A New Kind of Science: The NKS Forum > Applied NKS > Modelling the act of observation, not the result
Author
MikeHelland

Registered: Dec 2003
Posts: 179

Modelling the act of observation, not the result

Hello,

Physical theories are expressed as mathematical models.

Since Newton's time the mathematics has advanced, but the general idea
has remained the same:

You have an equation with variables; you can make measurements of
nature and plug those measurements into the equation; you can solve the
equations for the variables you do not know; and the solution should
tell what your next measurement will be.

In other words, the input and the output of these mathematical models
correlate to what is observed in nature.

That's very basic, right?

It might be so basic, that no one has really questioned that approach.

There are alternatives, consider this one:

We have a mathematical model where the inputs are not observed in
nature, only the output.

That means the data being operated on are not values observed in
nature, and thus do not need to adhere to the laws of nature. In other
words, we could build a model that has precisely determined absolute
values as the input, and we would not be violating the principles of
uncertainty or relativity because these values are not observed.

As long as the output of the program is indeterminate and relative, we
still have a valid model to investigate.

This can be accomplished very easily: instead of including an observer
axiomatically, include the observer explicitly.

In other words, don't model what is observed, model the act of
observation.

This is a very simple idea, and it seems to be a logical evolution of
relativity and quantum mechanics, yet it has never been done.

I have done a little work on this idea.

I don't have a theory. I don't have a complete model.

I just have some ideas and prototypes for a different approach to
physics.

You can learn about them here:

http://www.techmocracy.net/science/time.htm

If you've viewed my web page before, make sure to refresh your browser
to see the latest and greatest.

All I'm looking for are constructive comments.

Are the ideas expressed well?
Does it make sense?
Are there parts that sound like gibberish?
Did I spell anything wrong?

Thanks.

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01-03-2005 04:33 AM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Actually, not at all a new idea. Look up hidden markov models sometime, for example. It is a reasonably well developed area for formal modeling and data mining, particularly for things like time series. For what it is worth.

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01-05-2005 02:28 PM
MikeHelland

Registered: Dec 2003
Posts: 179

I'm not sure they are quite the same.

Correct me if I'm wrong, but doesn't HMM use probabilities to determine what is observed?

That's pretty different from what I'm suggesting. I'm suggesting a determinate model that simulates the observation.

Since the observer may only access the result of the observation and not the data of the simulation that lead to it, what is observed is still indeterminate from their point-of-view, but nothing probablistic was involved.

You would get a better idea of exactly what my suggestion is by reading the paper I provided a link to.

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01-05-2005 03:46 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Probabilities can be 1.

For the underlying state transitions, in which case you can still have random observation errors of a hidden deterministic process. Or for the observations only but not the underlying state transitions, in which case you have a deterministic (but potentially lossy) mapping from the underlying states to the observations. Or for both, in which case the two series are still distinct, because there is again an intervening mapping between hidden state and observation, even if the chain of hidden states is deterministic, and the mapping from states to observations is deterministic as well. The last just means various probabilities are 1 rather than something else. You still get a difference between observation sequence and underlying sequence from a potentially lossy mapping (e.g. only some average is observable, lower level state information is therefore lost).

It was noted long ago in the context of the black box problem, that a coarser graining or renaming of variables (that "lumps" distinguished states into some broader category) can make a deterministic system appear undetermined, from a single prior state, in the renamed variable. But that sometimes the appearence of determinism can be restored, by inputing hidden states to the system ("multiplying" the observable states, into e.g. B when it follows A as B2, vs. B when it follows B as B1) or by imputing "memory" aka path dependence, to the observed or remapped system.

Imagine a finite state machine with 10 states, with definite transitions from each to a following state, probabilities 1. Now, consider a remapping of that FSM that lumps states 0-4 into one category, A, and 5-9 into another, B. Then you have a new system with 2 states, A and B. Starting from any state in the underlying FSM, you pass through some series of underlying states, say 1 -> 3 -> 5 -> 4 -> 7 -> 1 and then cycles. The corresponding 2 state system then "says" A A B A B A and then repeats - from that initial underlying state (1). A is sometimes followed by A and sometimes by B, from that initial. From a different underlying FSM initial state, you will get a different trajectory. If the observor cannot tell whether the initial underlying FSM state is 1 or 2 or 3 or 4 or 0, then he may see different sequences from A. How much he can discover about the underlying system depends on how much data he has, whether all the possible sequences are represented within it, etc. Note also that there can be underlying distinctions that never matter in the mapped result. They will pass undetected, but will also be irrelevant to the behavior of the mapped variable. (To the extent that happens, we can say the mapped system is a successful "reduction" of the underlying one. The things the mapping "lumps together" really do "behave the same", at the mapped level).

It does not matter that one of the systems is considered an observed and another an unobserved system. The analysis does not depend on this. It is a formal property of lossy translations. Any mapping from one system to another that does not preserve absolutely all of the information in the previous system has this character. And any mapping that takes two or more distinguished states in one system, to the same state in the other, is an information destroying mapping. (We say, is a "contraction").

The useful formal correspondance in this whole area, is between a mapping from one system to another, and within one system, from one step to another. A lossy mapping within a system corresponds to an irreversible trajectory, or the presence of an attractor. (A typical CA's evolution is a many to one mapping - most states have a single successor but multiple possible predecessors. The special case of multi-way systems reverses this). Common lossy mappings between systems are averaging procedures, measurements that map multiple things about a system to a single number, and the like.

With times series from CAs, one can e.g. total black cells across a line, generating a numerical sequence. That is the average density through time, with all of the details of the underlying configuration thrown out by the lossy mapping "Total". Instead of an overall average, you can partition into blocks of cells. You can lump nearby time steps together. You can map a 3x3 block to an integer from 0 to 9 and preserve density information completely, but lose configuration information. Or you can map to just a 1 or 0 for mostly black or mostly white, and lose most of the density information, too. Then one asks, if given only this lossy signal, how much could I infer about the underlying rule or pattern? Can I tell whether the underlying rule is local, or deterministic, or detect the speed of information spread, or its complexity class? Etc.

There is plenty of reasonable pure NKS work to be done to explore this idea. Not much of the above has been done even for CAs. But it is not a new subject, and there is an existing literature you may want to explore - both the HMM stuff and previous black box problem stuff in control theory and cybernetics, etc.

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01-05-2005 05:01 PM
Tmaq
Kellie Kolonies
On The Move

Registered: Jan 2005
Posts: 17

Probabilities can also be > 1.

Are you familiar with the now infamous 'Lets Make a Deal' problem?

-Tom

__________________
-Tom McWilliams

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02-23-2005 11:18 AM
MikeHelland

Registered: Dec 2003
Posts: 179

Jason,

I think the idea I have explained is more similar to Bohmian mechanics and Hidden Variable hypotheses, but there is still a specific difference:

Where there are unobservable magnitudes in these models, the model I am suggesting consists *only* of unobservable magnitudes.

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05-04-2005 07:29 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

My exhaustive analysis of models with only unobservables in them - you can't see anything. Everything therefore looks like everything else. Om.

A magnitude, hidden or not, is a distinction or partial ordering. A variable varies, or it isn't one. Observed differences can have hidden causes or unhidden causes, but without observed differences (at the "emergent" level if you like) there is no thought at all, and nothing to model.

Different underlying states have different consquences, or they aren't different. Different posited underlying states that have the same observable consequences, aren't functionally different, and are purely optional in a theory.

In reality, the problem we face is the reverse - that the same observable antecedents have different observable consequences, aka the observed "protocol" is "multivalued". One can deal with that by positing unobserved distinctions, by looking for path dependence (temporal distinctness) or by imputing some fundamental randomness to some underlying process.

A theory that says we don't see things, or don't see different things, would just be wrong. We do. The problem is precisely to arrive at some posited underlying map or structure that predicts or generates the structure of quite entirely observable similarity and difference we observe. Including as the interesting or tricky bit, the case where similar observable priors seem to have different observable laters.

The NKS intuition in such matters is that the similiarity observed in the priors is some lossy averaging or condensation of a fundamentally much more intricate thing, one in general capable of arbitrarily complicated internal relations, "programmably" complicated in other words, such that its gross evolution is not readily predictable from just an average or condensed measure of the prior state.

You don't try to predict what your computer is going to do as you run some program, by measuring its temperature. That it does entirely different things sometimes from starting temperatures you can't tell apart, surprises no one. One knows the detailed behavior depends on an intricate internal state, not on an average anything.

Hidden variables says as much, in short hand. But there are strong theorems that show local deterministic hidden variable theories, locality understood classically and deterministic taken in the sense of single-valued, can't explain various QM observations. Accepting this, you can accept multi-valued transitions or you can accept non-local hidden variables. NKS has no particular need for locality, it is not trying to defend any classical set up. Actually you can model either in an NKS way, but NKS favors single valued ("deterministic") models when they are possible.

One might also track transitions rather than imputed states. Some supposedly "observed" multi-valuedness may stem from trying to draw distinctions finer than the underlying system actually supports. If the physical reality is transition A then transition B, and one has instead imputed (by hypothesis, imaginary) states X Y and Z such that X via A becomes Y which via B becomes Z, then there might appear to be "multivaluedness" from X or Y, without there really being any such multivaluedness to A or to B as transitions. Not because there is instead an X prime and a Y prime hidden from you, but because X and Y are made up to begin with, imposed equivalence classes of our own making, where in reality transitions A and B might simply be "atomic". (With whatever is actually determining for their sequencing, part of much larger webs of relations, say). There is no a priori reason to expect an entirely imputed local "state" to be single value determining. Maybe there isn't any such thing as a "state" at that scale, maybe one has "cut in half" (purely "mentally", in analysis) a (real) "indivisible", or shrunk the sense of "local" past the physically meaningful point.

These it seems to me are the ways one can think of mismatches between imputations and realities in a model that includes unobservables along with observables. You can impute more states than there really are, or fewer. Or you can have all of them exactly, in which case if you still see multivalued transitions, the cause is some objective indeterminacy. I believe that partial ordering of the possible modeling mismatches is exhaustive. Either one is lumping together truly distinguished states, or one is splitting real unities, or one isn't doing either.

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05-04-2005 08:20 PM
MikeHelland

Registered: Dec 2003
Posts: 179

>My exhaustive analysis of models with only unobservables in them - you can't see anything.

The third section of my paper describes how to use a model of unobservables to predict the observable.

If that can't be done, can you point out the specific mistakes in my paper?

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05-06-2005 05:31 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

My perhaps flippant point was just that all models have observables in them. Which items are predicted to be observable and which items are posited in addition but predicted by the model not to be observable, is one of the attributes of a given model. But they all have to predict as observable, what we actually observe, or they are wrong.

It was a response to your statement above "the model I am suggesting consists *only* of unobservable magnitudes" - which was presumably just loose usage. If it is trying to say something other than loosely, what it is saying is nonsense. The charitable reading is that you simply meant there are some unobservables as well as some observables, with the latter presumably consequences of the former (by whatever compression or mapping). Which is called "any theory with hidden variables", and is not a new idea.

My renewed advice is that you read the extensive existing literature on this subject, instead of telling yourself repeatedly that your modeling ideas are revolutionary and new. Lack of the imagination to make distinctions between underlying and observable processes is not a hold up anywhere.

Any theory can add all the non-observable constructs it likes, to get the observable answers to come out right. It doesn't need to use any previous theory's constructs (it can get to the observable "answers" some other way, perhaps), but can if it wants to. A non observable construct is plausible if it simplifies the whole model, or restores useful attributes (single valued determinism etc). Essentially every existing theory makes use of non-observable constructs, some more than others. It is normal, not revolutionary. (E.g. Nobody has ever seen a probability amplitude, as you see the position of a dial).

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05-06-2005 05:59 PM
MikeHelland

Registered: Dec 2003
Posts: 179

I meant that the model is defined only by unobservables.

The mathematical model is a set of values that change according to some rules.

None of the values within the model are observable. None represent the outcome of an experiment.

As far as I know, no scientific model does that.

And there's a good reason why:

It doesn't predict the outcome of an experiment, therefore, its not a scientific model.

But with my model you *can* predict the outcome of an experiment, it just isn't as simple as reading the result of a calculation as a value.

Say you measure your height to be 6 feet tall.

That is an observable, a measurement. Correct?

In an NKS universe, is there a "6" in the values of the universe that somehow, during measurement, leaves the logical system and enters our conscious experience?

Highly doubtful.

Agreed so far?

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05-06-2005 07:33 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

You don't have something to teach us, you have almost everything to learn, and I recommend you go get started by doing your homework. The most elementary aspect of your idea is common property to all modelers, not original, and is the only part of what you are talking about that is clear or correct. The only thing you are adding is blindness to other bits, and unawareness of the prior work of others. You confuse the resulting myopic view, with something original, because you have not seen that myopia exactly reproduced before.

You asked whether your overall presentation makes sense or is gibberish, and I am telling you. Told you on the first post, told you on the second, and on the third. I'll tell you in any level of detail you require, but the answer isn't going to change. You are clearly interested enough in these questions that it would be worth your while to actually go learn the relevant literature. You are clearly not well enough informed about the subject that you have anything to teach us before you have done so. Sorry, I can be polite a few iterations but sometimes the point is simply not grasped unless one is blunt.

Now in detail -

"I meant that the model is defined only by unobservables."

Equivocation on "defined by". Any model posits some underlying terms, rules, mechanisms, equations, what have you. Those have consequences in their own formal terms. Any model tells you how its posited underlyings map to observations (directly, by being averaged, by being sampled, whatever), or it fails to show any relation, let alone the relation of accurate correspondance, to the observations. No model *defines* a sequence of observables.

"None of the values within the model are observable."

Equivocation on "within the model". That which the model implies for a variable it predicts will be observable, is part of the model. It just is a different variable than some underlying or hidden one. You can't make a model with all the variables hidden or you don't have a map to observations, don't say anything about observations, and therefore do not say anything. "All my underlying variables flap about this way. I've no idea how they are connected to the observable sequence". Then they have no relation to it, you haven't modeled anything.

A model is a map from something posited to a set of observables, however restricted a map. The underlying can have a billion billion states, and the observable can have only two, one of which obtains 99% of the time. But if there isn't a map from the underlyings to an observable difference there isn't a model at all. And if there is, then the statement that none of the values within the model are observable is false. The model says, F of this underlying goes to, equals, follows, is, this observable.

"As far as I know, no scientific model does that."

And I am telling you, how far you know is not very far at all, because you are just wrong. Every model does this, not none.
Kepler does some math and predicts Jupiter will be here next Wednesday night. That is a map from some ellipse equation, which you can't observe, to the position of a dot in the night sky, which isn't a number. Any model already does this.

Any *hidden variable* model does more than this, it asserts that you can't measure something that is really going on, but can measure some resultant of it. It may say, for instance, you can't see the position and velocity of all of these particles I've posited as existing in this box of gas, but you can measure the pressure they exert on average on this wall of it. And then I can explain why that pressure goes up, when I put hotter gas in the box. The ensemble state of the gas is not an observable, the pressure is. The observable is predicted to reflect the ensemble state in a uniform way. The ensemble state is, further, expected on plausible but not certain arguments, to usually follow this or that statistical relation to another observable (some velocity distribution according to temperature).

A model posits an underlying formal system without requiring it to be observable, provides a map from any such system observable or not to a set of observables, and thereby tries to relate the sequence of observables to some formal system. No relation to observables at the top end means no model. But nowhere is it ever required that anything the model posits, must be observable. And in practice, practically no scientific model predicts everything it posits or refers to, will be observable. Nor does it try to fit every wiggle of the observed. It tries to get some potentially noisy and lossy map from some posited underlying formalism, to a selected, few-aspects-only, series of observations.

Don't congratulate yourself on reinventing the wheel, learn a little about how much is already known about these problems.

"But with my model you *can* predict the outcome of an experiment, it just isn't as simple as reading the result of a calculation as a value."

Um, of course it is, "calculation" just means more than you think it does. First I evolve the model, then I apply the underlying to "observable" map, to every scrap of it. What you are calling "the calculation" means state (t2) as some function g of state (t1), t2 = g (t1). But perpendicular to that, I also have another function f that takes state at t1 and state at t2 or anything like them, to observable at t1 - f ( t1 ) and f (g ( t1 ) ) aka f ( t2 ). f may be lossy - it may lump different things together; f may be noisy - it may introduce slight differences even when provided the same underlying. But no f provided, means the observable consequence left unspecified, means nothing modeled. A model maps something to observations or it fails to model. Nothing original is being said in this paragraph, this is news to no one, it is not an original idea, it is something everybody already knows.

"Say you measure your height to be 6 feet tall. That is an observable, a measurement. Correct?"

Strictly speaking, to be six feet tall means a succession of measurements by fair tape measures results in an equivalence class of visual inspections in which some pencil mark or what not is always within half an inch of this many ticks from where I started. Each of those is an observation, the posited external reality that rolls them all together is not an observation but a fact (except the right answer is 5 feet 9 inches in my case), and no model or theory has been advanced in the process. Some have been assumed or used in the deduction, such as I am not growing rapidly, tape measures are not wildly fluctuating, all pragmatically dismissed etc.

"is there a "6" in the values of the universe that somehow, during measurement, leaves the logical system and enters our conscious experience?"

Red herrring and a basic philosophical confusion, ascribed to others if not actually suffered. No model has anything to do with this. I prescribe Santayana and Popper in addition to the black box problem and the theory of hidden variable modeling and inference already suggested.

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05-06-2005 09:06 PM
MikeHelland

Registered: Dec 2003
Posts: 179

"That which the model implies for a variable it predicts will be observable, is part of the model."

And what I am saying is there are no such variables in the model.

Let's say you have a system of values operated on by rules.

Again, none of the variables of the rules, are observable.

Let's say the values represent things like electrons, photons, and quarks.

If you can make an atom out of them, or even further sophisticated molecular structures, you should be able to make something resembling an apple.

How tall is that apple?

If the model had positions for particles, or if a hidden variable model could tell you the observed position of particles, using that you could make a determination, probably through a little subtraction.

My claim is specfifically that if you want to make a prediction from a model, it requires a few more steps.

1. In addition to the modeled apple, you need to model a ruler

The ruler will have marks on it equally spaced.

2. In addition to all of that, you need a modeled neurocomputer

The neurocomputer would have to have the knowledge that the number of marks the apple covers up on the ruler is a length of the apple in the units of the ruler.

And a key ingredient here is that the neurocomputer would only knows the nubmer of marks covered by the apple if it interacted with light signals coming from both the ruler and the apple.

If the modeled neurocomputer happens to be in relative motion to the light signals it relies on to make its measurement, then even if the entire model is placed on a grid of absolute space, the measurements predicted using the method I described could vary, demonstrating the phenomenon of length contraction.

In addition to distance, time should be measured similarly, with a modeled clock and an observer. Even mass, position, and momentum shoudl be predicted from a mathematical this way.

I suggest that a computer programmer investigating models of physics has to go to the length of creating an internal observer of their model and learning what the internal observer knows in order to make investigate observables in an a model whose rules and values are completely unobservable.

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05-06-2005 09:45 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

"if you want to make a prediction from a model, it requires a few more steps"

And as so stated, the claim is merely false. Models that do not have this character make predictions and do so just fine. Thus the "requires" is false. It is an instance of that species of argument, unless you tell me everything you can't say anything etc. Other modelers do not require your permission or need any of your "shoulds". Their models concretely succeed in mapping aspects of phenomena or they don't. Others have had and suggested the idea (e.g. the whole "second order cybernetics" crowd) but recognize that there is nothing required about it. It merely shifts the system one is addressing.

Second, of course what you describe has predicted observables in it. You predict that light has these or those effects on whatever computer you embed etc. (Why should you think an internal of your model corresponds in any way to light?) Or, if you beg off and don't, then you don't have a model because you don't bother to map to consequences, you just have states that you urge others to consider, that flap around in this or that way, but do not have mapped observables tied to them. In which case the rest of us just say, that's nice, but doesn't say anything about the world, no thanks, I don't need the posited internals of your proposal and they don't do anything for me.

We all know how to put an observer in a model, we know our options on the subject, what sort of questions we can freely choose to address by doing so or not to bother about when we don't think it matters, etc. You aren't saying anything new, you are just very sure of its newness and that its brilliant importance can't possibly be correctly understood or we'd all say "gee" and flock to agree etc. Whether you are aware of it or not, these are the characteristics of a crank, who is unfamiliar with relevant prior thought on the subject, and is caught in well understood snares at the mere philosophy level. There is no science here.

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05-06-2005 11:45 PM
MikeHelland

Registered: Dec 2003
Posts: 179

If what I've said is not new I have one question.

The method I described for putting an observer in a model means that the only observables of the model are what can be deduced as the knowledge of the observer, all other magnitudes within the model are unobservable.

I think I made the case that a model universe like this, means that against an absolute grid of space length contraction can be predicted. It should also be pretty clear that even in a determinately evolving model the internal observer would deduce it to be evolving indeterminately, so it would appear to be compatible with modern physics.

But the way in which it predicts length contraction does not require a universal speed limit.

If two observers in the model are moving away from each other at a speed faster than other agents in the model can mediate an interaction, the observers won't know about each other. So in a manner of speaking nothing can move faster than the speed of light according to internal observers of the model, but that doesn't mean nothing in the model can move faster than the speed of light.

If what I say is not new, then please cite something that describes a model of unobservables that includes particles not bound by any speed limit, but still in harmony with the laws of physics due to the revised method of making predictions from the model.

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05-09-2005 04:02 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Look up second order cybernetics for models that build in an observer. Look up hidden variable anything for models in which there is determinism at an underlying level despite many-valued-ness aka apparent indeterminism at the phenomenal level. Everybody knows that you can have non determinism or you can have non locality - what nobody has is any plausible physical model of said non locality (aka immediate action at a distance etc), that still reproduces the full range of QM phenomena at the phenomenal level, in a straightforward way. Plenty is known about how little an underlying deterministic system needs to have to exhibit the apparent stochastic results at the phenomenal level - basically all it needs to do is show brownian motion type randomness when suitably aggregated. That's easy, all sorts of deterministic systems can do it. "You just have a non local hidden variable that is deterministic" is not a theory, everyone knows it is a modeling option as a basic scheme, but that is not the same as having a fully worked out rival to the standard model on that basis, e.g. I don't know how many times I have to tell you before you actually go read something you didn't write. At any right, this is a forum for NKS ideas, not for peddling yours. You have your own website, look to it.

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05-09-2005 05:10 PM