On 8/19/2012 6:03 PM, meekerdb wrote:
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.
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 such statements can point to
examples of 2+2=4 and communicate about such statements with each
other however far away in space and time they are from each other.
We can ignore the fact that there is a collection of entities to
whom the statement "I understand that 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 the concept. :_(
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 on demonstrability, e.g. I understand p if and only if I
can demonstrate that p implies q and q is not trivial and q is true
in the same context as p. I think that Bruno's idea of "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 actually implemented in at least one possible
physical world (i.e. satisfies thermodynamic laws and 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, that abstract computation requires that at least one
physical system actually can implement it. This is not ultrafinitism
since I am allowing for an uncountable infinity of physical worlds,
but almost none of them are accessible to each other (there exist
event horizons, etc.).
Consider the case where a computation X is generating an exact
simulation of the behavior of molecules in a two compartment tank
with a valve and there exists a computer Y that can use the output of
X to control the valve. We can easily see that X could be a
subroutine of Y. If the control of Y leads to an exact partition of
the fast (hot) and slow (cold) molecules and this difference can be
used to run Y then some might argue that we would have a computation
for free situation. The problem is that for the hot/cold difference
to be exploited to do work the entire apparatus would have to be
coupled 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.
Hi Brent,
Good point. I stand corrected! But did my remark about
understanding make any sense to you? I am trying to work out the
implication of the idea of Boolean algebras as entities capable of
evolving and interacting as it is a key postulate of the idea that I am
researching. The Maxwell Demon is just a nice and handy toy model of
this idea, IMHO. Could the Maxwell Computational Demon "understand" what
it is doing? We could add the capacity to have a self-model as a
subroutine and thus a way to gauge its actual efficiency against a
theoretical standard as a way to implement a "choice" mechanism... See
http://www.youtube.com/watch?v=ehno85yI-sA for a discussion of this
self-modeling idea.
The demon makes one tank hot an the other cold so a heat engine runs
on the difference.
Yes, the demon would act in a cycle: Compute the simulation to
operate the valve to segregate the hot from cold and then use the heat
engine to charge a battery, discharging the difference in temperatures.
Can this run forever? No, given real world things like friction and the
wearing out of parts, but in the idea case it might seem to be able to
run for ever.
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.
The idea case would shift the initial position/momentum question
into a synchronization question: how is a measurement different from the
"inverse" of a simulation? I do not have any good words to express my
thought here... Let's see where the discussion takes us.
See
http://www.nature.com/news/the-unavoidable-cost-of-computation-revealed-1.10186
for more on this.
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.
The reversibility argument only works if there is sufficient black
memory to work with such that erasure never is necessary. This is just
trading off the recource of energy for the resource of a read/write
medium. Given the wearing out of parts situation, could this be dealt
with so that it is not a problem for the idea case aka no friction, no
loss of heat to an external world...
See also http://www.csupomona.edu/~hsleff/MD-power-time.pdf
<http://www.csupomona.edu/%7Ehsleff/MD-power-time.pdf> for a nice
discussion...
I am trying to met Bruno half-way in his COMP idea... I just can't
let go of the apparent necessity of actual physical implementation, even
given that I really like his immaterialist hypothesis. It is too much
like Leibniz' PEH and its reliance on the logically impossible. How is
Bruno's idea not a proverbial floating castle in the sky?
Brent
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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