl> wrote in message
news:caeab7cb.02061...@posting.google.com...
For what it's worth:
Wolfram might mean "a new kind of physics". But he can't say that, because
that doesn't sound big enough.
And, well, he is a phycisist, and to physicists, physics is all the science
there is. (The audience for which his book is intended can't tell the
difference, too.)
And, if i understand his claim correctly, the 'novelty' is exactly that he
dismisses most of the technical results that you mention as 'irrelevant for
real understanding' (the only thing there is, if you can't make
predictions).
Sometimes in science, you must sacrifice ambitions for results. That has
happened before, you know.
One example: mathematics was a step backwards from philosophy, in the sense
that it refused to answer questions like "what is a line?", it just wanted
results;
Likewise for physics; experiments are not mathematical proofs, but without
them, no physical results.
Perhaps that is what Wolfram means when he talks about "A new kind of
science"? A "successor-science for physics"
Cheers,
Herman Jurjus
Doug Wedel
book? Many reviewers (predictably) find this more or less insufferable.
And why is Wolfram so unbelievably reticent and/or dismissive about the work
of other scientists who have contributed to the various fields he explores?
Again, many reviewers (predictably) find this a woeful lack.
For someone to fill his creative scientific work with braggadocio and to
fail to adequately cite predecessors, raises questions in my mind. Has
any other "great scientist" praised himself or herself to anything like this
extent in his or her seminal work? Has any other great work of science
failed so abysmally to adequately recognize the work of other scientists?
Herman Jurjus
"Doug Wedel" <doug...@yahoo.com> wrote in message
news:up6Q8.44728$LC3.3...@bgtnsc04-news.ops.worldnet.att.net...
> I wonder why Wolfram was so naive as to praise himself to the skies in his
> book? Many reviewers (predictably) find this more or less insufferable.
Maybe it is not naive, but part of a deliberate strategy.
I can imagine that this book will make quite some impression on some 15 year
old people. By the time they are the scientific establishment, they may be
very willing to make their hero famous, and scorn his predecessors.
> And why is Wolfram so unbelievably reticent and/or dismissive about the
work
> of other scientists who have contributed to the various fields he
explores?
> Again, many reviewers (predictably) find this a woeful lack.
>
Two possible reasons:
1. see above.
2. many people feel a great disappointment about science; it is complicated,
with all those differential equations and such, but little insight seems to
be ever gained that is easy to understand.
Perhaps Wolfram wants to get the attention and appreciation of this large
crowd of math-haters?
> For someone to fill his creative scientific work with braggadocio and to
> fail to adequately cite predecessors, raises questions in my mind.
In the minds of most people, great discoveries in science have never been
achieved without dismissing the establishment; the supposed history of
Galilei is too deeply ingrained in their minds. So, without a tone and
writing style as Wolfram's, there is little hope that the mainstream public
will have attention for (any) scientific messages.
Has
> any other "great scientist" praised himself or herself to anything like
this
> extent in his or her seminal work? Has any other great work of science
> failed so abysmally to adequately recognize the work of other scientists?
See above. Most people may think so, even if they have no clue, and that
might be enough.
Cheers,
Herman
Herman Jurjus
"Herman Jurjus" <h.ju...@hetnet.nl> wrote in message
news:aes2bt$9h3gm$1...@ID-110648.news.dfncis.de...
>
> "Doug Wedel" <doug...@yahoo.com> wrote in message
> news:up6Q8.44728$LC3.3...@bgtnsc04-news.ops.worldnet.att.net...
> > I wonder why Wolfram was so naive as to praise himself to the skies in
his
> > book? Many reviewers (predictably) find this more or less insufferable.
>
> Maybe it is not naive, but part of a deliberate strategy.
> I can imagine that this book will make quite some impression on some 15
year
> old people. By the time they are the scientific establishment, they may be
> very willing to make their hero famous, and scorn his predecessors.
To which i should add:
If i'm right about W's intentions, a strong critical attitude of the
'establishment' may very well *help* him to gain historical magnitude in
this way.
Cheers,
Herman
W. Edwin Clark
Herman Jurjus wrote:
>
> To which i should add:
> If i'm right about W's intentions, a strong critical attitude of the
> 'establishment' may very well *help* him to gain historical magnitude in
> this way.
>
Have you read the book and the reviews? The problem is not a critical
attitude of the establishment, it is his dismissal of the work of
others and attempts to take credit for ideas that he wishes he
had thought of first. A true critique of the establishment should
come with some testable hypothesis. For example, Newton and Einstein
were taken seriously when their ideas were used to make predictions
that were verified by observation.
Read some of the reviews I have linked to at
http://www.math.usf.edu/~eclark/ANKOS_reviews.html
and you will begin to understand the situation better.
--Edwin Clark