On 06 Jul 2012, at 15:07, David Nyman wrote:
On 6 July 2012 10:27, Bruno Marchal <[email protected]> wrote:
In which structure is that relative-frequency defined, and to whom
does it apply? How can we verify it?
The structure, if you like, is the total state of knowledge of the
"knower" (as you have characterised it in a post to Brent) which ex
hypothesi must embrace all possible occasions of sentience.
This might lead to perhaps interesting question. The knower I
described to Brent, was the knower that we might associate to the
universal machine. Usually (before salvia!) I would not have been open
to that idea, because, well, first the math is lacking, and might not
exist or be trivial. I would have said that the knower begin with the
Löbian entity. But that might be a detail in our setting: the Löbian
machine is basically the same as the universal machine, but having the
belief in some induction axioms. This gives the reflexive loop giving
them the rich and stable cognitive abilities of the Löbian machine
(with the 8 hypostases). Those hypostases will never get change on all
computational histories where the machine remains correct (that is
enough for the derivation of the physical laws, but is quite too much
simple for "real life psychology".
Now, such machine (the virgin universal or the Löbian which is
slightly less virgin) have basically no knowledge at all, and live in
a disconnected conscious state.
I am not sure it makes sense to ask for such a machine if there is a
probability that they become suddenly "me". I would say that may be
the first person indeterminacy of such a machine might have a
indeterminacy domain limited to slightly more complex universal state,
perhaps becoming a bacteria, before becoming a mammal, say. The idea,
is that you always survived in the most normal (Gaussian) neighborhood
available to you, and that normal state is given by the relative
proportion of computations going into that state. So in all situations
the indterminacy is relative to the actual state of the machine, as
brought by the universal dovetailer (or its arithmetical equivalent).
It is not impossible that a rich conscious state, like the one by a
Löbian mammals, necessitates a very long computation, so that the
probability to become such a Löbian mammals, directly from the
universal knower, would be a very rare event (possible, but
stochastically impossible).
Each such occasion is here conceived as a set of spatio-temporal
relations in the context of a particular personal history. Taken as
a whole the structure is of course timeless and eternal. Hoyle's
heuristic is then simply a way of thinking about this structure such
that occasions are given (i.e. from the pov of the knower) in
proportion to their measure, in mutually exclusive succession.
Hence the intrinsic spatio-temporal relations of the substrate are
conceived as unfolding experientially in the form of the myriad
personal histories. It's a way of rationalising the experiential
dynamic, if you like, from the pov of a universal knower, which as
you yourself point out, cannot be an arithmetical, or indeed a
physical, notion.
Indeed. But it is still describable in arithmetical terms, like
arithmetical truth, which is not arithmetical, but concerns only
arithmetical sentences.
I think that here you have a good intuition that the spatiol temporal
unfold experentially from the knower, and this is confirmed, as the
knower logic, with comp, is given by S4Grz (and the X logics) and this
defined indeed a sort of dynamic. In my (old) opinion: this confirmed
Brouwer theory of consciousness, which relates intrinsically
consciousness and time (and S4Grz has indeed been used as a logic of
time by some philosopher).
Now, the salvia experience has refuted this for me, as it generates an
hallucination which put some doubt on that perspective, and which is
why I am willing to attribute a consciousness to the non Löbian
universal machine. Indeed, it seems conceivable that we can be
conscious in a completely non spatio-temporal way. I thought comp
would prevent such possibility, even through an hallucination.
Here your thought might be helpful. But I am not sure it needs to
postulate an absolute indeterminacy. I am not sure it might make sense
to ask: "being a virgin UM, what is the probability of being David in
the next instant?".
But the plant salvia, I have to say, provides evidence for your idea
that it might make sense, for we can apparently get the virgin state
(or be close to it), and yet *it seems* that we survive. It remains
possible that actually, I am correct, and that the probability to
"become a bacteria" when smoking salvia is close to 1, from the 1-pov.
Of course the "third person view will not confirm this. Brrr...
You ask me how this could be tested; since it is a way of thinking,
rather than a theory, the only relevant test is whatever power it
may possess to reduce confusion and enhance conceptual clarity. I
became particularly aware of this when reading some of the posts
about jumping and backtracking, etc. When we reason about some
divergence of "my future moments" in copying scenarios it is
perfectly natural of course to relativise these to my personal
history as given, without consideration that the relevant reference
class might be any broader. Furthermore, since our reasoning here
seems naturally to "follow" the spatio-temporal evolution of some
underlying "real system" (as Bitbol calls it),
OK. Comp forces us to derive the spatio-temporal reality from the
statistics of the machines experiences, and this is the result of the
comp reduction of physics to arithmetic. Everett confirms the
existence of first person plural notion (which multiplies collections
of interacting universal machine), and if comp derives Everett QM,
comp is saved from solipsism, which is still a logical threat for comp.
it does not seem relevant to distinguish the logico-physical
relations of next or prior from the bare notion of succession itself.
I think we have to do that distinction, but I am not sure what you
mean by "bare notion of succession". There are many one. The barest is
probably the notion of successor of a natural number, axiomatize by
the successor axiom of robinson or peano arithmetic (0 ≠ s(x), x ≠
y -> s(x) ≠ s(y), etc.). The semantic of this is the usual function
y=x=& from n to N.
Then you have the succession of the step of the universal dovetailer.
This one will be defined from many application of the axioms of
arithmetic.
Then you have the succession of steps in particular computation,
including for example simulation of galaxies.
But comp makes the real galaxies and the real physics a first person
(hopefully plural) notion, which means that physical time and
subjective time are internal views, which borrows from what the UD
does in the limit (which defined the first person domain
indeterminacy, by the delay invariance of the first person view).
Those notion of time needs to be extracted from some of the machine's
hypostases.
Real problems of coherency in this way of thinking emerge, however,
when we begin to consider "future moments" of low intrinsic measure,
such as in quantum suicide scenarios, or extreme threats to
conscious survival. At this point, we seek to avoid cul-de-sacs or
occasions of extreme improbability by resorting to notions of
jumping or backtracking referred to a particular personal identity,
or even in extreme cases the idea of merging with the infant
consciousness of a different identity entirely. But here we are no
longer following - or at the very least least are forced to
undertake highly non-standard excursions within - the real system.
I see what you mean. This is difficult indeed. That is why in the
publication I try to avoid, amnesia, but of course, through quantum
erasure, we know that "nature" does not avoid this. Here my strategy
consists in trying to get QM from arithmetic, instead of trying to
figure out intuitively the indeterminacy domain for experience
involving amnesia or first person fusion of computational histories.
But we can try.
This reaches perhaps its reductio ad absurdum in Saibal Mitra's
treatment of memory erasure scenarios. He is forced by this mode of
reasoning to speculate, for example, that the "you" that "escapes"
disaster by memory erasure has "swapped histories" with another
"you" that would otherwise have avoided it! It is interesting to
speculate how one would test, or even recognise, this eventuality!
This is without doubt a difficult problem. Normally comp still
suggests that you survive in the closest possible computation. But as
salvia and even just sleep seems to illustrate, amnesia is always
computationally close. Simple switch that can transform a rich
computationally deep machine into a virgin baby seems to exist, which
make such bactracking available. I wish it is like that, because the
next option looks like an infinite agony!
It should, I hope, be obvious that all of the above incoherencies
can be resolved quite simply by adopting the heuristic under
discussion. The structure under consideration, as I have said, is
the total state of knowledge of the knower; all possible occasions
of sentience, duly distributed amongst distinguishable personal
histories in due measure, exist within it.
I fail to make sense of this, as I fail to see the necessity of this.
All that is required, conceptually, is to make explicit the
experiential notion of the mutually-exclusive succession of
occasions of sentience; all relativisation of personal identity and
past-future relations are referred to those aspects of the substrate
associated with a given occasion. There is no suggestion of prior
or next in the bare notion of experiential succession; no extrinsic
ordering whatsoever is implied. The logical consequence is that all
notions of personal history are referred to a singular point-of-
view: that of the knower.
But the knower "code" is intrinsic in all universal machine, (or all
Löbian one) making all of them in the state of having unique singular
experience, with huge, but not totally complete, first pov
indeterminacy domain. They become complete if you take all transitive
closures on the accessible computational states. The probability of a
bacteria becoming you is one, no doubt, but the probability that a
bacteria becomes you in one computational step, although non null, is
very close to zero. A fortiori this is the case for the universal
knower. Somehow, you are "him", but he is not always you. (A good
thing for that motivates for the meeting of others).
"I" am fundamentally that knower,
On this I can completely relate.
and the knowledge successively recoverable from occasions of
sentience is what informs me of who, where, when, and relative to
what, I am on any given occasion.
On this too, but I still don't see why we would need to make the
universal "I" being undetermined on all occasion of sentience, in one
strike, so to speak, even if salvia seems to agree with this (but
salvia is capable of making me doubting on comp too!).
Nor do I see how we can put a distribution probability on all moments.
It is not unfrequent that people thought to be able to refute the UDA
by pointing on the fact that such a global distribution of probability
does not exist, and my usual reply is that all the probabilities are
defined in the relative conditional way. To be sure I know now that
such global probabilities can exist, if we abandon the "sigma-
additivity" axiom in probability theory for example, but this remains
rather awkward, and unnecessary, because the universal knower is
"directly all of us": it is coded in your actual brain, and even cells
(admitting the non Löbian weak notion of knowing). If a computation
support knowledge, it automatically "run" the universal knower.
Of course this makes all indexical into a sort of illusion (like "me",
"here" and "now"), but the math explains, or should explain if comp is
true, why a deep spatio-temporal structure unfold, and why it is
stable and lawful. Comp makes somehow consciousness and arithmetic
absolutely real, and all the rest are relative opinions and knowledge.
I am sure your analysis might help to better apprehend consciousness,
and can perhaps better handle the amnesia situation. But you have not
(yet) convinced me that it has to be termed into a new form of
*assumed at the outset* indeterminacy. The probability of "being me"
is a sort of Dirac distribution: it is one, for "me", and zero for the
others. The probability of becoming "me", is perhaps close to one on
the transitive closure of the computations, and is complex to compute
for particular brain instantiation.
Bruno
http://iridia.ulb.ac.be/~marchal/
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