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I like your argument, Rafal. If I might summarise, I think this is what you

were saying...

- There are universes N which occur naturally, from "pure mathematics",

which contain humanlike civilisations (enough like our universe for purposes

of this argument).

- There are universes S which occur as simulations inside other universes,

which are humanlike civilisations (as above).

- The space of all mathematics of which N is the same order is larger than

the space of simulations S, thus we are more likely to be in N than S, and

thus not in a simulation.

Is that about right?

If so, I would counter by saying that the space N cannot be larger than the

space S, and in fact should be of a lower order (aleph thingy?) than S.

Take this from the hierarchical conception of the full space of applicable

universes. Note that universes in N spring out of "mathematics per se".

Whereas elements of S can derive from elements of N, or from other elements

of S.

So, if each n in N has some non-zero probability of creating a sub-hierarchy

of elements of S, where the depth of that hierarchy is infinite, we get an

infinite number s's in S for each n. ie: the order of S is higher than N, so

that you are vanishingly unlikely to actually exist in an n, rather than an

s.

Now, I am not sure if your argument shows below that the order of N is as

high as it can be (equating it with the space of all mathematics?). I'd

question that claim, if you are making it (not sure). If that was the case,

it would follow, I guess, that the space of simulations must be constrained

in some way to match it.

Emlyn

-----Original Message-----

From: Smigrodzki, Rafal [mailto:SmigrodzkiR@MSX.UPMC.EDU]

Sent: Tuesday, 11 December 2001 5:36

To: 'extropians@tick.javien.com'

Subject: RE: New website: The Simulation Argument

I just read Nick Bostrom's article:

http://www.simulation-argument.com/classic.html

<http://www.simulation-argument.com/classic.html>

Not being a physicist or mathematician I feel a bit apprehensive about

commenting on it, lest I say something embarrassing, but let me try to

explain how I could try to disagree with the article's conclusion:

1) Let's assume that the whole of reality is a mathematical construct - a

self-evolving formal system, not constrained by the laws of physics (such as

conservation laws), whose infinitesimally small subset is our observable

physical world, with it's laws ultimately derived from a set of axioms and

rules of production. No entity external to the totality of this system

exists, hence it is not a simulation, but rather an explosion of pure

mathematics, arising spontaneously and unavoidably from a true and absolute

nothingness, in all the unimaginable ways pure math could develop, with new

extensions of the axiom set adding themselves whenever undecidable theorems

arise.

2) We cannot place ourselves with absolute certainty within any level of the

system - there is an unknown and perhaps unknowable number of layers

separating our physical reality from the mathematical constructs which we

are capable of understanding (contain within our minds), such as the roots

of number theory, and the empty set.

3) Since the number of levels of the system (its axiomatic extensions) is as

large as mathematics itself, infinite in a way beyond the reach of our

minds, it follows that subsets of the system capable of supporting our

physics should arise in an infinity of levels, over and above any of the

branching patterns predicted by the multiuniverse interpretation of QM. It

is somewhat similar to the infinite formation of patterns in a fractal, such

as the Mandelbrot set, where the central black rosette comes up over and

over again, arbitrarily large or infinitesimally smaller than the first

instance you calculate, except the whole system is not fractal - new

extensions are not blowups of lower levels, although they do contain

repetitions of the smaller sets as their constituent parts.

4) Some of the instances of worlds indistinguishable from ours will occur

within computational devices used by sentient entities living on higher

levels, farther removed from the root of the system. Let's call them S

5) Some of the instances of worlds indistinguishable from ours will occur as

subsets of branches of mathematics per se, like fractals, without any

conscious entities producing them. Let's call them N.

6) Both N and S are infinities, and if most of the system consists of

branches which are not sentient, then N>>S.

7) If N>>S, then it is indeed possible that a vast majority of

instantiations of our minds would exist without being simulated, while

allowing a high likelihood of developing into posthumans, infinitely large

numbers of whom would run ancestor simulations (e.g. as part of applied

cosmology experiments, without any moral motivations).

So this is the fourth proposition. Metaphysics at it's worst, I'm afraid,

probably unprovable and unfalsifiable, but pleasant.

Rafal

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