The Atheist's Afterlife: can resurrection happen without magic?
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11-10-2015, 09:03 AM
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 08:59 AM)GirlyMan Wrote:  
(11-10-2015 07:45 AM)Chas Wrote:  I suspect that to simulate X requires a mechanism with a complexity on the order of P(X), the power set of X.

That's what I would think at first blush but apparently it depends.

THE COMPUTATIONAL COMPLEXITY OF COMPONENT SELECTION IN SIMULATION REUSE

That doesn't seem particularly applicable, but maybe I just need more coffee. Drinking Beverage

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11-10-2015, 09:21 AM
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 09:03 AM)Chas Wrote:  
(11-10-2015 08:59 AM)GirlyMan Wrote:  That's what I would think at first blush but apparently it depends.

THE COMPUTATIONAL COMPLEXITY OF COMPONENT SELECTION IN SIMULATION REUSE

That doesn't seem particularly applicable, but maybe I just need more coffee. Drinking Beverage

Where do you get the power set from if not from all possible combinations of the simulation components?

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11-10-2015, 11:36 AM
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 09:21 AM)GirlyMan Wrote:  
(11-10-2015 09:03 AM)Chas Wrote:  That doesn't seem particularly applicable, but maybe I just need more coffee. Drinking Beverage

Where do you get the power set from if not from all possible combinations of the simulation components?

There are an infinite number of possible components, so the power set's cardinality is Aleph one.

But that wasn't my point. My point was that to simulate something requires a platform of greater complexity than the thing being simulated.

However, that might not be strictly true as a Universal Turing Machine can run any algorithm. Just not in real time - and that's the rub.

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11-10-2015, 12:06 PM (This post was last modified: 11-10-2015 12:23 PM by GirlyMan.)
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 11:36 AM)Chas Wrote:  
(11-10-2015 09:21 AM)GirlyMan Wrote:  Where do you get the power set from if not from all possible combinations of the simulation components?

There are an infinite number of possible components, so the power set's cardinality is Aleph one.

Don't quote me on this but since components seem discrete instead of continuous I think the cardinality of their power set is [Image: aleph_2.png]

(11-10-2015 11:36 AM)Chas Wrote:  But that wasn't my point. My point was that to simulate something requires a platform of greater complexity than the thing being simulated.

That's an interesting point I haven't considered. Not sure it's without controversy. Don't think it's incontrovertible.

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11-10-2015, 12:45 PM
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 12:06 PM)GirlyMan Wrote:  
(11-10-2015 11:36 AM)Chas Wrote:  There are an infinite number of possible components, so the power set's cardinality is Aleph one.

Don't quote me on this but since components seem discrete instead of continuous I think the cardinality of their power set is [Image: aleph_2.png]

There can be a countably infinite (aleph nought) number of discrete simulation components and that makes the power set uncountably infinite (aleph one).

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(11-10-2015 11:36 AM)Chas Wrote:  But that wasn't my point. My point was that to simulate something requires a platform of greater complexity than the thing being simulated.

That's an interesting point I haven't considered. Not sure it's without controversy. Don't think it's incontrovertible.

It is a postulate, but a realistic simulation would require something of complexity equal to (or greater than) the thing being simulated running on something of some complexity.

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11-10-2015, 03:03 PM (This post was last modified: 11-10-2015 03:09 PM by GirlyMan.)
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 12:45 PM)Chas Wrote:  There can be a countably infinite (aleph nought) number of discrete simulation components and that makes the power set uncountably infinite (aleph one).

I don't agree. 2 raised to the power of aleph naught is aleph naught.

(11-10-2015 12:45 PM)Chas Wrote:  It is a postulate, but a realistic simulation would require something of complexity equal to (or greater than) the thing being simulated running on something of some complexity.

Not buying that on face value. I'm thinking of deep artificial neural networks and genetic algorithms. Deep-learning ANNs can be proven to apprroximate any arbitrary function to any arbitrary degree.

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11-10-2015, 08:51 PM
RE: The Atheist's Afterlife: can resurrection happen without magic?
(11-10-2015 03:03 PM)GirlyMan Wrote:  
(11-10-2015 12:45 PM)Chas Wrote:  There can be a countably infinite (aleph nought) number of discrete simulation components and that makes the power set uncountably infinite (aleph one).

I don't agree. 2 raised to the power of aleph naught is aleph naught.


In elementary set theory, Cantor's theorem states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by a much simpler proof than that given below. Counting the empty subset, subsets of A with just one member, etc. for a set with n members there are 2n subsets and the cardinality of the set of subsets n < 2n is clearly larger. But the theorem is true of infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite. The theorem is named for German mathematician Georg Cantor, who first stated and proved it.

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(11-10-2015 12:45 PM)Chas Wrote:  It is a postulate, but a realistic simulation would require something of complexity equal to (or greater than) the thing being simulated running on something of some complexity.

Not buying that on face value. I'm thinking of deep artificial neural networks and genetic algorithms. Deep-learning ANNs can be proven to apprroximate any arbitrary function to any arbitrary degree.

Maybe so.

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