> On 25 Sep 2019, at 14:15, Alan Grayson <[email protected]> wrote:
>
>
>
> On Wednesday, September 25, 2019 at 5:26:21 AM UTC-6, Bruno Marchal wrote:
>
>> On 24 Sep 2019, at 14:55, Alan Grayson <[email protected] <javascript:>>
>> wrote:
>>
>>
>>
>> On Tuesday, September 24, 2019 at 6:38:50 AM UTC-6, Bruno Marchal wrote:
>>
>>> On 23 Sep 2019, at 13:11, Alan Grayson <[email protected] <>> wrote:
>>>> <snip>
>>>> Stathis Papaioannou
>>>>
>>>> What I have shown is that it's hypothetically possible to have countable
>>>> universes wherein there are no repeats, no exact copies. AG
>>>
>>> It is a theorem, about *all* universal machinery phi_i that all programs
>>> repeat, with different codings.
>>>
>>> For all i there is a j such that i ≠ j, and for all x phi_j(x) = phi_i(x).
>>> That is obvious for a programmer, you can always add spurious instructions,
>>> for example.
>>>
>>> So, in the arithmetical reality (which is Turing universal) then if you can
>>> survive with a digital brain, you survive in all infinitely many
>>> computations which extends your current experiences.
>>> There is arguably a non countable set of (infinite!) computational
>>> extension, but at all time, a brain or a machine cannot distinguish more
>>> than a finite or countable states.
>>>
>>> Bruno
>>>
>>> If you have a countable set of programs, none of which can calculate an
>>> irrational number, how could they produce copies of everything? They have
>>> no contact with a set so large. AG
>>
>> First, the UD does compute many irrational numbers, like sqrt(2), PI, e,
>> etc. Those are computable real number, in the sense that an galorothm can
>> generate all decimals.
>>
>> But then you forget the first person indeterminacy, and the step 4 of the
>> UDA. The consciousness of the emulated entities cannot be aware of any
>> delay, and so will fork on a non computable set of “stream”, given by the
>> program dovetailing on all initial sequence of all (Turing) Oracles.
>>
>> I cannot generate one precise non-computable real number, but I can generate
>> them all. The following path illustrates this:
>>
>> 0
>> 1
>>
>> 00
>> 01
>> 10
>> 11
>>
>> 000
>> 001
>> 010
>> 011
>> 100
>> 101
>> 110
>> 111
>>
>> Etc.
>>
>> This generate each infinite sequence of 0 and 1, including all non
>> computable real numbers, in the limit, and as the machine cannot be aware of
>> the delays of “reconstitution’ in the universal dovetailing, their first
>> person indeterminacy domain is not countable.
>>
>> Bruno
>>
>> Because irrational numbers have non repeating decimal representations, they
>> can't be exactly calculated by any finite process. Period! AG
>
> OK, but that is not the standard definition of “computable” for a real
> number. Basically, a real number is computable if we have an algorithm to
> generate all its decimal (and actually we ask a bit more but I do not want
> enter in the details).
>
> Computable real number are represented in arithmetic by the code of total
> computable functions (the set of such code can be shown to be NOT computable).
>
> ??? Can you elaborate? AG
A total computable function from N to N is a function which is defined, and
computable, on each of its argument (total = everywhere defined). You can
represent a real number r by the code (the program, the digital machine, the
combinator, …, or their “Gödel number” description) of the total computable
function which on n gives the nth decimal of r, or first nth decimals of that
number. PI would be the (computable) function {(0, 3), (1, 1), (2, 4), (3,
1),(4, 5) …}, or {(0, 3), (1, 31), (2, 314), (3, 3141), (4, 31415), …)}.
>
> With your definition, only finite function and set would be computable, and
> that would make the notion of computability trivial.
>
>
> You agreed on a related thread that "most" real numbers are NOT computable
> since we don't have mathematical representations of them, unlike the case
> with PI. I think that set is dense in the reals with the cardinality of the
> continuum.
OK.
> My point was to suggest another problem with your version of the MWI; the
> severe restriction of what worlds are possible under the arithmetic MW
> scenario. AG
The restriction is not severe, much less than with “Digital Physics” where
people suppose that the physical universe is the result of one computation. The
universal dovetailer dovetails on all computations, including the computations
which need an Oracle (a non computable real number), by dovetailing on all
initial segment of that real numbers.
Imagine that Planck Constant is a non computable real number, and that it is
needed to emulate a human, then the universal dovetailer will still be able to
emulate such a human, as it will emulate the human (assumed to be Turing
emulable) on all initial segment of the Planck constant. The emulation will be
wrong on all oracle different of Planck Constant, but still correct on the one
thread where the subject got the correct decimal.
Oh, I see you say also:
>> I cannot generate one precise non-computable real number, but I can generate
>> them all.
>
>
> No. This you definitely NOT do. AG
Yes, I can, and this without naming the numbers or getting a code for each one.
Imagine that there is a non computable real number 0, 01000110111101100010111….
(In binary, and I will limit myself on the open interval ( 0 1 ).
Its first decimal is certainly among 0 and 1, so, I get the correct initial
segment among
0,0. (here!)
0,1
Its second decimal is certainly among 0 and 1, so, I get it among
0,00
0,01. (here!)
0,10
0,11
The third decimal is certainly among 0 and 1, so I get it among
0,000
0,001
0,010. (here!)
0,011
0,100
0,101
0,110
0,111
Etc. As the universal dovetailer never stops, it generates all real numbers. If
a guy is duplicated along the lines, at the start he can predict with
near-certainty that he will get white noise, although a (countable) infinities
of guy will assess getting a computable “recognisable” real number, like the
(binary) digits of PI, or of sqrt(7), but their measure will be negligible.
Now, the universal dovetailer dovetail on all computation, with all inputs and
all Oracle/stream. A priori it makes too much histories and too much “apparent
universes”. This is solved by the auto-refterential constraints inherited by
the fact that we assume the observer’s mind/consciousness to be determined by a
local program. At each step of the universal dovetailing the observer is
multiplied on an infinity of computations (step 3 and step 4 are needed, and
step 7) which realise local consistent extensions, and the logic of their
accessible realities is determined by the logic of the self-referential modes
(mainly, to get physics, []p, []p & p, []p & <>p, []p & <>t & p, with p being a
sigma_1 sentence, which corresponds to the partial computable possible events.
But for this you need a bit of theoretical computer science and mathematical
logic.
With mechanism, you have the arithmetical (sigma_1) reality, which is an
arithmetical universal dovetailing. By its emulation of all digital machines,
together with the first person indeterminacy, this generates a consciousness
flux, which differentiates (through different inputs/oracle). By the first
person invariance delays, the “physical appearance” are the one where the
histories get relatively rare, and get multiplies by large cardinal. They have
to be deep (in a sense made mathematical by Bennett), but that is provided by
the natural depth of the universal dovetailing itself.
The logics of physics can be tested with Nature, but we can also see that
Everett-Feynman presentation of physics already look like a mean to evacuate
explosions of histories. Feynman phase randomisation really looks like a clever
way to make consciousness focusing on shortest paths, like Nature.
This approach has the advantage that we can exploit incompleteness and
Solovay’s theorems (the logic G and G*) to distinguish the sharable laws of
verifiable and sharable physics, but also sharable laws on the non communicable
physical measurement, i.e. the qualia (which was the goal).
Bruno
>
> --
> 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]
> <mailto:[email protected]>.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/everything-list/67d32f3f-0ba5-4f5e-8450-6505c363c4ea%40googlegroups.com
>
> <https://groups.google.com/d/msgid/everything-list/67d32f3f-0ba5-4f5e-8450-6505c363c4ea%40googlegroups.com?utm_medium=email&utm_source=footer>.
--
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 view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/208DEF2D-27AC-47E1-96CC-4B3685AAF0D5%40ulb.ac.be.
