On 08 Jun 2014, at 14:28, David Nyman wrote:
On 7 June 2014 20:05, Bruno Marchal <[email protected]> wrote:
At step 7, it is not in principle. Like in the preceding protocol,
we just assume the existence of an infinite running of the UD in our
infinite (then) space-time structure.
The proposition is that if that is the case, and don't see white
rabbits, it means some computations are multiplied, and exploit
(perhaps) the random oracle inherent in that multiplication.
OK, so the pedagogic purpose of step 7 is to persuade us that our
experiences *could* be the consequence of the above, but it doesn't
yet force that conclusion (because it could still be avoided in the
way I have suggested).
The step 8 does not, and cannot, refute your point above, but it can
explain how far it goes near a god-of-the-gap move, or a magic move.
It is close to be proved, as to counteract to step 8 you are forced
(in the transfinite) to provide a matter which is non Turing
emulable, and non FPI recoverable. It looks like reifying a mystery
to prevent a possible partial solution to a mystery. Someone might
add that matter needs a "Gods" blessing, also.
Step 8, if I've understood it, shows that one can evacuate all
traces of "computation" from a "primordial" physical instantiation
(either by substituting a filmed record, under the particular
contingencies of the movie graph, or by systematically substituting
each of the "computational relations" by fortuitous physical
events). This renders the ascription of "computation" to the
physical events as entirely gratuitous. Hence what follows is either
the abandonment of CTM, or alternatively the reversal consequence.
The reversal could only then be avoided by an appeal, as you say, to
some (presumably presently unknown) aspect of "primordial matter"
that is not Turing emulable in principle (e.g. that required actual
computational infinities). Even after such a move, any naturally
motivated appeal to "computation" and its putative relation with
consciousness is hardly any clearer than before.
My own intuition, for what its worth, has always been that any
appeal to "computation" on the assumption of "primordial matter" is
somewhat suspect and ad hoc. ISTM that what is supposed to be
"primordial" about a specific set of entities and their relations is
precisely that they *exclusively* underlie (or more correctly,
comprise) everything that is "really real". So the hierarchical
structure of everything we observe thereafter - be it physical,
chemical, biological, physiological, etc. - would be deemed to be
underpinned, exclusively and exhaustively, by such a primordial
substratum.
The higher-order levels in the hierarchy could always, at least in
principle, be reduced without loss to the primordial entities and
their relations. They are, IOW, *re-descriptions* of primordial
reality, not independent realities in themselves. If so, the problem
in trying to add "computation" to such a hierarchy is that it must
suffer the same fate - i.e. that of being reduced and eliminated as
an ultimately supernumerary re-description of what is "really" just
the primordial substratum. And consequently, if we attempt to attach
consciousness to such a supernumerary re-description, it must
inevitably be exposed to similar reduction and elimination. This is,
I think, what the demonstrations in step 8 lay bare.
By contrast, after the reversal, the primordial entities and
relations are restricted to the natural numbers (or their
equivalents) and their additive and multiplicative relations. It
used to trouble me that the same arguments I have deployed above
could seemingly equally be directed at this alternative "primordial
substratum". That is, that whatever was deemed to "emerge" from
arithmetic could in the final analysis always be reduced to it again
without loss and hence ultimately eliminated as being independently
real. But the critical difference here, compared with the starting
point of "primordial matter", seems to be the natural emulation of
computation and the universal machine in arithmetic. Their
consequences in logic seem, at least in principle, to offer a route
out of the reduction/elimination impasse by connecting an "outer
structure" of basic arithmetical entities and relations with a much
larger and more complex "internal reality" consisting of the modes
of arithmetical truth. This latter reality is then no longer
vulnerable in the same way to either reduction or elimination,
though the task (substantially) remains, after a promising
beginning, to connect it systematically and robustly with "observed
reality".
It occurred to me that the relation between such a substratum and
its truth domain might be suggested, albeit rather imperfectly, by
an analogy with something like an LCD screen. The idea is that an
enormously large (infinite?) set of possible dramatic storylines can
potentially be realised by a finite set (in this case) of
"fundamental" entities and their relations (i.e. the pixels). Of
course, the analogy immediately breaks down because, in the case of
the screen, an external interpreter is necessary for any "dramatic
truth" whatsoever to be accessible. To complete the analogy one must
rather imagine something that is both self-interpreting and self-
filtering (at this point one also importing "The Library of Babel"
into the picture!). Et voila - the UDA!
Et voilà :)
Thanks for that impressive summarizing reasoning.
Note that the UD get the (infinite) library of babel + the infinity of
readings made by each universal numbers. The atemporal arithmetical
relation do the relative interpretations (and the measure problem as a
gift)
Now you should be ready to see that this + computer science makes it
all precise and testable (at least in its simplest classical
theoretical rendering), and that's AUDA.
Ready? Have you bought the Mendelson? I found here (thanks to the
moving) a quite excellent book by Daniel Cohen (Elis Horwood). But I
see it is out of print:
http://www.amazon.com/Computability-Logic-Mathematics-its-Applications/dp/0745807291
I really don't want to annoy you with technics, but I still think that
the main point of AUDA can be quickly understood, like the consequence
of the closure of the partial computable functions for the
diagonalization, and the necessities of the intensional variants of
"beweisbar".
Machines can perceive and study the (divine) geometry and music made
by what they cannot understand.
Bruno
David
On 07 Jun 2014, at 17:23, David Nyman wrote:
On 12 February 2014 11:17, Bruno Marchal <[email protected]> wrote:
At step seven, the primitive materialist can still invoke a
physicalist form of ultrafinitism, to prevent the comp reversal
between physics and arithmetic (or number theology).
If I've grasped this, it's that one could attempt to avoid the
reversal by claiming that the physical universe isn't (or mightn't
be) sufficiently "robust" (i.e. physically extended?) to
instantiate a physical UD that would run "forever". If so, this
would presumably side-step the need to take the consequent
infinities of computations into account.
Yees, that the whole point.
However, I've never felt fully in command of this step, actually.
For example, why couldn't one argue that the physical universe is
indeed sufficiently robust, in the sense intended, to support the
infinite running of a UD, but it simply be the case that - in fact
- *there is no such UD in existence*?
Yes, that certainly exists too. But it is not an interesting
protocol to get the partial reversal of step seven: if there is a
concrete UD* then the laws of physics = "the hunting of the
arithmetical rabbits".
Then in step eight we quasi-eliminate moves like "small universe, or
your robust but without UD, etc."
I seem to have missed the force of the implication (at step 7) that
a physically instantiated, infinitely-running UD *must* be taken
into account, given the simple fact of a physical universe
sufficiently robust, *in principle*, to support its existence.
At step 7, it is not in principle. Like in the preceding protocol,
we just assume the existence of an infinite running of the UD in our
infinite (then) space-time structure.
The proposition is that if that is the case, and don't see white
rabbits, it means some computations are multiplied, and exploit
(perhaps) the random oracle inherent in that multiplication.
IOW, even given the comp assumption, why couldn't one still argue
that all relevant computations - *absent actual physical evidence*
of an infinitely-running UD - in fact supervene on physical brains
and/or other non-biological physical digital machines?
By step 8. That moves above is shown introducing a "god-of-the-gap"
to select a reality. It entails a sort of magic distinguishing a
computation from all the others.
You can do this, as step 8 talk about "reality" and thus can only
suggest the implausibility of such a move.
It is almost like using an ideology (the belief in a primary
physical universe) to divert from a testable explanation of where
the physical laws come from, and why the physical can hurt.
It is the same than Omnes, who invoke literally the abandon of
rationalism to select one universe in his otherwise clear
description of a (QM) multiverse.
The step 8 does not, and cannot, refute your point above, but it can
explain how far it goes near a god-of-the-gap move, or a magic move.
It is close to be proved, as to counteract to step 8 you are forced
(in the transfinite) to provide a matter which is non Turing
emulable, and non FPI recoverable. It looks like reifying a mystery
to prevent a possible partial solution to a mystery. Someone might
add that matter needs a "Gods" blessing, also.
Bruno
David
--
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 [email protected].
To post to this group, send email to everything-
[email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
