On 2/14/2012 05:57, Stephen P. King wrote:
On 2/13/2012 11:18 PM, acw wrote:
On 2/14/2012 02:55, Stephen P. King wrote:
On 2/13/2012 5:27 PM, acw wrote:
[SPK] There is a problem with this though b/c
it assumes that the field is pre-existing; it is the same as the
"block
universe" idea that Andrew Soltau and others are wrestling with.
Why is a pre-existing field so troublesome? Seems like a similar
problem as the one you have with Platonia. For any system featuring
time or change, you can find a meta-system in which you can describe
that system timelessly (and you have to, if one is to talk about time
and change at all).
Dear Kermit,
OK, I will try to explain this in detail and check my math. I am good
with pictures, even N-dimensional ones, but not symbols, equations and
words...
Think of a collection of different objects. Now think of how many ways
that they can be arranged or partitioned up. For N objects, I believe
that there are at least N! numbers of ways that they can be arranged.
Now think of an Electromagnetic Field as we do in classical physics. At
each point in space, it has a vector and a scalar value representing its
magnetic and electric potentials. How many ways can this field be
configured in terms of the possible values of the potentials at each
point? At least 1x2x3x...xM ways, where M is the number of points of
space. Let's add a dimension of time so that we have a 3,1 dimensional
field configuration. How many different ways can this be configured?
Well, that depends. We known that in Nature there is something called
the Least Action Principle that basically states that what ever happens
in a situation it is the one that minimizes the action. Water flows down
hill for this reason, among other things... But it is still at least M!
number of possible configurations.
How do we compute what the minimum action configuration of the
electromagnetic fields distributed across space-time? It is an
optimization problem of figuring out which is the least action
configured field given a choice of all possible field configurations.
This computational problem is known to be NP-Complete and as such
requires a quantity of resources to run the computation that increases
as a non-polynomial power of the number of possible choices, so the
number is, I think, 2^M! .
The easiest to understand example of this kind of problem is the
Traveling Salesman problem
<http://en.wikipedia.org/wiki/Travelling_salesman_problem>: "Given a
list of cities and their pairwise distances, the task is to find the
shortest possible route that visits each city exactly once. " The number
of possible routes that the salesman can take increases exponentially
with the number of cities, there for the number of possible distances
that have to be compared to each other to find the shortest route
increases at least exponentially. So for a computer running a program to
find the solution it takes exponentially more resources of memory and
time (in computational steps) or some combination of the two.
Yet the problem is decidable in finite amount of steps, even if that
amount may be very large indeed. It would be unfeasible for someone
with bounded resources, but not a problem for any abstract TM or a
physical system (are they one and the same, at least locally?).
Hi ACW,
WARNING WARNING WARNING DANGER DANGER! Overload is Eminent!
OK, please help me understand how we can speak of computations for
situations where I have just laid out how computations can't exist.
Computations can be encoded in Peano Arithmetic and many others
"timeless" theories just as well. I'm not entirely sure I see what your
proof is. Although if you deny any form of Platonia or Plentitude and
any form of *primitive* physical reality, I'm not entirely sure what
you're left with to represent computations. You'll have to present an
understandable theory which is not primitively physical, nor platonic.
Currently I only consider the timeless platonic versions as primitive
physics: 1) doesn't make too much sense, especially since we're always
talking about it only through math, thus it can just be 'math' 2)
UDA+MGA show that it's superfluous if we do happen to admit a digital
substitution. Adding 3p time does not fix the issue (as shown in my
earlier thought experiment), and 1p time is too subjective to grant it
continuity over too large intervals (we cannot guarantee continuity each
time short term memory is cleared).
If we take CTT at face value, then it requires some form of implementation.
Implementation in arithmetic seems sufficient to me.
Some kind of machine must be run.
It's run by some sentences being either true or false.
Are you sure that you are not
substituting your ability to imagine the solution of a computation as an
intuitive proof that computations exist as purely abstract entities,
independent from all things physical?
If COMP, they have to.
Without COMP, but assuming a 3p, it's not hard to again get a similar
result if one is to consider reality consistent (which it has to be,
otherwise it wouldn't exist).
The term physical starts losing its meaning the more abstract and
mathematical the theory gets. I can't distinguish physical from
phenomenology if one gives up the primitively physical.
The platonic view is that reality or the 1p exists as an abstract
answerable "question" and we're that answer. Or to put it another way -
because some timeless abstract relations hold.
My difficulty may just be a simple
failure of imagination but how can it make any sense to believe in
something in whose very definition is the requirement that it cannot be
known or imagined?
It cannot be known? We can do math as much as we want, although we will
run into limitations (due to Godel and friends). Not all true sentences
are provable, although we can always construct a stronger system in
which more and more sentences are provable. If a system is allowed to
infinitely change their mind, they can be infinitely more right, at the
cost of being temporarily wrong - guess which kind of system we are.
As for imagination, I'm sorry, but I can't imagine what primitive
physics is either - it makes no sense to me. I can't imagine numbers too
much beyond the patterns and patterns of patterns my brain can conceive
- it's all abstract relations and meta-relations there. I may use
numerals or symbols to talk about them, but that doesn't mean that the
choice of numerals or symbols is relevant in any way.
I can't see how numbers/progressions can be reduced further, nor do I
see any reason to waste time on that. Yet, we can all use them.
Numbers aren't even the only entities that have such problems - try
substituting enough words with their definitions and so on, to realize
that you'll run into both cognitive limitations of our brain and the
fact that things are really abstract down there and trying to ground
them in *perceived* non-abstract entities does no good. Other things
like knowledge and experience are so incommunicable, that even grounding
them in the abstract is difficult.
Knowing and imagining are, at least, computations running in our brain
hardware.
Self-referential knowledge that you've gained by self-observation and
doing or reading science.
If your brained stopped, the knowing, imagining and even
dreaming that is "you" continues?
Is this about COMP's prediction of unusual continuations?
That's already in the assumption of surviving a digital substitution.
I consider my consciousness as existing due to a certain abstract
structure having an implementation. That structure is currently
implemented in my brain. If it would be implemented anywhere else, I
would continue existing there. If, for example, there was some machine
within the UD which ran all possible programs with some special
environment/functions and said machine instantiated the abstract
structure that is my mind, I would manifest relatively to that program,
which may have completely weird/different physics than our own, it may
be so weird that calling it 'physics' in any classical sense would be
non-sense. Of course, I don't really expect such continuations to be
high-measure, but if my brain truly ceased functioning and there were no
more "usual" high-measure continuations, I could expect that such a low
measure continuation to be experienced. Of course, such a machine could
also run here in our universe, if MWI happens to be true (or
alternatively, sufficiently large robust universe) - I've already
described such an example machine in an earlier thread.
So you do believe in disembodies
spirits, you are just not calling them that.
The term "spirit" would mean some strange embedding in this physical
world, yet without any physical effect. I don't see any point in such a
definition.
Instead I consider the meta-level at which our experiences exist, for
example: arithmetical or computational truth. Such truth may stand for
interconnected Observer Moments. If such OMs have unusual continuations
outside the current local physical structure, then sure. I do expect
continuations which do manifest within some other physical structure,
mostly because we evolved in such a structure ourselves and we are
*embodied*, we'd require physics or at least a VR to function,
regardless how that physics or VR was ultimately implemented.
Something like a theorem prover which needs no physical reality may very
well be more directly implemented within Platonia and wouldn't need such
layering as we would.
I apologize, but this is a
bit hard to take. The inconsistency that runs rampant here is making me
a bit depressed.
What exactly is physical anyway? Can we distinguish any difference
between Platonic phenomenology and primitive physics? I can't, but one
of them offers more interesting answers than the other (which just
refuses to give any).
Now, given all of that, in the concept of Platonia we have the idea of
"ideal forms", be they "the Good", or some particular infinite string of
numbers. How exactly are they determined to be the "best possible by
some standard". Whatever the standard, all that matters is that there
are multiple possible options of The Forms with the stipulation that it
is "the best" or "most consistent" or whatever. It is still an
optimization problem with N variables that are required to be compared
to each other according to some standard. Therefore, in most cases there
is an Np-complete problem to be solved. How can it be computed if it has
to exist as perfect "from the beginning"?
The problem is that you're considering a "from the beginning" at all,
as in, you're imagining math as existing in time. Instead of thinking
it along the lines of specific Forms, try thinking of a limited
version along the lines of: "is this problem decidable in a finite
amount of steps, no matter how large, as in: if a true solution
exists, it's there."
And what exactly partitions it away from all the other "true solutions"?
This idea seems to only work if there is "One True Theory of
Mathematics".... But we know that that is not the case, there are many
different Arithmetics. How exactly do you know that yours is the "true
standard" one?
True relative to some theory. Said theory may have implementation as a
theorem prover, thus a computation. I don't ask for undecidable truths.
There may be many non-standard arithmetics, but I only consider the
finite one: the standard model. If you don't like arithmetic, just pick
any other system capable of universal computation, it doesn't really matter.
I'm not entirely sure if we can include uncomputable values there,
such as if a specific program halts or not, but I'm leaning towards
that it might be possible.
OK, there is no beginning. Recursively enumerable functions exist
eternally. OK. Why notLittle Ponies
<http://www.hasbro.com/mylittlepony/en_US/>? My daughters tells me all
about How Princess Celestia rules the sky... This entire theory reminds
me of the elaborated Pascal's Gamble... How do we know that our "god" is
the true god? OK. So we Bet on Bp&p. OK... Then what? How do I know what
"Bp&p" means?
I'm sure MLP exists eternally within OMs of their many fans' minds. If
some worlds containing actual robust implementations of magical ponies
exist, I do not know - magical non-reductive worlds are likely very rare
in the landscape because of their sheer complexity.
Pascal's Gamble? Here's an interesting post:
http://lesswrong.com/lw/z0/the_pascals_wager_fallacy_fallacy/
Leaving that aside: if you do accept COMP's assumptions, then sure, you
can bet on it if you want. Most religions want you to accept infinitely
complex assumptions which have no evidence behind them and you can't
reason about them much - COMP's assumptions are reasonable enough given
what we know, it can be false, but most evidence points that it's
probably not (see other thread for list of assumptions). COMP tells you
if you have a few simple and reasonable assumptions, then there are some
major consequences as to what the ontology has to be, what is possible,
and good hints to solving the mind-body problem, figuring out physics
and so on. Unfortunately some of these problems are computationally
intractable with our current resources. COMP's conclusions may upset a
hardcore materialist - in which case, if you really hate them that much,
you'll have to deny that you have consciousness or believe in some
infinitely complex stuff to avoid them.
Bp&p? Provable and true sentence, that is, correct knowledge. If you
dislike AUDA, it's not like you can't formulate it within some other
framework - the reasoning should still stand. AUDA just examines UDA's
consequences for a class of idealized machines and makes some
interesting headway towards the nature of qualia and quanta. UDA's
conclusions still stand even without AUDA.
I figured this out when I was trying to wrap my head around Leindniz'
idea of a "Pre-Established Harmony". It was supposed to have been
created by God to synchronize all of the Monads with each other so that
they appeared to interact with each other without actually "having to
exchange substances" - which was forbidden to happen as Monads "have no
windows". For God to have created such a PEH, it would have to solve an
NP-Complete problem on the configuration space of all possible worlds.
Try all possible solutions for a problem, ignore invalid ones.
And how exactly do we distinguish valid from invalid ones? By what
process do we "try all possible solutions"? Process and timelessness do
not mix.
You'll need to define what makes something "invalid", for example, if PA
allows a proof of "0=1", you could consider PA inconsistent (I doubt it
is). Such a true/false distinction is a matter of a meta-theory. In the
end, it all reduces to computation or abstract relations. Obviously, one
cannot really reduce this any further and I won't make any attempt - I
just consider such computational systems as universal enough to build an
ontology around them. If that's not good enough - you'll have to answer
the same questions about physics, and you can't really avoid them. Just
hiding behind the name 'physics' isn't enough, especially if the answer
is "don't ask".
If the number of possible worlds is infinite then the computation will
require infinite computational resources. Given that God has to have the
solution "before" the Universe is created,
"before", what is this "before", it makes no sense to talk of time
when dealing with timeless structures. A structure either exists in
virtue of its consistence/soundness, or it doesn't (it can exist as
something considered by someone within some other structure, which
does happen to be consistent, thus it only exists as a(n incorrect)
thought). Introducing a ``God'' agent to actually do creation or
destruction will only lead to confusion, because creation or
destruction implies time or causality. Platonia only implies local
consistency. On the other hand, I'm not even asking for any full
Platonia, just recursively enumerable sets should be enough...
How does the existence on an entity determine its properties? Please
answer this question. What do "soundness" and "consistency" even mean
when there does not exist an unassailable way of defining what they are?
Look carefully at what is required for a proof, don't ignore the need to
be able to communicate the proof.
Soundness and consistency have precise definitions. If you want an
absolute definition of consistency, it could be seen as a particular
machine never halting. Due to circularity of any such definitions, one
has to take some notion of abstract computation fundamental (for example
through arithmetic or combinators or ...)
It cannot use the time
component of "God's Ultimate Digital computer". Since there is no space
full of distinguishable stuff, there isn't any memory resources either
for the computation. So guess what? The PEH cannot be computed and thus
the universe cannot be created with a PEH as Leibniz proposed.
You can encode computation in arithmetic or other timeless systems
just as well.
Encode computation? How does it even makes sense to juxtapose a process
that requires time in a situation that is timeless? We cannot have our
computational cake and eat it (eliminate its temporality) too.
Turing Machines can be encoded within diophantine equations, thus same
goes for UTMs and of course the UD.
Arithmetic can emulate computability and computability can emulate
arithmetic (standard model only).
Time is merely a relation between states, it's always possible to
express such a relation timelessly.
Is it? So there is no such thing as change?
Change is the relation between states.
Then why is the illusion of it so damned persistent?
Continuity of consciousness? I don't know if it's an illusion, but it's
what we expect to happen, regardless of what actually happens. It makes
sense to care about what our next probable moments will be. I don't know
if I'm able to experience anything more than OMs to some granularity or
if I retain continuity every day after sleep or even within just a few
seconds (surely the qualia from a few seconds ago is already gone, but I
have the qualia from 'here and now'). Maybe something like the
inference/connection between 2 states is what an OM is (the continuity
view of OMs?), in Platonia it could for example be the what the
existence of a complex deep inference between some 2 theorems feels like
(or similar). Timeless views don't deny the subjective continuity.
Surely we can start in a environment that is
transitory and change laden and think up systems of ideas that seem to
be timeless, but do they really have these properties?
Both views might be valid. The timeless view just seems more general and
more likely to yield interesting results.
Did you see my
argument about how invariants require a set and transformations on the
set to be defined. Take away the transformations and what you have? A
set with nothing like an invariance to be seen anywhere. We can
eliminate measure of Change, but we cannot eliminate Change itself.
Not sure I understood that argument, I'll have to review it again.
To be fair, I'm not sure how even a single computation can be
performed without there existing a consistent definition of that
computation (thus the existence of that sentence in Platonia).
Does my no-brand name Desktop that I built myself, with its hard drives,
mother board, power supply, etc, depend on its running this crappy
Windows 7 OS only if someone has defined what a computations is? Of
course not! Again, how exactly does the existence of an entity, be it a
computation, Pony, UD or whatever, determine the particular set of
properties that make that computation a computation, the Pony and Pony
and the UD a UD? This is like the Randians chanting "A is A" over and
over never minding questions like what the <expletive deleted> is A?
Hah. Well, you do have to postulate some universal computational system.
Fortunately it doesn't matter which - the results should be the same due
to CTT.
You cannot even compute 1+1 without it, much less NP-complete
problems. I don't see how a in-time universe solves the problems you
ascribe to Platonia - same problems are present in both and they can
only be avoided by giving some consistent system existence. As for
space? why would space be needed for deciding if some recursive
relations hold. Space is itself an abstraction and I don't see how
introducing it would solve anything about such abstract recursive
relations, except maybe making it simpler to reason for those that
like to imagine physical machines instead of purely abstract ones.
Without space or time the operation of "copying" is impossible. Try it
some time. How can you over come the identity of indiscernibles without
space or time?
Recursive numbers and relations are not indiscernible, they are governed
by an exact and well-defined theory. Some such theory is being
postulated, it doesn't matter which, merely that it support universal
computation and it's not hard to find one as few systems can escape
CTT's consequences.
The idea of a measure that Bruno talks about is just another way of
talking about this same kind of optimization problem without tipping his
hand that it implicitly requires a computation to be performed to "find"
it. I do not blame him as this problem has been glossed over for hundred
of years in math and thus we have to play with nonsense like the Axiom
of Choice (or Zorn's Lemma) to "prove" that a solution exists,
never-mind trying to actually find the solution. This so called 'proof"
come at a very steep price, it allows for all kinds of paradox
<http://en.wikipedia.org/wiki/Banach-Tarski_paradox>.
All possible OM-chains/histories do exist and one just happens to live
in one of them.
Sure.
A measure is useful for predicting how likely some next OM would be,
but that doesn't mean that our inability of listing all possible OMs
and deciding their probabilities means that no next OM will exist - we
all inductively expect that it will.
No! You are neglecting the fact that there are not just a set of
connected OMs floating out in Platonic NowhereLand. You have to consider
all possible OMs and show how the continuation works. You at least have
to have something like a fixed point and that requires a space with
closure and compactness and *a transformation* on that space. You cannot
define continuation without meeting this requirement.
Are we using the same definition of space? I think I was confused until
now and just considered space as 3D physical space. If you meant it in
the mathematical sense, you'll need to be more precise...
As for the continuation's existence - one can show how a particular mind
thinks the continuation worked (because its next state was computed
successfully and so on). Showing all possible continuations is immensely
harder as it's very subjective and related to exactly what some
particular mind's implementation happens to be - it may even allow for
change - what can you change and still remain 'you'? Finding all
continuations isn't even computable, but finding some particular
continuations is possible, just never the general case.
I'll give an example to show why it's not computable:
Consider UTM0 (an Universal Turing Machine), it's partially implementing
some physics P0 and eventually a brain B0 and that brain is implementing
OS0 (an Observer Structure, Turing Emulable). Consciousness itself
corresponds to OS0's expected future states (computable), for example
represented in Arithmetical Truth. Talk about an observer's Godel number
is talk about OS0 or something which indirectly implements OS0 (for
example, a very good brain emulator).
You might be able to run UTM0 a few more states and if it faithfully
implements P0, B0 and OS0, you have yourself one continuation, which you
can verify because it should also have computed OS0's next states (which
can be verified as you have the Godel number). OS0 within the UDA
typically means the substitution level. Now consider various other
possibilities:
- UTM0 only computed a few states of P0
- P0 itself may be implemented by an infinity of other machines, all
computable in part, but maybe not computable in their full history, in
the limit
- B0 might not be a straight abstraction layer above P0, P0 might
directly alter B0's functionality, yet not altering OS0.
- OS0 claims that it's itself when it finds itself in another OM and so on.
- OS0 itself is subject to change and it doesn't always know much about
what changes and how much. Most change is gradual, but change can be
from simple forgetting to total amnesia. Many other unusual changes can
also happen. OS0's change can be due to changes in B0, or influenced
from P0 (for example quantum uncertainty), but overall OS0 expects that
it won't be changed too much and OS0's structure is very robust to
change due to how evolution shaped it. There's no clear way to say when
OS0 is now something which is no longer itself, such a thing involves
reference to self and one cannot always know when self is changed
indirectly, especially when changes are small.
- OS0 depending too heavily on P0's workings would make most
continuations be local (very low subst. level). A different
implementation of OS0 (with some details lost) which no longer depends
on P0 (SIM, substrate independence) might have its measure/expected
continuations altered in practice (I described a thought experiment on
how a SIM can directly select some classes of continuations in my first
post). If such a SIM's continuations have too many white rabbits, it
might COMP be less useful in practice :(
Can we tell if some UTM is implementing OS0? Rice's theorem says no.
If you want a blatant example consider homomorphic encryption
implementing P0. However, even if one is to disregard such trickery
(which is nonetheless very real), we can't even formalize when a changed
you no longer constitutes 'you', and yet we live through such changes
constantly. Continuity (or its illusion) is possible because we have
short term memory (and long term memory) and it's not wiped too often.
Because we have priors as to how the world works and how we work, we're
using a relative measure as opposed to an absolute one: we care about
our continuations, but if anything is a continuation, it's only
something which we ourselves can know. OS0 will keep finding machines
that implement it and thus there will be a next continuation. What if
OS0 crashes? There is likely a way to modify OS0 to prevent that crash
(or that such a modified version exists).
Continuation as it is, is definable in arithmetic, but it's far too
subjective a thing to give a simple, precise definition, if one allows
self-modification.
Unfortunately the measure itself is likely to be uncomputable, unlike
finding some next OM (actually, I'm not so sure about this being
entirely computable as well, it might prove that it's only computable
in specific cases, just never in general; within COMP, finding a next
OM means finding a machine which implements the inner machine('you'),
that should always exist as UMs exist, however what if the inner
machine crashes? a slightly modified inner machine might not, yet that
machine would still identify mostly as 'you' - whatever this measure
thing is, it's way too subjective and self-referential, yet this is
complicated because the inner machine doesn't typically know their own
godel number, nor can they always trust their inputs to be exactly
what they 'expect').
"Know its own Godel number"? How exactly does that happen? Please
remember, all of this is *occurring*, (dammit, we cannot even use that
word consistently) in the Timelessness of Platonia. There is no
Occurring at all there. There isn't even any "there" there!
UTM0's states are contained within timeless arithmetic (TM's can be
implemented as Diophantine equations). OS0's relations are also
contained there. "Occur" is the relation between 2 states.
OS0 can't know its own Godel number without finding or becoming a good
physicist and doctor that studies P0 and B0 and then finds a way to make
an alternate version, but maybe not 100% accurate implementation of B0,
although presumably a good enough implementation of OS0.
Keep in mind, OS0 is the "subst. level", thus if a new implementation of
OS0 exists, then a continuations of it would exist (1p indeterminacy
occurs if original still stays exists after it).
A possible solution to this problem, proposed by many even back as far
as Heraclitus, is to avoid the requirement of a solution at the
beginning. Just let the universe compute its least action configuration
as it evolves in time, but to accept this possibility we have to
overturn many preciously held, but wrong, ideas and replace them with
better ideas.
In a way, you could avoid thinking of Platonia and just consider the
case of a machine's 1p always finding its next OM. As long as finding
one next OM doesn't take infinite steps, you could consider it alive.
What if no next step OM exists for it, but it exists in a version
where a single bit was changed?
Here is the problem, given the measure of a single number in an infinite
set is zero, The possibility of defining a continuance this way is also
zero.
The probability that I would experience this OM right now is 0, yet I
still experience it. If all OMs exist, then they are all experienced.
A machine finding its next OM seems magical enough, but it's not that
troublesome when viewed as an observer being a particular structure, and
that particular structure being capable of consciousness, thus anywhere
that structure is manifested, you have that structure's consciousness
and continuations. Considering such a structure as being represented in
arithmetical truth and thus being how some arithmetical truth feels from
the inside can allow one to obtain some interesting answers (such as in
AUDA), it also gives you a neutral foundation for both mental and
'physical'.
Onward!
Cranky and Tired Stephen
Take it easy and cheers ;)
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