On 17 Nov 2008, at 04:41, Brent Meeker wrote:
> But all possible implementations is a logical concept that exists only
> in platonia -
Any program for the universal dovetailer like this one
GEN & DU
implements all computations in our (apparently) material world we are
sharing now.
> so what is the distinction between implemented and
> un-implemented computations.
Suppose I am inviting you on the planet mars. We have to take a
digital teleporter though (I can afford a two place tickets for a
conventional rocket, sorry). So we are read and cut on the planet
earth, and the information read is send on mars. There, I am
reconstituted, and you, well, bad luck but the reconstitution-machine
just break down. In that case, I am implemented on the planet mars,
and you are not.
Implementation is a relative notion. A program P is implemented on a
universal machine M when P is translated in the language of the
machine M, and when M is trigged so that it evaluates or executes the
program P, on earth or in platonia.
Implementation is a purely mathematical notion for the theoretical
computer scientist. For the physicist, or the business man, it is true
that the word is sometimes used in the sense of concretely implemented
in a real machine in front of us.
But note that the UD has been implemented and executed, for a few
days, concretely on a Macintosh Computer in 1991. That is the key of
the whole construction. The deployment of the UD is a precise
concretisable object. This is made possible by the "Godel's miracle",
or "Church's thesis". It is the only place in math were an
epistemological notion (computation) admit a universal definition.
Godel did not believe in Chuch thesis for a long time, and after he
begin to accept it, he called it a miracle, because it is indeed hard
to believe in it, when you are aware of Cantor's proof and the power
of diagonalisation. As said Godel, it is amazing that Church thesis
can survive to diagonalization. This is the hidden difficulty of the
step seven. I thionk Tom Caylor grasped it through his redaing of the
Cutland book. The notion of computation is highly non trivial.
Computer (universal computing machine) are highly non trivial
mathematical object (implemented or not here or there).
Bruno
http://iridia.ulb.ac.be/~marchal/
--~--~---------~--~----~------------~-------~--~----~
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.domain.name.hidden
To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---
Received on Mon Nov 17 2008 - 11:03:26 PST