2012/9/8 benjayk <benjamin.jaku...@googlemail.com>

>
> I just respond to some parts of your posts, because I'd rather discuss the
> main points than get sidetracked with issues that are less fundamental.
>
>
> Jason Resch-2 wrote:
> >
> >>
> >> I admit that for numbers this is not so relevant because number
> relations
> >> can be quite clearly expressed using numerous symbols (they have very
> few
> >> and simple relations), but it is much more relevant for more complex
> >> relations.
> >>
> >
> > Complex relation can be expressed in terms of a series of interrelated
> > simpler relations (addition, multiplication, comparison, etc.).  You are
> > focused on the very lowest level and it is no wonder you cannot see the
> > higher-level possibilities for meaning, relations, intelligence,
> > consciousness, etc. that a machine can create.
> The complex relations can often only be expressed as simple relations on a
> meta-level (which is a very big step of abstraction). You can express
> rational numbers using natural numbers, but only using an additional layer
> of interpretation (which is a *huge* abstraction - it's the difference
> between description and what is being described).
>
> The natural numbers itself don't lead to the rational numbers (except by
> adding additional relations, like the inverse of multiplication).
>
>
> Jason Resch-2 wrote:
> >
> > The relation of hot vs. cold as experienced by you is also the
> > production of a long series of multiplications, additions, comparisons,
> > and
> > other operations.
> You assume reductionism or emergentism here. Of course you can defend the
> CT
> thesis if you assume that the lowest level can magically lead to higher
> levels (or the higher levels are not real in the first place).
> The problem is that this magic would precisely be the higher levels that
> you
> wanted to derive.
>
>
> Jason Resch-2 wrote:
> >
> >>
> >>
> >> Jason Resch-2 wrote:
> >> >
> >> >> For example it cannot directly compute
> >> >> >> -1*-1=1. Machine A can only be used to use an encoded input value
> >> and
> >> >> >> encoded description of machine B, and give an output that is
> >> correct
> >> >> >> given
> >> >> >> the right decoding scheme.
> >> >> >>
> >> >> >
> >> >> > 1's or 0's, X's or O's, what the symbols are don't have any bearing
> >> on
> >> >> > what
> >> >> > they can compute.
> >> >> >
> >> >> That's just an assertion of the belief I am trying to question here.
> >> >> In reality, it *does* matter which symbols/things we use to compute.
> A
> >> >> computer that only uses one symbol (for example a computer that adds
> >> >> using
> >> >> marbles) would be pretty useless.
> >> >> It does matter in many different ways: Speed of computations,
> >> effciency
> >> >> of
> >> >> computation, amount of memory, efficiency of memory, ease of
> >> programming,
> >> >> size of programs, ease of interpreting the result, amount of layers
> of
> >> >> programming to interpret the result and to program efficiently, ease
> >> of
> >> >> introspecting into the state of a computer...
> >> >>
> >> >
> >> > Practically they might matter but not theoretically.
> >> In the right theoretical model, it does matter. I am precisely doubting
> >> the
> >> value of adhering to our simplistic theoretical model of computation as
> >> the
> >> essence of what computation means.
> >>
> >>
> > What model do you propose to replace it?
> >
> > The Church-Turing thesis plays a similar role in computer science as the
> > fundamental theorem of arithmetic does in number theory.
> None. There is no one correct model of computations. There are infinite
> models that express different facets of what computation is. Different
> turing machines express different things, super-recursive turing machines
> express another thing, etc...
> I think computer scientists just don't want to accept it, because it takes
> their bible away. We like to have an easy answer, even if it is the wrong
> one.
>
>
> Jason Resch-2 wrote:
> >
> >>
> >> Jason Resch-2 wrote:
> >> >
> >> >>
> >> >> Why would we abstract from all that and then reduce computation to
> our
> >> >> one
> >> >> very abstract and imcomplete model of computation?
> >> >> If we do this we could as well abstract from the process of
> >> computation
> >> >> and
> >> >> say every string can be used to emulate any machine, because if you
> >> know
> >> >> what program it expresses, you know what it would compute (if
> >> correctly
> >> >> interpreted). There's no fundamental difference. Strings need to be
> >> >> interpreted to make sense as a program, and a turing machine without
> >> >> negative numbers needs to be interpreted to make sense as a program
> >> >> computing the result of an equation using negative numbers.
> >> >>
> >> >
> >> > I agree, strings need to be interpreted.  This is what the Turing
> >> machine
> >> > does.  The symbols on the tape become interrelated in the context of
> >> the
> >> > machine that interprets the symbols and it is these relations that
> >> become
> >> > equivalent.
> >> That is like postulating some magic in the turing machine. It just
> >> manipulates symbols.
> >>
> >
> > No, it is not magic.  It is equivalent to saying the laws of physics
> > interrelate every electron and quark to each other.
> It is more like saying that the laws of physics show how to create humans
> from atoms.
> This is not the case. Nothing in the laws of nature says that some atoms
> form a human. Still it is evidently the case that there are humans, meaning
> that the laws of nature just don't describe the higher levels
>
>
>
> Jason Resch-2 wrote:
> >
> >>
> >> Jason Resch-2 wrote:
> >> >
> >> >> First, our modern computers are pretty much strictly more
> >> computationally
> >> >> powerful in every practical and theoretical way.
> >> >
> >> >
> >> > They aren't any more capable.  Modern computers have more memory and
> >> are
> >> > faster, sure.  But if their memory could be extended they could
> emulate
> >> > any
> >> > computer that exists today.
> >> Using the right interpretational layer, meaning right output and input
> >> conversion, right memory content, correct user interface etc....
> >> What is the justifcation that all of this doesn't matter?
> >>
> >>
> > No program can determine its hardware.  This is a consequence of the
> > Church
> > Turing thesis.  The particular machine at the lowest level has no bearing
> > (from the program's perspective).
> If that is true, we can show that CT must be false, because we *can* define
> a "meta-program" that has access to (part of) its own hardware (which still
> is intuitively computable - we can even implement it on a computer).
>

It's false, the program *can't* know that the hardware it has access to is
the *real* hardware and not a simulated hardware. The program has only
access to hardware through IO, and it can't tell (as never ever) from that
interface if what's outside is the *real* outside or simulated outside.

Quentin


> Actually I will make another post about this, because it seems to be an
> important argument.
>
>
> Jason Resch-2 wrote:
> >
> >> Note that I am not saying it doesn't make sense to abstract from that. I
> >> am
> >> just saying it doesn't make sense to reduce our notion of computation to
> >> (near) the highest level of abstraction (which the CT thesis asserts).
> >> It is the same mistake as saying that all use of language is equivalent
> >> because you can map all strings to all other strings, and every word can
> >> in
> >> principle represent everything. On some level, it is correct, but it is
> >> not
> >> a useful level to think of as the foundation of language, because it
> >> takes
> >> away most of what actually matters about language.
> >>
> >>
> > Okay.  I can see your point that when looking all the way down at the
> > bottom layers, you can see a difference.  However, I am not sure how this
> > matters.  If our universe were a giant emulation on some computer, the
> > particular architecture of the computer could make no difference to us.
> > So
> > long as they emulated the same laws of physics there is no possible way,
> > even in theory, that we could ever discern which architecture was running
> > our universe.
> Do you realize that what you said is just a restatement of the belief in
> "only low level computation matters"? I think if the universe were an
> emulation we could indeed see no difference, because we wouldn't be in the
> emulation at all (though our behaviour may be mirrored in some way there).
>
>
> Jason Resch-2 wrote:
> >
> >
> >> Jason Resch-2 wrote:
> >> >
> >> >>
> >> >> Even if we grant that what you say is true, why would we define
> >> >> computation
> >> >> as being completely abstracted from the way something is expressed?
> >> >> Especially if languages are very different (and programming languages
> >> can
> >> >> be
> >> >> *very* different) the way we express actually does matter so much
> that
> >> it
> >> >> is
> >> >> quite meaningless to even say the express the same thing.
> >> >>
> >> >> Tell me, does "00000000000000000000000000000000000000000000" really
> >> >> practically express the same thing as "44"?
> >> >
> >> >
> >> > It depends on the interpreter.
> >> Right. And this means that the strings practically will express
> different
> >> things and are thus not equivalent in general. The same is true for
> >> computations.
> >>
> >
> > A Turing machine along with its tape has a unique definition and future
> > evolution.  All the meaning it has is also uniquely defined (though
> > perhaps
> > implicitly), anyone can follow it and see what it does.
> That's not true. The low-level action of a turing machine may have many
> high-level meanings, which can't be derived from the lower levels. For
> example, it is possible that some operation on data may represent graphical
> transformation, or change to a source code of a program, or change of an
> audio file, etc...
>
> It only practically mostly isn't the case because we encode and store and
> manipulate and decode the data in a way that is mostly not very ambigous
> (to
> us!). But that is a function of a higher-level. The computer itself doesn't
> know what data represents. We can use computers do display images as texts
> for example, and if we lack the right interpretational layer, then a given
> piece of data, or a given computatation is just meaingless rubbish.
>
>
> Jason Resch-2 wrote:
> >
> > Whereas with a lone bit string (with no definition of its interpreter),
> > there is no
> > inherent or definite meaning.
> Yes, just as with turing machines.
> The only inherent meaning of a bit string like 01 is first bit is zero,
> second bit is 1.
>
> Very long bit strings can have quite unique high-level meaning for us, just
> like long computations.
>
>
> Jason Resch-2 wrote:
> >
> >>
> >>
> >> Jason Resch-2 wrote:
> >> >
> >> >> will be easy to read, will be easily interpreted without error,
> >> >> will be easier to correctly use, etc...
> >> >> So using different symbols will expand what the system can express on
> >> a
> >> >> very
> >> >> relevant level.
> >> >>
> >> >
> >> > At the lowest level but not at higher levels.  You are using a
> computer
> >> to
> >> > type an email which uses a "tape" that has only 2 states.  Yet you are
> >> > still able to type "44".
> >> ???
> >> Did you mean at the higher level, but not at the lowest level?
> >>
> >
> > By lowest level I mean the raw hardware.  At the lowest level your
> > computer's memory can only represent 2 states, often labeled '1' and '0'.
> > But at the higher levels built upon this, you can have programs with much
> > larger symbol sets.
> >
> > Maybe this is the source of our confusion and disagreement?
> Yes, it seems like it. You say that the higher levels are contained in the
> lower level, while I argue that they are clearly not, though they may be
> relatively to a representational meta-level (but only because we use the
> low
> levels in the right way - which is big feat in itself).
>
>
> Jason Resch-2 wrote:
> >
> >> > The computer (any computer) can do the interpretation for us.  You can
> >> > enter a description of the machine at one point in time, and the state
> >> of
> >> > the machine at another time, and ask the computer is this the state
> the
> >> > machine will be in N steps from now.  Where 0 is no and 1 is yes, or A
> >> is
> >> > no and B is yes, or X is no and Y is yes.  Whatever symbols it might
> >> use,
> >> > any computer can be setup to answer questions about any other machine
> >> in
> >> > this way.
> >> The computer will just output zeroes and ones, and the screen will
> >> convert
> >> this into pixels. Without your interpretation the pixels (and thus the
> >> answers) are meaningless.
> >>
> >
> > When things make a difference, they aren't meaningless.  The register
> > containing a value representing a plane's altitude isn't meaningless to
> > the
> > autopilot program, nor to those on board.
> Right, but it is meaningless on the level we are speaking about. If you use
> a turing machine to emulate another, more complex one, than its output is
> meaningless until you interpret it the right way.
>
>
> Jason Resch-2 wrote:
> >
> >> If you don't know how to encode and decode the symbols (ie interpret
> them
> >> on
> >> a higher level than the level of the interpretation the machine is
> doing)
> >> the "interpretation" is useless.
> >>
> >
> > Useless to the one who failed to interpret them, but perhaps not
> > generally.  If you were dropped off in a foreign land, your speech would
> > be
> > meaningless to others who heard you, but not to you, or others  who know
> > how to interpret it.
> Right. I am not objecting to this. But this is precisely why we can't
> ignore
> the higher levels as being less important (or even irrelevant) than the low
> level language / computation.
> Unless we postulate some independent higher level, the lower levels don't
> make sense in a high level context (like emulation only makes sense to some
> observer that knows of the existence of different machines).
>
>
> Jason Resch-2 wrote:
> >
> >
> >> We always have to have some information beforehand (though it may be
> >> implicit, without being communicated first). Otherwise every signal is
> >> useless because it could mean everything and nothing.
> >>
> >>
> > How do infants learn language if they start with none?
> Because they still have something, even though it is not a language in our
> sense.
> Of course we can get from no information to some information in some
> relative realm.
>
> benjayk
>
> --
> View this message in context:
> http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34406957.html
> Sent from the Everything List mailing list archive at Nabble.com.
>
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