Re: The class of Boolean Algebras are a subset of the class of Turing Machines?

From: Stephen Paul King <stephenk1.domain.name.hidden>
Date: Tue, 26 Nov 2002 13:37:45 -0500

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" <ben.domain.name.hidden>
To: "Stephen Paul King" <stephenk1.domain.name.hidden>;
<everything-list.domain.name.hidden>
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:stephenk1.domain.name.hidden]
> > Sent: Tuesday, November 26, 2002 12:29 PM
> > To: Ben Goertzel; everything-list.domain.name.hidden
> > 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" <ben.domain.name.hidden>
> > To: "Stephen Paul King" <stephenk1.domain.name.hidden>;
> > <everything-list.domain.name.hidden>
> > 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:stephenk1.domain.name.hidden]
> > > > Sent: Tuesday, November 26, 2002 9:25 AM
> > > > To: everything-list.domain.name.hidden
> > > > 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
> > > >
> > > >
> > >
> > >
> >
> >
>
>
Received on Tue Nov 26 2002 - 13:38:52 PST