The Atheist's Afterlife: can resurrection happen without magic?



11102015, 09:03 AM




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 08:59 AM)GirlyMan Wrote:(11102015 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 doesn't seem particularly applicable, but maybe I just need more coffee. Skepticism is not a position; it is an approach to claims. Science is not a subject, but a method. 

11102015, 09:21 AM




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 09:03 AM)Chas Wrote:(11102015 08:59 AM)GirlyMan Wrote: That's what I would think at first blush but apparently it depends. Where do you get the power set from if not from all possible combinations of the simulation components? #sigh 

11102015, 11:36 AM




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 09:21 AM)GirlyMan Wrote:(11102015 09:03 AM)Chas Wrote: That doesn't seem particularly applicable, but maybe I just need more coffee. 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. Skepticism is not a position; it is an approach to claims. Science is not a subject, but a method. 

11102015, 12:06 PM
(This post was last modified: 11102015 12:23 PM by GirlyMan.)




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 11:36 AM)Chas Wrote:(11102015 09:21 AM)GirlyMan Wrote: Where do you get the power set from if not from all possible combinations of the simulation components? Don't quote me on this but since components seem discrete instead of continuous I think the cardinality of their power set is (11102015 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. #sigh 

11102015, 12:45 PM




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 12:06 PM)GirlyMan Wrote:(11102015 11:36 AM)Chas Wrote: There are an infinite number of possible components, so the power set's cardinality is Aleph one. There can be a countably infinite (aleph nought) number of discrete simulation components and that makes the power set uncountably infinite (aleph one). Quote:(11102015 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. 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. Skepticism is not a position; it is an approach to claims. Science is not a subject, but a method. 

11102015, 03:03 PM
(This post was last modified: 11102015 03:09 PM by GirlyMan.)




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 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. (11102015 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. Deeplearning ANNs can be proven to apprroximate any arbitrary function to any arbitrary degree. #sigh 

11102015, 08:51 PM




RE: The Atheist's Afterlife: can resurrection happen without magic?
(11102015 03:03 PM)GirlyMan Wrote:(11102015 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). 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. Quote:(11102015 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. Maybe so. Skepticism is not a position; it is an approach to claims. Science is not a subject, but a method. 



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