Registered: Jan 2005
Posts: 2

I am posing this question because, to date, I have not seen a similar question posted.

Wolfram once stated something to the effect that he felt that if all of reality comes into existence from a very simple rule (or rules), that the program for, "life, the universe and everything" (as Douglas Adams might put it) might be only a few lines long.

My question is this, what would be "running" that "program"? And what runs any of the "programs," "rules," what-have-you?

Now some might accuse me of being too literal here, but I think this is an important question to ask. Not just, "can simple rules be used to explain complexity or the mechanics of the universe?" or "what are the rules?", but "what medium does the rule interact with?"

Wolfram talks about simple computer programs, but can a program run without a computer? No.

I can send a hex dump of a program to my printer and set the paper on my desk, but without the CPU, it's worthless.

This "meta" problem plagues me.

Now certainly I understand a model might be best limited to a narrow study, but even in the narrowest application, you need something to "run" the rules or "programs."

This is a sincere question.

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Registered: Mar 2004
Posts: 132

Hello Roger.

I know the plague you're talking about, and I think there's a good reason for it being there.

I think that we only need to go so far as to say something to the effect of "...which implies that something such as ourselves would think that", where what we would be thinking is "what the hell!?, where do we come from?, what do we do now?"

And I believe the principle of computational equivalence does exactly this. For it implies that such undecidability is inevitable in systems as complex as ourselves.

The one thing I see happen with people who even may know this fact quite well is still the burden of traditional intuition that is in them – that makes the relentless attempt to define a seperation between the qualities of human behavior and the qualities of the external world. From that alone a crucial point that is so often missed is that not only does the PCE imply undecidability in us, but it also implies it in the whole universe as well.

I think it's sort of like the relationship between our conscious selves and the brains that are supposed to account for us. All the science leads to definite underlying structure, but we nevertheless have this constant curiosity of there being more there.

In a way the PCE seems to explain all of this quite well. For it's implications show us that simple rules really can make us in all our complexity, and that there really doesn't need to be something as complex as a god or a big computer behind it all for us to exist. It could be as simple as something like rule 30, but to the same level of satisfaction that would stop us from asking questions altogether I'm sure we would have to refine our models and polish our intuition to decide exactly what rule is for certain the fundamental mechanism at work.

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Registered: Jun 2004
Posts: 78

Wolfram made a number of very strong statements,
which, IMO, decrease the value of his work.
One of these statements is that Universe is
a computer controlled by some simple program.
What he REALLY proves in NKS is:
there're cases when programs deliver a better
description of natural processes than
differential equations. He provides a number
of pretty convincing examples. There's also
some reasoning in NKS to the effect that
differential equations, except the simplest ones,
can be solved only by numeric methods,
so why to bother considering these equations
in the first place - we could be better off
starting from programs right away. There's certainly a grain of truth in this observation.
If wish he had just stopped here...

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Registered: Mar 2004
Posts: 132

Vasily, there is no such statement in NKS saying that the universe is a giant computer. What he says is much stronger than that, and offers a kind of solution to the meta problem of which I talked about above.

Doesn't it? Am I missing something?

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Registered: Jun 2004
Posts: 78

The idea that the whole Universe is a computer is what NKS
is all about. People are computers, too. This statement
was also repeated many times. I don't want to provide
any quotes here, because I'd have to quote the whole
book.
To verify that I was not alone with this interpretation
of NKS, please google "universe as computer", and
follow the very first link.

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Registered: Oct 2003
Posts: 167

Roger Pingleton asked:

what medium does the rule interact with?

__________________
Tony Smith
Complex Systems Analyst
TransForum developer
Local organiser

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Registered: Jun 2004
Posts: 78

If behaviour of Universe can be simulated, with 100%
accuracy, by a computer, as Wolfram claims, this is equivalent
to the statement that Universe IS a computer. Why?
BY DEFINITION. These systems are computationally
equivalent, and the whole class of these computationally
equivalent systems is CALLED (!) "computer".

IMO, NKS is the ultimate formulation of materialistic doctrine.
Wolfram just brought it to logical conclusion.

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Registered: Jan 2005
Posts: 15

The fact that we do need complex pieces of hardware (say a PC)
and of software (say Mathematica)
for running CA rules and simulating some natural behaviour
is indeed misleading, since it may
suggest that the real universe also needs some 'computer'
for running its 'program'; this idea leads to problematic questions,
such as speculating on the nature and origin of that 'computer',
on whether or not it is itself part of the universe...

My understanding of what Tony says (and I support his view)
is that we do not need to postulate the existence of a huge
'computer' animating a huge network of particles:
the only 'computer' is the individual particle itself,
which is intrinsically capable of interacting with its neighbors
according to some simple, universal rule.
All the rest is purely emergent, large scale behaviour,
that does not require any higher-level control.

While the huge computer would be very costly,
the tiny computing particle is very cheap.
Of course, setting up a huge network of cheap computing particles
is still costly.
But it would become cheap again if the whole construction were
carried out by one initial particle, in a big bang (self-replication
being one of the required emergent features) -- if, in other words,
the very creation of the physical substratum (space, matter, and so on)
could be regarded as an emergent feature.

Is it conceivable to look for some experimental evidence
in support of the last scenario by exploring rules
and computations on a (regular) computer?
The apparent contradiction here is that a regular computer
does already provide its own substratum (memory space and computing power),
while our experiment would try to simulate
(also) the very creation of some substratum, without making use
of any substratrum...

__________________
========================================================================
Tommaso Bolognesi
Formal Methods && Tools Lab.
CNR - ISTI - Pisa - Italy
e-mail: t.bolognesi@iei.pi.cnr.it
web: http://matrix.iei.pi.cnr.it/FMT/

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Registered: Aug 2003
Posts: 712

I've moved this thread here because it strikes me as much more of an NKS way of thinking question than a pure investigation of the properties of simple programs question.

I think there is some confusion, or at least potential for it on the part of some readers, between the idea of a computer and the idea of a CPU. A CPU is part of a particular design for practical computers that we call the von Neumann architecture. (It is also, incidentally, not a physical object made out of carefully arranged sand, but anything that performs a certain functional role in such a set up). It is not a necessary part of the abstract nature of computation. It is an allowed and often convenient extra, a functional subsystem distinguished from other aspects of a computation.

Abstractly considered, a computation is a transformation operating on information. Information goes in, information comes out, differently. The difference can depend on the information or on any portion of it. But one set of rules must decide what happens to any variety of information given - that is the underlying regularity that makes it a computation.

(Note, information is not yet computation. Any number can be recorded on an abacus, but an abacus by itself is only a memory, not a computer. A memory is just an arrangement, what is arranged is a matter of indifference, electrons, beads, grains of sand... A set of rules for sliding beads back and forth on an abacus, on the other hand, may constitute a computer. Computers do not need to be made from electronics, that is just very convenient for handling large arrangements of delicate parts in a robust way, with minimal effort.)

In the von Neumann architecture, a portion of the information in the input is considered "instructions" and another portion is considered "data". But they are instantiated in precisely the same way in memory. A definite instruction set operates on the instruction portion of the input to determine the sequence of operations to be performed on the memory portion of the input. (When this division is relaxed, and the results of operations on the memory portion can change the instruction portion of the input during run-time, we speak of “dynamic programming”).

A computer is general purpose if it can be made to implement any finite algorithm by changing what is fed into it. In the von Neumann architecture, by changing only the instruction portion of the input, we get the general purpose computer to perform any computable transformation on the rest of the data.

This exploits a finite version of the principle of universality. It is not necessary to have a different underlying rule for each sort of computation we want to perform. We can instead fix an instruction set (a BIOS for a contemporary computer e.g.), and then arrange sequences composed out of that fixed instruction set so as to mimic the behavior of the overall algorithm we want, for this particular run.

(Notice I say, "a finite version of...". The strict mathematical sense of universality depends on countably infinite sets, and no actual computer has infinite memory or has run for an infinite time. But as we see in practice, real world computation depends on the underlying flexibility of the system and not on its cardinality. Universality in the strict mathematical sense describes what e.g. a Pentium chip might be able to do with infinite memory or running for an infinite run time. When the answer is “any computable algorithm”, we find in practice that we have a general purpose computer. Even though the exact logical conditions of universality have not, sensu stricto, been met).

All that is necessary is for the limited instruction set to have sufficient internal richness to support emulation of an arbitrary computation. That is, the instruction set needs to be past the threshold of universality. Once it is, we do not in principle need to make it any more complicated, nor do we need to alter it to perform a different computation. We can instead leave the instruction set fixed, and modify the data passed to it, to perform a different sequence of those instructions (longer, looped, whatever).

When computation was being discovered, systems were deliberately designed to have universality as a property. But Turing is deservedly famous and so are his machines, because he proved that a system with a very simple underlying structure was already sufficient for this. Previous results in mathematics had already shown that any finite algorithm could be encoded as a problem of arithmetic. And Turing showed that precisely those problems that could be solved there, could be solved by one of his simple machines (idealizations, in fact, of the process whereby human beings did arithmetic).

In Turing’s day, “computer” did not mean “box on a desk that performs general algorithms”. It was the job description of a human being who added, subtracted, multiplied, and divided numbers. We can encode any arrangement as a number, both an input and an ouput. Any computation can then be specified as a certain transformation between numbers.

Now, after NKS, we know that systems that nobody ever designed to be able to perform universal computations can in fact perform universal computations, and that this is true even of remarkably simple systems. So simple they might readily arise physically in everyday systems, all around us. That, Wolfram conjectures, is the underlying cause of apparent complexity, the unifying aspect or marker that we notice as complexity. Some systems have sufficient internal richness that they are as programmable (capable of behaving in different ways when fed different inputs) as any artificial system that was meant to be.

The claim about complexity and the universe is then that its ongoing evolution in time corresponds to a computation of arbitrary sophistication. From prior state to next state there is some simple transformation. But a repeated sequence of simple transformations can do all sorts of complicated things.

Any given configuration of the universe then corresponds to a state of data or “memory”, if one wants to pursue the analogy. With no internal division between an instruction portion and a data portion, and no use made of the von Neumann scheme of functional differences imposed over memory, for the conceptual convenience of a human programmer. What corresponds to the underlying set of possible transformations, (which can then be concatenated into any finite algorithm)? The laws of physics, or rather, any transformation the laws of physics entail.

When Wolfram speaks of looking for the rule that might define the universe, he means finding a functional form that specifies those entailed transformations, in some appropriate, underlying representation of real states. Memory in is state of the universe at time t0. Memory out is state of the universe at time t1. Rule of the universe aka laws of physics are the transformation, r: M(t0) -> M(t1). The trick of course is to find a simple r that can still give rise to the great complexity we see all around us.

I hope this helps.

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Registered: Jun 2004
Posts: 78

rule M(t0) -> M(t1) implies there's an absolute objective
time. One may argue (and Wolfram does exactly this) that the time measured by our clocks is not the same as real time of
universe, but still, the notion of time, in some or other
interpretation, is a basis for this theory. Which is not
surprising, because the notion of time is embedded in
our definition of computation (e.g., Turing machine employs
both space AND time). This theory
strikes me as being clearly antropocentric. From the fact that
we have an idea of time it eventually jumps to conclusion
that some variant of this idea is a basis of ULTIMATE
definition of Universe. On the same grounds, I can argue
that the notion of beauty (love, good, evil, etc.) is also ingrained in a fabric
of Universe -just because we happen to have these ideas in our
mind, too. Strangely, these notions never show up in Wolfram's
fundamental rules. I don't understand why the notion of
time is better than all those.

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Registered: Aug 2003
Posts: 712

Actually, strictly speaking it implies there is some underlying version of succession, but need not imply that this is invariant from place to place or corresponds to our sense of time in the emergent reality that results. A later time in the emergent sense in a certain frame of reference, may correspond to a whole series of update events having occurred in a whole subset of nodes in some underlying graph, such that locally considered, there are distinguishable predecessor and successor states of the local pattern of connections around whatever constitutes that frame of reference.

No globally synchronized absolute time is required for this. The minimal structure required for a rule-like mapping is succession, but how updating is sequenced is a free parameter to search on, not a prior assumption required by "rule-like-ness". There is deeper nesting of rule application here than there, in abstract data.

I should perhaps also point out that one can link chains of abstract states together with intervening events, or chains of abstract events together with intervening states. s-e-s-e-s-e sequences can be parsed in either "phase", starting from state and going to state s-e-s, or starting from event and going to event, e-s-e. You can have a space of mappings or functions as well as spaces they act on. That is formal tinkering, and just depends on the formal construct one thinks will produce a workable model (whether mathematical or program like). A local sequentially updating programmatic rule on an abstract network, is what Wolfram suggests.

Needless to say, any accurate model of reality must account for our emergent sense of time and the orderings it actually enables us to apply to real events. That is data; not corresponding to data implies any theory fails. But the manner in which the apparent ordering arises, may differ from theory to theory.

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Registered: Jun 2004
Posts: 78

Jason, I'm sorry, but the idea of "succession" is not enough.
Theory has to predict not only WHAT will happen with the
object, but also WHEN, and you have no choice but using
time parameter to describe WHEN. Which is exactly what
you are doing in YOUR formula M(t0)->M(t1).
If we stick to cellular automation model, this translates
to the problem: which substitution is performed NEXT?
If we say that substitution rule is applied to cell X,
and then substitution rule is applied to cell Y, and
nothing happens in between, we already introduce
the notion of ABSOLUTE time. Succession is enough
only when you deal with a SINGLE cell, but if you consider
ALL cells, you need some notion of time that can be applied
GLOBALLY, and it's absolutely unclear how this global
notion may emerge from local successions. Obviously, the
order of substitutions is important. Wolfram certainly realizes
this problem, but his treatment of it is pretty vague.
I'm surprised that he ventured to take on
this problem at all; so far no one was able to say anything
meaningful about the nature of time, and saying just ANYTHING
about it exposes the person to a slew of very hard questions
for which he has no answers;
this could be easily avoided if NKS took a bit more modest
approach - e.g., just demonstrating that SOMETIMES programs
are as good (or even better) as diff.equations while
describing natural phenomena.

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Registered: Jun 2004
Posts: 78

BTW, did anyone tried to play with CA driven by internal clock?
What I mean is: classic CA is driven by external clock: all the
rules ate applied simpltaneously to all cells, as if some external
clock generator was connected to each cell.
Instead, rule can be applied only if the state of neigbour changes.
E.g., if state of cell X is a function of states of cells Y and Z,
rule is applied only if either Y or Z (or both) changes its state.
If, as a result, state of X also changes, this recursively triggers
the changes in dependent cells, and so on (if state remains the same,
there's no further propagation). If change of state in
cell X affects several other cells, corresponding rules are applied
simulteneously. This is a natural definition of internal clock.
This process leads to natural definition of global (absolute) time,
as well as local time in each cell (the latter is defined simply
as a number of state changes within some interval of absolute time).

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Registered: Mar 2004
Posts: 1

Computers and the universe

Computers are artifacts just to transform input strings to output strings. The individual instructions of a CPU are like simple programs. Applying these instructions in certain sequences gives complex results.

Physics tries to find simple laws. Based on physics we know how atoms forms molecules and molecules forms even more complex structures like DNA. DNA created humans and humans created computers.

The thesis of Wolfram is that the metaphor of simple programs can be applied to the physical universe. The best way to proof that is to build programs that simulate the universe.

So: NKS = Virtual Reality.

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Registered: Jun 2004
Posts: 78

>> So: NKS = Virtual Reality
I agree with this. But note the irony: NKS is a manifesto of
20-th century materializm. However, this extreme form
of materializm immediately leads to negation of the very
idea of objective reality. I bet this wasn't Wolfram's intention.

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