Hi Hal,
At 22:30 17/01/05 -0500, Hal Ruhl wrote:
>I reject Schmidhuber Comp because a sequence of world states [world
>kernels] which may indeed be Turing machine [or some extension there of]
>emulable is nevertheless managed by the system's dynamic which is external
>to the machine.
>
>Any sub component of a world kernel [such as myself] is subject to the
>same result thus my rejection of Personal Comp.
I understand the sentences but I am completely lost to see relations with
previous sentences of you. Have you try to sum up your theory (your
theories) in a web page (like you did some years ago) ?
I really think we should focus on a well established theory or language to
make progress. As you
know my results are based on classical first order arithmetic. But recently
I came back to an old craving of me: lambda calculus and combinatory logic.
I have discovered that combinators make it possible to simplify
considerably my work (and this at many different levels). I will hardly
resist to say more on this in a near future. The advantage of combinatory
logic is that it is more quickly funny (as opposed to first order logic
which beginning is tedious and hard (and I usually refer to textbook or to
Podnieks pages).
Informal Combinatory logic can be presented as an "everything theory". It
has a static and a dynamic:
STATIC: K is a molecule
S is a molecule
if x and y are molecules then (x y) is a molecule. From this
you can easily enumerate all
possible molecules: K, S, (K K), (K S), (S K), (S S), ((K K)
K), ((K S) K) ...
DYNAMIC: For all molecules x and y, the molecules ((K x) y) produce x
For all molecules x, y z, the molecules (((S x) y) z)
produce y
Exercices: what gives ((K K) K) ? what gives (K (K K)) ?
Is there a molecule M such that (M x) gives x?
That theory has been discovered by Shoenfinkel in 1920 and rediscovered by
Curry and Church (the same as in "Church thesis") in the 1930, and has had
since many applications in practical and theoretical computer science. It
is very fine grained and useful to compare many theories. I am sure that if
you were willing to study it a little , it would inspire you for finding
more understandable presentation of your ideas. Note that it does not
subsumes comp, but, given that this theory is Turing complete, it is
perhaps one of the better road toward computer science and its
philosophies. It could interest everyone in this list and I am pretty sure
many know it or have heard about it. I am currently translating my thesis
in combinators language if only because I have discovered it provides huge
helps to make concrete some otherwise too much abstract notion for good
willing students and philosophers.
I am leaving Brussels for Paris (First European Congress in Philo of
Sciences) and I will be back in a few days.
Regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Wed Jan 19 2005 - 18:48:29 PST