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Richard J. Gaylord

Chicago, IL

Registered: Jul 2004
Posts: 31

how to do science?

CA's have been used extensivley to model various physical, biological, socioeconomic system. The way this has been done traditionally, is to use the CA cell(s) to represent the objects of the system and to apply a set of rules to govern the behavior of these 'objects'.

i wonder if this approach is sensible (and this applies also to the use of mathematics to represent
objects (and the wave function in QM can be considered an object) in these systems. iam beginning to think it is fundamentally misguided.

take for example, the Game of Life CA. If one were to 'observe' the behavior of one or more 'life-forms' (eg. gliders), i wonder what the likelihood is that one would ever deduce that the glider is an epiphenomenon (and not an object in itself)
produced by rules about the turning off and on of cells.

it even makes me wonder if we can ever learn the 'laws of any phenomenon' by studying the behavior of objects observed in the system (this would include objects like predators and prey in ecosystems or bubbles and crashes in financial systems). there is no compelling reason to think that these 'observables' are 'real' rather than simply behaviors based on rules that bear no direct resemblance (or connection) to what is observed.

i believe stephen has pointed this out in NKS, or at least it is an obvious (to me) implication of stephen's statements in NKS.

if this is correct, we have a FUNDAMENTAL dilemma as scientists. if we can't expect to find the laws of natural phenomena by studying the behavior of objects in objects, how do we go about looking for the 'laws'?

finally, perhaps there is already a historical example of this misguided approach. i am thinking of the attempt to study the mind as an object. it seems obvious to most of us (at least to me) that psychology has turned out to be a pseudo-science (i don't mean this in a condescending way) and only recently have we begun to make progress by studying neuropsychology (a branch of neuroscience).

i would like to hear the opiniions of others on this issue. it is disheartening to think that we have no real hope of finding out how (or what makes( 'things' work by studying the behavior of these 'things'.




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Old Post 07-30-2004 02:24 PM
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MikeHelland


Registered: Dec 2003
Posts: 181

>if this is correct, we have a FUNDAMENTAL dilemma as scientists. if we can't expect to find the laws of natural phenomena by studying the behavior of objects in objects, how do we go about looking for the 'laws'?

I agree. Here is how we find the laws:

1. Go outside,
2. Look at something
3. Take a guess at how it works
4. Make predictions

If the predictions match, and are convincing you have found a tentative law. This is the scientific method, which the study of simple programs does not deeply effect.

However I do think the study of simple programs is a useful tool.

We have found many laws, and even formalized them as equations, though putting all the equations into a single formalization has been very difficult.

In my opinion after the laws have been found and hashed out by scientists is where the value of simple programs comes in. We should be able to create programs whose output resembles what we've found in our laws. The laws guide is in the process of creating models, not the other way around as you note.

(I actually discuss NKS at the very end of this paper, I hope what I've said about it is accurate:
http://www.techmocracy.net/science/nature.htm)

Though, perhaps my comments are only relevant in the field of physics, which I know was not the original scope of your question. On the other hand, perhaps where parts of the universe are normally unobservable should we use our laws to create a model, it could be possible that our model shows us new phenomena that we create new laws from.

I don't think I've actually answered your question :-) But hopefully its another viewpoint that someone finds interesting.

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Old Post 07-30-2004 02:51 PM
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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

"Make predictions" is a looser concept than people sometimes suppose. It does not need to be a prediction of the exact value of a parameter. It just needs to be something logically entailed by the guess, that some observations could fail to fit with.

Thus, "it will be 4.567" clearly qualifies but is not necessary. "It could be anything imaginable" does not qualify (but see below). "It will be between 0.2 and 0.5 95% of the time" is fine. So is "it will be a normally distributed random variable" or "it will show a scale free power law distribution".

Predictions can also be about sensitivity analysis rather than values, or about constraints, or even about failure to remain within certain bounds that some other theory might expect. "For any bound A I can find an initial condition x that will exceed A by time t" is a perfectly good prediction.

The role it needs to perform is to critique the guess. Obviously the procedure is also meant to be iterated. The first rule is to keep going.

Is there any cosmic guarantee that this procedure must always find out what is actually causing some phenomenon? No. But no such guarantee is necessary. It does find useful general truths. A model is useful if it tells you things about the real system.

NKS suggests that the world is extensively modelable, but strictly predictable (in detail etc) only where the underlying behavior is simple enough. This is not a property of our procedures, but of the world. Some behaviors are generated by simple understandable rules, but have complicated results. In the real world, not just in our heads.

And the only way to see those results in detail is to perform a correspondingly complicated calculation - whether letting the system do it and reading off the result empirically, or using a model to do it.

Such a model can be as difficult to predict as the real system. It deliberately abstracts away secondary characteristics, to be sure, to focus on some key aspect of the phenomenon. But that need not be a simple aspect, and the basic cause of the complexity seen in the real system may not be abstracted away. In which case, the model will behave in ways as complicated as the real system, for the same sorts of formal reasons.

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Old Post 07-30-2004 04:21 PM
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Richard J. Gaylord

Chicago, IL

Registered: Jul 2004
Posts: 31

how to do science and what IS science?

i don't find mike's approach to be useful (no offense)

he says: here is how we find the laws:

1. Go outside,
2. Look at something
3. Take a guess at how it works
4. Make predictions

If the predictions match, and are convincing you have found a tentative law. This is the scientific method.

nor do i find jason's response helpful.


his proposal that a model is useful if it tells you things about the real system, assumes there is such a thing as a 'real system'. how are we to know that we are studying a real system.

i still think the game of life CA is a good example. at which point do we trealize that studying the 'life-forms' are not the basic constituents of the real system. in fact, it is not the cellls themselves that are the basic constituents but rather the cells plus the rules that govern the turning on and off of cells.

morever, there is no way to decide on the 'predictiveness' of a model. Ptolemy's model had predicitive value (although it has recently been found thast he fudged the data a bit; just as newton did).

feyerabend and kuhn argue that theories are incommensurable?

the whole idea of predictiveness is tied into the idea of measurement and that is problematic at best (the one- and two-slit experiment clearly illustrate the dilemma)

i read somewhere ' that the reason that mathematics has been so successful in physics is because the only things we can study are those that are amenable to mathematical analysis.

perhaps mach was correct in saying the only value of a theory (or a model) is in it's ability to fit data.

there is no TOE or even a TOLS (theory of lots of stuff).

i would say from my own research in that the value of a model (note that i don't distinguish between a model and a theory - is there one) is that having a model is a tool for thinking about a phenomenon.

i don't want this to turn into a 'philosophy of science' discussion (philosophers are especially unqualified to discuss any aspect of physics orscience) but this issue forms the very core of the 'value' of NKS to the sciences (not that NKS need justify itself by its usefulness in other scientific fields).

perhaps there is no such thing as 'the real world' at all. all there is in a practical sense, are those 'things' that our brain (mind is devoid of meaning) is capable of dealing with.

i am inclined to the few that there are alot of interesting (each person decides what's interesting) 'things' to study and we can choose what one's we want to study and that is a perfectly valid criterion for a field.

at this time, the best way for me to deal with these fundamental matters is to go have a pint of pale ale. :)

as robin williams said "reality is for those people who can't handle drugs" (he probably didn't mean theories or mathematics as a drug, but physicists seem to use it as their drug of choice).

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Old Post 07-30-2004 07:18 PM
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MikeHelland


Registered: Dec 2003
Posts: 181

First, I'd like to state the importance of "tentative" in my post and clarify that my personal opinion of the scientific method is that it doesn't exist beyond the method of critical rationalism. This has already been discussed on this board:
http://forum.wolframscience.com/sho...s=&threadid=401

Here's an example of Popper's view:
http://www.the-rathouse.com/poptheoryknow.html

I don't think predictions are important for science or knowledge. However we're talking about "laws" most of which involve predictions, which is why I posted the widely accepted (though as we both agree, philosophically unsound) version of the scientific method.

I agree with your other points too.

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Old Post 07-30-2004 07:35 PM
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Gunnar Tomasson


Registered: Oct 2003
Posts: 69

Re. the following:

if this is correct, we have a FUNDAMENTAL dilemma as scientists. if we can't expect to find the laws of natural phenomena by studying the behavior of objects in objects, how do we go about looking for the 'laws'?

Comment:

I suspect that the 'dilemma' consists in the imprecision of language since the dawn of the modern scientific revolution whereby observed regularities in the field of physical phenomena are labeled 'laws' once they have been given precise mathematical form.

What else, in any case, might the concept of "law" denote?

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Old Post 08-12-2004 07:26 PM
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Jesse Nochella
WRI

Registered: Mar 2004
Posts: 132

Denoting Law

I don't know where this thread is going, but I have a few things to say.

Personally, I do not see any fundamental dilemma in defining the role of any system that takes data and searches for ways to emulate it (say, the scientific method, human perception).

When I think about "law" the definition of one, I come to the conclusion that really there is nothing but only a system capable of universal computation fundamentally needed to denote what a law is.

All a law really seems to be from my eye is something that implies a set of axiom systems that are capable of full emulation of a set of data(say, any logical statment that you can formulate, or any percieved physical system) upon the assertion of its truth. Then, in language, we can say "all this is explainable *because* of this something, and won't work without it, so it's a law". Laws imply universal emulation.

And if this is all a law can really ever be argued to be, then rather strikingly, the validity of a law in itself can never be regarded as a natural phenomenon, and instead is only of metaphysical sorts. A mental phenomenon.

And so, if law is indeed just a mental phenomenon, then why should there exist laws for systems that are not capable of producing them? A system that is not universal is not capable on its own to find that a given set of data implies mechanisms that can emulate it -- because then it would be universal (or at least I've got a big a hunch that it would be). Is the real misguidance in believing that fundamental structure of the universe is based on laws?

If it is indeed a misguidance then, of course, there is no dilemma. The purposeful pursuit of information is a phenomenon exclusively upheld by universal systems, and so also is "the Law" in which they percieve.

In response to Jon Awbrey's post here, I am not convinced that laws constrain, or that some events that could possibly happen indeed do not. But thats another topic.

Last edited by Jesse Nochella on 08-17-2004 at 10:33 PM

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Old Post 08-16-2004 09:03 PM
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Jon Awbrey


Registered: Feb 2004
Posts: 558

I Sought The Law ...


One notion of law is constraint,
the very peculiar fact that not
everything that can happen does --
of course there's a catch about
virtual events that violate the
prima facie laws of nature, but
even these outlaws honor a code
all their own.

Jon Awbrey, 15 Aug 2004


Jesse,

On second or third thought I decided to delete that comment
in conformity with the Metaphor Emissions Reduction Act,
but since you were quick and kind enough to notice it
it would probably be even more confusing to leave it
left out now.

The stock notion that I referred
to is that "Law Is Constraint",
not that "Law Constrains".
There's a subtle difference --
perhaps we might capture it by
paraphrasing the first slogan as:

The presence of law is
the presence of constraint.

That way of saying it avoids the error
of deputizing any symbolic expression
of the law in question, as we do when
we say the "Long Arm Of The Law", and
other such metaphorical stretches of
of the imagery-producing faculties.

Here is one illustration of the "law as constraint" idea:
Consider the difference between a formal language L c A* --
which means that the language L is just a particular subset
of the set of all finite sequences on a finite alphabet A --
and a formal grammar G that accounts for L. The language
itself is uniquely defined as just that particular subset --
the existence of the constraint L c A* is the existence of
the law, independent of expression in a particular grammar --
but there may be many different grammars that account for
the very same language.

For natural languages, things are naturally a bit messier,
but the consistency of a natural language consists in the
empirical fact that "some things you can't say" without
violating the well-informed informant's sense of sense.
That is how we sense the presence of lawfulness in the
language, but there may never come a day when we have
a perfect grammar that can account for, justify, and
discharge all of the detectable linguistic facts.

As a parting shot/thought from this very same canon,
let me remind you of the analogy that Newton drew
between physics and cryptography.

Jon Awbrey

Last edited by Jon Awbrey on 08-19-2004 at 03:24 AM

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Old Post 08-19-2004 03:10 AM
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Jesse Nochella
WRI

Registered: Mar 2004
Posts: 132

Jon,

Thank you for correcting me on that. I wont claim to have intended that notion in the first place because really it's much, much clearer now.


I guess I let my post hang a bit with odd conclusions about law/constraint. They came across my mind while reading this thread in the form of questions, but by the time I had finished stating the questions, I had developed it a bit more and should of continued.

I would not be suprised if there is some logical flaw in the reasoning in my previous post, but as of now, i don't know how to argue otherwise.

Coming from Richards second post, saying that:
"perhaps there is no such thing as 'the real world' at all. all there is in a practical sense, are those 'things' that our brain (mind is devoid of meaning) is capable of dealing with. "
and Gunnar's comment:
"I suspect that the 'dilemma' consists in the imprecision of language since the dawn of the modern scientific revolution whereby observed regularities in the field of physical phenomena are labeled 'laws' once they have been given precise mathematical form."

The question I first asked myself was:
"If there are laws for us, what about physical processes?"

So, I gave my definition of law and concluded that a system must be universal to percieve law/constraint, and then therefore for any non universal system, there are no laws.

What I did not include in the post is this:
If our universe works anything like a mobile automaton / casual network, then it follows that any universal system, whether it be rule 110, a universal cyclic tag system, or some universal turing machine that is in effect being emulated directly by our universe rule would indeed look *exactly* the same to any system within that universe, being you and me.

And following from that, then the question arises:
How can we, as systems of this universe, be able to witness all this diverse phenomena which has behavior consistent enough for us to generalize it with traditional mathematics in the form of "laws", if the systems that are responsible for such behavior do not necessarily have to be universal?
In other words, since our universe rule most likely operates like a mobile antomaton / casual network, meaning that uderlying form of fundamental processes are undetectable, the patterns of behavior generated (programs emulated) by a our universe rule would seem to have infinite computational power / capabilities.
If thats true, then how can there be all these percieved limitations in behavior?

If I haven't missed something so far, then I see only but a few ways to explain this.

First, there's the possibility that all existing phenomena have some sort of special infinite capabilities that reside within their, seemingly constrained forms ( a unified version of this statement is that the universe has some sort of infinite/irreducible computation that is in effect unseen by all systems that are in it ).

Second, there is no indefinite power that exclusively fabricates constraint. But instead, there is in effect universal systems that for whatever reason, by whatever means, constrain themselves and behave appropriately within their own constraints ( again, a unified way of saying this is that the universe is in effect built up off of all possible (near all?) constraints that can be computed by our rule ). This, I believe, Leads to fairly definite entities that persist over time but are in great diversity of appearance, all reflections of eachother, shadows of the same thing (sound familiar?).

The third, I suppose would be if I am incorrect in some way, and that systems need not constrain themselves to be diffirent. However, even if this has a more palatable flavor, the concept does not appeal to me for some reason. It seems arguable, and in some wau just philosophically unsound, but at present I just dont know what to do with it.


Kind of like what most of this post is about!!

*sigh*, well now I've got myself going in vertical loops. Better close.

I guess the relevancy of all this is in that when you try to explain "how to do" inquiry, what you're really trying to explain is yourself -- because thats what we do. You're trying to explain everything.

Trying to explain everything is hard!
nuff said.




(p.s., I wrote this post last night and am now copying it to the forum in verbatim, despite my implulse to heavily revise it with a wakeful mind.
Please, if you feel like saying a thing or two about it, go ahead and dice it up to pieces. I want to unravel this ball of twine. Perhaps another thread would be appropriate. Well anyways, like I said, have at it.)

Jesse Nochella

Last edited by Jesse Nochella on 08-21-2004 at 05:51 PM

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Old Post 08-20-2004 09:06 PM
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Jon Awbrey


Registered: Feb 2004
Posts: 558

Law & Mercy

LAC. Note 3

Jesse, et al.

My attention is being pulled away in other directions, so
these comments will have to remain a bit elliptic. A more
intuitive name for constraint is "shape". The way that a
particular language L is embedded in its ambient space A*,
the biggest language on the same alphabet, is analogous to
the way that a geometric object is embedded in its geometric
space. The same thing goes for the way that a manifold of
physical possibility is situated within a manifold of logical
or mathematical possibility. One of the things that they harp
on a lot in math is the difference between a mathematical object,
mathematically speaking, a substantial reality -- for example,
a triangle, a space, a formal language, a manifold -- and the
many representations of it in that one finds with respect to
particular coordinate systems, grammars, or even alphabets.

Epi-Ellipsis. If you take the crytographic clue, I am suggesting
that the real language is a shape more invariant than what we may
observe in the frame of reference of a given alphabet, and that
one of the difficulties of disguise is just how hard it is to
transform this shape entirely away.

Now, what are you looking at when you watch a cellular automaton
wend its weavy way down the screen? Is it a mathematical object,
something with a substantial shape that you can get a real grip on,
or is a coordinate space, the labels of fable whose name is legion?
If you see it as a coordinate representation, a particular sequence
of boolean coordinate vectors, then it's a phenomenal appearance,
and the solid shapes that we seek beneath these superficial shades
have to be sought in the form of mathematical invariants. And that,
My Dear Watson, will take us several more steps of serious sleuthing,
if not a finer glass than we've eyed heretofore.

Jon Awbrey

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