Jul 1, 2015 06:31 PM
http://fqxi.org/community/articles/display/203
EXCERPT: David Wolpert has his tongue mostly in his cheek when he says that his theory puts limits on religions. "There cannot be two gods, both of which can perfectly observe everything, or both of which can make anything happen that they want," he says. In fact, there cannot even be two gods who both have perfect memory. In short, it is mathematically impossible to have a polytheistic universe with all-knowing gods.
[...] Inference devices are physical machines that obey the normal rules of mathematics and logic. The only a priori restriction on them is that they exist in the same physical universe as the system they want to know about. In Wolpert’s model, for an inference device to know something about the state of a system they must be able to correctly answer YES or NO to any binary question concerning the state of that system. The question could be something as simple as: Are there clouds in the sky? If its answer is always correct, no matter what the actual state of clouds in the sky, then the device knows whether there are indeed clouds in the sky.
Wolpert proved that it’s impossible for one inference device (device A) to both know its own answer to an arbitrary question and to also know the answer to the same question by a different inference device B. The same holds true for B. This limitation holds no matter what the laws of physics actually are—the limits apply in any universe.
[...] Laplace introduced the idea of a hypothetical super-intelligent ’demon’ that can predict the future state of the universe if it has complete knowledge of the current state. But, by using Wolpert’s framework, one can model the current avatar of any such demon as an inference device, while the future avatar of the demon must be regarded as another inference device. (This is because the state of the universe changes from one moment to another and inference devices can only be defined within the context of one given state of the universe.) Wolpert’s work shows that the current avatar of the demon cannot know with absolute certainty the future avatar’s knowledge about the state of the universe. In other words, Laplace’s demon cannot predict without uncertainty. (This is true even if one assumes a classical, finite, non-chaotic universe, as Laplace did.)....
EXCERPT: David Wolpert has his tongue mostly in his cheek when he says that his theory puts limits on religions. "There cannot be two gods, both of which can perfectly observe everything, or both of which can make anything happen that they want," he says. In fact, there cannot even be two gods who both have perfect memory. In short, it is mathematically impossible to have a polytheistic universe with all-knowing gods.
[...] Inference devices are physical machines that obey the normal rules of mathematics and logic. The only a priori restriction on them is that they exist in the same physical universe as the system they want to know about. In Wolpert’s model, for an inference device to know something about the state of a system they must be able to correctly answer YES or NO to any binary question concerning the state of that system. The question could be something as simple as: Are there clouds in the sky? If its answer is always correct, no matter what the actual state of clouds in the sky, then the device knows whether there are indeed clouds in the sky.
Wolpert proved that it’s impossible for one inference device (device A) to both know its own answer to an arbitrary question and to also know the answer to the same question by a different inference device B. The same holds true for B. This limitation holds no matter what the laws of physics actually are—the limits apply in any universe.
[...] Laplace introduced the idea of a hypothetical super-intelligent ’demon’ that can predict the future state of the universe if it has complete knowledge of the current state. But, by using Wolpert’s framework, one can model the current avatar of any such demon as an inference device, while the future avatar of the demon must be regarded as another inference device. (This is because the state of the universe changes from one moment to another and inference devices can only be defined within the context of one given state of the universe.) Wolpert’s work shows that the current avatar of the demon cannot know with absolute certainty the future avatar’s knowledge about the state of the universe. In other words, Laplace’s demon cannot predict without uncertainty. (This is true even if one assumes a classical, finite, non-chaotic universe, as Laplace did.)....