On 16 Jun 2010, at 01:04, Rabbi Rabbit wrote:
Dear Bruno,
Thank you for your ample and generous answer.
I want to play with my cards on the table and I take as a rule not to
pretend to understand what I do not understand.
That is a good idea, especially if you want understand.
I must confess you
that your answer was for me as promising as it was obscure.
I'll try to break down my doubts.
Ah! The divine intellect is a typical (neo)platonist notion. It is
Plato's Noûs, and its rôle is played by the modal logic G* all along
this list. It is the canonical divine intellect that you can
associate
to any self-referentially correct machine.
The (pegagogical) problem is that it assumes some background in
mathematical logic.
I have no idea what is the modal logic G*.
Nobody knows logic. Marijuana illegality, and the whole prohibition
politics are based on error in the most elementary part of logic. And
formal logic, a branch of mathematics, is virtually known only by
professional logicians.
Propositional logic is the mathematical analysis of argument involving
abstract propositions. The goal is to analyse the validity of
arguments independently of the meaning of the proposition. For
example, to deduce p from p & q, is valid. To deduce p from p OR q, is
not valid.
Propositional modal logic introduce new operator, like POSSIBLE p and
NECESSARY p.
There are many modal logics (when there is only one classical two-
valued propositional logic).
I may give you reference, but the work I was alluding too asks for a
rather big investment in mathematics.
I understand that I need to
go through the archives of the list to get the details, but I didn't
have the time yet to do so. I am also at lost with your concept of a
"self-referentially correct machine". As I understand it, If the
machine is self-referential, either it is a tautology to say that it
is correct or the categories of correct and false are irrelevant.
A machine is self-referential if it asserts something about itself.
Imagine a robot saying "I have five legs".
But that machine can be non self-referentially correct. Imagine that
the machine has six legs.
Likewise, if I tell you that I am 42 km tall, I am making a self-
reference, but I may be wrong (lying, distract, etc.).
I am not 42 km tall, to be sure :)
An altimeter in a plane is implicitly self-referential, when given the
altitude, and may be non correct.
Most mystics, including the introspective universal
machine, agree that God has simply no name at all.
The "little god" (the universal machine) has no definite name: each
time you give it a name or description it can change it (refute it)
and get other names (an infinity of names are then available). The
explosion of universal machines and programming languages can be
related to this phenomenon.
Do you mean that the so-called "introspective universal machine" is a
mystic?
At this stage, take it as a poetical shortcut for summing up the major
discoveries of Gödel (and others) and their consequences in
theoretical computer science.
We know that a proving machine, once above some treshold of
complexity, can discover and bet on the truth on some proposition, yet
without being able to prove them.
So machines, when looking inward, discover the gap between provable
and true.
I am still struggling to understand what you mean by the self-
referentially correct machine. Now there is an introspective universal
machine and a universal machine that it is also a "little god". In
Judaism, the "little god" is associated to the angel Metatron, as for
instance in Yom Kippur. On a second thought, "Metatron" sounds pretty
much like the name you would give to a machine! This is Metatron 2.0.
"Tron" is also the title of an early movie introducing the notion of
virtual environment. A key notion in mechanist philosophy.
A problem I have with Kabbalah, the Sufi and some other mystical is
that many forget the initial insight from numbers and develop many
"numerical superstition". This did already begin with Pythagoras.
What do you mean by "the initial insight from numbers"? This looks
particularly promising.
I mean the birth of elementary arithmetic. It seems that in Africa
(Mesopotamia?), people already knew that there is an infinity of
triples of natural numbers such that x^2 + y^2 = y^2.
(*) see the Universal Dovetailer Argument (in the list, or in my url
below, search the archive for UDA).
I visited your site, but unfortunately the only way to access the
article about UDA was to buy the whole magazine. I didn't find it
either in "The Theory of Nothing". Any CC version of your article
available? I would love to read it.
Weird!
A complete version of UDA (but quite quick at the eighth step) is in
this paper (click there on the PDF or HTML as you prefer. Click on PDF
slide for one slide summing up the argument diagrammatically).
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Hmm... remember that Pauli and Jung build their concept from the OLD
Quantum Mechanics.
My reference to Pauli and Jung was, actually, the story according to
which Pauli became obsessed with the number 317. It seems that in the
course of his research in physics, Pauli encountered this number over
and over again in all kind of different measurements and ratios,
apparently unrelated and with no connection to each other. As the
legend goes, Pauli became at some point a patient of Jung and
explained him about his obsession. Jung told him that, following
Jewish Gematria(*), 317 was the numerical value of the word Kabbalah.
A very amusing "coincidence". My favourite part of the story is that
through his research in physics and subsequent obsession with the
number 317, Pauli had up reconnecting with his Jewish roots! It is a
joke worth a God with sense of humour.
I guess you mean the number 137.
I am a but skeptical with the coincidences, theoretical statistics
shows that they are more numerous that our intuition accounts for.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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