On 8/19/2012 2:43 PM, Stephen P. King wrote:

On 8/19/2012 4:30 PM, meekerdb wrote:On 8/19/2012 12:51 PM, Stephen P. King wrote:I understand that 2+2 = 4. I still cannot explain how and why I understand "2+2 = 4". "2+2=4" is easy. "I understand 2+2=4" is quasi infinitely more complex.## Advertising

Dear Bruno,As I see it, the quasi-infiitely more complex aspect of "I understand that 2+2=4"follows, at least, from the requirement that many entities capable of making suchstatements can point to examples of 2+2=4 and communicate about such statements witheach other however far away in space and time they are from each other. We can ignorethe fact that there is a collection of entities to whom the statement "I understandthat 2+2=4" has a meaning. You need to get a grip on the nature of meaningfulness.Searle has tried to do this with his Chinese Room idea but failed to communicate theconcept. :_(Maybe Bruno will introduce a new modality to his logic Up="Understands p". :-) Brent --Hi Brent,That would be wonderful if possible. AFAIK, understanding is contingent ondemonstrability, e.g. I understand p if and only if I can demonstrate that p implies qand q is not trivial and q is true in the same context as p. I think that Bruno's ideaof "interviewing a machine" is a form of demonstration as I am trying to define it here.In my thesis, demonstrability requires that the model to be demonstrated is actuallyimplemented in at least one possible physical world (i.e. satisfies thermodynamic lawsand Shannon information theory) otherwise it could be used to implement a Maxwell Demon.BTW, it was an analysis of Maxwell's Demon that lead me to my current ideas, thatabstract computation requires that at least one physical system actually can implementit. This is not ultrafinitism since I am allowing for an uncountable infinity ofphysical worlds, but almost none of them are accessible to each other (there exist eventhorizons, etc.).Consider the case where a computation X is generating an exact simulation of thebehavior of molecules in a two compartment tank with a valve and there exists a computerY that can use the output of X to control the valve. We can easily see that X could be asubroutine of Y. If the control of Y leads to an exact partition of the fast (hot) andslow (cold) molecules and this difference can be used to run Y then some might arguethat we would have a computation for free situation. The problem is that for thehot/cold difference to be exploited to do work the entire apparatus would have to becoupled to a heat reservoir that would absorb the waste energy generated by the work.Heat Reservoirs are interesting beasts....

`If your computer simulation is acting as Maxwell's demon then you don't need a heat`

`reservoir. The demon makes one tank hot an the other cold so a heat engine runs on the`

`difference. Unfortunately this is impossible because such a simulation would require`

`defining the initial state of the particle's position and momentum in the two tanks. This`

`is not available for free. To determine it by measurement takes at least as much free`

`energy as can be recovered after implementing Maxwell's demon.`

See http://www.nature.com/news/the-unavoidable-cost-of-computation-revealed-1.10186 for

`But if you're doing a calculation once on a given machine it's not necessary to erase the`

`result. In Feynman's paper on quantum computing he note this gets around Landauer's`

`limit. So long as the evolution of the computation is unitary no energy need be`

`dissipated. So I don't see how the result is relevant to Bruno's UD.`

Brent

We ignore the role played by our physical world in ourphilosophical/mathematical/logical discussions to our peril!-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon --You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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