. Will
catch up hopefully soon.
Best wishes
John M
- Original Message -
From: Hal Finney [EMAIL PROTECTED]
To: everything-list@eskimo.com
Sent: Tuesday, June 14, 2005 7:41 PM
Subject: Re: White Rabbit vs. Tegmark
PROTECTED]
To: Hal Finney [EMAIL PROTECTED]
Cc: everything-list@eskimo.com
Sent: Tuesday, May 24, 2005 2:45 AM
Subject: Re: White Rabbit vs. Tegmark
John Mikes wrote:
... Those posts were accessible (for me) that started with a
statement of the writer and not a lot of copies with some reply-lines
interjected. I know (and like to use) to copy the phrases to reply to but
even in a 2-week archiving it turns sour. After the first 30-40
Jonathan Colvin writes:
That's rather the million-dollar question, isn't it? But isn't the
multiverse limited in what axioms or predicates can be assumed? For
instance, can't we assume that in no universe in Platonia can (P AND ~P) be
an axiom or predicate?
No, I'd say that you could indeed
- Original Message -
From: Hal Finney [EMAIL PROTECTED]
To: everything-list@eskimo.com
Sent: 27 May 2005 19:19
Subject: RE: White Rabbit vs. Tegmark
.
.
To summarize, logic is not a property of universes. It is a tool that
our minds use to understand the world, including possible
Le 27-mai-05, à 20:19, Hal Finney a écrit :
Brent Meeker writes:
I doubt that the concept of logically possible has any absolute
meaning. It
is relative to which axioms and predicates are assumed.
I agree but that is the reason why if we want to talk *about* or to
find measure *on*
Hal:
To summarize, logic is not a property of universes. It is a
tool that our minds use to understand the world, including
possible universes.
We may fail to think clearly or consistently or logically
about what can and cannot exist, but that doesn't change the
world out there.
Brent: I doubt that the concept of logically possible has any
absolute meaning. It is relative to which axioms and
predicates are assumed.
That's rather the million-dollar question, isn't it? But isn't the
multiverse limited in what axioms or predicates can be assumed? For
instance,
Hi Jonathan,
Should we not expect Platonia to be Complete?
Stephen
- Original Message -
From: Jonathan Colvin [EMAIL PROTECTED]
To: 'Everything-List' everything-list@eskimo.com
Sent: Saturday, May 28, 2005 1:30 PM
Subject: RE: White Rabbit vs. Tegmark
Brent: I doubt
Stephen: Should we not expect Platonia to be Complete?
I'd like to think that it should not be (by Godel?); or that it is not
completely self-computable in finite meta-time. Or some such. But that's
more of a faith than a theory.
Jonathan Colvin
Brent: I doubt that the concept of
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
To: Brent Meeker [EMAIL PROTECTED]
Cc: Everything-List everything-list@eskimo.com
Sent: 26 May 2005 19:54
Subject: RE: White Rabbit vs. Tegmark
.
.
.
* But the arbitrariness of the measure itself becomes the main argument
against
Le 26-mai-05, à 18:03, Hal Finney a écrit :
One problem with the UD is that the probability that an integer is even
is not 1/2, and that it is prime is not zero. Probabilities in general
will not equal those defined based on limits as in the earlier
paragraph.
It's not clear which is the
Bruno Marchal writes:
Le 26-mai-05, à 18:03, Hal Finney a écrit :
One problem with the UD is that the probability that an integer is even
is not 1/2, and that it is prime is not zero. Probabilities in general
will not equal those defined based on limits as in the earlier
paragraph.
-Original Message-
From: Alastair Malcolm [mailto:[EMAIL PROTECTED]
Sent: Friday, May 27, 2005 8:53 AM
To: Patrick Leahy
Cc: Everything-List
Subject: Re: White Rabbit vs. Tegmark
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
To: Brent Meeker [EMAIL PROTECTED]
Cc
Brent Meeker writes:
I doubt that the concept of logically possible has any absolute meaning. It
is relative to which axioms and predicates are assumed. Not long ago the
quantum weirdness of Bell's theorem, or special relativity would have been
declared logically impossible. Is it logically
I don't see what practical difference there is between saying all universes
exist and we need to think with logical consistency about the subject and all
logically possible universes exist.
Whatever the case, a related point might be worth considering: whether logic
is the only such invariant
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
To: Alastair Malcolm [EMAIL PROTECTED]
Cc: EverythingList everything-list@eskimo.com
Sent: 24 May 2005 22:10
Subject: Re: White Rabbit vs. Tegmark
.
[Patrick:]
This is very reminiscent of Lewis' argument. Have you read his
On Thu, 26 May 2005, Alastair Malcolm wrote:
An example occurs which might be of help. Let us say that the physics of
the universe is such that in the Milky Way galaxy, carbon-based SAS's
outnumber silicon-based SAS's by a trillion to one. Wouldn't we say that
the inhabitants of that galaxy
On Thu, May 26, 2005 at 11:20:35AM +0100, Patrick Leahy wrote:
A measure like this works for the continuum but not for the naturals
because you can map the continuum onto a finite segment of the real line.
In m6511 Russell Standish describes how a measure can be applied to the
naturals
Paddy Leahy writes:
For the continuum you can restore order by specifying a measure which just
*defines* what fraction of real numbers between 0 1 you consider to lie
in any interval. For instance the obvious uniform measure is that there
are the same number between 0.1 and 0.2 as between
On Thu, 26 May 2005, Brent Meeker wrote:
I agree with all you say. But note that the case of finite sets is not
really any different. You still have to define a measure. It may seem
that there is one, compelling, natural measure - but that's just
Laplace's principle of indifference
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
To: Alastair Malcolm [EMAIL PROTECTED]
Cc: EverythingList everything-list@eskimo.com
Sent: 26 May 2005 11:20
Subject: Re: White Rabbit vs. Tegmark
On Thu, 26 May 2005, Alastair Malcolm wrote:
An example occurs which might
On Thu, May 26, 2005 at 07:54:03PM +0100, Patrick Leahy wrote:
* Since the White Rabbit^** argument implicitly assumes a measure, as it
stands it can't be definitive.
* But the arbitrariness of the measure itself becomes the main argument
against the everything thesis, since the main
On Wed, 25 May 2005, Stathis Papaioannou wrote:
SNIP
Consider these two parallel arguments using a version of the anthropic
principle:
(a) In the multiverse, those worlds which have physical laws and
constants very different to what we are used to may greatly predominate.
However, it is no
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
To: Alastair Malcolm [EMAIL PROTECTED]
Cc: EverythingList everything-list@eskimo.com
Sent: 24 May 2005 22:10
Subject: Re: White Rabbit vs. Tegmark
.
.
This is very reminiscent of Lewis' argument. Have you read his book? IIRC
he
Stathis: I don't know if you can make a sharp distinction between the
really weird universes where observers never evolve and the
slightly weird ones where talking white rabbits appear now
and then. Consider these two parallel arguments using a
version of the anthropic principle:
(a)
Paddy writes
Stathis Papaioannou wrote:
(b) In the multiverse, those worlds in which it is a frequent occurrence
that the laws of physics are temporarily suspended so that, for example,
talking white rabbits materialise out of thin air, may greatly
predominate. However, it is no
On Mon, May 23, 2005 at 06:03:32PM -0700, Hal Finney wrote:
Paddy Leahy writes:
Oops, mea culpa. I said that wrong. What I meant was, what is the
cardinality of the data needed to specify *one* continuous function of the
continuum. E.g. for constant functions it is blatantly aleph-null.
Remember that Wolfram assumes a 1-1 correspondence between
consciousness and physical activity, which, as you, I have refuted (or
I pretend I have refuted, if you prefer).
the comp hyp predicts physical laws must be as complex as the solution
of the measure problem. In that sense, the apparent
Le 24-mai-05, à 01:10, Patrick Leahy a écrit :
On Mon, 23 May 2005, Hal Finney wrote:
I've overlooked until now the fact that mathematical physics
restricts
itself to (almost-everywhere) differentiable functions of the
continuum.
What is the cardinality of the set of such functions? I
Le 24-mai-05, à 00:17, Patrick Leahy a écrit :
On Mon, 23 May 2005, Bruno Marchal wrote:
SNIP>
Concerning the white rabbits, I don't see how Tegmark could even address the problem given that it is a measure problem with respect to the many computational histories. I don't even remember if
Russell writes
You've got me digging out my copy of Kreyszig Intro to Functional
Analysis. It turns out that the set of continuous functions on an
interval C[a,b] form a vector space. By application of Zorn's lemma
(or equivalently the axiom of choice), every vector space has what is
called
Lee Corbin writes:
Russell writes
You've got me digging out my copy of Kreyszig Intro to Functional
Analysis. It turns out that the set of continuous functions on an
interval C[a,b] form a vector space. By application of Zorn's lemma
(or equivalently the axiom of choice), every vector
Perhaps I can throw in a few thoughts here, partly in the hope I may learn
something from possible replies (or lack thereof!).
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
Sent: 23 May 2005 00:03
.
.
A very similar argument (rubbish universes) was put forward long ago
On Tue, 24 May 2005, Alastair Malcolm wrote:
Perhaps I can throw in a few thoughts here, partly in the hope I may learn
something from possible replies (or lack thereof!).
- Original Message -
From: Patrick Leahy [EMAIL PROTECTED]
Sent: 23 May 2005 00:03
.
SNIP
This is not a
Le 23-mai-05, à 06:09, Russell Standish a écrit :
On Mon, May 23, 2005 at 04:00:39AM +0100, Patrick Leahy wrote:
Hmm, my lack of a pure maths background may be getting me into trouble
here. What about real numbers? Do you need an infinite axiomatic
system to
handle them? Because it seems
On Sun, 22 May 2005, Hal Finney wrote:
Regarding the nature of Tegmark's mathematical objects, I found some
old discussion on the list, a debate between me and Russell Standish,
in which Russell argued that Tegmark's objects should be understood as
formal systems, while I claimed that they
Hi Patrick,
Sorry for having been short, especially on those notions for which some
background of logic is needed.
Unfortunately I have not really the time to explain with all the
nuances needed.
Nevertheless the fact that reals are simpler to axiomatize than natural
numbers should be a
On Mon, 23 May 2005, Bruno Marchal wrote:
SNIP
Concerning the white rabbits, I don't see how Tegmark could even address the
problem given that it is a measure problem with respect to the many
computational histories. I don't even remember if Tegmark is aware of any
measure relating the
Paddy Leahy writes:
Let's suppose with Wei Dai that a measure can be applied to Tegmark's
everything. It certainly can to the set of UTM programs as per Schmidhuber
and related proposals. Obviously it is possible to assign a measure which
solves the White Rabbit problem, such as the UP.
On Mon, May 23, 2005 at 11:17:04PM +0100, Patrick Leahy wrote:
And another mathematical query for you or anyone on the list:
I've overlooked until now the fact that mathematical physics restricts
itself to (almost-everywhere) differentiable functions of the continuum.
What is the
Paddy Leahy writes:
Oops, mea culpa. I said that wrong. What I meant was, what is the
cardinality of the data needed to specify *one* continuous function of the
continuum. E.g. for constant functions it is blatantly aleph-null.
Similarly for any function expressible as a finite-length
Without getting into a long hurrang, I think that Tegmark is correct, at least
in part. Briefly, there has to be a reason why these alternate worlds exist.
I'm referring to the Everett-Wheeler hypothesis and not just wishful thinking.
Granted, if I remember correctly, Tegmark does deal with the
On Mon, May 23, 2005 at 12:03:55AM +0100, Patrick Leahy wrote:
...
A very similar argument (rubbish universes) was put forward long ago
against David Lewis's modal realism, and is discussed in his On the
plurality of worlds. As I understand it, Lewis's defence was that there
is no measure
fight, so until I see
something about his theory that is simply untenable, I'll let it slide.
- Original Message -
From: Russell Standish
To: Patrick Leahy
Subject: Re: White Rabbit vs. Tegmark
Date: Mon, 23 May 2005 09:47:22 +1000
On Mon, May 23, 2005 at 12:03:55AM +0100, Patrick
On Mon, 23 May 2005, Russell Standish wrote:
I think most of us concluded that Tegmark's thesis is somewhat
ambiguous. One interpretation of it that both myself and Bruno tend
to make is that it is the set of finite axiomatic systems (finite sets
of axioms, and recusively enumerated
Patrick Leahy writes:
Sure enough, you came up with my objection years ago, in the form of the
White Rabbit paradox. Since usage is a bit vague, I'll briefly re-state
it here. The problem is that worlds which are law-like, that is which
behave roughly as if there are physical laws but not
Regarding the nature of Tegmark's mathematical objects, I found some
old discussion on the list, a debate between me and Russell Standish,
in which Russell argued that Tegmark's objects should be understood as
formal systems, while I claimed that they should be seen more as pure
Platonic objects
On Mon, May 23, 2005 at 04:00:39AM +0100, Patrick Leahy wrote:
Hmm, my lack of a pure maths background may be getting me into trouble
here. What about real numbers? Do you need an infinite axiomatic system to
handle them? Because it seems to me that your ensemble of digital strings
is
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