from:"Hal"

Re: Mathematical Logic, Podnieks'page ...

2004-07-02 Thread Hal Ruhl

Hi Bruno:
The idea of my model is that the foundation system has two components one 
is inconsistent because it is complete - it contains all - and the other is 
incomplete - it is empty of all.

These two components can not join but the incomplete one must attempt to do 
so - leading to the creation of metaverses.

Hal
At 10:36 AM 7/2/2004, you wrote:
At 10:14 01/07/04 -0400, Hal Ruhl wrote:
Re the discussion on mathematical realism etc. I ask for comments on 
whether or not definition that is the division of ALL in to two parts 
is a mathematical process.

To me definition seems arbitrary but some definitions result in 
mathematical concepts such as the one I use which results in the concepts 
of incompleteness and inconsistency
From this I can infer you are not following classical or more general 
standard logic where inconsistent theories are trivially complete in the 
sense that *all* propositions are provable (all the true one + all the 
false one!).
This explains probably why it is hard to me to follow your post. I 
suggested to you (some years ago) to follow simpler paths, for pedagogical 
reasons. I read your posts but I have not yet a clue of what are your more 
primitive beliefs. You over-use (imo) analogies, which can be inspiring 
for some constructive path, but you don't seem to be able to realize the 
lack of clarity of your most interesting posts in that regards. I respect 
your willingness to try, and I hope my frankness will not discourage you.

Bruno
http://iridia.ulb.ac.be/~marchal/

Re: Mathematical Logic, Podnieks'page ...

2004-07-02 Thread Hal Ruhl

Hi Bruno:
By the way if some systems are complete and inconsistent will arithmetic be 
one of them?

As I understand it there are no perfect fundamental theories.  So if 
arithmetic ever becomes complete
then it will be inconsistent.  In the foundation system which I believe 
contains mathematics from the beginning arithmetic is complete so its 
inconsistent.

Hal

Re: Mathematical Logic, Podnieks'page ...

2004-07-06 Thread Hal Ruhl

Hi Bruno:
At 01:15 PM 7/2/2004, you wrote:
Hi Hal,
At 12:44 02/07/04 -0400, Hal Ruhl wrote:
By the way if some systems are complete and inconsistent will arithmetic 
be one of them?

As I understand it there are no perfect fundamental theories.  So if 
arithmetic ever becomes complete
then it will be inconsistent.

Yes, if by arithmetic you mean an axiomatic system, or a formal theory, 
or a machine.
No if by arithmetic you mean a set so big that you cannot define it
define appears to be a two sided activity.   When you define a thing you 
also define the thing which it is not - a bag of the remainder of 
all.  Most of the time the latter may not be useful.  Since all of 
arithmetic [and mathematics] is in the Everything and the Everything in my 
system is the definitional pair to the Nothing, defining the Nothing [or 
the Everything] automatically defines all of arithmetic along with all of 
mathematics.

A Something is less than the Everything and may or may not contain 
mathematics or a portion thereof.

in any formal theory,
Well my theory seems concerned with the form of its statements that is 
the Somethings and how they alter.

I think my theory defines mathematics the way that The first number that 
can not be described in less than fourteen words  defines a number that we 
nevertheless may never actually have in hand.

Hal

Re: ... cosmology? KNIGHT KNAVE

2004-07-27 Thread Hal Finney

I am confused about how belief works in this logical reasoner of type 1.
Suppose I am such a reasoner.  I can be thought of as a theorem-proving
machine who uses logic to draw conclusions from premises.  We can imagine
there is a numbered list of everything I believe and have concluded.
It starts with my premises and then I add to it with my conclusions.

In this case my premises might be:

1. Knights always tell the truth
2. Knaves always lie
3. Every native is either a knight or a knave
4. A native said, you will never believe I am a knight.


Now we can start drawing conclusions.  Let t be the proposition that
the native is a knight (and hence tells the truth).  Then 3 implies:

5. t or ~t

Point 4 leads to two conclusions:

6. t implies ~Bt
7. ~t implies Bt

Here I use ~ for not, and Bx for I believe x.  I am ignoring some
complexities involving the future tense of the word will but I think
that is OK.

However now I am confused.  How do I work with this letter B?  What kind
of rules does it follow?

I understand that Bx, I believe x, is merely a shorthand for saying that
x is on my list of premises/conclusions.  If I ever write down x on
my numbered list, I could also write down Bx and BBx and BBBx as far
as I feel like going.  Is this correct?

But what about the other direction?  From Bx, can I deduce x?  That's
pretty important for this puzzle.  If Bx merely is a shorthand for
saying that x is on my list, then it seems fair to say that if I ever
write down Bx I can also write down x.  But this seems too powerful.

So what are the correct rules that I, as a simple machine, can follow for
dealing with the letter B?

The problem is that the rules I proposed here lead to a contradiction.
If x implies Bx, then I can write down:

8. t implies Bt

Note, this does not mean that if he is a knight I believe it, but rather
that if I ever deduce he is a knight, I believe it, which is simply the
definition of believe in this context.

But 6 and 8 together mean that t implies a contradiction, hence I can conclude:

9. ~t

He is a knave.  7 then implies

10. Bt

I believe he is a knight.  And if Bx implies x, then:

11. t

and I have reached a contradiction with 9.

So I don't think I am doing this right.

Hal Finney

Re: regarding QM and infinite universes

2004-07-27 Thread Hal Finney

Danny Mayes writes:
First, regarding the idea of magical universes or quantum immortality
for that matter, doesn't this assume a truly infinite number of
universes? However, if you start with the idea that the reality we
experience is being created by a mechanical/computational process,
isn't it more likely that the number of universes is just extremely
large?Why should we assume the creator (however you choose to
define that) has access to infinite resources? Also, everything that
makes up our universe appears to have finite characteristics (per QM),
so it seems like every possibility within the parameters of the
multiverse could be covered by an enormous, but not infinite range of
possibility.

In some ways, infinity is a more plausible choice than some large number.
After all, what number will you pick? A billion? 1.693242 sextillion?
10 to the 10 to the 10... repeated precisely 142,857 times? Any such
number would be completely arbitrary. A fundamental theory about
the universe should not have such magical constants in it. The only
plausible numbers are 0, 1, and infinity. Maybe I'll throw in 2 if
I'm feeling generous. Since evidently it takes more than 2 bits of
information to create the universe, I think the simplest proposal is
that there are no limits.

I think we are overlooking something here. It seems like there should
be a quanta of probabilty, just as there is (apparently) with time,
space, and matter. In other words, once the probability of something
happening falls below a certain threshold, it is not realized. Could
there be a Planck scale of probability? Does decoherence somehow keep
these strange events from occurring on a macro scale?

It's possible. The concept of a special Planck scale is not part
of QM. It is an incomplete attempt to merge QM with general relativity.
Many physicists are coming to view our current attempts along these lines
as unpromising. See Lawrence Krauss' interview in the new Scientific
American,
http://www.sciam.com/article.cfm?chanID=sa006colID=1articleID=0009973A-D518-10FA-89FB83414B7F
.

We don't really know how it will work out, whether there are these kinds
of thresholds for matter or space or energy. But if it does, then I
suspect you are right and similar limits could exist for probability
as well. Sufficiently improbable events might not occur in the MWI
multiverse. (Of course there are other ways to get a multiverse.)

Hal Finney

Re: Does Omega point theory allow for an eternally self-creating universe?

2004-07-27 Thread Hal Finney

Danny Mayes writes:
 Assuming MWI is correct, and that Tipler's Omega point theory is correct 
 in that in at least some portion of the multiverse there will exist the 
 physical capacity for a computer to exist with infinite computing power, 
 even in the confines of a finite universe,  does this then allow for an 
 eternally self-recreating universe with no outside explanation necessary?

I think there are some problems with this, which I'll get to in a
moment.  But first it is good to keep in mind that current cosmological
observations contradict Tipler's predictions.  There is strong evidence
that the universal expansion is increasing and that there will be no
collapse and no Omega Point.

 Specifically, the question is whether the Omega point computer could 
 simulate the birth of a new, fully intact multiverse and run it through 
 to the creation of a new virtual omega point computer, that would then 
 continue the process in an endless cycle (or chain)?  Does one computer 
 with infinite computing power (and only a millisecond to exist from an 
 objective viewpoint) allow for this infinite layer of creation?  Does it 
 matter whether the multiverse itself is infinite or just very large?

I see a few problems with this.  First, the OP computer could in
fact simulate many universes, including those different from itself.
Perhaps it could even simulate all possible universes.  So its actions
don't go too far in explaining why it, itself, exists.

Second, if you study the details of the OP you learn that it is a
difficult time to live.  It is not a stable situation.  Life will grow
exponentially more difficult as the collapse intensifies.  At the same
time, life grows perhaps exponentially more powerful, so there would
be reason to hope that it could manage to survive forever.  However,
this is not assured.

In particular, there is no guarantee that the OP computation project
will be maintained forever.  The beings in charge of the computer might
change their minds and start using it to play video games.  Or survival
may become so challenging that they can't waste their time simulating all
possible universes, or even their own.

Keep in mind that even though it only takes a finite amount of time from
the outside, the appropriate time scale is the internal one, and that
one lasts forever.  The OP is the product of life and intelligence, and
for this model to work, these entities must live forever and run their
computer forever.  Literally, forever and ever and ever.  That's the only
way the philosophical model works.  Such stability seems inconsistent
with the nature of life and intelligence as we know it.

Third, it's not clear how exactly this explanation works.  If the
universe is real, it doesn't need to simulate itself in order to exist.
If it isn't real, the fact that it simulates itself doesn't seem like
enough to bring it into existence.  I can imagine no end of universes
that simulate themselves, in fact most of them would have a much easier
time of it than the OP beings struggling with their chaotic collapse.
Does that mean they are all just as real as our universe would be, if
the OP's simulations were what made us real?

In fact among the simplest of such self-simulating universes is Bruno's
Universal Dovetailer, a trivial program which runs all programs
(including, by definition, itself).  If the OP brings itself into
existence, so does the UD, which is much simpler.  And the UD then makes
us exist along with all other universes, whether the OP turns out to be
cosmologically plausible or not.

Hal Finney

Re: ... cosmology? KNIGHT KNAVE

2004-07-28 Thread Hal Finney

This is confusing because I believe p has two different meanings.
One is that I have written down p with a number in front of it,
as one of my theorems.  The other meaning is the string Bp.

But that string only has meaning from the perspective of an outside
observer.  To me, as the machine, it is just a pair of letters.  B doesn't
have to mean believe.  It could mean Belachen, which is German for
believe.

All I need to know, as a formal system, is what rules the letter B
follows.

Bruno wrote:

 At 09:54 27/07/04 -0700, Hal Finney wrote:
 If I ever write down x on
 my numbered list, I could also write down Bx and BBx and BBBx as far
 as I feel like going.  Is this correct?

 Well, not necessarily. Unless you are a normal machine, which
 I hope you are!
 So let us accept the following definition: a machine is normal when,
 if it ever assert x, it will sooner or later asserts Bx.
 Normality is a form of self-awareness: when the machine believes x,
 it will believe Bx, that is it will believe that it will believe x.


 But what about the other direction?  From Bx, can I deduce x?  That's
 pretty important for this puzzle.  If Bx merely is a shorthand for
 saying that x is on my list, then it seems fair to say that if I ever
 write down Bx I can also write down x.  But this seems too powerful.

 You are right. It is powerful, but rather fair also.
 let us define a machine to be stable if that is the case. When the
 machine believes Bx the machine believes x.

So in my terms, I can add two axioms:

0a. x implies Bx
0b. Bx implies x

The first is the axiom of normality, and the second is the axiom of
stability.  I don't find these words to be particularly appropriate,
by the way, but I suppose they are traditional.

It also seems to me that these axioms, which define the behavior of
the letter B, don't particularly well represent the concept of belief.
The problem is that beliefs can be uncertain and don't follow the law
of the excluded middle.  If p is that there is life on Mars, then (p or
~p) is true.  Either there's life there or there isn't.  But it's not
true that (Bp or B~p).  It's not the case that either I believe there
is life on Mars or I believe there is no life on Mars.  The truth is,
I don't believe either way.

But axioms 0a and 0b let me conclude (Bp or B~p).  Obviously they
collectively imply p if and only if Bp.  Therefore from (p or ~p)
we can immediately get (Bp or B~p).  Hence for normal people, the law
of the excluded middle applies to beliefs.

This proof is pure logic and has no dependence on the meaning of B.
If B is Belachen, I have showed that if p implies Belachen(p), then
it follows that (Belachen(p) or Belachen(~p)) is true.  That's all.

It's a step outside the system to say that B follows rules which make it
appropriate for us to treat it as meaning believes.  But do 0a. and
0b. really capture the meaning of belief?  I question that.  B looks
more like an identity operator under those axioms.

 The problem is that the rules I proposed here lead to a contradiction.
 If x implies Bx, then I can write down:
 
 8. t implies Bt
 
 Note, this does not mean that if he is a knight I believe it, but rather
 that if I ever deduce he is a knight, I believe it, which is simply the
 definition of believe in this context.


 Here you are mistaken. It is funny because you clearly see
 the mistake, given that you say 'attention  (t implies Bt) does
 not mean if he is a knight the I believe it. But of course (t implies Bt)
 *does* mean if he is a knight the I believe it.

I don't see this.  To me as the machine, there is no meaning.  I am just
playing with letters.  t implies Bt is only a shorthand for if he is a
knight then B(if he is a knight).  There is no more meaning than that.
The letter B is just a letter that follows certain rules.

We only get meaning from outside, when we look at what the machine is
doing and try to relate the way the rules work to concepts in the real
world.  It is at this point that we bring in the interpretation of Bx as
the machine believes x.

Suppose for some proposition q the machine deduces it on step 117:

117. q

Does this mean that q is true?  No, it means that that the machine
believes q.  Does it mean that Bq is true?  Yes.  Bq is true, because Bq
is a shorthand for saying that the machine believes q, and by definition
the machine believes something when it writes it down in its numbered
list.  We can see it right there, number 117.  So the machine believes
q and Bq is true.  But q is not (necessarily) true.  The machine writing
something down does not mean it is true.  By definition, it means the
machine believes it.

Consider a different example:

191. Bp

What does this mean?  Does it mean that Bp is true?  No, it means that the
machine believes Bp, because by definition, what the machine writes down
in its numbered list is what it believes.  Is BBp true?  Yes, it is true,
because that says that the machine believes Bp, and that means that Bp

Re: Omega Point theory and time quanta

2004-08-01 Thread Hal Finney

 difficulties implied
by quantum theory, and a wildly unlikely theory becomes that much less
plausible.

Then of course there is the new problem that the Big Crunch no longer
is a plausible outcome, tossing Tipler's theories into the trash.

In short, while the Omega Point theory was an interesting speculation
on how infinite computation might be possible in a universe based on
General Relativity, it was never very plausible and is much less so now.

Hal Finney

Re: Djinni vs. White Rabbit

2004-08-19 Thread Hal Finney

. previously-discussed 
 Champernowne machine / everything algorithm.)  But what if the 
 dynamics of the simulation are such that these jinni exist as a priori 
 structural parameters, roots if you will of the computation?  In such 
 an environment, every computable universe is NOT every possible 
 universe.

It sounds like you are suggesting that it would be simpler to suppose
that all universes exist which contain jinn than all universes exist.
That doesn't seem at all plausble to me.  My heuristic is that any rule
of the form all universes exist except X is going to be more complicated
than one of the form all universes exist.

Hal Finney

Re: Errata (for the origin of physical laws)

2004-09-24 Thread Hal Ruhl

I once saw a quote attributed to Niels Bohr to the effect that an expert is 
a person who has made all the mistakes its possible to make in a narrow 
field of endeavor.

Hal
At 07:11 AM 9/24/2004, you wrote:
The curious and amusing thing is that in FU, Smullyan
call that error the beginners error (page 46).
It consists in believing that the formula (a- -b)  (a - b) is
a contradiction, where actually the formula is true in case a is false.
A simpler example is (p- -p). This is true for p false.
What is curious and amusing is that Smullyan made that very error
page 42 (of the first edition, and it is wrongly corrected in the second
edition). Can you see it.
Morality: consistent machines *can* be inconsistent,
as any Loebian machine believes (-Bf - -B- Bf).
Well; that is neither a justification nor a consolation ...
At 12:26 23/09/04 +0200, Bruno Marchal wrote:
Hi,
In the second paragraph of the physics and sensations section
of my paper the origin of physical laws and sensations I made
a rather stupid error (what a shame!).
Indeed I say Note that neither G nor G* does prove it
[where it is for Bp - -B-p]. This is ridiculous, because
G* proves Bp-p, for any p, and thus G* proves B-p - -p,
and thus (by contraposition) G* proves p--B-p, and by
propositional calculus Bp--B-p.
Worst, my justification was that Bf-B-f  (where f = false).
This is correct, but I infer from that that Bf--B-f is not provable by G*.
But G* proves both Bf-B-f and Bf--B-f, that is Bf-f.
The error has no consequences for the rest of the paper, but
still, why did I wrote that???
Please, don't hesitate to ask ANY questions, so that perhaps
other errors will be single out.
You can also propose more general
critics. Don't be shy. (You can also ask questions about FU).
http://iridia.ulb.ac.be/~marchal/

Re: S, B, and a puzzle by Boolos, Smullyan, McCarthy

2004-10-11 Thread Hal Finney

 And here is another puzzle, which is not entirely
 unrelated with both the KK puzzles and the current probability
 discussion: I put three cards, two aces and a jack, on their
 face in a row. By using only one yes-no question and pointing
 one of the card, you must with certainty find one of the aces.
 I know where the cards are, and if you point on a ace, I will
 answer truthfully (like a knight), but if you point on the jack, I
 will answer completely randomly!
 How will you proceed?   (The puzzle is one invented by Boolos,
 as a subpuzzle of a harder one by Smullyan  McCarthy.
 Cf Boolos'  book Logic, logic, and logic. According to
 Boolos, it illustrates something nice about the practical
 importance of the excluded middle principle. And this is
 a hint, perhaps.)

Although it is true that if you point at a Jack the answer doesn't give
you any information, you don't really need much info in that case as
you know that the other two cards are Aces.  As long as you are going to
finally choose a card different than the one you point at, any mistaken
info you get from the Jack won't hurt you.  You need to come up with
a question which will work when you are pointing at an Ace, and which
will lead to you choosing another card.

For example, point at the card at one end and ask Is the card on the
other end an Ace?  If he says yes, choose that card on the other end,
and if he says no, choose the middle card.  This of course works if you
are pointing at an Ace because he will tell the truth, and if you are
pointing at a Jack it will work because both other cards are Aces.

Hal Finney

RE: Observation selection effects

2004-10-02 Thread Hal Finney

Stathis Papaioannou writes:
 Here is another example which makes this point. You arrive before two 
 adjacent closed doors, A and B. You know that behind one door is a room 
 containing 1000 people, while behind the other door is a room containing 
 only 10 people, but you don't know which door is which. You toss a coin to 
 decide which door you will open (heads=A, tails=B), and then enter into the 
 corresponding room. The room is dark, so you don't know which room you are 
 now in until you turn on the light. At the point just before the light goes 
 on, do you have any reason to think you are more likely to be in one room 
 rather than the other? By analogy with the Bostrom traffic lane example you 
 could argue that, in the absence of any empirical data, you are much more 
 likely to now be a member of the large population than the small population. 
 However, this cannot be right, because you tossed a coin, and you are thus 
 equally likely to find yourself in either room when the light goes on.

Again the problem is that you are not a typical member of the room unless
the mechanism you used to choose a room was the same as what everyone
else did.  And your description is not consistent with that.

Suppose we modify it so that you are handed a biased coin, a coin which
will come up heads or tails with 99% vs 1% probability.  You know about
the bias but you don't know which way the bias is.  You flip the coin
and walk into the room.  Now, I think you will agree that you have a
good reason to expect that when you turn on the light, you will be in
the more crowded room.  You are now a typical member of the room so the
same considerations that make one room more crowded make it more likely
that you are in that room.

This illustrates another problem with the lane-changing example, which
is that the described mechanism for choosing lanes (choose at random)
is not typical.  Most people don't flip a coin to choose the lane they
will drive in.  Instead, they have an expectation of which lane they will
start in based on their long experience of driving in various conditions.
It's pretty hard to think of yourself as a typical driver given the wide
range of personality, age and experience among drivers on the road.

Hal Finney

Re: Observation selection effects

2004-10-08 Thread Hal Finney

Stathis Papaioannou writes:
 Hal Finney writes:
 Not to detract from your main point, but I want to point out that
 sometimes there is ambiguity about how to count worlds, for example in
 the many worlds interpretation of QM.  There are many examples of QM
 based world-counting which seem to show that in most worlds, probability
 theory should fail.

 I'm not sure what examples you have in mind here,

The specific kind of example goes like this.  Suppose you take a
vertically polarized photon and pass it through a polarizer that is
tilted slightly from the vertical.  Quantum mechanics predicts that
there is a high chance, say 99%, that the photon will pass through,
and a low chance, 1%, that it will not make it and be absorbed.

Now, the many worlds interpretation can be read to say that the universe
splits into two when this experiment occurs.  There are two possible
outcomes: either it passes through or it is absorbed.  So there are two
universes corresponding to the two results.

However, the universes are not of equal probability, according to QM.
One should be observed 99% of the time and the other only 1% of the
time.

The discrepancy gets worse if we imagine repeating the experiment multiple
times.  Each time the multiverse splits again in two.  If we did it, say,
20 times, there would be 2^20 or about 1 million universes.  In only
one of those universes did the photon take the 99% chance each time,
yet that is the expected result.  By a counting argument, the chance
of getting that result is only one in a million since only one world
out of a million sees it.  This is the apparent contradiction between
the probability predictions of orthodox quantum mechanics and the MWI,
assuming that we count worlds in this way.


 but this is actually the 
 general point I was trying to make: probability theory doesn't seem to work 
 the same way in a many worlds cosmology, due to complications such as 
 observers multiplying and then not being able to access the entire 
 probability space after the event of interest.

 Consider these three examples:

 (A) In a single world cosmology, I claim that using my magic powers, I have 
 bestowed on you, and you alone, the ability to pick the winning numbers in 
 this week's lottery. If you then buy a lottery ticket and win the first 
 prize, I think it would be reasonable to concede that there was probably 
 some substance to my claim (if not magic powers, then at least an effective 
 way of cheating).

 (B) In a single world cosmology, I announce that using my magic powers, I 
 have bestowed on some lucky gambler the ability to pick the winning numbers 
 in this week's lottery. Now, someone does in fact win the first prize this 
 week, but that is not surprising, because there is almost always at least 
 one winner each week. I cannot reasonably claim to have helped the winner 
 unless I had somehow tagged him or otherwise uniquely identified him before 
 the lottery was drawn, as in (A).

 (C) In a many worlds cosmology, I seek you out as in (A) and make the same 
 claim about bestowing on you the ability to pick the winning numbers in this 
 week's lottery. You buy a ticket, and win first prize. Should you thank me 
 for helping you win, as in (A)? In general, no; this situation is actually 
 more closely analogous to (B) than to (A). For it is certain that at least 
 one future version of you will win, just as it is very likely that at least 
 one person will win in the single world example. I can only claim that I 
 helped you win if I somehow identified which version in which world is going 
 to win before the lottery is drawn, and that is impossible.

I'm afraid I don't agree with the conclusion in (C).  I definitely should
thank you.  To see this, let's make my thanks a little more sincere,
in the form of a payment.  Suppose I agree in advance to pay you $1000
if you succeed in helping me win the lottery.  I say that is a wise
decision on my part.  It doesn't cost me anything if you don't help,
and if you do have some way of rigging the lottery then I can easily
afford to pay you this modest sum out of my winnings.

But I think your reasoning suggests that it is unwise, since I will win
anyway, so why should I pay anything to you?  I don't need to thank you
in this way.  Do you agree that this follows from your reasoning?

Hal Finney

An All/Nothing multiverse model

2004-11-13 Thread Hal Ruhl

I would appreciate comments on the following.
Proposal: The Existence of our and other universes and their dynamics are 
the result of unavoidable definition and logical incompleteness.

Justification:
1) Given definitions 1, 2, and 3:
2) These definitions are interdependent because you can not have one 
without the whole set.

3) Notice that Defining is the same as establishing a boundary between 
what a thing is and what it is not.  This defines a second thing: the is 
not.  A thing can not be defined in isolation.

4) These definitions are unavoidable because at least one of the [All, 
Nothing] pair must exist.  Since they form an [is, is not] pair they 
bootstrap each other into existence.

5) The Nothing has a logical problem: since it is empty of concept it can 
not answer any meaningful question about itself including the unavoidable 
one of its own stability.

6) To answer this unavoidable question the Nothing must at some point 
penetrate the boundary between itself and the All in an attempt to 
complete itself.  This could be viewed as a spontaneous symmetry breaking.

7) However, the boundary is permanent as required by the definitions and a 
Nothing remains.

8) Thus the penetration process repeats in an always was and always will 
be manner.

8) The boundary penetration produces a shock wave [a boundary] that moves 
into the All as the old example of Nothing tries to complete itself.  This 
divides the All into two evolving Somethings - evolving 
multiverses.  Notice that half the multiverses are contracting - loosing 
concepts.

9) Notice that the All also has a logical problem.  Looking at the same 
meaningful question of its own stability it contains all possible answers 
because just one would constitute a selection i.e. net internal information 
which is not an aspect of the complete conceptual ensemble content of the 
All.   Thus the All is internally inconsistent.

10) Thus the motion of a shock wave boundary in the All must be consistent 
with this inconsistency - That is the motion is at least partly random.

11) Some of these evolving Somethings - multiverses will admit being 
modeled as a computer computation but with true noise - definition 5.

Definitions:
1) The All: The complete conceptual ensemble (including the concept of 
itself).  Some concepts and collections of concepts may or may not have a 
separate physical reality.

2) The Nothing: That which is empty of all concepts.
3) The Everything: That which contains the All and separates it from the 
Nothing.  Thus it also contains the Nothing.

4 A Something: A division of the All into two subparts.
5) True noise: The random content of the evolution of the Somethings 
introduces random information into each component of a multiverse from a 
source external to that component.

Hal

RE: An All/Nothing multiverse model

2004-11-13 Thread Hal Ruhl

Sorry, I placed the definitions at the end of my post for easy group 
reference and forgot to mention it.

Hal

RE: An All/Nothing multiverse model

2004-11-13 Thread Hal Ruhl

[The whole post]:
I would appreciate comments on the following.
I placed the definitions at the end for easy group reference.
Proposal: The Existence of our and other universes and their dynamics are 
the result of unavoidable definition and logical incompleteness.

Justification:
1) Given definitions 1, 2, and 3:
2) These definitions are interdependent because you can not have one 
without the whole set.

3) Notice that Defining is the same as establishing a boundary between 
what a thing is and what it is not.  This defines a second thing: the is 
not.  A thing can not be defined in isolation.

4) These definitions are unavoidable because at least one of the [All, 
Nothing] pair must exist.  Since they form an [is, is not] pair they 
bootstrap each other into existence.

5) The Nothing has a logical problem: since it is empty of concept it can 
not answer any meaningful question about itself including the unavoidable 
one of its own stability.

6) To answer this unavoidable question the Nothing must at some point 
penetrate the boundary between itself and the All in an attempt to 
complete itself.  This could be viewed as a spontaneous symmetry breaking.

7) However, the boundary is permanent as required by the definitions and a 
Nothing remains.

8) Thus the penetration process repeats in an always was and always will 
be manner.

8) The boundary penetration produces a shock wave [a boundary] that moves 
into the All as the old example of Nothing tries to complete itself.  This 
divides the All into two evolving Somethings - evolving 
multiverses.  Notice that half the multiverses are contracting - loosing 
concepts.

9) Notice that the All also has a logical problem.  Looking at the same 
meaningful question of its own stability it contains all possible answers 
because just one would constitute a selection i.e. net internal information 
which is not an aspect of the complete conceptual ensemble content of the 
All.   Thus the All is internally inconsistent.

10) Thus the motion of a shock wave boundary in the All must be consistent 
with this inconsistency - That is the motion is at least partly random.

11) Some of these evolving Somethings - multiverses will admit being 
modeled as a computer computation but with true noise - definition 5.

Definitions:
1) The All: The complete conceptual ensemble (including the concept of 
itself).  Some concepts and collections of concepts may or may not have a 
separate physical reality.

2) The Nothing: That which is empty of all concepts.
3) The Everything: That which contains the All and separates it from the 
Nothing.  Thus it also contains the Nothing.

4) A Something: A division of the All into two subparts.
5) True noise: The random content of the evolution of the Somethings 
introduces random information into each component of a multiverse from a 
source external to that component.

Hal

Re: Who believe in Concepts ? (Was: An All/Nothing multiverse model)

2004-11-14 Thread Hal Ruhl

At 07:56 AM 11/14/2004, you wrote:
Hal Ruhl wrote:

I would appreciate comments on the following.
I placed the definitions at the end for easy group reference.
Proposal: The Existence of our and other universes and their dynamics are 
the result of unavoidable definition and logical incompleteness.
Justification:
1) Given definitions 1, 2, and 3: [see original post]
I have already a problem here. It might not be specific to this proposal
but this is a good opportunity to raise the question.
Defintion 1 and everything that follows depends in a strong way of the
concept of concept and on strong properties of that concept (like the
possibilty to discrimate what is a concept from what is not and to gather
all concepts in a set/ensemble/collection with a consistent meaning).
Perhaps I could find a more neutral word or define what I mean by concept.
Please note however that the complete ensemble can not be consistent - 
after all it contains a completed arithmetic.  Generally smaller sets can 
not prove their own consistency.

snip

Let's assume nothingness exists. Therefore something (nothingness) exists.
That is one of my points if one replaces your nothingness with my 
nothing and your something with my All.

Any definition defines two entities simultaneously.  Generally but not 
necessarily the smaller of the two entities is the one about which the 
definition says: This entity is:.  The definition creates a boundary 
between this entity and a second entity which is all that the first is 
not.  Most of the second entities may have no apparent usefulness but 
usefulness of an entity is not relevant.


Therefore nothingness doesn't exist.
Not at all.  One can not define a something without simultaneously 
defining a nothing and vice versa.

That is the usually unnoticed aspect of the definitional process.  This 
leads you to the exclusionary statement below.

That's why there's something rather than noting.
To the contrary both exist if either does.
Hal

< 1 2 3 4 5 6 7 >

501 - 600 of 644 matches

Mail list logo