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, 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, 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.
'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 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.
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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