Re: The class of Boolean Algebras are a subset of the class of Turing Machines?
Stephen Paul King wrote: I am asking this to try to understand how Bruno has a problem with BOTH comp AND the existence of a stuffy substancial universe. It seems to me that the term machine very much requires some kind of stuffy substancial universe to exist in, even one that is in thermodynamic equilibrium. I fail to see how we can reduce physicality to psychology all the while ignoring the need to actually implement the abstract notion of Comp. I really would like to understand this! Sets of zero information fail to explain how we have actual experiences of worlds that are stuffy substancial ones. It might help if we had a COMP version of inertia! Even Descartes realised the incompatibility between Mechanism and Weak Materialism (the doctrine that Stuff exits), in his Meditation. I think Stuff has been introduced by Aristotle. Plato was aware, mainly through the dream argument, that evidence of stuff is no proof, and he conjectured that stuff was shadows of a deeper, invariant and ideal reality, which is beyond localisation in space or time. My question is why do you want postulate the existence of stuff. The only answer I can imagine is wanting that physics is fundamental. But that moves makes both physics and psychology, plus the apparent links between, quite mysterious. No doubt that Aristotle errors has accelerated the rise of experimental science and has made possible the industrial revolution. But Aristotle stuff has been only use to hide fundamental question which neither science nor technics will be able to continue to hide. Dennett argues that consciousness, for being explained at all, must be explained without postulating it. I think the same is true for matter, space, time, and any sort of stuff. But, now, with comp, what I say here becomes a consequence of the movie graph argument or of Maudlin's article computation and consciousness. See Maudlin or movie in the archive for more explanation or references. You can also dismiss the movie/Maudlin argument if both: 1) You grant me the comp apparition of physics through the proof of LASE 2) You accept some form of OCCAM razor (the concetual form used by Everett or by most 'everythingers'). Regards, Bruno
RE: The class of Boolean Algebras are a subset of the class of Turing Machines?
The statement Boolean Algebras are a subset of the class of Turing Machines doesn't seem quite right to me, I guess there's some kind of logical typing involved there. A Turing machine is a kind of machine [albeit mathematically modeled], whereas a boolean algebra is an algebra. Boolean algebra is a mathematical framework that is sufficient to model/design the internals of Turing machines... In a conceptual sense, they're equivalent ... -- Ben -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 12:29 PM To: Ben Goertzel; [EMAIL PROTECTED] Subject: The class of Boolean Algebras are a subset of the class of Turing Machines? Dear Ben, So you are writing that the class of Boolean Algebras are a subset of the class of Turing Machines? Kindest regards, Stephen - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, November 26, 2002 9:58 AM Subject: RE: turing machines = boolean algebras ? Essentially, you can consider a classic Turing machine to consist of a data/input/output tape, and a program consisting of -- elementary tape operations -- boolean operations I.e. a Turing machine program is a tape plus a program expressed in a Boolean algebra that includes some tape-control primitives. -- Ben G -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 9:25 AM To: [EMAIL PROTECTED] Subject: Re: turing machines = boolean algebras ? Dear Ben and Bruno, Your discussions are fascinating! I have one related and pehaps even trivial question: What is the relationship between the class of Turing Machines and the class of Boolean Algebras? Is one a subset of the other? Kindest regards, Stephen
Re: The class of Boolean Algebras are a subset of the class of Turing Machines?
Dear Ben, So then it is: Boolean Algebras /equivalent Turing Machines in the mathematical sense. I am asking this to try to understand how Bruno has a problem with BOTH comp AND the existence of a stuffy substancial universe. It seems to me that the term machine very much requires some kind of stuffy substancial universe to exist in, even one that is in thermodynamic equilibrium. I fail to see how we can reduce physicality to psychology all the while ignoring the need to actually implement the abstract notion of Comp. I really would like to understand this! Sets of zero information fail to explain how we have actual experiences of worlds that are stuffy substancial ones. It might help if we had a COMP version of inertia! Kindest regards, Stephen - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, November 26, 2002 12:49 PM Subject: RE: The class of Boolean Algebras are a subset of the class of Turing Machines? The statement Boolean Algebras are a subset of the class of Turing Machines doesn't seem quite right to me, I guess there's some kind of logical typing involved there. A Turing machine is a kind of machine [albeit mathematically modeled], whereas a boolean algebra is an algebra. Boolean algebra is a mathematical framework that is sufficient to model/design the internals of Turing machines... In a conceptual sense, they're equivalent ... -- Ben -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 12:29 PM To: Ben Goertzel; [EMAIL PROTECTED] Subject: The class of Boolean Algebras are a subset of the class of Turing Machines? Dear Ben, So you are writing that the class of Boolean Algebras are a subset of the class of Turing Machines? Kindest regards, Stephen - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, November 26, 2002 9:58 AM Subject: RE: turing machines = boolean algebras ? Essentially, you can consider a classic Turing machine to consist of a data/input/output tape, and a program consisting of -- elementary tape operations -- boolean operations I.e. a Turing machine program is a tape plus a program expressed in a Boolean algebra that includes some tape-control primitives. -- Ben G -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 9:25 AM To: [EMAIL PROTECTED] Subject: Re: turing machines = boolean algebras ? Dear Ben and Bruno, Your discussions are fascinating! I have one related and pehaps even trivial question: What is the relationship between the class of Turing Machines and the class of Boolean Algebras? Is one a subset of the other? Kindest regards, Stephen
RE: The class of Boolean Algebras are a subset of the class of Turing Machines?
Among other things, Bruno is pointing out that if we assume everything in the universe consists of patterns of arrangement of 0's and 1's, the distinction btw subjective and objective reality is lost, and there's no way to distinguish simulated physics in a virtual reality from real physics. I accept this -- there is no way to make such a distinction. Tough luck for those who want to make one!! ;-) -- Ben G -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 1:38 PM To: [EMAIL PROTECTED] Subject: Re: The class of Boolean Algebras are a subset of the class of Turing Machines? Dear Ben, So then it is: Boolean Algebras /equivalent Turing Machines in the mathematical sense. I am asking this to try to understand how Bruno has a problem with BOTH comp AND the existence of a stuffy substancial universe. It seems to me that the term machine very much requires some kind of stuffy substancial universe to exist in, even one that is in thermodynamic equilibrium. I fail to see how we can reduce physicality to psychology all the while ignoring the need to actually implement the abstract notion of Comp. I really would like to understand this! Sets of zero information fail to explain how we have actual experiences of worlds that are stuffy substancial ones. It might help if we had a COMP version of inertia! Kindest regards, Stephen - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, November 26, 2002 12:49 PM Subject: RE: The class of Boolean Algebras are a subset of the class of Turing Machines? The statement Boolean Algebras are a subset of the class of Turing Machines doesn't seem quite right to me, I guess there's some kind of logical typing involved there. A Turing machine is a kind of machine [albeit mathematically modeled], whereas a boolean algebra is an algebra. Boolean algebra is a mathematical framework that is sufficient to model/design the internals of Turing machines... In a conceptual sense, they're equivalent ... -- Ben -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 12:29 PM To: Ben Goertzel; [EMAIL PROTECTED] Subject: The class of Boolean Algebras are a subset of the class of Turing Machines? Dear Ben, So you are writing that the class of Boolean Algebras are a subset of the class of Turing Machines? Kindest regards, Stephen - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, November 26, 2002 9:58 AM Subject: RE: turing machines = boolean algebras ? Essentially, you can consider a classic Turing machine to consist of a data/input/output tape, and a program consisting of -- elementary tape operations -- boolean operations I.e. a Turing machine program is a tape plus a program expressed in a Boolean algebra that includes some tape-control primitives. -- Ben G -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED]] Sent: Tuesday, November 26, 2002 9:25 AM To: [EMAIL PROTECTED] Subject: Re: turing machines = boolean algebras ? Dear Ben and Bruno, Your discussions are fascinating! I have one related and pehaps even trivial question: What is the relationship between the class of Turing Machines and the class of Boolean Algebras? Is one a subset of the other? Kindest regards, Stephen
