re:Re: The number 8. A TOE?

2002-11-21 Thread Marchal Bruno
Tim May wrote

(I was struck by the point that the sequence 1, 2, 4, 8 is the only 
sequence satisfying certain properties--the only scalars, vectors, 
quaternions, octonions there can be--and that the sequence 3, 4, 6, 
10, just 2 higher than the first sequence, is closely related to 
allowable solutions in some superstring theories, and that these facts 
are related.)


That's indeed what amazes me the more. I always thought that the dimension
justification in string theories was unconvincing, but with the octonion
apparition there, I must revised my opinion.
Needless to say I hope octonions will appear in the Z1* semantics!
(so we could extract string theory from comp directly).

Do you know that Majid found a monoidal category in which the octonions
would naturally live, even (quasi)-associatively, apparently.

I think the sedenions (16 dim) could play a role too, even if they do not
make a division algebra. cf the (not really easy) 1998 paper by Helena
Albuquerque and Shahn Majid quasialgebra structure of the octonions.
For the paper and some other see 
http://arXiv.org/find/math/1/ti:+octonions/0/1/0/1998/0/1
All that gives hope for finding the generalized statistics we need
on the (relative) consistent histories or observer-moments 
(i.e, with AUDA,  a Z1* semantics). 
Well... let us dream a bit...  ;-)

Bruno
 




RE: Re: The number 8. A TOE?

2002-11-21 Thread Ben Goertzel

Regarding octonions, sedenions and physics

Tony Smith has a huge amount of pertinent ideas on his website, e.g.

http://www.innerx.net/personal/tsmith/QOphys.html

http://www.innerx.net/personal/tsmith/d4d5e6hist.html

His ideas are colorful and speculative, but also deep and interesting.

One could spend a very long time soaking up all the ideas on the site.

By the way, Tony is a very nice guy, who did a postdoc under Finkelstein (of
quantum set theory fame) and earns his living as a criminal-law attorney.

I spent some time a few years back trying to create a novel physics theory
based on discrete Clifford algebras, which relate closely to quaternions and
octonions.  My effort was unfinished, and I turned my attention to other
types of science, but some of my notes are at:

http://www.goertzel.org/papers/main.htm

(scroll to the bottom to see a list of documents under the heading

Some Incomplete Speculations on the Foundations of Physics

-- Ben Goertzel




Re: Algorithmic Revolution?

2002-11-21 Thread vznuri
RS wrote on one level how the algorithmic revolution 
was epistemological. I objected to this partly. let me
quote the dictionary defn of epistemology

epistemology-- the branch of philosophy that deals with 
the nature and theory of knowledge.

now in newtons time, science was seen as a branch of philosophy.
however in modern times, philosophy has become somewhat disconnected
from science and followed its own course. so to me to label a genuine
scientific paradigm shift epistemological seems to downplay its
significance somewhat as a little too abstract. the scientific revolution
is not merely about a different way of seeing the universe, but a different
way of interacting with it. (experimental method, etc.) 

this is exactly
the way in which I insist the algorithmic revolution be interpreted
as I outlined..  not merely a shift in the way 
we view the world. (unfortunately 
paradigm shift terminology sometimes implies a merely conceptual,
subjective shift in view, partly due to kuhns perspective, but a
paradigm shift means much more than a mere psychological rearrangement.)


next, RS defines the clockwork metaphor in terms of the newtonian
revolution. this is very reasonable and there is a high correlation.
however I would argue the clockwork paradigm is ongoing. the
clockwork universe involved multiple new ways of seeing the
world. one of them, indeed, was newtonian mathematical laws
for physics, gravitation, etcetera. another was determinism,
ala the famous laplacian quote re: atoms as billiard balls. 

however another was simply, universe as mechanistic. the clock is a 
machine. the clock metaphor proposes the universe runs like a kind
of automated machine subject to mathematical/physical laws. 

lets be very careful to define clockwork universe metaphor in terms
of the accurate history of its origination, not from our modern point
of view. note that in the middle ages, prior to
the newtonian revolution, the previous paradigm for the concept
of force was something sometimes involving supernatural aspects.
the world was presumed to be set in motion by god  influenced
by various spirits, entities, etcetera in ways not fully conceivable.
this is what the clockwork metaphor replaced.

the universe as mechanistic theme from the clockwork metaphor
persists to this day. einsteins relativistic theory involved the
consideration at clocks in moving frames. 
when physicists analyze particle dynamics,
or even search for a TOE as we are here, I would say the clockwork
metaphor is still alive. its still ticking, so to speak.. wink

again, let me contrast the algorithmic metaphor for the universe
with the clockwork one. even in newtons time, the idea was
that the universe ran **like** a clock. it was a metaphor. but
the zuse-fredkin-wolfram idea of the universe is that the
universe evolves not merely **as** a computation, but that it
**is** a computation. 

therefore, imho the algorithmic metaphor
is actually more than a metaphor, more than the clockwork model
was a metaphor.  its not merely a paradigm shift I would say, its
something more. its a new model, a new system, a new framework. 
its comparable to newtons discovery
of the law of gravitation if the program can be successfully
carried out.

is the algorithmic idea incorrect? someday we will probably
notice that it has its deficiencies just as the clockwork idea
did, but we will not discard it entirely, just as we have
not discarded the clockwork universe idea.

so imho to say the clockwork metaphor for reality is wrong,
is (uh) wrong. imho its a simplistic/facile rejection of a 
still-legitimate paradigm.




wolfram speaks at comdex

2002-11-21 Thread vznuri

wolfram at comdex on the universe as software idea etc

http://news.com.com/2100-1040-93.html