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From: Kory Heath <kory.heath.domain.name.hidden>

Date: Sat, 17 Jan 2004 21:40:22 -0500

At 1/17/04, Eric Hawthorne wrote:

*>1. All cellular automata which are computationally universal are reducible
*

*>to each other, by the definition of universality, so it doesn't matter
*

*>which D the automaton program itself is. The subject matter that they can
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*>represent and compute is equivalent.
*

That's correct on one level, but what we're really interested in is the

dimensionality of space that SASs within the computation would perceive

their world as having. For instance, we know that there is a very simple 1D

CA that's computation universal (Wolfram's rule 110), so we know that we

can implement any higher-dimensional cellular automata in rule 110.

However, if we implement in rule 110 some 3D CA which contains SASs, these

SASs would go right on moving around in their 3D world and perceiving their

space as 3D. In an important sense, it would be incorrect to say that those

SASs live in a 1D world, even though ultimately their "substrate" is 1D.

This is really just another example of the familiar concept of "substrate

neutrality".

*>So at the least the 2D or 4 or 5D sentient creatures would be frustrated
*

*>(remember, they are SUBSTRUCTURES, they're not computing the space itself,
*

*>they're
*

*>part of the space and perceiving and acting on other parts of it).
*

But what possible reason do we have for believing that 4D or 5D cellular

automata (or, to be more careful, cellular automata which would be

perceived as 4D or 5D by the SASs within them) are somehow hostile to the

existence of SASs? The arguments in Tegmark's paper about how universes

with more than 3 spacial dimensions can't support stable structures like

atoms simply don't apply to 4D cellular automata. Those arguments are very

specific, applying only to quantum-physical and string-theory models.

-- Kory

Received on Sat Jan 17 2004 - 21:47:21 PST

Date: Sat, 17 Jan 2004 21:40:22 -0500

At 1/17/04, Eric Hawthorne wrote:

That's correct on one level, but what we're really interested in is the

dimensionality of space that SASs within the computation would perceive

their world as having. For instance, we know that there is a very simple 1D

CA that's computation universal (Wolfram's rule 110), so we know that we

can implement any higher-dimensional cellular automata in rule 110.

However, if we implement in rule 110 some 3D CA which contains SASs, these

SASs would go right on moving around in their 3D world and perceiving their

space as 3D. In an important sense, it would be incorrect to say that those

SASs live in a 1D world, even though ultimately their "substrate" is 1D.

This is really just another example of the familiar concept of "substrate

neutrality".

But what possible reason do we have for believing that 4D or 5D cellular

automata (or, to be more careful, cellular automata which would be

perceived as 4D or 5D by the SASs within them) are somehow hostile to the

existence of SASs? The arguments in Tegmark's paper about how universes

with more than 3 spacial dimensions can't support stable structures like

atoms simply don't apply to 4D cellular automata. Those arguments are very

specific, applying only to quantum-physical and string-theory models.

-- Kory

Received on Sat Jan 17 2004 - 21:47:21 PST

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