On 11 Mar 2011, at 13:07, Andrew Soltau wrote:
On 10/03/11 14:10, Bruno Marchal wrote:
Yes, but you still require an explanation of how the machine
actually runs. All possible states of the machine exist 'already' in
an arithmetical universe.
On 10 Mar 2011, at 13:47, Andrew Soltau wrote:
All the moments exist, and as Deutsch points out, as you
summarise, 'The appearance of change is already explained by the
fact that there are different frames that have an implicit
sequence and in which the observers state is different', but for
change to actually happen, the magic finger must move. Otherwise
reality would be like a movie film sitting in the can in storage.
The change in the "working program" is brought by the "universal
machine" which interprets it.
States "alone" do not make sense. What makes a state a machine's state
is that there is a universal number, or the "initial" universal system
itself (elemantary arithmetic, say), which includes it in a
computation. It is a bit similar to Rovelli's relational idea, but in
the context of arithmetic. It is standard to define states and
(universal) machines, and pieces of computations in arithmetic. What
makes a computation emulated in arithmetic is an infinity of true
relations between numbers, and in this case most are provable in a
tiny part of any formal arithmetic (like RA, that is Robinson
arithmetic, which I use to fix the idea).
All you need is an initial universal "machine". It happens that
addition and multiplication, with first order logic is enough to
define such an initial universal system, and the UDA+MGA shows that
the laws of mind, including the laws of matter, does not depend on
the choice of the initial universal system.
Naturally. But you still require an explanation of how such
arithmetic, or how such computations, are carried out. This is where
you need an 'external' time.
So elementary arithmetic does emulate, in the mathematical sense,
Why? The internal time defined by the basic sequence of the natural
numbers is enough. It can be used to define the notion of
computational steps, and of sequence of computational steps. Assuming
comp, you are "here and now" because it exists a sequence of
computational steps leading to your current computational state, at
the right level. Of course, there is an infinity of such sequences,
and we will have to develop a relative uncertainty calculus on them
(or prove that they cannot exist and refute comp).
Arithmetic does not just describe all those computations: it
literally emulate them. This is not trivial to show, although
computer science gives the insight. Computations in arithmetic are
not like movie, they are like a observer line universe in a block
Ok. And you still require an explanation of how something moves
along the line. This is what is missing from physics. It is
inherently absent in any concept of straightforward existence.
Nothing moves in the "block-universe", be it arithmetical or primary
physical. But we can explain why machines will develop discourse about
moving things, and, in the case of comp, we can even explain why a
part of that moving will be considered as incommunicable by the
machine from its first person point of view.
Provided you can explain how we come to be experiencing change, in
other words, how it comes to be that the computation is running, as
opposed to simply existing.
To add an external time reintroduces a mystery where it is not
"Running" is defined in term of sequence of steps. For all universal
number, there will be a notion of steps associated with it, and a
notion of running, which will be defined by reference to the successor
That use of time is like the use of "God" as gap explanation by the
pseudo-religious (authoritative) people. You will end up with a
primitive time, a primitive matter, and why not a primitive "god"
responsible for all this.
In which case you have to accept that the passage of time is an
That is, in my opinion, the correct insight of Deutsch.
I would not call it an illusion. It is only an illusion from the point
of view of "God" (arithmetical truth, say). I would call it a personal
(first person plural or not) subjective reality. Bergson's subjective
duration is retrieved in the "Bp & p" hypostase, and physical time is,
or should be, retrieved in the material hypostase Bp & Dp (& p).
Physical time (and physical space) appears as first person plural
All we need is a good theory of self-reference, but this is provided
by theoretical computer science/ mathematical logic.
(The consequence of UDA are admittedly "unbelievable". That is why the
original name of the Universal Dovetailer Argument was "Universal
Dovetailer Paradox". But AUDA explains the paradox. The "divine
intellect", that is the modal logic G*, proves the equivalence, with
respect to arithmetical proposition, between all hypostases, but
explains why machine cannot see that equivalence, and why such
hypostases (definition of person's view) are all different and obeys
different logics (intuitionist temporal logic for the first person,
quantum logic for the material views).)
This is also why in none of my papers I separate UDA from AUDA,
because UDA is too much unbelievable in the Aristotelian era, but AUDA
explains why it has to be like that. The genuine Gödel's bomb is not
that machine are limited, it is that machine can study their own
limitation, up to the geometry/topology of their relative consistent
In this case, you are not a being which witnesses change.
Er ... you confuse me with God I'm afraid.
Once I develop special memories, by virtue of being in a state
belonging to a computation, I will have the feeling of witnessing
change. For many computations, if the measure problem admits a
solution, that change will have a referent in term of locally stable
If the measure problem does not admit a solution, then comp is false.
You are simply, at each moment in time, that which exists at that
moment in time, and has the illusion, at that moment in time, that
you have existed at other moments in time. Objectively this is
unassailable. Subjectively I personally, for one, consider that it
does not account for my experience.
Up to now, no theory account for experience, except perhaps the
classical theory of knowledge. This is made transparent in the comp
frame, where we can see that the machine is unable to be aware of that
"illusion" aspect of its experience. When the machine refers to its
subjective experience, it refers to its knowledge, defined by Bp & p
(By Plato in the Theaetetus).
But the machine can explain that IF she is a correct machine, then she
has to make that distinction, between Bp (what she can communicate in
a third person scientific way) and (Bp & p), what she knows, and
cannot prove to know as such. This entails that machine will not find
more easier than us that they are machine, and for them too, "saying"
yes to the doctor will need a leap of faith.
I don't really think that there is a lot more one can say about it.
Except that he mentions an "implicit sequence", which is typically
made explicit by the universal machine which emulates, albeit
statically or arithmetically-realistically, the computation. All
computations in that setting are ultimately based on the explicit
sequence 0, s(0), s(s(0)), ... (or the equivalent in the
How the sequence is defined, and whether it is fundamentally
physical or arithmetical, is of no consequence to this - admittedly
highly philosophical - point.
What about step 4?
At the seventh step, in the case your remark could be developed as
making comp and its 8th conclusion false, the seventh step would still
prove that the primary physical universe has to be "little" (non-
robust). No Tipler omega-point!
In the whole possible multi-multi ... verse, there would be no
universal dovetailing, because this one does entail a global
indeterminacy (unpredictability) similar to arithmetic. That would
already refute the MWI applied to the quantum vacuum, because it
provides a universal dovetailing in the multiverse.
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