Hi Mark,

   Interleaving
----- Original Message ----- From: "Mark Buda" <her...@acm.org>
To: "Everything List" <everything-list@googlegroups.com>
Sent: Tuesday, January 12, 2010 10:25 PM
Subject: Re: the theory of everything?


On Jan 12, 5:51 pm, "Stephen Paul King" <stephe...@charter.net> wrote:
1) What is the cardinality of this infinite collection/set/class/whatever of
machines?

I believe that would have to be the cardinality of the continuum, but
I'm not entirely sure. Why does the cardinality matter?

***
[SPK]

It would seem to because there is a difference in the properties of the various infinities. I think that any infinity other than that of the integers, aleph_0, is such that any set that is not a proper subset has a measure of zero.In other words, "A set of points capable of being enclosed in intervals whose total length is arbitrarily small. " http://mathworld.wolfram.com/MeasureZero.html

   Your chance of picking it out of a pile is zero.

This is the case because in considering comptutations we are effectively treating numbers the same way that topologists and geometers treat points, thus the same rules and theorems apply.

See: http://en.wikipedia.org/wiki/Null_set and http://en.wikipedia.org/wiki/Lebesgue_measure
http://en.wikipedia.org/wiki/There_is_no_infinite-dimensional_Lebesgue_measure
http://planetmath.org/encyclopedia/AlephNumbers.html

   But there is, I think, a problem with the infinity of the integers.

How do we distinguish one subset of numbers, a string, from another unless there is a set of functions whose role is to map all of the numbers that generate the "same computation" to each other. The problem I see is where is the set of mapping functions encoded? Is it just another string of numbers itself and if so what keeps it from just being another computation itself. Maybe that's a good thing.

***
2) What measure is it that might be used to partition the set or class of
machines such that at least one subset of them can be identified as
corresponding to consciousness?

I don't know. They may all correspond to some kind of conscious
experience. (What is it like to be a rock?) The ones that correspond
to human consciousness are the ones that do not terminate or repeat.

****
[SPK]

We need some kind of measure to constider the abstract properies of these notions that we are playing with. ;) When we say that "the abstract immaterial computations are all that there is" we have to take the notion along with all of the logical implications and attachements. We firt see that there are more than one computation that could implement a rock. The same for any qualia. We use the notion of an equivalence class to gather together all of the computational strings that "implement the same computation". When we are trying to identify the content of consciouness to a computation, does it not make sense that there has to be some difference between the sub-computation (equivalence class) that *is* a tree and the sub-computation (equivalence class) that *is* a car? There would have to exists equivalence classes for any qualia up to and including the "experience of what it is like to be a bat" and "what it is like to be Buda", etc. Ok, so that implies that there is something that is different about each equivalence class of computations, thus there has to exist something that can be considered as a measure of the difference. If I recall correctly, information is a "difference that makes a differense" and computations, loosely, are transformation of sets/collections/etc. of information. So, we must have a measure to have a "difference".
***

3) How can we differentiate between Machines and not-Machines unless there
exists some measure to do so?

You've lost me here. What not-Machines are you talking about?

***
[SPK]

Would there not be strings that are purely noise or the computational equivalent: random number generators? These would only be "machines" in that sense but they do not have any notion of information associated with them, thus I consider them non-machines. Make sense?
***

4) How does mere existence of a Machine give any accounting for its
implementation?

I don't understand the question.

***
[SPK]

Existence is passive, it does nothing to inform in itself. We can use the presence or non-presence of a particular number in a particular position in a string to identify a state of the Platonic Turing machine tape or head, but the mere existence of a string or individual number that can represent that PTM does not inform the "happening" of the state. Its merely a passive identification. In a lightless room, does the color of the walls make any difference?

This is the difficulty that I have with Platonic Computational Idealism, try as hard as I might, I can not see how we can speak meaningfully of any notion that involves some form of chance when we have from the onset disallowed for its existence. Becoming can not obtain from pure Being. OTOH, its easy to get Being out of Becoming. Just figure out the fixed Points. http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29 Those subsets of Becoming that are invariant with respect to some other subset of Becoming. ;)

The big Problem I see is that there is no notion of a relationship between "numbers" and Becoming that is both unique and one-to-one and onto. We can quantify aspects of change with numbers....derivatives... My mind is decohereing...
***

5) Are you secretly attempting to construct a reductio ad absurdum proof?

Nope. I'm not secretly attempting to do anything. I am just trying to
understand the universe.
***

[SPK]

   Me too! And its fun. ;)

Onward!

Stephen
----- Original Message -----
From: "Mark Buda" <her...@acm.org>
To: "Everything List" <everything-list@googlegroups.com>
Sent: Tuesday, January 12, 2010 2:55 PM
Subject: Re: the theory of everything

snip

But the abstract immaterial computations are all that there is. There
is no machine, no physical universe, no nothing, without the
computations - the consciousnesses. And all of them "happen", and all
of them are equally real. Each of them is like the execution of a
universal Turing machine given a particular input tape. The initial
portion of the tape encodes some algorithm executed by the machine;
the rest of the tape serves as input to the machine (observations, in
the quantum mechanical sense).

Some (infinite) subset of these machines correspond to consciousnesses
that believe they are you. I am asserting that they, in fact, *are*
you. The first-person you, including your mind, body, and the entire
observable universe (as seen by you). That's why you can say "yes,
Doctor" and still continue - your consciousness was never really in
your body in the first place. Learning that as an infant was one of
the first mistakes you made, and one of the hardest to unlearn, but it
was necessary for you to be able to learn all the other stuff, the
important stuff, most of which you have yet to learn.

snip



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