RE: Algorithmic Revolution?
Colin Hales wrote > ... >Not really TOE stuff, so I?ll desist for now. I remain ever hopeful that one >day I?ll be able to understand Bruno?. :-) Ah! Thanks for that optimistic proposition :-) Let us forget the AUDA which needs indeed some familiarity with mathematical logic. But the UDA? It would help me to understand at which point you have a problem. For example I understand where Hall Finney stops, although I still does not understand why. I got a pretty clear idea where and why Stephen King disagrees. This can help me to ameliorate the presentation. You could also help yourself through the formulation of precise questions. Perhaps you did and I miss it? (*) Bruno (*) My computer crashed badly some weeks ago and I use the university mailing system which is not so stable. Apology for funny spellings, "RE:RE:"-addition in replies, lack of signature, etc.
Re: Algorithmic Revolution?
> Colin Hales wrote: > > Here is another possible confusion: emergence as a descriptive artefact vs > > emergence as real layered behaviour in a real system. The wording > > initially looks as if you think emergence is not real. The emergence is real > > (whatever we consider real is!). Example: There are at least 6 fundamental > > layers of emergence from quantum froth to mind. The agreed view appears to > > be that any formal mathematics of each layer stops at each layer whereas an > > algorithmic approach generates/spans the layers, which are delineated by an > > appropriately sensitised observer. Both styles of description seem > > appropriate and able to coexist provided their character is understood. I presented a general systems model of complexity~emergence at the first Complexity conference held in Nashua, New Hampsire USA by NECSI in 1997 in which I stipulated a very specific relationship involved in inter-tier production of emergent complexity. The layers do couple in very specific ways - at any level of layering~tiering identifiable. Info~energy which recursively loops between the state-nodes of two or more agents in a reference frame binds the agents into a narrower behavior mode. I.e., increased distribution of information~energy in one tier of organization can cause behavior localization in an adjacent tier. Rephrased: natural or induced entropy increases in one tier can effectively produce negentropic complexity formation in the next higher tier of organixation (Rose, 1973). Designing the algorithm involved is the key to human survival and evolution. Jamie Rose Ceptual Institute
Re: Algorithmic Revolution?
Colin Hales wrote:
> Here is another possible confusion: emergence as a descriptive artefact vs
> emergence as real layered behaviour in a real system. The wording
> initially looks as if you think emergence is not real. The emergence is real
> (whatever we consider real is!). Example: There are at least 6 fundamental
> layers of emergence from quantum froth to mind. The agreed view appears to
> be that any formal mathematics of each layer stops at each layer whereas an
> algorithmic approach generates/spans the layers, which are delineated by an
> appropriately sensitised observer. Both styles of description seem
> appropriate and able to coexist provided their character is understood.
Remember my insistence on the models being "good" (by whatever
criterion "good" is). Emergence in a poor model is most definitely not
real. But we expect good models to be capturing something about
reality, so emergence in these models is in some sense a real
phenomenon.
However, all I really insist upon is that two observers discussing a
phenomenon agree that a particular model (or language as it were) is
good. Then they can agree upon the emergence in that case. For the
billions of people who believe in God, presumably God is equally a
real emergent phenomenon.
>
> Not really TOE stuff, so Ill desist for now. I remain ever hopeful that one
> day Ill be able to understand Bruno
. :-)
>
Same here!
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
RE: Algorithmic Revolution?
Russell Standish wrote: >> Colin Hales wrote: >> Hi Folks, >> I have chewed this thread with great interest. >> >> Our main gripe is the issue of emergent behaviour and the mathematical >> treatment thereof? Yes? This is the area in which Wolfram claims to have >> made progress. (I am still wading my way through his tome). >> >> ***Isnt the 'algorithmic revolution' really a final acceptance that there >> are behaviours in numbers that are simply inaccessible to "closed form" >> mathematical formulae? - That closed-form mathematics cannot traverse the >> complete landscape of the solution space in all contexts? >> > >If this were the case, the 'algorithmic revolution' is at least 200 years old, as people have >known at least this long that most integrals cannot be written in "closed form". > >Of course, from a practical point of view, it was so expensive to solve mathematical problems numerically, > that hardly anyone bothered until the advent of the electronic computer. Since then, of course > computational science has taken off like a rocket, and keeps the likes of me employed. But this is > hardly new news, or philosophically interesting. > Cheers We have a small confusion here (probably caused by my own choice of words). Im not talking about the numerical solution to a given mathematical formula. Agreed: Mundane++. Memories of laboriously iterating on my calculator come to mind! :-) What Im saying (as you seem to agree) is that for some aspects of the universe (including those aspects we identify as emergent phenomena) there are no formulae possible in the first place. I think I find the answer to my original question in the last 2 paragraphs of your paper section 2. http://life.csu.edu.au/ci/vol09/standi09/, as well in your emergence thread para where I think you have nailed it: . As to mathematics predicting emergent phenomena, I believe that the answer is categorically no. Emergent phenomena are a result of a modelling process - eg what a brain does, not an analytic process. Mathematics can be used to describe the emergent phenomenon after it is discovered, but I don't think the discovery process can really be called mathematics.. Here is another possible confusion: emergence as a descriptive artefact vs emergence as real layered behaviour in a real system. The wording initially looks as if you think emergence is not real. The emergence is real (whatever we consider real is!). Example: There are at least 6 fundamental layers of emergence from quantum froth to mind. The agreed view appears to be that any formal mathematics of each layer stops at each layer whereas an algorithmic approach generates/spans the layers, which are delineated by an appropriately sensitised observer. Both styles of description seem appropriate and able to coexist provided their character is understood. I think we do have a revolution and it is a revolution that will force us to use a wolfamesque rule-based numerical combination descriptive/predictive method to deal with emergence whether we like it or not because its the only technique that can traverse the layers and there are a multitude of problems where we need to do exactly that. It seems more than a passing fad. I can foresee industry based on derivation of elaborate CA to fulfil useful requirements that cannot be achieved otherwise. I can see scientific method and Cog. Sci. in particular undergoing a transformation of a sort as a result. Not really TOE stuff, so Ill desist for now. I remain ever hopeful that one day Ill be able to understand Bruno . :-) Cheers, Colin Hales
Re: Algorithmic Revolution?
I don't think I received the first of my two messages written today on Wolfram, but it made it to the archive. In case anyone missed it I'll just point to it rather than re-sending. It's available at http://www.escribe.com/science/theory/m4156.html. Hal Finney
Re: Algorithmic Revolution?
Hal Finney wrote:
>
> My one concern is that if Wolfram is right and our universe is a random
> program from some set, and if there are much more than on the order
> of 100 bits in the program, we will never be able to find the right
> program. If the nature of the program space is similar to what Wolfram's
> explorations suggest, that most of the space is unstructured and there
> is no way to identify the likely fruitful programs, there will be no
> way for us to know if we are on the right track or not. We won't have
> the hope of finding a program that "almost works" and then successively
> refining it to get closer and closer, because the true program will be
> completely different from an almost-true program.
>
> The situation will be something like the search for a cryptographic key,
> where you can't really hope to get closer and closer until you get it.
> You're stabbing totally in the dark until you fall upon the right one.
> And if the search space is too large, you will never find the answer.
>
> Hal Finney
>
This is exactly the problem I have with the idea that we live within
one particular computational history, for all time, but can never know
which.
There will be constraints on the set of possible histories in which
can be lived, which can be uncovered and linked to a theory of
conscious observation. All else is pure contingency. So other ideas
proposed on this list - that we can be identified with a whole sheaf
of computations that are continually diverging - seem far more appropriate.
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
Re: Algorithmic Revolution?
One more point with regard to Wolfram and our list's theme. I think that implicit in his conception of the underlying rules of the universe you have to assume some kind of all-universe model. The reason is that he does not expect our universe's program to be particularly special or unique. He thinks it will be relatively short, but given the kind of computational structures that might be the basis for the universe, the program is expected to be basically random. Every computational system has a certain percentage of its programs that can produce interesting-looking structure, and the expectation is that the same thing will hold for whatever computational model turns out to most simply express the universe's program. Whatever our program is, it will turn out to be one of the ones that produces structure. But these are almost certainly a tiny percentage of the whole, based on Wolfram's results. And the specifics of which ones will produce structure are very difficult to define. Making a tiny change in a program will often produce a completely different output, at least with the computational systems Wolfram investigates. The ones which produce structure are scattered very randomly throughout the space of all possible programs. For example, among the nearest-neighbor, 2-state, 1-dimensional CAs that Wolfram uses as his simple exemplars, there are 256 possible different programs, which Wolfram numbers from 0 to 255. As it turns out, only one of them, program number 110, produces a certain kind of complex structure that has particle-like behavior with very complex kinds of interactions. Of all of them, this is the one which at least superficially would be the most likely to be able to evolve life (although it's almost certainly too simple to actually do so). But let's suppose that we learned that we lived in a universe based on rule 110. Why would that be? Why, of all the 256 possible programs, would only rule 110 exist? Well, there are two plausible answers. One is that someone selected rule 110, but that raises all kinds of insurmountable problems of its own. The other is that all of the programs were instantiated, and then of course we turned out to live in rule 110 because it was the only one that could sustain life. So Wolfram's approach leads very naturally to the assumption that all possible programs are being run. If it does turn out that our universe's program is relatively simple but still densely packed and "random" among a vast space of comparable programs, most of which would produce sterile universes, then I think we would be forced to seriously consider that all of the other programs were being run, too. My one concern is that if Wolfram is right and our universe is a random program from some set, and if there are much more than on the order of 100 bits in the program, we will never be able to find the right program. If the nature of the program space is similar to what Wolfram's explorations suggest, that most of the space is unstructured and there is no way to identify the likely fruitful programs, there will be no way for us to know if we are on the right track or not. We won't have the hope of finding a program that "almost works" and then successively refining it to get closer and closer, because the true program will be completely different from an almost-true program. The situation will be something like the search for a cryptographic key, where you can't really hope to get closer and closer until you get it. You're stabbing totally in the dark until you fall upon the right one. And if the search space is too large, you will never find the answer. Hal Finney
Re: Algorithmic Revolution?
I think there are a couple of things about Wolfram's book which aren't well understood. Most importantly, he is not specifically commited to cellular automata. He does focus on them, especially 1-dimensional, 2-state CAs, as a particularly simple model of computation, which also has the property that a relatively high percentage of randomly chosen programs produce apparent complexity. But he explores a number of other computational systems, including higher dimensional and higher state CAs; mobile CAs; Turing machines; substitution systems; sequential substitution systems; tag systems; cyclic tag systems; register machines; symbolic systems; arithmetic; recursive sequences; iterated maps; continuous (non-quantized) CAs; partial differential equations; network systems; multiway systems; constraint satisfaction systems; and higher dimension versions of many of these. The lesson he draws is that generally, the same kinds of patterns are seen in virtually all of these ways of expressing computation. You see simple, constant outputs; simple repetition; chaotic patterns; and occasionally, the mysterious "structure" on the edge of chaos, which often shows tantalizing particle-like phenomena and other interesting analogs to real-world phenomena. Where he does fall back on CAs, I don't think his point is so much that the phenomena are based precisely on CAs, but that random, simple algorithms when implemented in CAs often produce very similar patterns to what we see in the real world. And that this is probably not coincidence. It suggests that these kinds of patterns could be considered attractors in pattern space. They are easier to produce than other patterns that might seem superficially similar. Their algorithm complexity is lower. And this insight might inform our efforts to understand the true nature of the phenomena which create these patterns. Where Wolfram turns to physics, his speciality, he explicitly departs the CA model as he tries to sketch a possible mathematical basis for the universe that is consistent with the paradoxical phenomena of QM and relativity. He uses network systems, hypothetical sub-quantum "nodes" which are connected to one another and whose connections might change under simple rules. This is not completely original; I think Wheeler and others pursued ideas similar to this back in the 70s. Wolfram takes it a little farther in showing how you could get some relativity-style phenomena, but it's a very bare beginning effort. My main point is that characterizing Wolfram as saying that the universe is a CA, or biological patterns or fluid turbulence or any other phenomena are caused by CAs, is not correct. He is not saying these phenomena are caused by CAs, he is saying that extremely simple CA programs produce similar phenomena, suggesting that such phenomena emerge spontaneously from computational systems. As for the universe, I think his point is that the grand, mathematical elegance of string theory and similar methods is the wrong approach. These beautiful mathematical models are too rigid and brittle to describe a universe like ours. The universe is more likely to be built out of a messy, random and simple little program that just happens to create patterns that have the properties necessary for life to evolve. In the context of our list, this can be thought of as a philosophical bias towards Schmidhuber and away from Tegmark. In Tegmark's model, string theory is relatively near the origin of the tree of mathematical structure; it is simple. If it produced enough particles and interactions of the right kinds to allow for life, it would be an excellent candidate for the place where we live. But in Schmidhuber's model, it's just as likely that some random hodgepodge of a program a few thousand bits in length will "just happen" to produce a very robust, dynamic and varied universe with all kinds of structure at different size scales. Such a universe is an inherently friendly home for life as there are so many possible niches for it to grow. Of course, at this point we are in no position to decide between these two philosophies. Wolfram's book is ultimatly a call to our intuition, an appeal for equal time to be given to Schmidhuber-ish approaches based on random programs, as for the traditional Tegmarkian mathematical modelling which is done in physics. I think there is something to be said for this shift in perspective, and I hope that at least a small minority of researchers will attempt to move Wolfram's program forward. Hal Finney
Re: Algorithmic Revolution?
Colin Hales wrote:
>
> Hi Folks,
>
> I have chewed this thread with great interest.
>
> Our main gripe is the issue of emergent behaviour and the mathematical
> treatment thereof? Yes? This is the area in which Wolfram claims to have
> made progress. (I am still wading my way through his tome).
>
> ***Isnt the 'algorithmic revolution' really a final acceptance that there
> are behaviours in numbers that are simply inaccessible to "closed form"
> mathematical formulae? - That closed-form mathematics cannot traverse the
> complete landscape of the solution space in all contexts?
>
If this were the case, the 'algorithmic revolution' is at least 200
years old, as people have known at least this long that most
integrals cannot be written in "closed form".
Of course, from a practical point of view, it was so expesnive to
solve mathematical problems numerically, that hardly anyone bothered
until the advent of the electronic computer. Since then, of course
computational science has taken off like a rocket, and keeps the likes
of me employed. But this is hardly new news, or philosophically
interesting.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
Re: Algorithmic Revolution?
My caveat before commenting: I'm an opinionated person, but I really
don't have any particular theory of everything to share with you. No
dreams theory, no soap bubble theory, no 18-dimensional cellular
automaton theory. I'm currently doing a lot of reading in logic, topos
theory, quantum mechanics, and math in general. I'm more interested
right now in really grasping why the Kochen-Specher says what it says,
for example. Some of you are way ahead of me. Anyway, these are some of
my caveats before plunging in.
On Sunday, November 24, 2002, at 04:26 AM, Colin Hales wrote:
Hi Folks,
I have chewed this thread with great interest.
Our main gripe is the issue of emergent behaviour and the mathematical
treatment thereof? Yes? This is the area in which Wolfram claims to
have
made progress. (I am still wading my way through his tome).
***Isnt the 'algorithmic revolution' really a final acceptance that
there
are behaviours in numbers that are simply inaccessible to "closed form"
mathematical formulae? - That closed-form mathematics cannot traverse
the
complete landscape of the solution space in all contexts?
And I believe Charles Bennett said all this more clearly and
convincingly with his "logical depth" arguments. (See, for example, his
long essay in an excellent book called "Fifty Years of the Turing
Machine.")
The argument goes like this: suppose one is walking on a beach and
finds a gold watch. The watch has many moving parts, many non-natural
things like the crystal, the case, and much internal structure. (I'm
deliberately mixing in parts of Dawkins' "Blind Watchmaker," as the
arguments are closely related.)
The watch shows evidence that a lot of "processes" have run for a very
long time. Not computer processes, but processes of manufacturing the
components, of fitting them together, of learning what doesn't work and
what does work, and of a serious industrial infrastructure.
Or consider an e. coli organism. Something like 4 GB of genetic
material, measured in bits and bytes (if I recall this correctly...it
doesn't affect the argument if I am off by some factor).
The "complexity" of the e. coli genome is, by some measures, just this
4 GB. But nearly all 4 GB strings (which is a very, very large number!)
produce dead organisms. In the space of 4 GB strings, some relatively
small "patch" of them produce functioning, reproducing organisms like
e. coli.
Both the watch and the e. coli appear to have been the result of a lot
of shuffling and processing of the "apparent" number of bits.
Charles Bennett calls this "logical depth." This is closely related to
algorithmic information theory, where the shortest description of a
string (or other object) is essentially the program or process which
produces the object. Bennett has placed more emphasis on the "depth" of
a series of iterated processes, but the idea is basically the same.
(And there may have been good syntheses of the ideas in recent years...)
Another way to look at this, metaphorically, is in terms of compression
of a spring. The evolutionary pressures and differential reproduction
rates with e. coli, or with watches!, takes a spring and puts more
energy into it...the energy to do things later. Even a fixed-length
string, like 4 GB in e. coli, can be seen as being "compressed" in this
sense. More and more logical depth is compressed into a string of fixed
length. (Imagine a program in a competing robot, perhaps in one of
those "Battlebots" arena shows, where the program is perhaps, by
coincidence, limited to about 4 GB of Pentium 4 main memory. The
program gets shuffled and changed, via either genetic algorithms (GA)
or genetic programming (GP) or whatever. The same 4 GB program space
("string," seen abstractly) gets more and more capable.
A cellular automaton can also have high logical depth. In fact, back
when I read (some of ) Wolfram's earlier book on CAs, "Cellular
Automata and Complexity," I believe it is called, this is the viewpoint
I was reading it from.
But the fact that cellular automata exhibit this kind of logical depth
does not mean that gold watches and e. coli are proof that the universe
is a cellular automaton!
Q.E.D.
Now, pace Zuse, Fredkin, Lloyd, and all the others, it may in fact be
the case that a Theory of Everything somehow involves CA-like
computations or interactions at perhaps the Planck scale.
But nothing in Wolfram's recent book is at all convincing to me that he
has shown this in any meaningful sense. The phenomena he has been
experimenting with are at least 25-30 orders of magnitude away from the
Planck scale. Believing snowflakes, crystals, and sea shells accrete
material in CA-like ways, which I think physicists and biologists have
been convinced of for a
RE: Algorithmic Revolution?
Hi Folks, I have chewed this thread with great interest. Our main gripe is the issue of emergent behaviour and the mathematical treatment thereof? Yes? This is the area in which Wolfram claims to have made progress. (I am still wading my way through his tome). ***Isnt the 'algorithmic revolution' really a final acceptance that there are behaviours in numbers that are simply inaccessible to "closed form" mathematical formulae? - That closed-form mathematics cannot traverse the complete landscape of the solution space in all contexts? My own approach has been to regard emergence as the repositioning of the observer of a system such that the mathematical descriptions you have been using fall over/cease to be relevant. The idea that the math can seamlessly transcend an observers scope is, I concluded, simply meaningless as the math is defined by the observers scope. The prejudices of our position as observers are therefore automatically destined to be embedded in our descriptors of things. If this is the case then one cannot overlook the use of computers or the AIT approach if you need to study, understand and replicate real-world phenomena (in particular, MIND) that transcend the boundaries of emergence. Will the historians look back on our obsession with closed form math and see it as the machinations of mathematical youth? Para *** above is the clincher and I have been unable to distil a definitive stance from all the writings. Clues anyone? regards, Colin Hales * somewhat perplexed *
Re: Algorithmic Revolution?
George, beautiful. Maybe I propose a line at the end: "With a LOT of ego attached" Best wishes John Mikes - Original Message - From: "George Levy" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, November 22, 2002 12:55 AM Subject: Re: Algorithmic Revolution? > When you look at the bottom of the well, > all the way > deep down, > you see yourself staring right back at you. > > And right now you look like an algorithm. > Oh well, there was a time when you looked like clockwork > Maybe tomorrow you'll be a brain. > And the day after tomorrow maybe a quantum device. > > The universe that we perceive is in our own image. > It can only be in our own image. > Bruno is right, the foundation of physics may well be psychology. > It could even be neurology. > > George
Re: Algorithmic Revolution?
When you look at the bottom of the well, all the way deep down, you see yourself staring right back at you. And right now you look like an algorithm. Oh well, there was a time when you looked like clockwork Maybe tomorrow you'll be a brain. And the day after tomorrow maybe a quantum device. The universe that we perceive is in our own image. It can only be in our own image. Bruno is right, the foundation of physics may well be psychology. It could even be neurology. George
Re: Algorithmic Revolution?
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.
Re: Algorithmic Revolution?
At 11/21/02, you wrote: The clockwork universe was shown to be wrong with Qunatum Mechanics. My gut feeling is that the computer universe will also be shown to be wrong. In my view there are two types of universes. Type 1 have internal rules of state succession that are like computers - UD's and the like could generate them. Type 2 have rules that have a degree of "do not care" in determining the valid next state and this "do not care" component is a channel to an external random oracle. However, I attempt to show in my approach that Type 1 are also subject to the external random oracle but the channel differs. This means that all universes have open logic systems and can have exploding cows and other white rabbit events. I believe ours to be a Type 2 universe with a rule set that allows few rabbit events of a macro nature and many of a micro nature. I suspect that in some aspects we agree. I also think that Bruno's UDA to the extent I think I understand it is a candidate for one of a Type 1 universe's channels to the external random oracle. I believe Juergen's work to be a candidate for the rule set of some Type 1 universes. However, I see no bias towards one type or the other in terms of quantity or in terms of any any other system wide measure. Hal
Re: Algorithmic Revolution?
[EMAIL PROTECTED] wrote:
>
>
> RS reformulates/reduces the term "algorithmic revolution" as:
>
> >1. A social revolution..
> >2. A scientific revolution..
> >3. An epistemological revolution..
> >4. A mathematical revolution..
>
> all true. however, wolfram-fredkin-zuse et al are not merely proposing a
> mere "epistemological revolution" as you state with (3). they're
> saying, the "next state" of the universe _really_is_ a
> computation, that we really are (and all reality is)
> built out of cells in a very large 3D or 4D cellular automaton. its
> not merely a metaphor. in this sense it probably cannot be seen on
> the same level as the clockwork mechanism for the universe, or
> the "universe-as-energy" from the thermodynamic/industrial/steam
> engine perspective.
Where did the "mere" come from? Epistemological as in a revolution of
our understanding of the world.
Zoom back 150 years, and you will find that people believed that the
universe really did follow Newton's equations of motion exactly, and
that all you needed to know everything about the universe at all times
was the positions and velocities of all constituent particles _at one
moment in time_. This is what is described by the clockwork metaphor.
The Wolfram-Fredkin-Zuse thesis that the universe is a Turing machine
is described metaphorically as a "computer universe" - just as real
computers are only metaphors for Turing machines.
I'm afraid I don't appreciate the difference here. The clockwork
universe was shown to be wrong with Qunatum Mechanics. My gut feeling
is that the computer universe will also be shown to be wrong.
>
> this is a physical hypothesis about the universe. so far it
> is not yet testable or falsifiable. but I would argue there
> is very good circumstantial evidence.
>
> RS says (3) is "potentially as wrong as the clockwork model
> of the universe". but, I would argue the clockwork model
> is not really "wrong", only that it was a steppingstone that
> is now obsolete or incomplete relative to new data. it was an
> outstanding metaphor for reality & is arguably still a very strong
> element of all modern scientific thought.
>
> with 4, RS says this refers to "algorithmic information theory"
> and "the jury is still out" on it.
> technically this is the name for the field that is
> involved with compressibility, i.e. chaitin-kolmogorov ideas
> (is this what RS meant?). which
> is mostly seen as a specialized subfield of computational
> complexity theory. this is a strange reduction from my point of
> view & is definitely not the mathematical revolution associated
> with "the algorithmic revolution" I referred to earlier.
>
>
Yes - the usual name for it is algorithmic information theory, and
Greg Chaitin was probably the prolific contributer. Ming Li has
demonstrated some very interesting applications for the theory in
solving mathematical problems otherwise unsolvable. I wouldn't be
surprised if AIT turns out to be as important as differential
equations or Hilbert space theory, for example. As I said though, it
is still too early to say.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
Re: Algorithmic Revolution?
RS reformulates/reduces the term "algorithmic revolution" as: >1. A social revolution.. >2. A scientific revolution.. >3. An epistemological revolution.. >4. A mathematical revolution.. all true. however, wolfram-fredkin-zuse et al are not merely proposing a mere "epistemological revolution" as you state with (3). they're saying, the "next state" of the universe _really_is_ a computation, that we really are (and all reality is) built out of cells in a very large 3D or 4D cellular automaton. its not merely a metaphor. in this sense it probably cannot be seen on the same level as the clockwork mechanism for the universe, or the "universe-as-energy" from the thermodynamic/industrial/steam engine perspective. this is a physical hypothesis about the universe. so far it is not yet testable or falsifiable. but I would argue there is very good circumstantial evidence. RS says (3) is "potentially as wrong as the clockwork model of the universe". but, I would argue the clockwork model is not really "wrong", only that it was a steppingstone that is now obsolete or incomplete relative to new data. it was an outstanding metaphor for reality & is arguably still a very strong element of all modern scientific thought. with 4, RS says this refers to "algorithmic information theory" and "the jury is still out" on it. technically this is the name for the field that is involved with compressibility, i.e. chaitin-kolmogorov ideas (is this what RS meant?). which is mostly seen as a specialized subfield of computational complexity theory. this is a strange reduction from my point of view & is definitely not the mathematical revolution associated with "the algorithmic revolution" I referred to earlier.
Re: Algorithmic Revolution?
There seems to be more heat that light in this discussion. There's
several things going on here:
1. A social revolution in the use of information technology (mobile
phones, internet and all that). This is beyond dispute, I believe, and
I didn't see anyone on this list disputing that.
2. A scientific revolution - use of computer simulations as a 3rd way
from theory and experiment. This is using computing technology, as
opposed to information technology, and is about 2 decades older thatn
the social revolution. Again, there is little dispute in this.
3. An epistemological revolution - a paradigm shift that sees reality
cast in terms of a computational or algorithmic metaphor. This is how
Tim May interpreted "algorithmic revolution", as did I.
4. A mathematical revolution - algorithmic information theory has been
explosive since it was founded in the mid-60s. It has profound
consequences to the roots of mathematics.
No. 3 is the type of thesis promoted by Wolfram, and goes back at
least to Konrad Zuse in the 1960s. It is worth treating with a
considerable grain of salt - it is a paradigm, as potentially wrong
as the clockwork model in the late 19th century.
No. 4 - I think the jury is still out. Practical applications of AIT
are still rather meagre compared with more traditional areas of
mathematics. But I do think it is a fascinating area of study.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
Re: Algorithmic Revolution?
hi all. re the term "algorithmic revolution" here are a few more ideas along this thread Id like to point out. TCM wrote >My belief is that basic mathematics is much more important than >computer use, in terms of understanding the cosmos and the nature of >reality. ok, fair disclosure, I have a BS software engr, writing code since age ~10, and it affects my worldview bigtime. or, one could say, I really know how to pick a winning horse, haha.. seriously, I recognized & planned my life around the "algorithmic revolution" from a young age. at an early point I realized that software is like "animated mathematics". this is a very,very deep & cosmic way of looking at algorithmics. it captures some of the revolutionary flavor. we can suggest that mathematics has previously attempted to grasp the concept of change, via calculus, differential eqns etc. but something is fundamentally new about simulation. it captures worlds that cannot be expressed via mathematical generalities. there are no equations we can write down that describe the outcome of, say, a climate simulation-- its all locally defined & then globally simulated & the outcome is "emergent". & what are the differential equations that describe the game of life?? imho algorithmics captures the extraordinary, currently very poorly understood property of "emergence". just as in the game of life there are thousands of glider types, none of which one would expect/anticipate from the simple rules. we can argue that algorithmics is a fundamentally new way to look at mathematics. and one could argue, all mathematics up until now has been transformed. at this point, it seems much more correct to classify mathematics as a subbranch of algorithmics than vice versa. I believe much mathematics of the future will be taught from the "algorithmic point of view" instead. imho, the invention & harnessing of the algorithm is roughly as significant in human intellectual development as pythagoras's original realization about how mathematics modelled nature. its easily on that order of magnitude as far as a milestone in human thought, possibly surpassing it. it seems to me, fundamentally, algorithmics entails and surpasses mathematics as a new simultaneously conceptual and physical tool for analyzing the universe and its variegated phenomena. so think. we've basically got several millenia of mathematical thought, dating all the way back to the babylonians (who played with perfect triangles, fractions etc), and quite well developed in greece 2000 years ago. reaching heights of sophistication with calculus, or the abstraction in the 20th century. Im saying to some degree, all that is childs play compared to the new universe of algorithmics. re: TCMs questions about some of my points. 1st, I believe that we will eventually get the math for a TOE that matches accelerator/particle physics so perfectly that it will be considered redundant or wasteful to do the expensive supercollider experiments, because the accelerators will never find anything that does not match the comprehensive theory. that is, after all, one of the big reasons to look for a TOE. but I agree, until that point, physicists are not going to give up the "big science".. a crazy thought? perhaps. but lets look at atomic weaponry testing-- thats essentially whats happened. the US has been simulating atomic weapons testing for many years now with powerful supercomputers. and obviously the results are considered ***extremely*** accurate. it can indeed be done on some level. 2nd-- alas, I wish I could cite a reference. but software is used extremely heavily in particle physics experiments to automatically analyze particles and classify them & find anomalous events. its basically AI-like software, extremely sophisticated. it can look at very complicated particle tracks & collisions and name all the particle tracks based on analyzing the "big picture". this used to be done by humans & by hand, and (as I understand it) the discovery of many particles from the last decade or around that range could not have been done with this highly sophisticated sorting software that can run through millions of events very quickly. so there is a hidden story behind massive particle accelerators. the software infrastructure for them is all invisible and mostly unknown to the public, but its a vast edifice at the core of the analysis, and has gone through revolutionary changes in a short amount of time, mirroring the algorithmic revolution elsewhere. how much is that software worth?? I cant really estimate, but I wouldnt be surprised if a significant percent of supercollider budgets was spent on developing it. if anyone knows references on software used in particle physics analysis, I would really like to know myself. a nice reference on the culture behind accelerators is "beamtimes & lifetimes" by sharon traweek.
Re: Algorithmic Revolution?
On Tuesday, November 19, 2002, at 05:12 PM, [EMAIL PROTECTED] wrote: I would take all of TCMs own citations and turn them around in my favor. I would classify all the following as occurring under the heading "algorithmic revolution" (not the greatest moniker I admit.. a provisional one for me right now) - advent of cyberspace, web, email, browsers etcetera - advent of mass software - PC revolution - microsoft & intel from zero to billion dollar companies in short decades - quantum computing is on the way - fractals. could not be discovered without algorithms. a new metaphor for not only nature but all reality. - complexity theory. again, not possible before the algorithmic metaphor and mass computational capabilities - simulation, "in silico science" - moore's law - photorealistic rendering - (relational) databases - mass economic shift into information technology as driving force.. "bits versus atoms".. (negroponte) - video games - etcetera!! I agree that these are all huge changes. I interpreted your "algorithmic revolution," in the context of this list and the Kevin Kelly article and the Wolfram brouhaha, to be about a revolution in terms of thinking of the universe (or multiverse) as being primarily computational. My point is that the verdict on the Zuse/Fredkin/Wheeler/Lloyd/Wolfram/Tegmark/Schmidhuber/etc. views of reality is still way, way out. I stand by this point. If by "algorithmic revolution" you meant that computers are increasingly important, then of course I agree. ... ahem!!! what is the relevance to a TOE??? well historically it is clear our perception of reality is based on our favorite metaphor of the times. in recent ages it was (a) the clock, "clockwork universe", (b) the steam engine. and now it is (c) computer/algorithm/information. clearly it is no coincidence whatsoever that new TOEs are essentially algorithmic. its the human race's latest-and-greatest metaphor for reality. Yes, and our past experience in going through all of these metaphors or "mathematical fictions" has made many of us wary of saying things like "The universe is like a hologram" or "The universe is about connection" or even "The universe is a gigantic Game of Life." The issue of an ontology being a metaphor is an interesting one. I currently have no view of any particular metaphor for what the universe "is." It may have computational aspects, and mathematics (superset of computer science, of course) may be woven throughout the structure of reality. It may even have "holographic" or "clockwork" or "cellular"-like aspects. But aspects are not the same thing as equivalence. Greg Egan makes a good point in "Diaspora" about the limitation of the mathematical models we sometimes use as metaphors for reality. A mass falling through a borehole through the Earth acts exactly as if it's a mass on a spring tethered at one end. Same precise equation of motion. Yet a spring is not at all what the Earth is, and confusing the mathematical model with reality is dangerous. Of course, at this point we have much, much less reason to speculate that the universe "is" a cellular automaton of some sort. scientists have been slow to adopt to this shift, and I would argue they are still underutilizing simulation to some extent. science & physics is still yet to be influenced fully by the algorithmic revolution. one striking example I think will happen-- I believe billion dollar particle accelerators may be downgraded in importance in favor of extremely effective simulations. The reason experiments are still done is because they are the real proof of the pudding about what the universe really _is_. (besides-- does anyone fully realize how much software plays already such a crucial, foremost role in existing accelerators??) Not sure what you mean. I did some coding of Monte Carlo simulations in my physics days, and I hired some of the coders from SLAC to work on some of the stuff we were doing at Intel. Software is used to design the accelerators, the detectors, the experiments, etc. As with the rest of the world, computers and software are undeniably important. I'm not doubting the importance of computers. Nor the importance of clocks and wristwatches. But just as we know "the universe as a clockwork mechanism" was not the whole picture, I think "the universe as a computer" is not, without a lot more evidence, very compelling. To me, at least. (I am interested in being convinced otherwise. And I have my own interests. Today I ordered the Peter Johnstone 2-volume set "Sketches of an Elephant: A Topos Theory Compendium." Not that I am saying "the universe is a topos.") --Tim May
Algorithmic Revolution?
TCM challenges me on the claim that we seem to be living through
an algorithmic revolution or paradigm shift, instead apparently
preferring a big ho, hum, shrug as more apropos.
I dont really know what the disagreement
is yet, it seems to be artificial/manufactured.
in one sense I am referring to nothing other than what KK outlined in his
wired article I posted.
unfortunately for TCM I think he's
barking up the wrong tree, I could cite huge piles of evidence.
also, I would credit TCM as being one of the earlier commentators
on key aspects of this revolution.
unfortunately, it is difficult to realize one is living in the
middle of a revolution, and historically most revolutions are only
identified in retrospect.
I would take all of TCMs own citations and turn them around in my
favor. I would classify all the following as occurring under
the heading "algorithmic revolution" (not the greatest moniker I admit..
a provisional one for me right now)
- advent of cyberspace, web, email, browsers etcetera
- advent of mass software
- PC revolution
- microsoft & intel from zero to billion dollar companies in short decades
- quantum computing is on the way
- fractals. could not be discovered without algorithms. a new metaphor
for not only nature but all reality.
- complexity theory. again, not possible before the algorithmic metaphor
and mass computational capabilities
- simulation, "in silico science"
- moore's law
- photorealistic rendering
- (relational) databases
- mass economic shift into information technology as driving force..
"bits versus atoms".. (negroponte)
- video games
- etcetera!!
its difficult to discriminate the distinction between 3 revolutions that
cross pollinate each other: revolution in computing power (including
storage & access of data), revolution
in communication (cyberspace), and the algorithmic revolution.
I think it is fair to say the former two are subsumed into
the latter. the fastest chips are completely valueless unless
there is something to do with them (run software). moreover, we dont
care which chips or technology our software runs on. (it may all be
quantum computers in not-so-distant future).
cyberspace is stitched out of software, such as internet protocols,
web servers, email servers, etcetera; it is in
fact a sort of "real-time algorithm". tim berners lee invented a
set of **protocols** ("communication algorithm").
this fact becomes clearer
as the algorithmic aspects of that communication system are enhanced.
for example, ebay is not merely a communication system, its a complex
cyberspatial-algorithmic system for auctions. google is a complex
algorithmic system for traversing web pages & serving them up in
a search engine, and worth billions because they do it more effectively
than anyone, i.e. have the best and most finely tuned "algorithms".
etcetera ..
we see that the most valuable aspects of
cyberspace are not about passive communication but active algorithmic
enhancements and optimizations of information flow.
lately I have been tracking the mass commoditization of video games.
recently video game industry revenue for the 1st time just outdistanced
hollywood box office receipts.
"the sims" has sold 18 million copies. new video games are starting to
replace movies as a core entertainment venue. this will all pale in the
future as mass group games are invented that run over cyberspace,
inciting further cultural shifting. the human race is getting married
to its algorithms, so to speak.
note that we still dont know the full implications or possibilities
of algorithms. new breakthrough ones are waiting to
be devised. for an example of an amazing
embodiment, look at what genetic algorithms are capable of. and its still
an open question whether true AI is an algorithm.
ahem!!! what is the relevance to a TOE??? well historically it is clear
our perception of reality is based on our favorite metaphor of the times.
in recent ages it was (a) the clock, "clockwork universe", (b) the
steam engine. and now it is (c) computer/algorithm/information. clearly
it is no coincidence whatsoever that new TOEs are essentially algorithmic.
its the human race's latest-and-greatest metaphor for reality.
scientists have been slow to adopt to this shift, and I would argue they
are still underutilizing simulation to some extent. science & physics
is still yet to be influenced fully by the algorithmic revolution. one
striking example I think will happen-- I believe billion
dollar particle accelerators
may be downgraded in importance in favor of extremely effective simulations.
(besides-- does anyone fully realize how much software plays already such a
crucial, foremost role in existing accelerators??)
now, Ive veered into some wild stuff, but I propose that a new TOE
will fully embody the "algorithmic revolution" Ive outlined above, it will
b
Re: Algorithmic Revolution?
Tim wrote:To: <[EMAIL PROTECTED]> Tuesday, November 19, 2002 4:50 AM SNIP >... > I just don't see any such sign of a revolution. No more so than 10 > years ago, 20 years ago. Yes, computers are now more powerful. >Problems > tend to grow faster in size than computers do, however, and often > having 100x the power only yields a slight improvement in accuracy, not > qualitative leaps or breakthroughs. (Paralleling, no pun intended, the > spacing of the Mersenne primes, where it's taking longer and longer to > brute force find the next one, even with dramatically more computer > power. Or the accelerator energy gap, where 10 times the accelerator > energy doesn't produce much more new physics.) > > There are aspects of computers that are always touching on cultural > issues. This last sentence tries to rectify your narrow view of a "revolution", understood not so much restricted in the quarters of Physics and other 'sciences' but in the entire life of humanity: The information-spread all over and in all topics. Todays use of computers is not computer-stuff: it is human lifestyle. Revolutionarily different from the lifestyle of 30 years ago. The "industrial revolution" was not an improved weaving machine. Revolutions are not results of a factual change, not changing a specific (scientific?) topical technique, they are trends, developing slowly within human development and observable only after a period as instrumental alterations in the facets of the entire life. And this is, what computers *helped* to occur, not by their technological gadgetal or theoretical improvements, but the universality of the world-information exchange - unparallelled earlier. Internet and stuff. The appreciable survey of newer segmental ideas and topical bestsellers you provide pertains to the technicalities and periferals of this revolution. There is a bigger (wider) one going on than your search for as a 'real' "scientific revolution", which is a segmental development anyway. > My belief is that basic mathematics is much more important than > computer use, in terms of understanding the cosmos and the nature of > reality. That may be an opinion and I respect it without subscribing to it. > > --Tim May Respectfully John Mikes
Algorithmic Revolution?
On Monday, November 18, 2002, at 10:15 PM, [EMAIL PROTECTED] wrote:
as just noted by TCM, kevin kelly on a computational/algorithmic TOE,
wolfram, wheeler, etcetera, from current issue of wired.
http://www.wired.com/wired/archive/10.12/holytech.html
I would say we are all in the midst of some kind
of "algorithmic revolution" that is sweeping across
culture, industry, & scientific fields etc. .. more
on that theme here
I just don't see any such sign of a revolution. No more so than 10
years ago, 20 years ago. Yes, computers are now more powerful. Problems
tend to grow faster in size than computers do, however, and often
having 100x the power only yields a slight improvement in accuracy, not
qualitative leaps or breakthroughs. (Paralleling, no pun intended, the
spacing of the Mersenne primes, where it's taking longer and longer to
brute force find the next one, even with dramatically more computer
power. Or the accelerator energy gap, where 10 times the accelerator
energy doesn't produce much more new physics.)
There are aspects of computers that are always touching on cultural
issues. In the 60s and 70s there was much hype about "general systems
theory" and modeling (a la Bertanlanffy, Arrow, others). Some social
scientists expected a revolution. In the 1980s it was chaos theory, and
fractals, with books on how financial markets are chaotic, how art is
fractal, how civilization lives at the boundary between order and
chaos, and so on. Trendy, and probably implicated somewhere in the
Sokal hoax ("Transgressing the Boundaries," the quantum
mechanics/litcrit/hermeneutics put-on). Not much of lasting value came
out of it, insofar as the revolutions outside of the narrow fields
directly involved are concerned.
In recent years it's been stuff about string theory, to some extent.
The Brian Greene book, "The Elegant Universe," became a best-seller,
even if probably fewer than one out of a hundred buyers got past the
first 20 pages. I don't think many of the coffee table book buyers are
expecting many revolutions outside of physics qua physics.
And of course Wolfram's book is a big seller. I won't comment, except
that I see no particularly strong evidence that he has changed the way
science is done, or will be done. Others have written harsher reviews.
I admire him for his dedication, but I think he missed the boat by not
working with others and working on specific problems.
(Tegmark works on lots of cosmology and observational astronomy
problems, with his Everything paper as just one small facet, almost a
hobby. Working on that theory full-time might make him a frequent
contributor to this list, but would probably not be good either for his
career or for getting any kind of progress or confirmation (!).)
My belief is that basic mathematics is much more important than
computer use, in terms of understanding the cosmos and the nature of
reality.
--Tim May
