On 13 Aug 2012, at 17:55, Platonist Guitar Cowboy wrote:
When this cowboy has to write a score, there are always the
constraints of what client/audience expect; even if they expect
breaking a set of conventions.
But the actual writing, the 1p experience of it, is out of my
control. If I am afforded conditions to be allowed to be open for
surprise, this control loss is ecstatic and overwhelming, in the
sense that I can't keep up with the seemingly "foreign?!" streams of
notes and melodies filling my head. Kind of like, when you start
dreaming and you're sort of conscious that you're dreaming pre-
sleep, then complex imagery/thought starts to unfold "automatically"
without our control, at a rate much higher and denser than we would
ever be able to code in real time, with interfaces available to us
today. Mahler said to Bauer Lechner upon conducting his symphonies
later in life: "I don't feel like I wrote the damned things. I feel
like I'm conducting somebody else's score." And although I can't
write anything close to a Mahler symphony, I feel the same towards
"my" own scores.
The craft part, tools of formal music theory and so on, are only
useful after this "generation" phase; serving merely to organize,
make presentable, to perfume, polish and make palatable the highly
dense strings of musical info passing through us all the time (if I
remain quiet and thoughtless enough, and my local universe doesn't
interrupt, including my analytical thinking, I'll begin to hear it).
Contrary to Tom Waits, who is a much better song writer than yours
truly, I do not believe that "the muse just happens to strike you
when you get lucky". For this cowboy, it's more a problem, to create
the conditions that make surprise possible: for me when my
analytical faculties are weakened sufficiently.
Yes, I would subscribe to "every symphony/song exists" outside of
time or is pre-established. But they are infinite.
Yes.
And they fork infinitely into new songs. I want my musical
redundancy pure and free and the problem is all the functional,
analytical noise, and biological need's stuff in the way ;)
:)
After I've gone fishing, then the formal theory and craft becomes
central; and you discover: Funny, "I" did that, would've never
crossed "my" mind...
OK.
I've never solved a NP-Complete problem though :)
The classical satisfiability problem of propositional logic is NP
complete, so I am pretty sure you did solve some of them. When looking
if p -> (q -> p) is a tautology, you do solve a NP-complete problem
instantiation. There are two variables, p and q, so you will need 2^2
lines in the truth table. So that truth table algorithm is intractable
if the number of variable is too big. With 64 variables you would need
2^64 lines.
NP problem are algorithmically solvable, but not necessarily
tractable, and necessarily non tractable in case P ≠ NP, as almost
everyone believe, but it is still a major open problem in computer
science.
Bruno
On Mon, Aug 13, 2012 at 3:19 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 12 Aug 2012, at 20:05, Stephen P. King wrote:
Hi Roger,
I will interleave some remarks.
On 8/11/2012 7:37 AM, Roger wrote:
Hi Stephen P. King
As I understand it, Leibniz's pre-established harmony is analogous
to
a musical score with God, or at least some super-intelligence, as
composer/conductor.
Allow me to use the analogy a bit more but carefully to not go
too far. This "musical score", does it require work of some kind to
be created itself?
This prevents all physical particles from colliding, instead they
all move harmoniously together*. The score was composed before the
Big Bang-- my own explanation is like Mozart God or that
intelligence
could hear the whole (symphony) beforehand in his head.
I argue that the Pre-Established Harmony (PEH) requires solving
an NP-Complete computational problem that has an infinite number of
variables. Additionally, it is not possible to maximize or optimize
more than one variable in a multivariate system. Unless we are
going to grant God the ability to contradict mathematical facts,
which, I argue, is equivalent to granting violations of the basis
rules of non-contradiction, then God would have to run an eternal
computation prior to the creation of the Universe. This is absurd!
How can the existence of something have a beginning if it requires
an an infinite problem to be solved first?
Here is the problem: Computations require resources to run,
That makes sense, but you should define what you mean by resources,
as put in this way, people might think you mean "primitively
physical resource".
and if resources are not available then there is no way to claim
access to the information that would be in the solution that the
computation would generate. WE might try to get around this problem
the way that Bruno does by stipulating that the "truth" of the
solution gives it existence, but the fact that some mathematical
statement or sigma_1 sentence is true (in the prior sense) does not
allow it to be considered as accessible for use for other things.
For example, we could make valid claims about the content of a
meteor that no one has examined but we cannot have any certainty
about those claims unless we actually crack open the rock and
physically examine its contents.
The state of the universe as "moving harmoniously together" was
not exactly what the PEH was for Leibniz. It was the
synchronization of the simple actions of the Monads. It was a
coordination of the percepts that make up the monads such that, for
example, my monadic percept of living in a world that you also live
in is synchronized with your monadic view of living in a world that
I also live in such that we can be said to have this email chat.
Remember, Monads (as defined in the Monadology) have no windows and
cannot be considered to either "exchange" substances nor are
embedded in a common medium that can exchange excitations. The
entire "common world of appearances" emerges from and could be said
to supervene upon the synchronization of internal (1p subjective)
Monadic actions.
I argue that the only way that God could find a solution to the
NP-Complete problem is to make the creation of the universe
simulataneous with the computations so that the universe itself is
the computer that is finding the solution. <snip>
Even some non universal machine can solve NP-complete problem.
Bruno
http://iridia.ulb.ac.be/~marchal/
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