A New Kind of Science: The NKS Forum > NKS Way of Thinking > Processing power pb
Author
Mike Pearson

Registered: Apr 2004
Posts: 3

Processing power pb

Hello,

the idea that the whole universe is just a simple CA (or another system studied in ANKS) is indeed very sexy but I see one major problem:

Suppose we have the winner CA in our hands ... How do we recognize that it is indeed the one that the universe is running ?
The problem is that we'll never have enough processing power to run the CA on a big enough grid and for long enough to be able to recognize familiar properties of our universe ...

So in order to recognize these familiar properties of our universe, we'd have to somehow study the CA and find properties about it. But doesn't this contradict the assumption that the only way to find out what a non-trivial CA is going to to is to run it ?

What are you thoughts on this ?

Best,

Mike.

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04-18-2004 08:33 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

In general we can't verify, but we can falsify. If a rule has consequences that we can see would violate known observed laws (if, e.g. special relativity would not hold or something like that) then we can reject it. Compact rules will tend to get all sorts of things wrong if any part of them is wrong, simply because there isn't a lot of room in them, so to speak. Any change in one of the features of the rule would generally have large consequences for its behavior. Most of the possible rules one can imagine trying fail to work in obvious ways. These can in effect be set up as filters - as you have a computer try rule after rule, you throw out the ones that can't meet specification A, or B, ...

If we find one that doesn't fail the filter tests, then we'd have to look at large scale limits of the behavior of the rule, and check their compatibility with known physics. That is not trivial, but passing the filters already helps. Then, ideally, we might notice some detailed feature of the rule and look for it experimentally. The point of any model is to try calculating with or experimenting on the model rather than the real system, and see if you can discover anything about the real system from observing the model. There is indeed no assurance we will be able to see any specific much larger scale behavior, in the size system we can calculate. A lot depends on how the rule's behavior seems to scale, when it comes to whether we will notice observable consequences.

If the rule is simple enough we may be able to find it (the previous step). We still have to see its consequences which you are right, is not a trivial step; and then in addition find ways to "stress" what we found and try to reject it. The overall method is simply trial and error. The overall guess could be right and we might still miss. Might just isn't "must", so it is worth trying.

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04-19-2004 04:18 AM
MikeHelland

Registered: Dec 2003
Posts: 179

Mike Pearson,

Your question is interesting, but I think that the problem you identifiy is the least of the worries. Let me make a pass at it like this:

Lets say we're not talking about nature, but we're talking about something like consciousness. Consciousness is experienced only from the context of self. If this is true then a program that is supposed to also be consciouss can never really be verified to have a consciousness identical to the consciousness you experience and are trying to duplicate. In order to verify this you would have to actually exist inside the program because you could only experience the consciousness created by the program in the context of self.

That might sound trippy, but think about it for a while.

Now, consider that you as a human are nature, a pile of particles interacting by the rules of nature. Realize that as you are made of nature, and you are attempting to understand nature, then any model of the universe will have the same fundamental limitation as any model of consciousness: because our observations of nature are equal to natures observation of itself, any model we create to mimic these observations can only be verified from within the context of the model itself.

Because we would be the creators of the model, we obviouslly exist outside of the model and are prohibitied from these experiences.

The above, and your question, are really mathematically proved by the Incompleteness Theorem.

If we consider nature to be a logical system, and we consider humans, and human knowledge to be contained in this system, then it is a FACT that we will never be able to prove that our model of nature _is_ nature because the model exists as a result of nature itself.

Again, I apoligize if this is way too trippy. But then, if you like this sort of thing, and your questions seem to suggest that you do, you might give the following a contemplative read:
http://www.techmocracy.net/science/time.htm

To answer your question directly, you are right (as Goedel has demonstrated) that we can never prove that we have the correct model, but it is not because we lack the processing power. It is because we are prohibited from the context required to mimic the experiences we have as creatures in nature.

Last edited by MikeHelland on 04-19-2004 at 02:42 PM

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04-19-2004 04:39 AM
Mike Pearson

Registered: Apr 2004
Posts: 3

Response to Jason Cawley:

But how do you "rule out" a given rule ?

For instance, if we take rule 110, maybe if we could run the CA on a huge grid, for a huge number of steps (far greater than what our current processing power gives us), then we might eventually recognize patterns that can be interpreted as space, time and so on ... And then we would eventually recognize all the properties of our universe ...

How can you prove that this is not the case ?

Best,

Mike.

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04-24-2004 08:07 PM
Mike Pearson

Registered: Apr 2004
Posts: 3

Response to Mike Helland:

Mike,

I am not really interested in "proving" that a given model is actually *the* model of the universe (and if you say that this would be impossible, then I gladly believe you :-)

What I am interested in is to find a model (maybe a CA or more generally a "computational model") that *exhibits* many of the properties that we can see in our universe.
The ultimate goal is of course to find new properties of this system and to check if by any chance they also apply to our universe ...
After all, isn't this what physics is all about ?

I am more of a software engineer than a physicist and this is probably why I am more attracted to models based on CA rather than models based on equations ...

If our universe is nothing more than a turing-complete system, then there is no reason why it could not run a sub-universe within itself with the same properties (only "slower", whatever that means :-)

I am afraid that we are far from being able to run this sub-universe because our processing power is way too small ...
And if we can't run it then we won't be able to find new properties of the universe, which would be rather disapointing ...

Best,

Mike.

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04-24-2004 09:22 PM

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