Bruno Marchal wrote:
On 02 Apr 2015, at 15:04, Bruce Kellett wrote:
Bruno Marchal wrote:
On 02 Apr 2015, at 04:08, Bruce Kellett wrote:
Emulation is a dynamical process in time. I wonder where you get a
time variable for your UTM.
By a variable on the computational steps. It has nothing to do with a
physical time a priori.
What variable? A simple numbering of steps? But that will not work, or
at least, you have hidden an assumption of an external time in your
notation.
The external time is given by the universal machine running the
computation. It can be the basic level (elementary arithmetic, or the
universal dovetailer), or it can be some other universal layer, running
on some other universal layer, running on some other .... running on the
basic level.
At the basic level, we have the block mindscape, like the UD* (the
infinite "cone" of all computations).
This does not do the work you require of it. See below.
"At the end of step 27, move to step 28." That contains an implicit
notion of time -- 'ending' and 'moving' are temporal concepts. I do
not see that you can remove all traces of the idea of an external
temporal parameter. Otherwise the machine could just halt arbitrarily
at some point and never know that it had halted.
I think you ned to flesh your ideas here out a great deal more.
Well, this is a forum, and I explain things already explained with all
details in much longer text (which sometime does not help, because busy
people tend to skip even more the long texts nowadays).
Let me try to help a bit though. Fix some universal programming
language, like Fortran, say. Enumerate all programs computing function
with 1 argument, p_0, p_1, p_2, ....
Let us denote by [p_i(j)^k] the kième step of the execution of the ième
program on argument j, by the universal dovetailer (which dovetails then
on all such [p_i(j)^k] .
Then we can define, indeed already in Robinson arithmetic, a computation
by a sequence of such steps, when i and j are fixed. So a computation is
given by the sequence
[p_456(666)^0]
[p_456(666)^1]
[p_456(666)^2]
[p_456(666)^3]
[p_456(666)^4]
etc.
This sequence is a subsequence of the general universal dovetailing,
which dovetails on all [p_i(j)^k].
It is a computation, only in virtue of the universal dovetailing, and
the universal dovetailing can be defined in arithmetic. I can translate
the proposition "the UD access to [p_345(898786)^89]" entirely in term
of arithmetic, using only the notion of addition, multiplication,
successor (of natural numbers) and 0, and predicate logic.
The only external time used is the ordering of the natural number, which
is easily translated in arithmetic: x < y means Ez(x + z) = y).
OK?
I got this much from reading your paper and other things you have said.
But this, at best, provides and ordering (indexing if you like) on the
computational steps. It does not provide a time parameter. In fact, it
is entirely static, and you get no more than some ordering imposed on
sequences that can be found in any normal number.
Let me be more specific in my criticism.
In step 7 of your argument you introduce the dovetailer. But you then
say "Suppose now, for the sake of argument, that out concrete and
'physical' universe is a sufficiently robust expanding universe so that
a 'concrete' UD can run forever..." Why do you need infinite time in an
expanding universe to run the dovetailer if it is not a physical
machine? You put the words 'physical' and 'concrete' in scare quotes,
but that is merely a device to mislead -- you actually are talking about
the everyday physical, concrete universe that we all know and love.
There is no Platonia here, or else why worry about time limitations and
require an infinite expanding universe in order to get all your
computations in?
In step 8 you introduce the idea that the 'physical universe' really
'exists' and is too small, in the sense of not being able to generate
the entire UD*, nor any reasonable portions of it. You call this move
/ad hoc/ and *disgraceful*, but that is again just a rhetorical trick to
divert attention from the fact that you really are talking about a
physical computer running in our physical universe. In which case, at
any finite time from the beginning of the universe the dovetailer will,
in general, not have generated any sequence of computations that would
correspond to us or anything else. Far from being a disgracefully /ad
hoc/ manoeuvre, this actually undoes your whole enterprise.
The only reason that the dovetailer might have to worry about time
limitations is if it is actually a physical computer. Physical computers
have to contend with such things as physical laws, the finite speed of
light, the properties of materials, the generation of heat (entropy) and
the need to remove that heat to a safe distance before everything melts
down. If your computer is not a physical device, then it has none of
these limitations, and there is no such concept available as the 'speed'
of the computation, the 'time for each step', or anything of this sort.
From our external concrete perspective, the whole thing is
instantaneous, or it enters statis at some point and gets nowhere. For a
non-physical computer these things are equivalent.
So without a physical computer you have no dynamics. A mere ordering of
states is still a static thing, and the dovetailer does nothing useful
that could not more easily be done by referring to a normal number.
This is why I have said several times in previous posts that you rely on
an underlying notion of physical time, and an underlying physical
computer, in order to make your computation dynamic and not static. What
you say above does not let you escape from this conclusion, it merely
reinforces it. The problem of time is your undoing.
Bruce
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