On 08 Apr 2011, at 06:55, meekerdb wrote:
On 4/7/2011 9:48 AM, Bruno Marchal wrote:
I indulge myself in a slight correction on a statement, that you
were just doing for a second time, despite I thought having already
insisted on the point. I am sorry because it is not completely in
On 07 Apr 2011, at 17:42, John Mikes wrote:
Thanks, Brent, - however:
I did not restrict myself to physics (lest: 'fundamental') and had
a shorthand-typo in my text:
- - - (=cause) - - -
which indeed means: "a change, effected by - what we call: a
I was referring to our (conventional) system looking only inside
the 'model' of already knowable knowledge, even those applied only
"as needed" to identify cause - or effect.
The unknown 'rest of the world' also influences those changes we
may experience within our model so our consclusions are incomplete.
That does not apply to a universal machine which 'knows it all' -
Universal machine knows about nothing.
They are universal with respect to computability, or emulability,
or simulability. Not on provability, believability or knowability.
Typically all humans being are universal machines. I can argue that
bacteria are already universal machine.
The UMs know about nothing, but they can become wise, that is
Löbian. This is when they realize that they are universal (in some
sense which I can make precise) in that case, they still know about
nothing, but they know that they know nothing, and they can know
why it is necessary that they know nothing. They also know that if
they develop knowledge, their ignorance-space will grow even more,
so that by learning, they can only be proportionnally more
ignorant. that is why they become extremely modest.
In the arithmetical interpretation of Plotinus hypostases, the
universal machine is the arithmetical correspondent of man. God is
arithmetical truth, and for "Him/It/Her" there is a sense to say
that He/It/her knows everything, but It is far beyond what *any*
machine can grasp. Machines cannot even give It a name, unless they
assume that they are machine, in which case the label "Truth" can
indirectly be applied.
Universal machine are more like universal baby than omniscient
With the Church-Turing Thesis, your laptop *is* a universal machine.
I doubt that it has enough memory.
Universality in Turing sense has nothing to do with the amount of
memory available. Turing's discovery of the universal machine is the
discovery of a *finite* code, a number, capable of (encoding a program
capable of) computing all partial computable function, like in Wolfram
cellular automata competition. The confusion comes from the fact that
Turing modeled his machine with an infinite tape, but this is needed
already for computing multiplication. It is more correct to put the
infinite tape in the environment. Typically all computers will ask for
some more memory during their computation. Humans' universality is
witnessed by the fact that at some point they decide to extend their
memory with cave's wall, books, ... magnetic tapes, etc. The
mathematical (and a fortiori the 'concrete one') universal machine are
finite object. That is why I have decided to talk on universal
*number*, for emphasizing that such universal 'device' are finite thing:
If phi_0, phi_1, phi_2, ... is an enumeration of partial computable
functions, u is a universal number if and only if phi_u(<x, y>) =
phi_x(y), with <x,y> some number code for (x, y).
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