On 6/11/2018 8:32 AM, Bruno Marchal wrote:
Hi Telmo,
On 11 Jun 2018, at 13:53, Telmo Menezes <te...@telmomenezes.com> wrote:
Hi Bruno,
Sorry for the delay, had a friend visiting.
No problem. From tomorrow (Tuesday) to Friday, I have many oral exams (+ a
conference in Nivelles, a city nearby). So take your time to comment and
express the dissatisfaction.
Ah! Let me try to answer.Keep in mind that I assume elementary arithmetic and
thus computations, etc.
(I am not sure I need YD here, but it can help).
- Why does consciousness even exist?
Consciousness is somehow the doubt between consistency and truth (<>p v p).
All universal number self introspecting meet this, and it is felt as
immediately obvious, and thus true, and undoubtable, yet non rationally
justifiable, and even non definable.
I follow your reasoning, from one of your recent articles. This leaves
me dissatisfied, but if I try to verbalize this dissatisfaction I feel
stuck in a loop. Perhaps this illustrates your point.
We might need to do some detour about what it would mean to explain
consciousness, or matter.
I might ask myself if you are not asking too much, perhaps. Eventually,
something has to remain unexplainable for reason of self-consisteny. I suspect
it will be just where our intuition of numbers or combinators, or of the
distinction finite/infinite comes from (assuming mechanism), or just why we
trust the doctor!
It goes from the rough dissociated universal consciousness of Q to the
elaborate self-consciousness of PA or ZF, or us.
Darwinism does not seem to require it.
It does. When the machine opts for <>p in the doubt between p and <>p, if it
let it go, in some sense, it transforms itself into a more speedy and more efficacious
machine, with respect to its most probable history.
So, consciousness brings a self-speedable ability, which is quite handy for
self-moving being living in between a prey and a predator.
I'm not convinced. Consider a simple computer simulation where agents
are controlled by evolving rules. Agents can eat blue or red pills.
90% of the time blue pills give them energy and red pills cause
damage. 10% of the time the opposite happens. It is not possible to
know before eating a pill. Let's say the rule system evolves to make
the agents always eat blue pills and never red pills. Most of the time
this helps the agents, precisely because it assumes the most probable
histories. This is a simplified version of the sort of "decisions"
that evolution makes, and I would say that it is reasonable to assume
that our own evolutionary story consists of the accumulation of a
great number of such decisions. I still don't see how consciousness
makes a difference in such a mechanism.
The reason why consciousness makes the difference is not related to the
environment, but is intrinsic to the machine itself.
I am aware to be quick on this, but the reason is a bit mathematically
involved, and again, depends crucially of a discovery made by Gödel, and
exposed in his paper “the length of proof”.
Gödel discovered the existence that if you have some essentially undecidable theory, like
RA, PA, ZF, there are always undecidable sentences, like <>RA in RA, of <>ZF in
ZF, etc, then if you add an undecidable sentence (in the theory T, say) to T, you get a
theory which not only will prove infinitely more sentence than T, but that infinitely many
proofs will be arbitrarily shorter in T+the undecidable sentence than the proof of it in T,
making “somehow” T+the undecidable sentence much faster than T.
Even if the added sentence is false, we get that speeding-up
?? What does it mean that it is false? I thought "true" was
undefinable. Do you mean it contradicts some theorem of T? But in that
case it would make T+the undecidable (false) sentence speed up the proof
of every sentence.
(even for interesting sentences as Eric Vandenbussche convinced me (He thought
that this was false, but eventually he proved that statement true).
Blum has got a similar result in computer science, and eventually Blum &
Marquez characterised the spedable machine/set (he used the w_i instead of the
phi_i), and he obtained the class of sub-creative set, which generalised the
creative set (which correspond to the universal machine).
This means that if you take a slow universal machine, like the Babbage Machine,
and a very efficacious machine, like a super-quantum computer, then you can by
make the Babbage machine more rapid than the quantum computer on *almost* all
inputs (= all except a finite number of exceptions), and even arbitrarily more
rapid. Of course the “almost” limit seriously the applicability of that
theorem, but in arithmetic, and for the FPI, that can play a rôle.
In particular, take a machine which observe itself, and as some inductive-inference
ability. By Gödel, or G, the machine can prove that if she is consistent, then her
consistency is not provable. The machine can also see that she never succeed in proving her
consistency, and eventually link this with the fact that her consistency (<>t) is not
provable. Then, the machine can guess that she is consistent, by the adductive
inductive-inference ability, and she can transform itself in a new machine with “<>t”
added as a new axiom. That machine will be (theoretically) more efficacious (with some
practical drawback). She can easily prove that his “ancestor” is consistent (in one line:
“see the new axiom!”), and can prove infinitely more theorem, and can prove old theorem
with shorter proofs. And she can continue on the (constructive, and then non constructive)
transfinite.
Can you give some non-trivial example of this speed-up?
This does not mean that a conscious machine is necessarily more efficacious on
all task,
What is the added undecideable sentence implied by consciousness?
Brent
due notably to those finite number of exception, but it can be used to argue
that in the long run, that make the machine more efficacious.
Your exemple above is a sort of particular counter-example, but it take into
account a social changing environment. Here I suppose the environment fixed.
But if the environment changed, it will be even more benefices to compute more
rapidly, even to find more quickly that she is wrong about its theory about her
environment.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
