2012/9/8 benjayk <[email protected]> > > 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. > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > -- All those moments will be lost in time, like tears in rain. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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