On 08 Apr 2011, at 06:55, meekerdb wrote:

On 4/7/2011 9:48 AM, Bruno Marchal wrote:
Hi John,

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 the topic:

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 cause". 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 knower.
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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