Re: Why the Church-Turing thesis?
2012/9/12 Quentin Anciaux > > > 2012/9/12 benjayk > >> >> >> >> Quentin Anciaux-2 wrote: >> > >> > 2012/9/12 Quentin Anciaux >> > >> >> >> >> >> >> 2012/9/12 benjayk >> >> >> >>> >> >>> >> >>> Quentin Anciaux-2 wrote: >> >>> > >> >>> > 2012/9/11 Quentin Anciaux >> >>> > >> >>> >> >> >>> >> >> >>> >> 2012/9/11 benjayk >> >>> >> >> >>> >>> >> >>> >>> >> >>> >>> Quentin Anciaux-2 wrote: >> >>> >>> > >> >>> >>> > 2012/9/11 benjayk >> >>> >>> > >> >>> >>> >> >> >>> >>> >> >> >>> >>> >> Quentin Anciaux-2 wrote: >> >>> >>> >> > >> >>> >>> >> > 2012/9/11 benjayk >> >>> >>> >> > >> >>> >>> >> >> >> >>> >>> >> >> >> >>> >>> >> >> Quentin Anciaux-2 wrote: >> >>> >>> >> >> > >> >>> >>> >> >> > 2012/9/10 benjayk >> >>> >>> >> >> > >> >>> >>> >> >> >> >> >>> >>> >> >> >> >> >>> >>> >> >> >> > > 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. >> >>> >>> >> >> >> <\quote> >> >>> >>> >> >> >> Yes that is true. If anything it is true because the >> >>> hardware >> >>> >>> is >> >>> >>> >> not >> >>> >>> >> >> even >> >>> >>> >> >> >> clearly determined at the base level (quantum >> uncertainty). >> >>> >>> >> >> >> I should have expressed myself more accurately and >> written >> >>> " >> >>> >>> >> >> "hardware" >> >>> >>> >> >> " >> >>> >>> >> >> >> or >> >>> >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs >> that >> >>> >>> have >> >>> >>> >> >> access >> >>> >>> >> >> >> to >> >>> >>> >> >> >> their "hardware" in the sense of knowing what they are >> >>> running >> >>> >>> on >> >>> >>> >> >> >> relative >> >>> >>> >> >> >> to some notion of "hardware". They cannot be emulated >> using >> >>> >>> >> universal >> >>> >>> >> >> >> turing >> >>> >>> >> >> >> machines >> >>> >>> >> >> > >> >>> >>> >> >> > >> >>> >>> >> >> > Then it's not a program if it can't run on a universal >> >>> turing >> >>> >>> >> machine. >> >>> >>> >> >> > >> >>> >>> >> >> The funny thing is, it *can* run on a universal turing >> >>> machine. >> >>> >>> Just >> >>> >>> >> that >> >>> >>> >> >> it >> >>> >>> >> >> may lose relative correctness if we do that. >> >>> >>> >> > >> >>> >>> >> > >> >>> >>> >> > Then you must be wrong... I don't understand your point. If >> >>> it's >> >>> a >> >>> >>> >> program >> >>> >>> >> > it has access to the "outside" through IO, hence it is >> >>> impossible >> >>> >>> for a >> >>> >>> >> > program to differentiate "real" outside from simulated >> >>> outside... >> >>> >>> It's >> >>> >>> >> a >> >>> >>> >> > simple fact, so either you're wrong or what you're describing >> >>> is >> >>> >>> not >> >>> >>> a >> >>> >>> >> > program, not an algorithm and not a computation. >> >>> >>> >> OK, it depends on what you mean by "program". If you presume >> that >> >>> a >> >>> >>> >> program >> >>> >>> >> can't access its "hardware", >> >>> >>> > >> >>> >>> > >> >>> >>> > I *do not presume it*... it's a *fact*. >> >>> >>> > >> >>> >>> > >> >>> >>> Well, I presented a model of a program that can do that (on some >> >>> level, >> >>> >>> not >> >>> >>> on the level of physical hardware), and is a program in the most >> >>> >>> fundamental >> >>> >>> way (doing step-by-step execution of instructions). >> >>> >>> All you need is a program hierarchy where some programs have >> access >> >>> to >> >>> >>> programs that are below them in the hierarchy (which are the >> >>> "hardware" >> >>> >>> though not the *hardware*). >> >>> >>> >> >>> >> >> >>> >> What's your point ? How the simulated hardware would fail ? It's >> >>> >> impossible, so until you're clearer (your point is totally fuzzy), >> I >> >>> >> stick >> >>> >> to "you must be wrong". >> >>> >> >> >>> > >> >>> > So either you assume some kind of "oracle" device, in this case,
Re: Why the Church-Turing thesis?
2012/9/12 benjayk > > > > Quentin Anciaux-2 wrote: > > > > 2012/9/12 Quentin Anciaux > > > >> > >> > >> 2012/9/12 benjayk > >> > >>> > >>> > >>> Quentin Anciaux-2 wrote: > >>> > > >>> > 2012/9/11 Quentin Anciaux > >>> > > >>> >> > >>> >> > >>> >> 2012/9/11 benjayk > >>> >> > >>> >>> > >>> >>> > >>> >>> Quentin Anciaux-2 wrote: > >>> >>> > > >>> >>> > 2012/9/11 benjayk > >>> >>> > > >>> >>> >> > >>> >>> >> > >>> >>> >> Quentin Anciaux-2 wrote: > >>> >>> >> > > >>> >>> >> > 2012/9/11 benjayk > >>> >>> >> > > >>> >>> >> >> > >>> >>> >> >> > >>> >>> >> >> Quentin Anciaux-2 wrote: > >>> >>> >> >> > > >>> >>> >> >> > 2012/9/10 benjayk > >>> >>> >> >> > > >>> >>> >> >> >> > >>> >>> >> >> >> > >>> >>> >> >> >> > > 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. > >>> >>> >> >> >> <\quote> > >>> >>> >> >> >> Yes that is true. If anything it is true because the > >>> hardware > >>> >>> is > >>> >>> >> not > >>> >>> >> >> even > >>> >>> >> >> >> clearly determined at the base level (quantum > uncertainty). > >>> >>> >> >> >> I should have expressed myself more accurately and written > >>> " > >>> >>> >> >> "hardware" > >>> >>> >> >> " > >>> >>> >> >> >> or > >>> >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs > that > >>> >>> have > >>> >>> >> >> access > >>> >>> >> >> >> to > >>> >>> >> >> >> their "hardware" in the sense of knowing what they are > >>> running > >>> >>> on > >>> >>> >> >> >> relative > >>> >>> >> >> >> to some notion of "hardware". They cannot be emulated > using > >>> >>> >> universal > >>> >>> >> >> >> turing > >>> >>> >> >> >> machines > >>> >>> >> >> > > >>> >>> >> >> > > >>> >>> >> >> > Then it's not a program if it can't run on a universal > >>> turing > >>> >>> >> machine. > >>> >>> >> >> > > >>> >>> >> >> The funny thing is, it *can* run on a universal turing > >>> machine. > >>> >>> Just > >>> >>> >> that > >>> >>> >> >> it > >>> >>> >> >> may lose relative correctness if we do that. > >>> >>> >> > > >>> >>> >> > > >>> >>> >> > Then you must be wrong... I don't understand your point. If > >>> it's > >>> a > >>> >>> >> program > >>> >>> >> > it has access to the "outside" through IO, hence it is > >>> impossible > >>> >>> for a > >>> >>> >> > program to differentiate "real" outside from simulated > >>> outside... > >>> >>> It's > >>> >>> >> a > >>> >>> >> > simple fact, so either you're wrong or what you're describing > >>> is > >>> >>> not > >>> >>> a > >>> >>> >> > program, not an algorithm and not a computation. > >>> >>> >> OK, it depends on what you mean by "program". If you presume > that > >>> a > >>> >>> >> program > >>> >>> >> can't access its "hardware", > >>> >>> > > >>> >>> > > >>> >>> > I *do not presume it*... it's a *fact*. > >>> >>> > > >>> >>> > > >>> >>> Well, I presented a model of a program that can do that (on some > >>> level, > >>> >>> not > >>> >>> on the level of physical hardware), and is a program in the most > >>> >>> fundamental > >>> >>> way (doing step-by-step execution of instructions). > >>> >>> All you need is a program hierarchy where some programs have access > >>> to > >>> >>> programs that are below them in the hierarchy (which are the > >>> "hardware" > >>> >>> though not the *hardware*). > >>> >>> > >>> >> > >>> >> What's your point ? How the simulated hardware would fail ? It's > >>> >> impossible, so until you're clearer (your point is totally fuzzy), I > >>> >> stick > >>> >> to "you must be wrong". > >>> >> > >>> > > >>> > So either you assume some kind of "oracle" device, in this case, the > >>> thing > >>> > you describe is no more a program, but a program + an oracle, the > >>> oracle > >>> > obviously is not simulable on a turing machine, or an infinite > regress > >>> of > >>> > level. > >>> >
Re: Why the Church-Turing thesis?
Quentin Anciaux-2 wrote: > > 2012/9/12 Quentin Anciaux > >> >> >> 2012/9/12 benjayk >> >>> >>> >>> Quentin Anciaux-2 wrote: >>> > >>> > 2012/9/11 Quentin Anciaux >>> > >>> >> >>> >> >>> >> 2012/9/11 benjayk >>> >> >>> >>> >>> >>> >>> >>> Quentin Anciaux-2 wrote: >>> >>> > >>> >>> > 2012/9/11 benjayk >>> >>> > >>> >>> >> >>> >>> >> >>> >>> >> Quentin Anciaux-2 wrote: >>> >>> >> > >>> >>> >> > 2012/9/11 benjayk >>> >>> >> > >>> >>> >> >> >>> >>> >> >> >>> >>> >> >> Quentin Anciaux-2 wrote: >>> >>> >> >> > >>> >>> >> >> > 2012/9/10 benjayk >>> >>> >> >> > >>> >>> >> >> >> >>> >>> >> >> >> >>> >>> >> >> >> > > 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. >>> >>> >> >> >> <\quote> >>> >>> >> >> >> Yes that is true. If anything it is true because the >>> hardware >>> >>> is >>> >>> >> not >>> >>> >> >> even >>> >>> >> >> >> clearly determined at the base level (quantum uncertainty). >>> >>> >> >> >> I should have expressed myself more accurately and written >>> " >>> >>> >> >> "hardware" >>> >>> >> >> " >>> >>> >> >> >> or >>> >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs that >>> >>> have >>> >>> >> >> access >>> >>> >> >> >> to >>> >>> >> >> >> their "hardware" in the sense of knowing what they are >>> running >>> >>> on >>> >>> >> >> >> relative >>> >>> >> >> >> to some notion of "hardware". They cannot be emulated using >>> >>> >> universal >>> >>> >> >> >> turing >>> >>> >> >> >> machines >>> >>> >> >> > >>> >>> >> >> > >>> >>> >> >> > Then it's not a program if it can't run on a universal >>> turing >>> >>> >> machine. >>> >>> >> >> > >>> >>> >> >> The funny thing is, it *can* run on a universal turing >>> machine. >>> >>> Just >>> >>> >> that >>> >>> >> >> it >>> >>> >> >> may lose relative correctness if we do that. >>> >>> >> > >>> >>> >> > >>> >>> >> > Then you must be wrong... I don't understand your point. If >>> it's >>> a >>> >>> >> program >>> >>> >> > it has access to the "outside" through IO, hence it is >>> impossible >>> >>> for a >>> >>> >> > program to differentiate "real" outside from simulated >>> outside... >>> >>> It's >>> >>> >> a >>> >>> >> > simple fact, so either you're wrong or what you're describing >>> is >>> >>> not >>> >>> a >>> >>> >> > program, not an algorithm and not a computation. >>> >>> >> OK, it depends on what you mean by "program". If you presume that >>> a >>> >>> >> program >>> >>> >> can't access its "hardware", >>> >>> > >>> >>> > >>> >>> > I *do not presume it*... it's a *fact*. >>> >>> > >>> >>> > >>> >>> Well, I presented a model of a program that can do that (on some >>> level, >>> >>> not >>> >>> on the level of physical hardware), and is a program in the most >>> >>> fundamental >>> >>> way (doing step-by-step execution of instructions). >>> >>> All you need is a program hierarchy where some programs have access >>> to >>> >>> programs that are below them in the hierarchy (which are the >>> "hardware" >>> >>> though not the *hardware*). >>> >>> >>> >> >>> >> What's your point ? How the simulated hardware would fail ? It's >>> >> impossible, so until you're clearer (your point is totally fuzzy), I >>> >> stick >>> >> to "you must be wrong". >>> >> >>> > >>> > So either you assume some kind of "oracle" device, in this case, the >>> thing >>> > you describe is no more a program, but a program + an oracle, the >>> oracle >>> > obviously is not simulable on a turing machine, or an infinite regress >>> of >>> > level. >>> > >>> > >>> The simulated hardware can't fail in the model, just like a turing >>> machine >>> can't fail. Of course in reality it can fail, that is beside the point. >>> >>> You are right, my explanation is not that clear, because it is a quite >>> subtle thing. >>> >>> Maybe I shouldn't have used the word "hardware". The point is just that >>> we >>> can define (met
Re: Why the Church-Turing thesis?
On 12 Sep 2012, at 13:30, benjayk wrote: Quentin Anciaux-2 wrote: 2012/9/11 Quentin Anciaux 2012/9/11 benjayk Quentin Anciaux-2 wrote: 2012/9/11 benjayk Quentin Anciaux-2 wrote: 2012/9/11 benjayk Quentin Anciaux-2 wrote: 2012/9/10 benjayk 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. <\quote> Yes that is true. If anything it is true because the hardware is not even clearly determined at the base level (quantum uncertainty). I should have expressed myself more accurately and written " "hardware" " or "relative 'hardware'". We can define a (meta-)programs that have access to their "hardware" in the sense of knowing what they are running on relative to some notion of "hardware". They cannot be emulated using universal turing machines Then it's not a program if it can't run on a universal turing machine. The funny thing is, it *can* run on a universal turing machine. Just that it may lose relative correctness if we do that. Then you must be wrong... I don't understand your point. If it's a program it has access to the "outside" through IO, hence it is impossible for a program to differentiate "real" outside from simulated outside... It's a simple fact, so either you're wrong or what you're describing is not a program, not an algorithm and not a computation. OK, it depends on what you mean by "program". If you presume that a program can't access its "hardware", I *do not presume it*... it's a *fact*. Well, I presented a model of a program that can do that (on some level, not on the level of physical hardware), and is a program in the most fundamental way (doing step-by-step execution of instructions). All you need is a program hierarchy where some programs have access to programs that are below them in the hierarchy (which are the "hardware" though not the *hardware*). What's your point ? How the simulated hardware would fail ? It's impossible, so until you're clearer (your point is totally fuzzy), I stick to "you must be wrong". So either you assume some kind of "oracle" device, in this case, the thing you describe is no more a program, but a program + an oracle, the oracle obviously is not simulable on a turing machine, or an infinite regress of level. The simulated hardware can't fail in the model, just like a turing machine can't fail. Of course in reality it can fail, that is beside the point. You are right, my explanation is not that clear, because it is a quite subtle thing. Maybe I shouldn't have used the word "hardware". The point is just that we can define (meta-)programs that have access to some aspect of programs that are below it on the program hierarchy (normal programs), that can't be accessed by the program themselves. They can't emulated in general, because sometimes the emulating program will necessarily emulate the wrong level (because it can't correctly emulate that the meta-program is accessing what it is *actually* doing on the most fundamental level). They still are programs in the most fundamental sense. They don't require oracles or something else that is hard to actually use, they just have to know something about the hierarchy and the programs involved (which programs or kind of programs are above or below it) Below it, there is a non Turing emulable ocean of universal machines, by fist person plural and singular indeterminacy. No machine can know which machines support her below its substitution level, and whatever ability you can give to the program above its substitution level, it will be Turing emulable. and have access to the states of other programs. Both are perfectly implementable on a normal computer. They can even be implemented on a turing machine, but not in general. They can also be simulated on turing machines, just not necessarily correctly (the turing machine may incorrectly ignore which level it is operating on relative to the meta-program). We can still argue that these aren't programs in every sense but I think what is executable on a normal computer can be rightfully called program. If by normal you mean "physical", then you give a reason to say "No" to the doctor. In that case there is no more any substitution level. Bruno
Re: Why the Church-Turing thesis?
2012/9/12 Quentin Anciaux > > > 2012/9/12 benjayk > >> >> >> Quentin Anciaux-2 wrote: >> > >> > 2012/9/11 Quentin Anciaux >> > >> >> >> >> >> >> 2012/9/11 benjayk >> >> >> >>> >> >>> >> >>> Quentin Anciaux-2 wrote: >> >>> > >> >>> > 2012/9/11 benjayk >> >>> > >> >>> >> >> >>> >> >> >>> >> Quentin Anciaux-2 wrote: >> >>> >> > >> >>> >> > 2012/9/11 benjayk >> >>> >> > >> >>> >> >> >> >>> >> >> >> >>> >> >> Quentin Anciaux-2 wrote: >> >>> >> >> > >> >>> >> >> > 2012/9/10 benjayk >> >>> >> >> > >> >>> >> >> >> >> >>> >> >> >> >> >>> >> >> >> > > 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. >> >>> >> >> >> <\quote> >> >>> >> >> >> Yes that is true. If anything it is true because the hardware >> >>> is >> >>> >> not >> >>> >> >> even >> >>> >> >> >> clearly determined at the base level (quantum uncertainty). >> >>> >> >> >> I should have expressed myself more accurately and written " >> >>> >> >> "hardware" >> >>> >> >> " >> >>> >> >> >> or >> >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs that >> >>> have >> >>> >> >> access >> >>> >> >> >> to >> >>> >> >> >> their "hardware" in the sense of knowing what they are >> running >> >>> on >> >>> >> >> >> relative >> >>> >> >> >> to some notion of "hardware". They cannot be emulated using >> >>> >> universal >> >>> >> >> >> turing >> >>> >> >> >> machines >> >>> >> >> > >> >>> >> >> > >> >>> >> >> > Then it's not a program if it can't run on a universal turing >> >>> >> machine. >> >>> >> >> > >> >>> >> >> The funny thing is, it *can* run on a universal turing machine. >> >>> Just >> >>> >> that >> >>> >> >> it >> >>> >> >> may lose relative correctness if we do that. >> >>> >> > >> >>> >> > >> >>> >> > Then you must be wrong... I don't understand your point. If it's >> a >> >>> >> program >> >>> >> > it has access to the "outside" through IO, hence it is impossible >> >>> for a >> >>> >> > program to differentiate "real" outside from simulated outside... >> >>> It's >> >>> >> a >> >>> >> > simple fact, so either you're wrong or what you're describing is >> >>> not >> >>> a >> >>> >> > program, not an algorithm and not a computation. >> >>> >> OK, it depends on what you mean by "program". If you presume that a >> >>> >> program >> >>> >> can't access its "hardware", >> >>> > >> >>> > >> >>> > I *do not presume it*... it's a *fact*. >> >>> > >> >>> > >> >>> Well, I presented a model of a program that can do that (on some >> level, >> >>> not >> >>> on the level of physical hardware), and is a program in the most >> >>> fundamental >> >>> way (doing step-by-step execution of instructions). >> >>> All you need is a program hierarchy where some programs have access to >> >>> programs that are below them in the hierarchy (which are the >> "hardware" >> >>> though not the *hardware*). >> >>> >> >> >> >> What's your point ? How the simulated hardware would fail ? It's >> >> impossible, so until you're clearer (your point is totally fuzzy), I >> >> stick >> >> to "you must be wrong". >> >> >> > >> > So either you assume some kind of "oracle" device, in this case, the >> thing >> > you describe is no more a program, but a program + an oracle, the oracle >> > obviously is not simulable on a turing machine, or an infinite regress >> of >> > level. >> > >> > >> The simulated hardware can't fail in the model, just like a turing machine >> can't fail. Of course in reality it can fail, that is beside the point. >> >> You are right, my explanation is not that clear, because it is a quite >> subtle thing. >> >> Maybe I shouldn't have used the word "hardware". The point is just that we >> can define (meta-)programs that have access to some aspect of programs >> that >> are below it on the program hierarchy (normal programs), that can't be >> accessed by the program themselves. They can't emulated in general, >> because >> sometimes the emulating program wil
Re: Why the Church-Turing thesis?
2012/9/12 benjayk > > > Quentin Anciaux-2 wrote: > > > > 2012/9/11 Quentin Anciaux > > > >> > >> > >> 2012/9/11 benjayk > >> > >>> > >>> > >>> Quentin Anciaux-2 wrote: > >>> > > >>> > 2012/9/11 benjayk > >>> > > >>> >> > >>> >> > >>> >> Quentin Anciaux-2 wrote: > >>> >> > > >>> >> > 2012/9/11 benjayk > >>> >> > > >>> >> >> > >>> >> >> > >>> >> >> Quentin Anciaux-2 wrote: > >>> >> >> > > >>> >> >> > 2012/9/10 benjayk > >>> >> >> > > >>> >> >> >> > >>> >> >> >> > >>> >> >> >> > > 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. > >>> >> >> >> <\quote> > >>> >> >> >> Yes that is true. If anything it is true because the hardware > >>> is > >>> >> not > >>> >> >> even > >>> >> >> >> clearly determined at the base level (quantum uncertainty). > >>> >> >> >> I should have expressed myself more accurately and written " > >>> >> >> "hardware" > >>> >> >> " > >>> >> >> >> or > >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs that > >>> have > >>> >> >> access > >>> >> >> >> to > >>> >> >> >> their "hardware" in the sense of knowing what they are running > >>> on > >>> >> >> >> relative > >>> >> >> >> to some notion of "hardware". They cannot be emulated using > >>> >> universal > >>> >> >> >> turing > >>> >> >> >> machines > >>> >> >> > > >>> >> >> > > >>> >> >> > Then it's not a program if it can't run on a universal turing > >>> >> machine. > >>> >> >> > > >>> >> >> The funny thing is, it *can* run on a universal turing machine. > >>> Just > >>> >> that > >>> >> >> it > >>> >> >> may lose relative correctness if we do that. > >>> >> > > >>> >> > > >>> >> > Then you must be wrong... I don't understand your point. If it's a > >>> >> program > >>> >> > it has access to the "outside" through IO, hence it is impossible > >>> for a > >>> >> > program to differentiate "real" outside from simulated outside... > >>> It's > >>> >> a > >>> >> > simple fact, so either you're wrong or what you're describing is > >>> not > >>> a > >>> >> > program, not an algorithm and not a computation. > >>> >> OK, it depends on what you mean by "program". If you presume that a > >>> >> program > >>> >> can't access its "hardware", > >>> > > >>> > > >>> > I *do not presume it*... it's a *fact*. > >>> > > >>> > > >>> Well, I presented a model of a program that can do that (on some level, > >>> not > >>> on the level of physical hardware), and is a program in the most > >>> fundamental > >>> way (doing step-by-step execution of instructions). > >>> All you need is a program hierarchy where some programs have access to > >>> programs that are below them in the hierarchy (which are the "hardware" > >>> though not the *hardware*). > >>> > >> > >> What's your point ? How the simulated hardware would fail ? It's > >> impossible, so until you're clearer (your point is totally fuzzy), I > >> stick > >> to "you must be wrong". > >> > > > > So either you assume some kind of "oracle" device, in this case, the > thing > > you describe is no more a program, but a program + an oracle, the oracle > > obviously is not simulable on a turing machine, or an infinite regress of > > level. > > > > > The simulated hardware can't fail in the model, just like a turing machine > can't fail. Of course in reality it can fail, that is beside the point. > > You are right, my explanation is not that clear, because it is a quite > subtle thing. > > Maybe I shouldn't have used the word "hardware". The point is just that we > can define (meta-)programs that have access to some aspect of programs that > are below it on the program hierarchy (normal programs), that can't be > accessed by the program themselves. They can't emulated in general, because > sometimes the emulating program will necessarily emulate the wrong level > (because it can't correctly emulate that the meta-program is accessing what > it is *actually* doing on the most fundamental level). > They still are programs in the most fu
Re: Why the Church-Turing thesis?
Quentin Anciaux-2 wrote: > > 2012/9/11 Quentin Anciaux > >> >> >> 2012/9/11 benjayk >> >>> >>> >>> Quentin Anciaux-2 wrote: >>> > >>> > 2012/9/11 benjayk >>> > >>> >> >>> >> >>> >> Quentin Anciaux-2 wrote: >>> >> > >>> >> > 2012/9/11 benjayk >>> >> > >>> >> >> >>> >> >> >>> >> >> Quentin Anciaux-2 wrote: >>> >> >> > >>> >> >> > 2012/9/10 benjayk >>> >> >> > >>> >> >> >> >>> >> >> >> >>> >> >> >> > > 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. >>> >> >> >> <\quote> >>> >> >> >> Yes that is true. If anything it is true because the hardware >>> is >>> >> not >>> >> >> even >>> >> >> >> clearly determined at the base level (quantum uncertainty). >>> >> >> >> I should have expressed myself more accurately and written " >>> >> >> "hardware" >>> >> >> " >>> >> >> >> or >>> >> >> >> "relative 'hardware'". We can define a (meta-)programs that >>> have >>> >> >> access >>> >> >> >> to >>> >> >> >> their "hardware" in the sense of knowing what they are running >>> on >>> >> >> >> relative >>> >> >> >> to some notion of "hardware". They cannot be emulated using >>> >> universal >>> >> >> >> turing >>> >> >> >> machines >>> >> >> > >>> >> >> > >>> >> >> > Then it's not a program if it can't run on a universal turing >>> >> machine. >>> >> >> > >>> >> >> The funny thing is, it *can* run on a universal turing machine. >>> Just >>> >> that >>> >> >> it >>> >> >> may lose relative correctness if we do that. >>> >> > >>> >> > >>> >> > Then you must be wrong... I don't understand your point. If it's a >>> >> program >>> >> > it has access to the "outside" through IO, hence it is impossible >>> for a >>> >> > program to differentiate "real" outside from simulated outside... >>> It's >>> >> a >>> >> > simple fact, so either you're wrong or what you're describing is >>> not >>> a >>> >> > program, not an algorithm and not a computation. >>> >> OK, it depends on what you mean by "program". If you presume that a >>> >> program >>> >> can't access its "hardware", >>> > >>> > >>> > I *do not presume it*... it's a *fact*. >>> > >>> > >>> Well, I presented a model of a program that can do that (on some level, >>> not >>> on the level of physical hardware), and is a program in the most >>> fundamental >>> way (doing step-by-step execution of instructions). >>> All you need is a program hierarchy where some programs have access to >>> programs that are below them in the hierarchy (which are the "hardware" >>> though not the *hardware*). >>> >> >> What's your point ? How the simulated hardware would fail ? It's >> impossible, so until you're clearer (your point is totally fuzzy), I >> stick >> to "you must be wrong". >> > > So either you assume some kind of "oracle" device, in this case, the thing > you describe is no more a program, but a program + an oracle, the oracle > obviously is not simulable on a turing machine, or an infinite regress of > level. > > The simulated hardware can't fail in the model, just like a turing machine can't fail. Of course in reality it can fail, that is beside the point. You are right, my explanation is not that clear, because it is a quite subtle thing. Maybe I shouldn't have used the word "hardware". The point is just that we can define (meta-)programs that have access to some aspect of programs that are below it on the program hierarchy (normal programs), that can't be accessed by the program themselves. They can't emulated in general, because sometimes the emulating program will necessarily emulate the wrong level (because it can't correctly emulate that the meta-program is accessing what it is *actually* doing on the most fundamental level). They still are programs in the most fundamental sense. They don't require oracles or something else that is hard to actually use, they just have to know something about the hierarchy and the programs involved (which programs or kind of programs are above or below it) and have access to the states of other programs. Both are perfectly implementable on a n
Re: Why the Church-Turing thesis?
2012/9/11 Quentin Anciaux > > > 2012/9/11 benjayk > >> >> >> Quentin Anciaux-2 wrote: >> > >> > 2012/9/11 benjayk >> > >> >> >> >> >> >> Quentin Anciaux-2 wrote: >> >> > >> >> > 2012/9/11 benjayk >> >> > >> >> >> >> >> >> >> >> >> Quentin Anciaux-2 wrote: >> >> >> > >> >> >> > 2012/9/10 benjayk >> >> >> > >> >> >> >> >> >> >> >> >> >> >> >> > > 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. >> >> >> >> <\quote> >> >> >> >> Yes that is true. If anything it is true because the hardware is >> >> not >> >> >> even >> >> >> >> clearly determined at the base level (quantum uncertainty). >> >> >> >> I should have expressed myself more accurately and written " >> >> >> "hardware" >> >> >> " >> >> >> >> or >> >> >> >> "relative 'hardware'". We can define a (meta-)programs that have >> >> >> access >> >> >> >> to >> >> >> >> their "hardware" in the sense of knowing what they are running on >> >> >> >> relative >> >> >> >> to some notion of "hardware". They cannot be emulated using >> >> universal >> >> >> >> turing >> >> >> >> machines >> >> >> > >> >> >> > >> >> >> > Then it's not a program if it can't run on a universal turing >> >> machine. >> >> >> > >> >> >> The funny thing is, it *can* run on a universal turing machine. Just >> >> that >> >> >> it >> >> >> may lose relative correctness if we do that. >> >> > >> >> > >> >> > Then you must be wrong... I don't understand your point. If it's a >> >> program >> >> > it has access to the "outside" through IO, hence it is impossible >> for a >> >> > program to differentiate "real" outside from simulated outside... >> It's >> >> a >> >> > simple fact, so either you're wrong or what you're describing is not >> a >> >> > program, not an algorithm and not a computation. >> >> OK, it depends on what you mean by "program". If you presume that a >> >> program >> >> can't access its "hardware", >> > >> > >> > I *do not presume it*... it's a *fact*. >> > >> > >> Well, I presented a model of a program that can do that (on some level, >> not >> on the level of physical hardware), and is a program in the most >> fundamental >> way (doing step-by-step execution of instructions). >> All you need is a program hierarchy where some programs have access to >> programs that are below them in the hierarchy (which are the "hardware" >> though not the *hardware*). >> > > What's your point ? How the simulated hardware would fail ? It's > impossible, so until you're clearer (your point is totally fuzzy), I stick > to "you must be wrong". > So either you assume some kind of "oracle" device, in this case, the thing you describe is no more a program, but a program + an oracle, the oracle obviously is not simulable on a turing machine, or an infinite regress of level. Halting problem is not new, I still don't see your point or something new here. Quentin > >> So apparently it is not so much a fact about programs in a common sense >> way, >> but about a narrow conception of what programs can be. >> >> benjayk >> -- >> View this message in context: >> http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417762.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 everything-list@googlegroups.com. >> To unsubscribe from this group, send email to >> everything-list+unsubscr...@googlegroups.com. >> 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. > -- 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. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/gr
Re: Why the Church-Turing thesis?
2012/9/11 benjayk > > > Quentin Anciaux-2 wrote: > > > > 2012/9/11 benjayk > > > >> > >> > >> Quentin Anciaux-2 wrote: > >> > > >> > 2012/9/11 benjayk > >> > > >> >> > >> >> > >> >> Quentin Anciaux-2 wrote: > >> >> > > >> >> > 2012/9/10 benjayk > >> >> > > >> >> >> > >> >> >> > >> >> >> > > 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. > >> >> >> <\quote> > >> >> >> Yes that is true. If anything it is true because the hardware is > >> not > >> >> even > >> >> >> clearly determined at the base level (quantum uncertainty). > >> >> >> I should have expressed myself more accurately and written " > >> >> "hardware" > >> >> " > >> >> >> or > >> >> >> "relative 'hardware'". We can define a (meta-)programs that have > >> >> access > >> >> >> to > >> >> >> their "hardware" in the sense of knowing what they are running on > >> >> >> relative > >> >> >> to some notion of "hardware". They cannot be emulated using > >> universal > >> >> >> turing > >> >> >> machines > >> >> > > >> >> > > >> >> > Then it's not a program if it can't run on a universal turing > >> machine. > >> >> > > >> >> The funny thing is, it *can* run on a universal turing machine. Just > >> that > >> >> it > >> >> may lose relative correctness if we do that. > >> > > >> > > >> > Then you must be wrong... I don't understand your point. If it's a > >> program > >> > it has access to the "outside" through IO, hence it is impossible for > a > >> > program to differentiate "real" outside from simulated outside... It's > >> a > >> > simple fact, so either you're wrong or what you're describing is not a > >> > program, not an algorithm and not a computation. > >> OK, it depends on what you mean by "program". If you presume that a > >> program > >> can't access its "hardware", > > > > > > I *do not presume it*... it's a *fact*. > > > > > Well, I presented a model of a program that can do that (on some level, not > on the level of physical hardware), and is a program in the most > fundamental > way (doing step-by-step execution of instructions). > All you need is a program hierarchy where some programs have access to > programs that are below them in the hierarchy (which are the "hardware" > though not the *hardware*). > What's your point ? How the simulated hardware would fail ? It's impossible, so until you're clearer (your point is totally fuzzy), I stick to "you must be wrong". > > So apparently it is not so much a fact about programs in a common sense > way, > but about a narrow conception of what programs can be. > > benjayk > -- > View this message in context: > http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417762.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 everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > 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. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
Quentin Anciaux-2 wrote: > > 2012/9/11 benjayk > >> >> >> Quentin Anciaux-2 wrote: >> > >> > 2012/9/11 benjayk >> > >> >> >> >> >> >> Quentin Anciaux-2 wrote: >> >> > >> >> > 2012/9/10 benjayk >> >> > >> >> >> >> >> >> >> >> >> > > 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. >> >> >> <\quote> >> >> >> Yes that is true. If anything it is true because the hardware is >> not >> >> even >> >> >> clearly determined at the base level (quantum uncertainty). >> >> >> I should have expressed myself more accurately and written " >> >> "hardware" >> >> " >> >> >> or >> >> >> "relative 'hardware'". We can define a (meta-)programs that have >> >> access >> >> >> to >> >> >> their "hardware" in the sense of knowing what they are running on >> >> >> relative >> >> >> to some notion of "hardware". They cannot be emulated using >> universal >> >> >> turing >> >> >> machines >> >> > >> >> > >> >> > Then it's not a program if it can't run on a universal turing >> machine. >> >> > >> >> The funny thing is, it *can* run on a universal turing machine. Just >> that >> >> it >> >> may lose relative correctness if we do that. >> > >> > >> > Then you must be wrong... I don't understand your point. If it's a >> program >> > it has access to the "outside" through IO, hence it is impossible for a >> > program to differentiate "real" outside from simulated outside... It's >> a >> > simple fact, so either you're wrong or what you're describing is not a >> > program, not an algorithm and not a computation. >> OK, it depends on what you mean by "program". If you presume that a >> program >> can't access its "hardware", > > > I *do not presume it*... it's a *fact*. > > Well, I presented a model of a program that can do that (on some level, not on the level of physical hardware), and is a program in the most fundamental way (doing step-by-step execution of instructions). All you need is a program hierarchy where some programs have access to programs that are below them in the hierarchy (which are the "hardware" though not the *hardware*). So apparently it is not so much a fact about programs in a common sense way, but about a narrow conception of what programs can be. benjayk -- View this message in context: http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417762.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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
2012/9/11 benjayk > > > Quentin Anciaux-2 wrote: > > > > 2012/9/11 benjayk > > > >> > >> > >> Quentin Anciaux-2 wrote: > >> > > >> > 2012/9/10 benjayk > >> > > >> >> > >> >> > >> >> > > 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. > >> >> <\quote> > >> >> Yes that is true. If anything it is true because the hardware is not > >> even > >> >> clearly determined at the base level (quantum uncertainty). > >> >> I should have expressed myself more accurately and written " > >> "hardware" > >> " > >> >> or > >> >> "relative 'hardware'". We can define a (meta-)programs that have > >> access > >> >> to > >> >> their "hardware" in the sense of knowing what they are running on > >> >> relative > >> >> to some notion of "hardware". They cannot be emulated using universal > >> >> turing > >> >> machines > >> > > >> > > >> > Then it's not a program if it can't run on a universal turing machine. > >> > > >> The funny thing is, it *can* run on a universal turing machine. Just > that > >> it > >> may lose relative correctness if we do that. > > > > > > Then you must be wrong... I don't understand your point. If it's a > program > > it has access to the "outside" through IO, hence it is impossible for a > > program to differentiate "real" outside from simulated outside... It's a > > simple fact, so either you're wrong or what you're describing is not a > > program, not an algorithm and not a computation. > OK, it depends on what you mean by "program". If you presume that a program > can't access its "hardware", I *do not presume it*... it's a *fact*. Quentin > then what I am describing is indeed not a > program. > > But most definitions don't preclude that. Carrying out instructions > precisely and step-by-step can be done with or without access to your > hardware. > > Anyway, meta-programs can be instantiated using real computer (a program > can, in principle, know and utilize part of a more basic computational > layer > if programmed correctly), so we at least know that real computers are > beyond > turing machines. > > benjayk > > -- > View this message in context: > http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417676.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 everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > 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. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
Quentin Anciaux-2 wrote: > > 2012/9/11 benjayk > >> >> >> Quentin Anciaux-2 wrote: >> > >> > 2012/9/10 benjayk >> > >> >> >> >> >> >> > > 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. >> >> <\quote> >> >> Yes that is true. If anything it is true because the hardware is not >> even >> >> clearly determined at the base level (quantum uncertainty). >> >> I should have expressed myself more accurately and written " >> "hardware" >> " >> >> or >> >> "relative 'hardware'". We can define a (meta-)programs that have >> access >> >> to >> >> their "hardware" in the sense of knowing what they are running on >> >> relative >> >> to some notion of "hardware". They cannot be emulated using universal >> >> turing >> >> machines >> > >> > >> > Then it's not a program if it can't run on a universal turing machine. >> > >> The funny thing is, it *can* run on a universal turing machine. Just that >> it >> may lose relative correctness if we do that. > > > Then you must be wrong... I don't understand your point. If it's a program > it has access to the "outside" through IO, hence it is impossible for a > program to differentiate "real" outside from simulated outside... It's a > simple fact, so either you're wrong or what you're describing is not a > program, not an algorithm and not a computation. OK, it depends on what you mean by "program". If you presume that a program can't access its "hardware", then what I am describing is indeed not a program. But most definitions don't preclude that. Carrying out instructions precisely and step-by-step can be done with or without access to your hardware. Anyway, meta-programs can be instantiated using real computer (a program can, in principle, know and utilize part of a more basic computational layer if programmed correctly), so we at least know that real computers are beyond turing machines. benjayk -- View this message in context: http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417676.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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
2012/9/11 benjayk > > > Quentin Anciaux-2 wrote: > > > > 2012/9/10 benjayk > > > >> > >> > >> > > 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. > >> <\quote> > >> Yes that is true. If anything it is true because the hardware is not > even > >> clearly determined at the base level (quantum uncertainty). > >> I should have expressed myself more accurately and written " "hardware" > " > >> or > >> "relative 'hardware'". We can define a (meta-)programs that have access > >> to > >> their "hardware" in the sense of knowing what they are running on > >> relative > >> to some notion of "hardware". They cannot be emulated using universal > >> turing > >> machines > > > > > > Then it's not a program if it can't run on a universal turing machine. > > > The funny thing is, it *can* run on a universal turing machine. Just that > it > may lose relative correctness if we do that. Then you must be wrong... I don't understand your point. If it's a program it has access to the "outside" through IO, hence it is impossible for a program to differentiate "real" outside from simulated outside... It's a simple fact, so either you're wrong or what you're describing is not a program, not an algorithm and not a computation. Quentin > We can still use a turing > machine to "run" it and interpret what the result means. > > So for all intents and purposes it is quite like a program. Maybe not a > program as such, OK, but it certainly can be used precisely in a > step-by-step manner, and I think this is what CT thesis means by > algorithmically computable. > Maybe not, but in this case CT is just a statement about specific forms of > algorithms. > > -- > View this message in context: > http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417440.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 everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > 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. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
Quentin Anciaux-2 wrote: > > 2012/9/10 benjayk > >> >> >> > > 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. >> <\quote> >> Yes that is true. If anything it is true because the hardware is not even >> clearly determined at the base level (quantum uncertainty). >> I should have expressed myself more accurately and written " "hardware" " >> or >> "relative 'hardware'". We can define a (meta-)programs that have access >> to >> their "hardware" in the sense of knowing what they are running on >> relative >> to some notion of "hardware". They cannot be emulated using universal >> turing >> machines > > > Then it's not a program if it can't run on a universal turing machine. > The funny thing is, it *can* run on a universal turing machine. Just that it may lose relative correctness if we do that. We can still use a turing machine to "run" it and interpret what the result means. So for all intents and purposes it is quite like a program. Maybe not a program as such, OK, but it certainly can be used precisely in a step-by-step manner, and I think this is what CT thesis means by algorithmically computable. Maybe not, but in this case CT is just a statement about specific forms of algorithms. -- View this message in context: http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34417440.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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
On 9/10/2012 11:40 AM, benjayk wrote: 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. <\quote> Yes that is true. If anything it is true because the hardware is not even clearly determined at the base level (quantum uncertainty). I should have expressed myself more accurately and written " "hardware" " or "relative 'hardware'". We can define a (meta-)programs that have access to their "hardware" in the sense of knowing what they are running on relative to some notion of "hardware". They cannot be emulated using universal turing machines (in general - in specific instances, where the hardware is fixed on the right level, they might be). They can be simulated, though, but in this case the simulation may be incorrect in the given context and we have to put it into the right context to see what it is actually emulating (not the meta-program itself, just its behaviour relative to some other context). We can also define an infinite hierarchy of meta-meta--programs (n metas) to show that there is no universal notion of computation at all. There is always a notion of computation that is more powerful than the current one, because it can reflect more deeply upon its own "hardware". See my post concerning meta-programs for further details. Dear benjayk, Is there any means by which the resource requirements paly a role for a single program? No, because of this indeterminacy (the 1p indeterminacy) as Bruno has explained well. But while this is true, if you consider multiple computations that are accessing shared resources things are not so clear. I wish that some thought might be given to the problem of concurrency. -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
2012/9/10 benjayk > > > > > 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. > <\quote> > Yes that is true. If anything it is true because the hardware is not even > clearly determined at the base level (quantum uncertainty). > I should have expressed myself more accurately and written " "hardware" " > or > "relative 'hardware'". We can define a (meta-)programs that have access to > their "hardware" in the sense of knowing what they are running on relative > to some notion of "hardware". They cannot be emulated using universal > turing > machines Then it's not a program if it can't run on a universal turing machine. > (in general - in specific instances, where the hardware is fixed on > the right level, they might be). They can be simulated, though, but in this > case the simulation may be incorrect in the given context and we have to > put > it into the right context to see what it is actually emulating (not the > meta-program itself, just its behaviour relative to some other context). > > We can also define an infinite hierarchy of meta-meta--programs (n > metas) to show that there is no universal notion of computation at all. > There is always a notion of computation that is more powerful than the > current one, because it can reflect more deeply upon its own "hardware". > > See my post concerning meta-programs for further details. > -- > View this message in context: > http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34413719.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 everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > 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. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
> > 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. <\quote> Yes that is true. If anything it is true because the hardware is not even clearly determined at the base level (quantum uncertainty). I should have expressed myself more accurately and written " "hardware" " or "relative 'hardware'". We can define a (meta-)programs that have access to their "hardware" in the sense of knowing what they are running on relative to some notion of "hardware". They cannot be emulated using universal turing machines (in general - in specific instances, where the hardware is fixed on the right level, they might be). They can be simulated, though, but in this case the simulation may be incorrect in the given context and we have to put it into the right context to see what it is actually emulating (not the meta-program itself, just its behaviour relative to some other context). We can also define an infinite hierarchy of meta-meta--programs (n metas) to show that there is no universal notion of computation at all. There is always a notion of computation that is more powerful than the current one, because it can reflect more deeply upon its own "hardware". See my post concerning meta-programs for further details. -- View this message in context: http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34413719.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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
2012/9/8 benjayk > > 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 > >> be
Re: Why the Church-Turing thesis?
As far as I see, we mostly agree on content. I just can't make sense of reducing computation to emulability. For me the intuitive sene of computation is much more rich than this. But still, as I think about it, we can also create a model of computation (in the sense of being intuitively computational and being implementable on a computer) where there are computations that can't be emulated by universal turing machine, using "level breaking" languages (which explicitly refer to what is being computed on the base level). I'll write another post on this. benjayk -- View this message in context: http://old.nabble.com/Why-the-Church-Turing-thesis--tp34348236p34406986.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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
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
Re: Why the Church-Turing thesis?
On 07 Sep 2012, at 12:24, benjayk wrote:
Bruno Marchal wrote:
On 28 Aug 2012, at 21:57, benjayk wrote:
It seems that the Church-Turing thesis, that states that an
universal turing
machine can compute everything that is intuitively computable, has
near
universal acceptance among computer scientists.
Yes indeed. I think there are two strong arguments for this.
The empirical one: all attempts to define the set of computable
functions have led to the same class of functions, and this despite
the quite independent path leading to the definitions (from Church
lambda terms, Post production systems, von Neumann machine, billiard
ball, combinators, cellular automata ... up to modular functor,
quantum topologies, quantum computers, etc.).
OK, now I understand it better. Apparently if we express a
computation in
terms of a computable function we can always arrive at the same
computable
function using a different computation of an abitrary turing universal
machine. That seems right to me.
But in this case I don't get why it is often claimed that CT thesis
claims
that all computations can be done by a universal turing machine, not
merely
that they lead to the same class of computable functions (if
"converted"
appriopiately).
This is due to a theorem applying to all universal programming
language, or universal system. They all contain a universal machine.
This makes CT equivalent with the thesis that there is a universal
machine with respect to (intuitive) computability.
It entails also an intensional Church thesis. Not only all universal
system can compute what each others can compute, but they can compute
the function in the same manner. This comes from the fact that a game
of life pattern (say) can exist and compute the universal function of
some other universal system, like a lisp interpreter for example. This
makes all result on computations working also on the notions of
simulation and emulation.
The latter is a far weaker statement, since computable functions
abstract
from many relevant things about the machine.
And even this weaker statement doesn't seem true with regards to more
powerful models like super-recursive functions, as computable
functions just
give finite results, while super-recursive machine can give
infinite/unlimited results.
Computability concerns finite or infinite generable things.
Then you can weaken comp indeed, and many results remains valid, but
are longer to prove. I use comp and numbers as it is easier.
Bruno Marchal wrote:
The conceptual one: the class of computable functions is closed for
the most transcendental operation in math: diagonalization. This is
not the case for the notions of definability, provability,
cardinality, etc.
I don't really know what this means. Do you mean that there are just
countable many computations? If yes, what has this do with whether all
universal turing machines are equivalent?
It means that the notion of computability, despite being epistemic, is
well defined in math. It is the only such notion. The diagnonalization
cannot been applied to find a new computable function already not in
the class of the one given by any universal machine.
It makes comp far more explanatively close than any concept in math
and physics.
Bruno Marchal wrote:
I really wonder why this is so, given that there are simple cases
where we
can compute something that an abitrary turing machine can not
compute using
a notion of computation that is not extraordinary at all (and quite
relevant
in reality).
For example, given you have a universal turing machine A that uses
the
alphabet {1,0} and a universal turing machine B that uses the
alphabet
{-1,0,1}.
Now it is quite clear that the machine A cannot directly answer any
questions that relates to -1. 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.
But for me this already makes clear that machine A is less
computationally
powerful than machine B.
Church thesis concerns only the class of computable functions.
Hm, maybe the wikipedia article is a bad one, since it mentioned
computable
functions just as means of explaining it, not as part of its
definition.
Bruno Marchal wrote:
The alphabet used by the Turing machine, having 1, 2, or enumerable
alphabet does not change the class. If you dovetail on the works of 1
letter Turing machine, you will unavoidably emulate all Turing
machines on all finite and enumerable letters alphabets. This can be
proved. Nor does the number of tapes, and/or parallelism change that
class.
Of course, some machine can be very inefficient, but this, by
definition, does not concern Church thesis.
Even so, CT thesis makes a claim about the equivalence of machines,
not of
emulability.
It does, by the intensional CT, which follows e
Re: Why the Church-Turing thesis?
On 9/7/2012 6:24 AM, benjayk wrote: Why are two machines that can be used to emlate each other regarded to be equivalent? In my view, there is a big difference between computing the same and being able to emulate each other. Most importantly, emulation only makes sense relative to another machine that is being emulated, and a correct interpretation. Dear benjayk, This is what is discussed under the header of "Bisimilarity" and bisimulation equivalence iff simulation = emulation. http://en.wikipedia.org/wiki/Bisimulation "a bisimulation is a binary relation between state transition systems, associating systems which behave in the same way in the sense that one system simulates the other and vice-versa." My own use of the term seeks a more generalized version that does not assume that the relation is necessarily binary nor strictly monotonic. The key is that a pair of machines can have an "image" of each other and that they are capable of acting on that image. -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Why the Church-Turing thesis?
Jason Resch-2 wrote:
>
> On Thu, Sep 6, 2012 at 12:47 PM, benjayk
> wrote:
>
>>
>>
>> Jason Resch-2 wrote:
>> >
>> > On Tue, Aug 28, 2012 at 2:57 PM, benjayk
>> > wrote:
>> >
>> >>
>> >> It seems that the Church-Turing thesis, that states that an universal
>> >> turing
>> >> machine can compute everything that is intuitively computable, has
>> near
>> >> universal acceptance among computer scientists.
>> >>
>> >> I really wonder why this is so, given that there are simple cases
>> where
>> >> we
>> >> can compute something that an abitrary turing machine can not compute
>> >> using
>> >> a notion of computation that is not extraordinary at all (and quite
>> >> relevant
>> >> in reality).
>> >> For example, given you have a universal turing machine A that uses the
>> >> alphabet {1,0} and a universal turing machine B that uses the alphabet
>> >> {-1,0,1}.
>> >> Now it is quite clear that the machine A cannot directly answer any
>> >> questions that relates to -1.
>>
>
> I see this at all being the case at all. What is the symbol for -1
> supposed to look like? Do you agree that a turing machine that used A, B,
> and C as symbols could work the same as one that used -1, 0, and 1?
Well, the symbol for -1 could be "-1"?
To answer your latter question, no, not necessarily. I don't take the
symbols not to be mere symbols, but to contain meaning (which they do), and
so it matters what symbols the machine use, because that changes the meaning
of its computation. Often times the meaning of the symbols also constrain
the possible relations (for example -1 * -1 normally needs to be 1, while A
* A could be A, B or C).
CT thesis wants to abstract from things like meaning, but I don't really see
the great value in acting like this is necessarily the correct theoretical
way of thinking about computations. It is only valuable as one possible,
very strongly abstracted, limited and representational model of computation
with respect to emulability.
Jason Resch-2 wrote:
>
> Everything is a representation, but what is important is that the Turing
> machine preserves the relationships. E.g., if ABBBABAA is greater than
> AAABBAAB then 01110100 is greater than 00011001, and all the other
> properties can hold, irrespective of what symbols are used.
The problem is that relationships don't make sense apart from symbols. We
can theoretically express the natural numbers using an infinite numbers of
unique symbols for both numbers and operations (like A or B or C or X for
10, ´ or ? or [ or ° for +), but in this case it won't be clear that we are
expresing natural numbers at all (without a lengthy explanation of what the
symbols mean).
Or if we are using binary numbers to express the natural numbers, it will
also be not very clear that we mean numbers, because often binary
expressions mean something entirely else. If we then add 1 to this "number"
it will not be clear that we actually added one, or if we just flipped a
bit.
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.
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.
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
Re: Why the Church-Turing thesis?
Bruno Marchal wrote:
>
>
> On 28 Aug 2012, at 21:57, benjayk wrote:
>
>>
>> It seems that the Church-Turing thesis, that states that an
>> universal turing
>> machine can compute everything that is intuitively computable, has
>> near
>> universal acceptance among computer scientists.
>
> Yes indeed. I think there are two strong arguments for this.
>
> The empirical one: all attempts to define the set of computable
> functions have led to the same class of functions, and this despite
> the quite independent path leading to the definitions (from Church
> lambda terms, Post production systems, von Neumann machine, billiard
> ball, combinators, cellular automata ... up to modular functor,
> quantum topologies, quantum computers, etc.).
>
OK, now I understand it better. Apparently if we express a computation in
terms of a computable function we can always arrive at the same computable
function using a different computation of an abitrary turing universal
machine. That seems right to me.
But in this case I don't get why it is often claimed that CT thesis claims
that all computations can be done by a universal turing machine, not merely
that they lead to the same class of computable functions (if "converted"
appriopiately).
The latter is a far weaker statement, since computable functions abstract
from many relevant things about the machine.
And even this weaker statement doesn't seem true with regards to more
powerful models like super-recursive functions, as computable functions just
give finite results, while super-recursive machine can give
infinite/unlimited results.
Bruno Marchal wrote:
>
> The conceptual one: the class of computable functions is closed for
> the most transcendental operation in math: diagonalization. This is
> not the case for the notions of definability, provability,
> cardinality, etc.
I don't really know what this means. Do you mean that there are just
countable many computations? If yes, what has this do with whether all
universal turing machines are equivalent?
Bruno Marchal wrote:
>
>>
>> I really wonder why this is so, given that there are simple cases
>> where we
>> can compute something that an abitrary turing machine can not
>> compute using
>> a notion of computation that is not extraordinary at all (and quite
>> relevant
>> in reality).
>> For example, given you have a universal turing machine A that uses the
>> alphabet {1,0} and a universal turing machine B that uses the alphabet
>> {-1,0,1}.
>> Now it is quite clear that the machine A cannot directly answer any
>> questions that relates to -1. 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.
>> But for me this already makes clear that machine A is less
>> computationally
>> powerful than machine B.
>
> Church thesis concerns only the class of computable functions.
Hm, maybe the wikipedia article is a bad one, since it mentioned computable
functions just as means of explaining it, not as part of its definition.
Bruno Marchal wrote:
>
> The alphabet used by the Turing machine, having 1, 2, or enumerable
> alphabet does not change the class. If you dovetail on the works of 1
> letter Turing machine, you will unavoidably emulate all Turing
> machines on all finite and enumerable letters alphabets. This can be
> proved. Nor does the number of tapes, and/or parallelism change that
> class.
> Of course, some machine can be very inefficient, but this, by
> definition, does not concern Church thesis.
Even so, CT thesis makes a claim about the equivalence of machines, not of
emulability.
Why are two machines that can be used to emlate each other regarded to be
equivalent?
In my view, there is a big difference between computing the same and being
able to emulate each other. Most importantly, emulation only makes sense
relative to another machine that is being emulated, and a correct
interpretation.
benjayk
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Re: Why the Church-Turing thesis?
On 28 Aug 2012, at 21:57, benjayk wrote:
It seems that the Church-Turing thesis, that states that an
universal turing
machine can compute everything that is intuitively computable, has
near
universal acceptance among computer scientists.
Yes indeed. I think there are two strong arguments for this.
The empirical one: all attempts to define the set of computable
functions have led to the same class of functions, and this despite
the quite independent path leading to the definitions (from Church
lambda terms, Post production systems, von Neumann machine, billiard
ball, combinators, cellular automata ... up to modular functor,
quantum topologies, quantum computers, etc.).
The conceptual one: the class of computable functions is closed for
the most transcendental operation in math: diagonalization. This is
not the case for the notions of definability, provability,
cardinality, etc.
I really wonder why this is so, given that there are simple cases
where we
can compute something that an abitrary turing machine can not
compute using
a notion of computation that is not extraordinary at all (and quite
relevant
in reality).
For example, given you have a universal turing machine A that uses the
alphabet {1,0} and a universal turing machine B that uses the alphabet
{-1,0,1}.
Now it is quite clear that the machine A cannot directly answer any
questions that relates to -1. 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.
But for me this already makes clear that machine A is less
computationally
powerful than machine B.
Church thesis concerns only the class of computable functions. The
alphabet used by the Turing machine, having 1, 2, or enumerable
alphabet does not change the class. If you dovetail on the works of 1
letter Turing machine, you will unavoidably emulate all Turing
machines on all finite and enumerable letters alphabets. This can be
proved. Nor does the number of tapes, and/or parallelism change that
class.
Of course, some machine can be very inefficient, but this, by
definition, does not concern Church thesis.
There was a thesis, often attributed to Cook (but I met him and he
claims it is not his thesis), that all Turing machine can emulate
themselves in polynomial time. This will plausibly be refuted by the
existence of quantum computers (unless P = NP, or things like that).
It is an open problem, but most scientists believe that in general a
classical computer cannot emulate an arbitrary quantum computer in
polynomial time. But I insist, quantum computer have not violated the
Church Turing Post Markov thesis.
Its input and output when emulating B do only make
sense with respect to what the machine B does if we already know what
machine B does, and if it is known how we chose to reflect this in
the input
of machine A (and the interpretation of its output). Otherwise we
have no
way of even saying whether it emulates something, or whether it is
just
doing a particular computation on the alphabet {1,0}.
I realize that it all comes down to the notion of computation. But
why do
most choose to use such a weak notion of computation? How does
machine B not
compute something that A doesn't by any reasonable standard?
Saying that A can compute what B computes is like saying that
"orange" can
express the same as the word "apple", because we can encode the word
"apple"
as "orange". It is true in a very limited sense, but it seems mad to
treat
it as the foundation of what it means for words to express something
(and
the same goes for computation).
If we use such trivial notions of computation, why not say that the
program
"return input" emulates all turing-machines because given the right
input it
gives the right output (we just give it the solution as input).
I get that we can simply use the Church-turing as the definition of
computation means. But why is it (mostly) treated as being the one
and only
correct notion of computation (especially in a computer science
context)?
The only explanation I have is that it is dogma. To question it
would change
to much and would be too "complicated" and uncomfortable. It would
make
computation an irreducibly complex and relative notion or - heaven
forbid -
even an inherently subjective notion (computation from which
perspective?).
That was what everybody believed before the rise of the universal
machine and lambda calculus. Gödel called the closure of the
computable functions for diagonalization a "miracle", and he took time
before assessing it. See:
DAVIS M., 1982, Why Gödel Didn't Have Church's Thesis, Information and
Control
54,.pp. 3-24.
http://iridia.ulb.ac.be/~marchal/
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To
Re: Why the Church-Turing thesis?
On Thu, Sep 6, 2012 at 12:47 PM, benjayk wrote:
>
>
> Jason Resch-2 wrote:
> >
> > On Tue, Aug 28, 2012 at 2:57 PM, benjayk
> > wrote:
> >
> >>
> >> It seems that the Church-Turing thesis, that states that an universal
> >> turing
> >> machine can compute everything that is intuitively computable, has near
> >> universal acceptance among computer scientists.
> >>
> >> I really wonder why this is so, given that there are simple cases where
> >> we
> >> can compute something that an abitrary turing machine can not compute
> >> using
> >> a notion of computation that is not extraordinary at all (and quite
> >> relevant
> >> in reality).
> >> For example, given you have a universal turing machine A that uses the
> >> alphabet {1,0} and a universal turing machine B that uses the alphabet
> >> {-1,0,1}.
> >> Now it is quite clear that the machine A cannot directly answer any
> >> questions that relates to -1.
>
I see this at all being the case at all. What is the symbol for -1
supposed to look like? Do you agree that a turing machine that used A, B,
and C as symbols could work the same as one that used -1, 0, and 1?
Everything is a representation, but what is important is that the Turing
machine preserves the relationships. E.g., if ABBBABAA is greater than
AAABBAAB then 01110100 is greater than 00011001, and all the other
properties can hold, irrespective of what symbols are used.
> 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.
>
> 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.
>
>
> Jason Resch-2 wrote:
> >
> > Consider: No physical computer today uses 1's or 0's, they use voltages,
> > collections of more or fewer electrons.
> OK, but in this case abstraction makes sense for computer scientist because
> progamers don't have access to that level. You are right, though that a
> chip
> engineer shouldn't abstract from that level if he actually wants to build a
> computer.
>
>
> Jason Resch-2 wrote:
> >
> > This doesn't mean that our computers can only directly compute what
> > electrons do.
> In fact they do much more. Electrons express strictly more than just 0 and
> 1. So it's not a good anology, because 0 and 1 express *less* than 0, 1 and
> -1.
>
>
> Jason Resch-2 wrote:
> >
> > But for me this already makes clear that machine A is less
> computationally
> >> powerful than machine B. Its input and output when emulating B do only
> >> make
> >> sense with respect to what the machine B does if we already know what
> >> machine B does, and if it is known how we chose to reflect this in the
> >> input
> >> of machine A (and the interpretation of its output). Otherwise we have
> no
> >> way of even saying whether it emulates something, or whether it is just
> >> doing a particular computation on the alphabet {1,0}.
> >>
> >
> > These are rather convincing:
> > http://en.wikipedia.org/wiki/Video_game_console_emulator
> >
> > There is software that emulates the unique architectures of an Atari,
> > Nintendo, Supernintendo, PlayStation, etc. systems. These emulators can
> > also run on any computer, whether its Intel X86, x86_64, PowerPC, etc.
> > You
> > will have a convincing experience of playing an old Atari game like space
> > invaders, even though th
Re: Why the Church-Turing thesis?
Jason Resch-2 wrote:
>
> On Tue, Aug 28, 2012 at 2:57 PM, benjayk
> wrote:
>
>>
>> It seems that the Church-Turing thesis, that states that an universal
>> turing
>> machine can compute everything that is intuitively computable, has near
>> universal acceptance among computer scientists.
>>
>> I really wonder why this is so, given that there are simple cases where
>> we
>> can compute something that an abitrary turing machine can not compute
>> using
>> a notion of computation that is not extraordinary at all (and quite
>> relevant
>> in reality).
>> For example, given you have a universal turing machine A that uses the
>> alphabet {1,0} and a universal turing machine B that uses the alphabet
>> {-1,0,1}.
>> Now it is quite clear that the machine A cannot directly answer any
>> questions that relates to -1. 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...
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.
Jason Resch-2 wrote:
>
> Consider: No physical computer today uses 1's or 0's, they use voltages,
> collections of more or fewer electrons.
OK, but in this case abstraction makes sense for computer scientist because
progamers don't have access to that level. You are right, though that a chip
engineer shouldn't abstract from that level if he actually wants to build a
computer.
Jason Resch-2 wrote:
>
> This doesn't mean that our computers can only directly compute what
> electrons do.
In fact they do much more. Electrons express strictly more than just 0 and
1. So it's not a good anology, because 0 and 1 express *less* than 0, 1 and
-1.
Jason Resch-2 wrote:
>
> But for me this already makes clear that machine A is less computationally
>> powerful than machine B. Its input and output when emulating B do only
>> make
>> sense with respect to what the machine B does if we already know what
>> machine B does, and if it is known how we chose to reflect this in the
>> input
>> of machine A (and the interpretation of its output). Otherwise we have no
>> way of even saying whether it emulates something, or whether it is just
>> doing a particular computation on the alphabet {1,0}.
>>
>
> These are rather convincing:
> http://en.wikipedia.org/wiki/Video_game_console_emulator
>
> There is software that emulates the unique architectures of an Atari,
> Nintendo, Supernintendo, PlayStation, etc. systems. These emulators can
> also run on any computer, whether its Intel X86, x86_64, PowerPC, etc.
> You
> will have a convincing experience of playing an old Atari game like space
> invaders, even though the original creators of that program never intended
> it to run on a computer architecture that wouldn't be invented for another
> 30 years, and the original programmers didn't have to be called in to
> re-write their program to do so.
Yes, I use them as well. They are indeed convincing. But this doesn't really
relate to the question very much.
First, our modern computers are pretty much strictly more computationally
powerful in every practical and theoretical way. It would be more of an
argument if you would simulate a windows on a nintendo (but you can't). I am
not saying that a turing machine using 0, 1 and -1 can't emulate a machine
using only 0 and 1.
Secondly, even this emulations are just correct as far as our playing
experience goes (well, at least if you are not nostalgic about hardware).
The actual process going on in the computer is very different, and thus it
makes sense to say that it computes something else. Its computation just
have a similar results in terms of experience, but they need
Re: Why the Church-Turing thesis?
On Tue, Aug 28, 2012 at 2:57 PM, benjayk wrote:
>
> It seems that the Church-Turing thesis, that states that an universal
> turing
> machine can compute everything that is intuitively computable, has near
> universal acceptance among computer scientists.
>
> I really wonder why this is so, given that there are simple cases where we
> can compute something that an abitrary turing machine can not compute using
> a notion of computation that is not extraordinary at all (and quite
> relevant
> in reality).
> For example, given you have a universal turing machine A that uses the
> alphabet {1,0} and a universal turing machine B that uses the alphabet
> {-1,0,1}.
> Now it is quite clear that the machine A cannot directly answer any
> questions that relates to -1. 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.
Consider: No physical computer today uses 1's or 0's, they use voltages,
collections of more or fewer electrons.
This doesn't mean that our computers can only directly compute what
electrons do.
But for me this already makes clear that machine A is less computationally
> powerful than machine B. Its input and output when emulating B do only make
> sense with respect to what the machine B does if we already know what
> machine B does, and if it is known how we chose to reflect this in the
> input
> of machine A (and the interpretation of its output). Otherwise we have no
> way of even saying whether it emulates something, or whether it is just
> doing a particular computation on the alphabet {1,0}.
>
These are rather convincing:
http://en.wikipedia.org/wiki/Video_game_console_emulator
There is software that emulates the unique architectures of an Atari,
Nintendo, Supernintendo, PlayStation, etc. systems. These emulators can
also run on any computer, whether its Intel X86, x86_64, PowerPC, etc. You
will have a convincing experience of playing an old Atari game like space
invaders, even though the original creators of that program never intended
it to run on a computer architecture that wouldn't be invented for another
30 years, and the original programmers didn't have to be called in to
re-write their program to do so.
> I realize that it all comes down to the notion of computation. But why do
> most choose to use such a weak notion of computation? How does machine B
> not
> compute something that A doesn't by any reasonable standard?
> Saying that A can compute what B computes is like saying that "orange" can
> express the same as the word "apple", because we can encode the word
> "apple"
> as "orange".
System A (using its own language of representation for system A), can
predict exactly all future states of another system B (and vice versa). A
and B have different symbols, states, instructions, etc., so perhaps this
is why you think system A can't perfectly emulate system B, but this is a
little like saying there are things that can only be described by Spanish
speakers that no other language (French, English, etc.) could describe.
Sure, a translation needs to occur to communicate a Spanish idea into an
English one, but just because spanish and english speakers use a different
language doesn't mean there are problems only speakers of one language can
solve.
> It is true in a very limited sense, but it seems mad to treat
> it as the foundation of what it means for words to express something (and
> the same goes for computation).
> If we use such trivial notions of computation, why not say that the program
> "return input" emulates all turing-machines because given the right input
> it
> gives the right output (we just give it the solution as input).
>
Many programs have no input and/or no output, but they still can be
rightfully said to perform different computations.
> I get that we can simply use the Church-turing as the definition of
> computation means. But why is it (mostly) treated as being the one and only
> correct notion of computation (especially in a computer science context)?
I think it more comes into play in the a definition of a universal machine,
than in the definition of computation.
It is useful because it makes it easy to prove. All you need to do is show
how some machine can be used to emulate any other known turning universal
machine.
>
The only explanation I have is that it is dogma. To question it would change
> to much and would be too "complicated" and uncomfortable. It would make
> computation an irreducibly complex and relative notion or - heaven forbid -
> even an inherently subjective notion (computation from which perspective?).
Reverse engineering machine language code is very difficult, but there are
automated programs for doing this that can provide much more readable
program code. Cod
