Dear LizR, I am trying to figure something out. I am looking for relations between mathematical limits on computations and physical limits on computations. My hypothesis implies that there should be an isomorphism between the class of mathematical computations and the class of physical systems that could implement those computations. There has to be a reason why we only observe computations that either terminate, or do not terminate in less than the age of the universe, 14e9 years. We have no hope of observing a computation that requires an infinite number of discrete steps. (This seems to make the falsification of Bruno's result difficult.) From astronomical observations, our universe appears to be finite and is calculated to have a finite quantity of matter in it. If this is all the result of computations, an infinite quantity of computations (as each observer in the universe is defined as the intersection of an infinite quantity of computations -is that Bruno's exact definition?-) then how is it that the universe we observe is finite?
A related question: If the matter in the universe where the "hardware" for the computation of the universe, would the universe that any observer in that universe be required to be finite? Observers seem to involve, individually, an infinite number of computations so my question above follows again: Why do we observe a finite universe? I can see two reasons: 1) Mathematical: Infinite sets are such that there is a bijection between the infinity and its proper subsets, thus if an observer is defined by some infinity it is also defined by any proper subset of that infinity. It seems to me that finite sets that are subsets of an infinite set, will not observe the infinite proper subsets of the infinity as they cannot be distinguished from each other or the whole! There is no difference that makes a difference between them. Computations that do not terminate are those that run forever or get stuck in a loop. 2) Physical: Assuming the universe is finite, there will only be a finite quantity of computation associated with any subset of that universe. We can identify the resources required to "run" a computation that terminates in some finite time. A finite universe with a certain set of properties could be simulated in finite time, assuming maximal efficiency, etc. There will be computations that cannot be run is a finite universe because they either do not terminate 'in time' or they do not terminate at all. I am assuming that any realistic use of clever configurations of matter allowed by the laws of physics, which seem to disallow for hypercomputing ala Tipler <http://en.wikipedia.org/wiki/Frank_J._Tipler> and others. The expansion of the distance between cosmic objects would not improve prospects of hypercomputing <http://en.wikipedia.org/wiki/Hypercomputation>unless the total quantity of matter and "fields" in the universe changes; the computational resources available do not change (or they go down as they go outside of each others event/causal horizons). A conjecture of mine is that the reason why we observe a finite universe is that only finite processes and products of finite processes, like our physical bodies, can only observe finite things because we can only communicate about finite things. A reality requires the ability to coherently communicate between its observers. On Fri, Jan 17, 2014 at 6:02 PM, LizR <[email protected]> wrote: > On 18 January 2014 11:39, Stephen Paul King <[email protected]>wrote: > >> Dear John, >> >> I invite your comment on a statement and question: *There is not >> observable difference between "X is non-computable" and "there does not >> exist sufficient resources to complete the computation of Y".* >> >> Are X and Y effectively the same thing, everything else being equal? If >> there is a difference that makes a difference, what might it be? >> > > In other words, is anything non-computable because of some theoretical > reason, rather than "merely local geographical" ones (which might cease to > be restrictions if, say, our local even horizon expands, or we construct > wormholes to other universe) ? > > Surely the halting problem? > > -- > You received this message because you are subscribed to a topic in the > Google Groups "Everything List" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/everything-list/TBc_y2MZV5c/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 [email protected] http://www.provensecure.us/ “This message (including any attachments) is intended only for the use of the individual or entity to which it is addressed, and may contain information that is non-public, proprietary, privileged, confidential and exempt from disclosure under applicable law or may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify sender immediately and delete this message immediately.” -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
