On 24 Oct 2014, at 19:35, meekerdb wrote:
On 10/24/2014 9:04 AM, Bruno Marchal wrote:
Hi Jesse,
Sorry for replying late.
On 27 Jul 2014, at 18:27, Jesse Mazer wrote:
On Sun, Jul 27, 2014 at 10:46 AM, David Nyman
<[email protected]> wrote:
On 23 July 2014 17:49, Jesse Mazer <[email protected]> wrote:
> 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?
Essentially because of the argument of Step 7 of the UDA. The
assumption here is that consciousness (i.e. the logic of the
first-person) is derived from computation. It then follows that we
cannot ignore the possibility in principle of "building a computer"
that not only implements a UD but also runs it for long enough to
generate its infinite trace, UD* (incorporating, by the way, a
"fractal-like" infinity of such dovetailing). If denying such a
possibility on grounds of a lack of "primitively-physical" resources
is evasive, to deny it on grounds of a lack of "mathematical"
resources is surely merely incoherent.
But if we do not deny it, but rather embrace it, we can see that
such
a structure would inevitably dominate any "observational reality".
I don't see why that should follow at all, as long as there are
multiple infinite computations running rather than the UDA being
the only one, there's no particular reason why the UDA computation
should "dominate" in terms of its contribution to measure.
The UD computation, the one appearing at the step 7 or the "UD
Argument (UDA)". The UD is the complete set of the possible
executions of a universal machines, including an extreme
redundancies of those computations, and which does not depend on
the choice of the universal base chosen. To fix the thing I choose
either Robinson Arithmetic (Predicate logic + seven axioms, using
the non logical symbols s, 0, +, *.), or the combinators, using
only the parentheses, =, S, and K.
'formal provability" in those theories is Sigma_1 complete. By the
intensional Church Thesis, which follows from the usual extension
al one, that is equivalent with a universal dovetailing. They
instantiate it in arithmetic.
See my most recent post to Bruno at http://www.mail-archive.com/[email protected]/msg55617.html
, particularly this paragraph where I give a possible definition
for how one could define "physical measure":
'For example, say after N steps of the universal computation U, we
can count the number of times that some computation A has been
executed within it, and the number of times that another
computation B has been executed within it,
What would "some computation" be? To compare to experience we need
the relative measure of some event conditioned on our experiencing it.
I agree (you comment on Jesse here). I think Jess takes this into
account later.
As I understand it, in the UD this will be represented by infinitely
many threads of computation. Since the computation does not go to
completion the relative number of these threads compared to some
other event thread doesn't exist.
I am not sure you take into account the difference of the points of
view, and notably the 1p invariance for the delays introduced in the
UD*.
and take the ratio of these two numbers; if this ratio approaches
some limit in the limit as N goes to infinity, then this limit
ratio could be defined as the ratio of the "physical" measure of A
and B within the universe/multiverse. So if A and B are two
possible future observer-moments for my current observer moment
(say, an observer-moment finding itself in Washington and another
finding itself in Moscow in your thought-experiment), then the
ratio of their physical measure could be the subjective
probability that "I" will experience either one as my next-
observer moment.'
Not exactly, because this could lead to an equivocal of "[]p" (the
machine utters/believes p") and "[]p & p", the non really definable
the machine utters/believes-truly p, which obeys a different logic,
and structures the observer moments differently than the "third
person" machines.
The frequentist approach works locally in the normal worlds,
How do you get frequentist measures from the UD?
We need the right "projectors" and the logic of the yes-no observable,
to get the general statistics, indeed.
but for having the normal worlds to begin with,we must take into
account that the logic(s) is (are) constrained by the cognitive
ability of the machine; notably in perception and observation.
Would you say that even if we define "physical measure" this way,
and even if multiple infinite computations are running alongside
the UDA computation, for some reason the UDA computation will
dominate? Consider the situation I imagined in this paragraph of
the same post:
The UD, with Church thesis, defines the battle field where the
winners will win. The Z logics illustrate that the winner seems to
be quantum universal machine. If QM is correct, the Z logic might
explain why it has to be like that, and, by the
difference between Z and Z*, it would explain the qualia.
So are you simply assuming there is a "winner", i.e. that the
relevant statistics exist in the limit? Even if they do, it's not
clear that they exist for our experience which is not "in the limit".
Yes, it is. You keep forgetting that the 1p are invariant for the
delays of computation. That is why we have infinite sums below the
comp substitution level. That is why we expect some continuum and some
non computable things, hopeng for not too much white rabbits.
It seems that you are assuming something like "The probability of a
number being even is 1/2."
That makes sense, and is used in number theory. There are tuns of ways
to put probabilities on numbers, by notably relinquishing the sigma-
additivity. But it is of no use here, because the probabilities are
structured by self-reference, and the infinities involve in the
indeterminacies.
'Also note that even if we have two different candidates for the
"physical universe" computation, call them U and U',
Oops! I intepreted you "U" above by the running of the UD, or the
sigma_1 truth.
and even if both contain a never-ceasing universal dovetailer
computation within them, it seems to me this is not enough to
guarantee that U and U' will both assign the same physical measure
to any two computations A and B, if we use a procedure like the
one I outlined to define "physical measure". Even though U and U'
will both compute all the same programs eventually since they both
contain a universal dovetailer, some programs might be computed
more frequently (more copies have been run after N steps) in U
than in U'. For example, U might be a physical simulation of a
universe containing one physical computer that's computing the
universal dovetailer along with 1000 physical computers computing
copies of my brain experiencing being in Washington, while U'
might be a physical simulation of a universe containing one
physical computer that's computing the
universal dovetailer along with 1000 physical computers computing
copies of my brain experiencing being in Moscow.'
To be more specific, imagine that these 1000 other simulated
computers are running *infinite* iterations of the "me in
Washington" simulation--for example, first it could spawn a copy
of me arriving in Washington at 3 PM and simulate my 1st hour
experienced in Washington from 3 PM to 4 PM, then it could spawn a
newly-minted copy #2 of my brain and newly-minted copy of
Washington at 3 PM and re-simulate my brain's 1st hour in
Washington from 3 PM to 4 PM, then it could go back to copy #1 and
simulate its second hour in Washington, then it could simulate
copy #1's third hour, then it could simulate copy #2's second
hour, then it could spawn a new copy #3 and simulate its first
hour, and keep going this way following the same ordering that
Cantor used to order the rational numbers as shown at http://www.homeschoolmath.net/teaching/rationals-countable.gif
(with the numerator as the copy # and the denominator as the hour
#). Since such a computer is constantly simulating copies of me in
Washington, while the UDA is only very occasionally
This seems to rely on time as measured by number of steps of the UD;
which is quite different from experienced time.
I agree. I made the same answer, basically, to Jesse.
Does the measure of one's experience depend on the number of times
the UD computes that experience? I expect that is infinitely many
times, so there is the problem of taking the relative measure of
infinities; which have one-to-one maps to proper subsets.
simulating copies of me in Washington or Moscow between all the
other Turing machine programs it must simulate, then if I want to
compare the measure of "me experiencing Washington" vs. "me
experiencing Moscow", the contribution of the computers dedicated
solely to the "me experiencing Washington" should dwarf the
contribution of the UDA. At least that should be true if "physical
measure" is defined the way I suggested above, where you compare
how many copies of each program have been run so far after N steps
of the universal program U.
I don't think this comparison has a limit; i.e. it varies
arbitrarily between 0 and 1 as the UD runs.
Well, if you can prove that... (nice idea, but I am not sure). Anyway,
I take into account what machine can rationalize and bet from the very
fact that there are machine. people thinks it is trivial, but
incompleteness detrivialize this in the extreme, as it entails the
difference between all the points of view.
It will have some definite value after a finite number of steps N,
but those steps don't map into a contiguous interval of the
calculate (physical) time.
Of course. But I am not sure Jesse was implying that the physical
times could be linked in such direct way with the "UD-time".
Bruno
Brent
All Universal dovetailing will brought such U and U', but also
their counterparts. Such extravagance exists in all UD, you can't
beat them algorithmically.
But those sigma_1 sentences and proofs, are structured by the need
of machines to have a self-referential ability, and explore its
possible universal neighbors.
Bruno
Jesse
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