Hi Jason,
I snipped the portion of the thread out to cut of the tail... Interleaving
in Blue.
I am also interested to hear what Bruno has to say. My perspective is that
>> most of the computations that support you and I are not isolated and
>> short-lived "computational Boltzmann brains" but much larger, long-running
>> computations such as those that correspond to a universe in which life
>> adapts and evolves.
>>
>
> I agree. I have never been happy with the Boltzman brain argument because
> it seems to assume that the probability distribution of "spontaneous" BBs
> is independent of the complexity of the content of the minds associated
> with those brains. I have been studying this relationship between
> complexity or "expressiveness" of a B.B. My first guesstimation is that
> there is something like a Zift's Law in the distribution: the more
> expressive a BB the less chance it has to exist and evolve at least one
> "cycle" of its computation. (After all, computers have to be able to run
> one clock cycle to be said that they actually "compute" some program...)
>
>
>
>> The starting conditions for these is much less constrained, and
>> therefore it is far more probable to result in conscious computations such
>> as ours than the case where the computation supporting your brain
>> experiencing this moment is some initial condition of a very specific
>> program. Certainly, those programs exist too, but they are much rarer.
>>
>
> RIght, but how fast do they get rarer?
>
It's hard to say. We would have to develop some model for estimating the
Kolmogorov complexity (and maybe also incorporate frequency) of different
programs and their relation to a given mind.
{spk} Do you have an candidate "toy models" of a mind that would work? What
can be constructed following Bruno's idea of an observer: an intersection
of infinitely many computations (of finite length?)
Would any "universal number do"? Isn't a Universal number always at max
Kolmogorov entropy? If we add arbitrary prefixes to a Universal number,
does it remain "Universal"?
>
>
>
>
>> They appear in the UD much less frequently than say the program
>> corresponding to the approximate laws of physics of this universe.
>>
>
> It takes far more data to describe your brain than it does to describe
>> the physical system on which it is based.
>>
>
>
> How do you estimate this?
>
The UDA is a comparatively short program, and provably contains the program
that is identical to your mind. Similarly, all of the known laws of
physics could fit on a couple sheets of paper. QM seems to suggest that
all possible solutions to certain equations exist, and so there is no need
to specify the initial conditions of the universe (which would require much
more information to describe than your brain).
{spk} Sure! Any finite program will be "smaller" an an infinite one! LOL.
But I am skeptical of the claim that even if it exists, finding it is HARD.
If you don't actually have a means to implement it on a physical machine
what good is an existential proof of it in some theory?
This is why I often wonder if this entire conversation exercise in
futility! :_( What does it really mean to say that a mind is a finite
program when such has measure zero in the Reals (which is where we should
embed the NxN->N idea in the first place. I loath Kronecker's claim! It is
synonymous to "Man is the measure of all things".
> Are you assuming that a lot of data can be compressed using symmetries and
> redundancies. This looks like a Kolmogorov complexity/entropy...
>
>
Somewhat. I think how frequently a program is referenced / instantiated by
other non-halting programs may play a role.
{spk} Like citations or Friending. LOL, nice! But what prevents such a
scheme from being regular, generating a complete graph with a homogeneous
connectedness or a purely random connectedness?
Real world networks are, at best, "small
world<http://en.wikipedia.org/wiki/Small-world_network>"
on average and thus are far different from what we expect from our
considerations of ensembles of NxN->N strings.
http://en.wikipedia.org/wiki/Small-world_network
"A *small-world network* is a type of mathematical
graph<http://en.wikipedia.org/wiki/Graph_(mathematics)>
in which most nodes are not neighbors of one another, but most nodes can
be reached from every other by a small number of hops or steps.
Specifically, a small-world network is defined to be a network where the
typical distance *L* between two randomly chosen nodes (the number of steps
required) grows proportionally to the logarithm of the number of nodes *N* in
the network, that
is:[1]<http://en.wikipedia.org/wiki/Small-world_network#cite_note-1>
[image: L \propto \log N]
>
>
>>
>> So we are (mostly) still "in the same universe", and so we can interact
>> with and affect the consciousness of other people.
>>
>
>
> From my reasoning, the appearance that we are "in the same universe" is a
> by product of bisimilarities in the infinity of computations that are each
> of us. In other words, there are many computations that are running
> Stephen that are identical to and thus are the same computation to many of
> the computations that are running Jason.
>
Yes. We would be programs instantiated within a (possibly but not
necessarily) shared, larger program.
{spk} So we get the UD at the end of the day thinking that way?.
> This gives an overlap between our worlds and thus the appearance of a
> common world for some collection of "observers".
>
Right.
> The cool thing is that this implies that there are underlaps; computations
> that are not shared or bisimilar between all of us.
>
Yes, I agree. In some branches of the MW, perhaps you were born but I was
not, or I was, and you weren't.
{spk} I am wanting to think of this as a massive constraint scheme. The
interaction of any one observer limits the possible interactions with
other observers. This limits the total set of set of possible interactions
for all observers all the way down to only a few possible interactions are
allowed for all observers if they are interacting.
> COuld those be the ones that we identify as "ourselves"?
>
>
>
Personal identity can become a very difficult subject, since there may be
paths through which my program evolves to become you, and vice versa.
{spk} I agree and this implies that in a deep way, we are one and the same
observer! Deciding the path that connects a pair of observers, I think, is
equivalent to computing the smooth diffeomorphism between the pair of
manifolds that each experiences as a "world".
On Fri, Dec 27, 2013 at 7:56 PM, Jason Resch <jasonre...@gmail.com> wrote:
>
>
>
> On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King <
> stephe...@provensecure.com> wrote:
>
>> Dear Jason,
>>
>> Interleaving below.
>>
>>
>> On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch <jasonre...@gmail.com>wrote:
>>
>>>
>>>
>>>
>>> On Fri, Dec 27, 2013 at 6:03 PM, LizR <lizj...@gmail.com> wrote:
>>>
>>>> On 28 December 2013 11:55, Stephen Paul King <
>>>> stephe...@provensecure.com> wrote:
>>>>
>>>>> Hi LizR,
>>>>>
>>>>> That is what is not explicitly explained! I could see how one might
>>>>> make an argument based on Godel numbers and a choice of a numbering scheme
>>>>> could show the existence of a string of numbers that, if run on some
>>>>> computer, would generate a description of the interaction of several
>>>>> actors. But this ignores the problems of concurrency and "point of view".
>>>>> The best one might be able to do, AFAIK, is cook up a description of the
>>>>> interactions of many "observers" -each one is an intersection of
>>>>> infinitely
>>>>> many computations, but such a description would itself be the content of
>>>>> some observer's point of view that assumes a choice of Godel numbering
>>>>> scheme.
>>>>> Something doesn't seem right about this!
>>>>>
>>>>> It seems to suggest "multi-solipsism" or something along those lines -
>>>> which doesn't make it wrong, of course.
>>>>
>>>> I await Bruno's answer with interest. I think he has already said
>>>> something about this, but I don't recall it being satisfactory, at least to
>>>> my limited understanding.
>>>>
>>>
>>> I am also interested to hear what Bruno has to say. My perspective is
>>> that most of the computations that support you and I are not isolated and
>>> short-lived "computational Boltzmann brains" but much larger, long-running
>>> computations such as those that correspond to a universe in which life
>>> adapts and evolves.
>>>
>>
>> I agree. I have never been happy with the Boltzman brain argument because
>> it seems to assume that the probability distribution of "spontaneous" BBs
>> is independent of the complexity of the content of the minds associated
>> with those brains. I have been studying this relationship between
>> complexity or "expressiveness" of a B.B. My first guesstimation is that
>> there is something like a Zift's Law in the distribution: the more
>> expressive a BB the less chance it has to exist and evolve at least one
>> "cycle" of its computation. (After all, computers have to be able to run
>> one clock cycle to be said that they actually "compute" some program...)
>>
>>
>>
>>> The starting conditions for these is much less constrained, and
>>> therefore it is far more probable to result in conscious computations such
>>> as ours than the case where the computation supporting your brain
>>> experiencing this moment is some initial condition of a very specific
>>> program. Certainly, those programs exist too, but they are much rarer.
>>>
>>
>> RIght, but how fast do they get rarer?
>>
>
> It's hard to say. We would have to develop some model for estimating the
> Kolmogorov complexity (and maybe also incorporate frequency) of different
> programs and their relation to a given mind.
>
>
>>
>>
>>
>>
>>> They appear in the UD much less frequently than say the program
>>> corresponding to the approximate laws of physics of this universe.
>>>
>>
>> It takes far more data to describe your brain than it does to describe
>>> the physical system on which it is based.
>>>
>>
>>
>> How do you estimate this?
>>
>
> The UDA is a comparatively short program, and provably contains the
> program that is identical to your mind. Similarly, all of the known laws
> of physics could fit on a couple sheets of paper. QM seems to suggest that
> all possible solutions to certain equations exist, and so there is no need
> to specify the initial conditions of the universe (which would require much
> more information to describe than your brain).
>
>
>> Are you assuming that a lot of data can be compressed using symmetries
>> and redundancies. This looks like a Kolmogorov complexity/entropy...
>>
>>
> Somewhat. I think how frequently a program is referenced / instantiated by
> other non-halting programs may play a role.
>
>
>>
>>
>>>
>>> So we are (mostly) still "in the same universe", and so we can interact
>>> with and affect the consciousness of other people.
>>>
>>
>>
>> From my reasoning, the appearance that we are "in the same universe" is
>> a by product of bisimilarities in the infinity of computations that are
>> each of us. In other words, there are many computations that are running
>> Stephen that are identical to and thus are the same computation to many of
>> the computations that are running Jason.
>>
>
> Yes. We would be programs instantiated within a (possibly but not
> necessarily) shared, larger program.
>
>
>> This gives an overlap between our worlds and thus the appearance of a
>> common world for some collection of "observers".
>>
>
> Right.
>
>
>> The cool thing is that this implies that there are underlaps;
>> computations that are not shared or bisimilar between all of us.
>>
>
> Yes, I agree. In some branches of the MW, perhaps you were born but I was
> not, or I was, and you weren't.
>
>
>> COuld those be the ones that we identify as "ourselves"?
>>
>>
>>
>
> Personal identity can become a very difficult subject, since there may be
> paths through which my program evolves to become you, and vice versa.
>
> Jason
>
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--
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