HI Jesse, David,
On 23 Jul 2014, at 18:49, Jesse Mazer wrote:
Had some trouble following your post (in part because I don't know
all the acronyms), but are you talking about the basic problem of
deciding which computations a particular physical process can be
said to "implement" or "instantiate"? If so, see my post at http://www.mail-archive.com/everything-list%40googlegroups.com/msg43484.html
and Bruno's response at http://www.mail-archive.com/everything-list%40googlegroups.com/msg43489.html
. I think from Bruno's response that he agrees that there is a well-
defined way of deciding whether one abstract computation implements/
instantiates some other abstract computation "within itself" (like
if I have computation A which is a detailed molecular-level
simulation of a physical computer, and the simulated computer is
running another simpler computation B, then the abstract computation
A can be said to implement computation B within itself).
So, why not adopt a Tegmark-like view where a "physical universe" is
*nothing more* than a particular abstract computation, and that can
give us a well-defined notion of which sub-computations are
performed within it by various "physical" processes? This approach
could also perhaps allow us to define the "number of separate
instances" of a given sub-computation within the larger computation
that we call "the universe", giving some type of measure on
different subcomputations within that computational universe (useful
for things like Bostrom's self-sampling assumption, which in this
case would say we should reason as if we were randomly chosen from
all self-aware subcomputations). So for example, if many copies of a
given AI program are run in parallel in a computational universe,
that AI could have a larger measure within that computational
universe than an AI program that is only ever run once within
it...of course, this does not rule out the possibility that there
are other "parallel" computational universes where the second
program is run more often, as would be implied by Tegmark's thesis
and also by Bruno's UDA. But there is still at least the theoretical
possibility that the multiverse is false and that only one unique
computational universe exists, so the idea that all possible
universes/computations are equally real cannot be said to follow
logically from COMP.
To have the computations, all you need is a sigma_1 complete theory
and/or a Turing universal machine, or system, or language.
It would take many pages to describe formally elementary arithmetic
(including the formal predicate calculus), which is indeed already
such a sigma_1 complete system/machine/theory, but a simpler one can
be given in less line, like the Putnam-Davis-Robinson-Matiyazevic-Jone
universal diophantine polynomials. Or the combinators, whose sigma_1
complete theory is given by the axioms
x = x
x = y & y = z ->. x = z
xy = xz / y = z
yx = zx / y = z
Kxy = x
Sxyz = xz(yz)
(I recall that a combinator is either K or S, or a combination of
combinators (X, Y), so a combinator is for example
(K (K S)) S) which we abbreviate K(KS)S as we can suppress all the
left parenthesis for ease of readability.
You can compute ((K K) K), or better KKK. By the second axiom you get
KKK = K. But K(KK) does not match any axioms, and thus stay calm:
K(KK) gives K(KK) as a stopping result.
For the theory of everything, we need no more. Oh, well to avoid
having just one combinators, you can add the axiom
~(K = S),
but for the ontology it is not really needed. It is a Turing universal
language, and all universal interpreters can be coded through a
combinator. In particular, you can easily find combinators which
mirrors faithfully the sigma_1 complete part of arithmetic, like you
can find combinators which solves the PDRMJ universal diophantine
polynomial equation.
In that theory, we can define those very theories formally, and they
all are instances of universal combinators, or universal numbers. A
computation is what a number do relatively to a universal number. But
by the FPI, a physical computation will be the one done, strictly
speaking, by infinities of universal (and non universal also) numbers/
combinators.
The absolute (relative measure) laws does not depend of choosing
arithmetic, or combinators, that is, the laws of physics will not
depend on the choice of the universal numbers. But the "winner", or
"winners" which support(s) and stabilize(s) your current state of mind
is "unknown", today. Except that when you interview the löbian
machine, which are those who knows that they are sigma_1 complete,
that they know that they are Turing universal, then you get that the
winner has some quantum favor, as the many dreams in the combinatoric
reality (the FPI on the sigma_1 complete reality).
David, I think that with the combinators, I might more quickly
explains different senses of "going at a higher level description",
making possible to better delineate where I agree with Brent and where
I agree with you.
I mean I will think about it.
Liz? Is it not time to study at least one, conceptually simple,
computer programing language?
The point is that we need a universal system, and then we can define
computations, the UD and and all finite portions of UD*, guided
through the FPI on the limit "winning measure(s)".
Or we use the phi_i?
All this already gives a very rich 3p reality, and does not address
the 1p, except by that FPI. But the löbian numbers have the
introspective ability to distinguish the representational (belief)
from the non representational (knowledge, hope).
The löbian number can already understand that they are "lost" in the
arithmetical reality, and confronted with the arithmetical truth, most
part of it being non justifiable. Yet, those non justifiable truth
obey a mathematics of their own, constraining different modes of the
apprehension of truth (arithmetical truth, combinatorical truth, c++al
truth, whatever).
David, The modes (like []p, []p & p, etc) emerges from the fact that
universal numbers develops complex 3p objects, like when proving
theorems, or building planes, or getting self-referential (even just
in the 3p way). We have to be platonist on the 3p constructions (the
programs, the data, the activity of a machines relatively to another
machine), to be able to be platonist on the 3p realities given by []p
& p, which are much more evanescent, as they create an umbilic cord
with truth, and pay the big price, as they loose their name/identity/
description.
Here your argument against Brent is at risk to be extended into an
argument against CTM. You gently save me by observing that I do
justify the existence of the modes, but that works only because
ultimately we say that "yes" to the doctor and on the fact that we bet
the doctor get the right "[]p" concerning us. We "know" already that
the *truth* of p will take care of itself (by the minimal realism
asked to have a notion of numbers or combinators, to begin with.
There is 31° celcius, without much air, and my head is boiling hot,
apologies for the typos.
Bruno
Jesse
On Wed, Jul 23, 2014 at 9:38 AM, David Nyman <[email protected]>
wrote:
Recent discussions, mainly with Brent and Bruno, have really got me
thinking again about the issues raised by CTM and the UDA. I'll try
to summarise some of my thoughts in this post. The first thing to
say, I think, is that the assumption of CTM is equivalent to
accepting the existence of an effectively self-contained
"computationally-observable regime" (COR). By its very definition,
the COR sets the limits of possible physical observation or
empirical discovery. In principle, any physical phenomenon, whatever
its scale, could be brought under observation if only we had a big
enough collider. But by the same token, no matter how big the
collider, no such observable could escape its confinement within the
limits of the COR.
If we accept that the existence of a COR is entailed by assuming
CTM, we come naturally to the question of what might be "doing the
computation". In terms of the UDA, by the time we get to Step 7, it
should be obvious that, in principle, we could build a computer from
"primitive" physical components that would effectively implement the
infinite trace of the UD (UD*). Furthermore, if such a computer were
indeed to be implemented, the COR would necessarily exist in its
entirety somewhere within the infinite redundancy of that trace.
This realisation alone might well persuade us, on grounds of
explanatory parsimony and the avoidance of somewhat strained or ad
hoc reservations, to accept FAPP that UD*->COR. Should we be so
persuaded, any putative underlying "physical computer" would have
already become effectively redundant to further explanation.
Notwithstanding this, we may still feel the need to retain
reservations of practicability. Perhaps the physical universe isn't
actually sufficiently "robust" to permit the building of such a
computer? Or, even if that were granted, could it not just be the
case that no such computer actually exists? Reservations of this
sort can indeed be articulated, although worryingly, they may still
seem to leave us rather vulnerable to being "captured" by Bostrom-
type simulation scenarios. The bottom line however seems to be this:
Under CTM, can we justify the "singularisation", or confinement, of
a computation, and hence whatever is deemed to be observable in
terms of that computation, to some particular physical computer
(e.g. a brain)? More generally, can we limit all possibility of
observation to a particular class of computations wholly delimited
by the activity of a corresponding sub-class of physical objects
(uniquely characterisable as "physical computers") within the limits
of a definitively "physical" universe?
This is where Step 8 comes in. Step 7 seeks to destabilise our naive
intuition about an exclusive 1-to-1 relationship between
computations and particular physical objects by pointing to the
consequences of a physical implementation of UD*. Step 8 however is
a change of tactic. First, it postulates a scenario where physical
tokens have been contrived to represent a "conscious
computation" (either in terms of a brain or in terms of a substitute
"computer"). Then it sets out to shows how all putatively
"computational" relations between such tokens could in principle be
disrupted without change in the net physical action or environmental
relations of the system that embodies them. Step 8 differs from Step
7 in that it seeks in the first instance to undermine the very
notion that physical activity can robustly embody *any* second-order
relations above and beyond those of net physical action. Accepting
such a stringent conclusion would then seem to rule out CTM prima
facie. The only possibility of salvaging it would lie in an
explanatory strategy in terms of which computational relations take
logical precedence over physical ones. Given that computational
relations are effectively arithmetical, this in turn leads to the
conclusion that CTM->UD*->COR (or more generally, that each implies
the others).
Notwithstanding this it would seem that Step 8 is not wholly
persuasive to everybody, so is there yet another tack? The line of
argument that I've been pursuing with Brent has led me to consider
the following analogy, which I'm sure you'll recognise. Consider
something like an LCD screen as constituting the "universe of all
possible movie-dramas". In terms of this analogy, what are the
referents of any "physical observations" on the part of the dramatis
personae featured in such presentations? IOW what are we to suppose
Joe Friday to be referring to when he asks for "Just the facts,
ma'am"? Well, the one thing we can be sure of is that NO such
reference can allude to the "underlying physics" (i.e. the pixels
and their relations) of the LCD display. If this analogy holds, at
least in general outline, what justification, under CTM, could
remain for any assumption that our own observations and references
might "accidentally" allude to some "LCD-physics" postulated,
mutatis mutandis, as underlying the COR? Would it not seem
extraordinary that any such underlying physics could contrive to
"refer to itself" through the medium of its merely computational
derivatives?
This last point might seem determinative, but might there not still
be a last-ditch redemption, of a physics underlying computation, in
terms of "evolution"? IOW, might it not be argued that the
acquisition of internal "computational" models of their physical
environment confers a survival advantage on the physical creatures
that embody them? But any such argument would, of course, be
completely circular; assuming CTM, it begins and ends in the COR.
IOW, arguing in this way would be to ignore the fact that the
history of such creatures, their survival, and the environment in
which this is supposed to take place, all lie within the COR, not
the putative regime of any "underlying physics". THAT "physics"
would necessarily be entirely inscrutable and inaccessible for
reference at the level of the COR (think of the LCD analogy). And
hence we simply would have no a priori justification for assuming
the observational physics of the COR to be isomorphic with some
notional underlying "LCD-physics". In fact, once having assumed CTM,
we would have no further basis for assigning THAT physics any role
whatsoever in our explanatory strategy.
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 [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.
