[Laurence Payne]

On 5 Sep 2006 13:40:05 -0700, wrote:

It would not contain the substring that enumerates pi, I suspect.

Why not? What would exclude it from being included?

Well, unless we're back to different sorts of infinite... :_)

[Laurence Payne]

On Tue, 05 Sep 2006 13:44:40 -0700, Bob Cain
wrote:

Can't quite see how your answer applies to the question. Seems like a
yes or no would, however. Anyway, I really meant to ask: will an
infinite random string contain all possible _finite_ sub-strings?

And must an infinite universe contain all imaginable objects? What
about un-imaginable ones? And impossible ones? (Before you start,
you KNOW curved space etc. are just cop-out arguments :-)

[Bob Cain]

Laurence Payne wrote:
On Tue, 05 Sep 2006 13:44:40 -0700, Bob Cain
wrote:

Can't quite see how your answer applies to the question. Seems like a
yes or no would, however. Anyway, I really meant to ask: will an
infinite random string contain all possible _finite_ sub-strings?

And must an infinite universe contain all imaginable objects? What
about un-imaginable ones? And impossible ones?

You got ahead of me. :-)

It does indeed seem to be the same question as whether or not all
possible quantum states of any finite volume must exist in an infinite
universe. If so, and if this one is infinite (which I don't yet
subscribe to), then all the mystery about how something as utterly
improbable as what we are immersed in could have happened. It did
because, however improbable, it was obviously a possibility and that's
all that is required.

Now, back to your regularly scheduled whatever before mother steps in
to slap my naughty fingers.

(Before you start,
you KNOW curved space etc. are just cop-out arguments :-)

:-)


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein

[Dirk Bruere at NeoPax]

Bob Cain wrote:
Laurence Payne wrote:
On Tue, 05 Sep 2006 13:44:40 -0700, Bob Cain
wrote:

Can't quite see how your answer applies to the question. Seems like a
yes or no would, however. Anyway, I really meant to ask: will an
infinite random string contain all possible _finite_ sub-strings?
And must an infinite universe contain all imaginable objects? What
about un-imaginable ones? And impossible ones?

You got ahead of me. :-)

It does indeed seem to be the same question as whether or not all
possible quantum states of any finite volume must exist in an infinite
universe. If so, and if this one is infinite (which I don't yet
subscribe to), then all the mystery about how something as utterly
improbable as what we are immersed in could have happened. It did
because, however improbable, it was obviously a possibility and that's
all that is required.

Now, back to your regularly scheduled whatever before mother steps in
to slap my naughty fingers.

(Before you start,
you KNOW curved space etc. are just cop-out arguments :-)

:-)


Bob

All Universes Hypothesis
http://space.mit.edu/home/tegmark/toe_frames.html

This is also very interesting
http://www.cs.umaine.edu/~chaitin/lm.html

FFF
Dirk

--
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[David Carter]

Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26 letters!
How do you know the next character wasn't going to be "s"? Or "2"?
Then it wouldn't be "the alphabet". And the series is either as he
defined,
or it's not. I already stated that any seemingly non random sequence
could
be part of an infinite random sequence. That sequence would *not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite strings that
do not seem at all random. In fact, it contains infinitely many strings
that, if used as a computer program, would generate the universe and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although it
wasnt stated, I assumed we were talking about real integers.

Carter

[Mr.T]

"Bob Cain" wrote in message
...
Will an infinite random string contain all possible sub-strings?

Maths doesn't allow you to divide one infinity by another - they
aren't equivalent.

Can't quite see how your answer applies to the question. Seems like a
yes or no would, however. Anyway, I really meant to ask: will an
infinite random string contain all possible _finite_ sub-strings?

In that case the answer is yes, because given a finite string length, there
must be a finite number of unique combinations.

MrT.

[Mr.T]

"Bob Cain" wrote in message
...
Laurence Payne wrote:
On Tue, 05 Sep 2006 13:44:40 -0700, Bob Cain
wrote:

Can't quite see how your answer applies to the question. Seems like a
yes or no would, however. Anyway, I really meant to ask: will an
infinite random string contain all possible _finite_ sub-strings?

And must an infinite universe contain all imaginable objects? What
about un-imaginable ones? And impossible ones?

You got ahead of me. :-)

It does indeed seem to be the same question as whether or not all
possible quantum states of any finite volume must exist in an infinite
universe. If so, and if this one is infinite (which I don't yet
subscribe to), then all the mystery about how something as utterly
improbable as what we are immersed in could have happened. It did
because, however improbable, it was obviously a possibility and that's
all that is required.

Sounds like Douglas Adams infinite probability drive :-)

MrT.

[Bob Cain]

Dirk Bruere at NeoPax wrote:
Bob Cain wrote:

All Universes Hypothesis
http://space.mit.edu/home/tegmark/toe_frames.html

That about covers it. :-) Great link, thanks.

This is also very interesting
http://www.cs.umaine.edu/~chaitin/lm.html

I used to work at Watson and just walking by Chaitin's office made my
brain hurt. I have a couple of his books but am saving them for
retirement.


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein

[Dirk Bruere at NeoPax]

Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Bob Cain wrote:

All Universes Hypothesis
http://space.mit.edu/home/tegmark/toe_frames.html

That about covers it. :-) Great link, thanks.

This is also very interesting
http://www.cs.umaine.edu/~chaitin/lm.html

I used to work at Watson and just walking by Chaitin's office made my
brain hurt. I have a couple of his books but am saving them for
retirement.


Bob

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[Dirk Bruere at NeoPax]

David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26 letters!
How do you know the next character wasn't going to be "s"? Or "2"?
Then it wouldn't be "the alphabet". And the series is either as he
defined,
or it's not. I already stated that any seemingly non random sequence
could
be part of an infinite random sequence. That sequence would *not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite strings
that
do not seem at all random. In fact, it contains infinitely many
strings
that, if used as a computer program, would generate the universe and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although it
wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).

--
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[[email protected]]

Dirk Bruere at NeoPax wrote:
Or any other non-rational numbers. Nor i for that matter. Although it
wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).

Yes, well the keyword here is "arbitrary." The design specs
for such a computer would be:

"Simulates universe when instruction code = pi."

This "arbitrary" machine need have only a single operand. Think
of the machine language programming manual:

OPERANDS

Mnemonic: PI
Opcode: 3.1415926535....
Description: simulates universe

Yep, that'll do it, for sure!

Be a bitch to build it though.

It'd be a lot easier just to let some quantum process
tunnel in a false vacuum, hit inflation, and the rest, as
we will eventually be heard to say 20 billion years
hence, will be history.

[David Carter]

Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26 letters!
How do you know the next character wasn't going to be "s"? Or
"2"?
Then it wouldn't be "the alphabet". And the series is either as he
defined,
or it's not. I already stated that any seemingly non random sequence
could
be part of an infinite random sequence. That sequence would *not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite strings
that
do not seem at all random. In fact, it contains infinitely many
strings
that, if used as a computer program, would generate the universe and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although it
wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).



Well in a way you are right though it cannot simulate the universe, it
does describe the relationship between the circumference of a circle and
the centre. in this respect it can be held as a symbol fr creation.

The Divine name ALHIM which characterises the difference between
Chockmah and Binah can also represent Pi.

Carter

[Dirk Bruere at NeoPax]

David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26
letters!
How do you know the next character wasn't going to be "s"? Or
"2"?
Then it wouldn't be "the alphabet". And the series is either as he
defined,
or it's not. I already stated that any seemingly non random
sequence
could
be part of an infinite random sequence. That sequence would
*not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite
strings that
do not seem at all random. In fact, it contains infinitely many
strings
that, if used as a computer program, would generate the universe and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although it
wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).



Well in a way you are right though it cannot simulate the universe, it
does describe the relationship between the circumference of a circle and
the centre. in this respect it can be held as a symbol fr creation.

The Divine name ALHIM which characterises the difference between
Chockmah and Binah can also represent Pi.

Pi (which is infinite in extent) and passes most tests for randomness.
Therefore it may well contain a long but finite sequence which, used as
machine code, would simulate the entire visible (finite) universe.

Infinity is BIG, especially at the fat end, even though it starts off
small...

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[David Carter]

Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in
message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26
letters!
How do you know the next character wasn't going to be "s"?
Or "2"?
Then it wouldn't be "the alphabet". And the series is either as he
defined,
or it's not. I already stated that any seemingly non random
sequence
could
be part of an infinite random sequence. That sequence would
*not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite
strings that
do not seem at all random. In fact, it contains infinitely many
strings
that, if used as a computer program, would generate the universe
and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although
it wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).



Well in a way you are right though it cannot simulate the universe, it
does describe the relationship between the circumference of a circle
and the centre. in this respect it can be held as a symbol fr creation.

The Divine name ALHIM which characterises the difference between
Chockmah and Binah can also represent Pi.

Pi (which is infinite in extent) and passes most tests for randomness.
Therefore it may well contain a long but finite sequence which, used as
machine code, would simulate the entire visible (finite) universe.

Infinity is BIG, especially at the fat end, even though it starts off
small...

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Sure, this is reminiscent of the monkeys in a junkyard. A reasonable
theory but of little value. I prefer to take the value I can get.

Carter

[Dirk Bruere at NeoPax]

David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Dirk Bruere at NeoPax wrote:
David Carter wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Mr.T wrote:
"Laurence Payne" lpayne1NOSPAM@dslDOTpipexDOTcom wrote in
message
...
On Mon, 4 Sep 2006 18:16:19 +1000, "Mr.T" MrT@home wrote:

If "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y ,z" is
random how
is it made any less random by being compressed to:
"the alphabet".
It isn't even slightly random at all, it repeats every 26
letters!
How do you know the next character wasn't going to be "s"?
Or "2"?
Then it wouldn't be "the alphabet". And the series is either
as he
defined,
or it's not. I already stated that any seemingly non random
sequence
could
be part of an infinite random sequence. That sequence would
*not* be
"compressed to the alphabet" though.
True.
And an infinite string will contain infinitely many finite
strings that
do not seem at all random. In fact, it contains infinitely many
strings
that, if used as a computer program, would generate the
universe and
ourselves in full virtual reality.


Will an infinite random string contain all possible sub-strings?


Bob


Would it? Set theory suggests it would - no?

It would not contain the substring that enumerates pi, I suspect.

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Or any other non-rational numbers. Nor i for that matter. Although
it wasnt stated, I assumed we were talking about real integers.

I rather like the idea that Pi embodies the code that simulates the
universe (if run on an arbitrary, rather fast, machine).



Well in a way you are right though it cannot simulate the universe,
it does describe the relationship between the circumference of a
circle and the centre. in this respect it can be held as a symbol fr
creation.

The Divine name ALHIM which characterises the difference between
Chockmah and Binah can also represent Pi.

Pi (which is infinite in extent) and passes most tests for randomness.
Therefore it may well contain a long but finite sequence which, used
as machine code, would simulate the entire visible (finite) universe.

Infinity is BIG, especially at the fat end, even though it starts off
small...

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM


Sure, this is reminiscent of the monkeys in a junkyard. A reasonable
theory but of little value. I prefer to take the value I can get.

The 'monkeys in a junkyard' question is quite amenable to a statistical
analysis. And the odds are finite, which means Pi contains infinitely
many monkeys operating forever.

--
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[Bob Cain]

Dirk Bruere at NeoPax wrote:

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.

How does AUH address the former rather than the latter?


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein

[Dirk Bruere at NeoPax]

Bob Cain wrote:
Dirk Bruere at NeoPax wrote:

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.

How does AUH address the former rather than the latter?

Well, one of the constraints that must be imposed on the selection of
all possible universes is conditions for intelligent life to perceive
them. So there is obviously an anthropic selection effect for starters.

For example, simple 'triangle universes' would not be complex enough to
give rise to intelligence.

--
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[Randy Yates]

Dirk Bruere at NeoPax writes:
[...]
Pi ... is infinite in extent ...

Not in base pi. In base pi, pi = 1.
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

[Bob Cain]

Dirk Bruere at NeoPax wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.

How does AUH address the former rather than the latter?

Well, one of the constraints that must be imposed on the selection of
all possible universes is conditions for intelligent life to perceive
them. So there is obviously an anthropic selection effect for starters.

I was remaining within what Tegmark calls Level I. He says that with
inflation (which requires infinite extent as it is formulated) and
quantum fluctuation there are bound to be instances and repeats of
this or any possible quantum state of a Hubble volume within the Level
I universe. The only constraints that are imposed at Level I are the
values we see for the fundamental constants. Level I assumes that the
universe is isotropic in that regard. Since we live in a
demonstration of an adequate state, it was inevitable. That may be
what the "strong" anthropic principle requires, I don't remember.

As I read Tegmark, there is no need at all for anthropic selection
since, one way or another, all possible states are "explored"
(redundantly) even at Level I. Selection implies a narrowing,
inflation implies the opposite.

BTW, thanks again for that link.

For example, simple 'triangle universes' would not be complex enough to
give rise to intelligence.

Whooosh again. :-)


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein

[Dirk Bruere at NeoPax]

Randy Yates wrote:
Dirk Bruere at NeoPax writes:
[...]
Pi ... is infinite in extent ...

Not in base pi. In base pi, pi = 1.

Then 1 is infinite in extent.

--
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[Dirk Bruere at NeoPax]

Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.
How does AUH address the former rather than the latter?
Well, one of the constraints that must be imposed on the selection of
all possible universes is conditions for intelligent life to perceive
them. So there is obviously an anthropic selection effect for starters.

I was remaining within what Tegmark calls Level I. He says that with
inflation (which requires infinite extent as it is formulated) and
quantum fluctuation there are bound to be instances and repeats of
this or any possible quantum state of a Hubble volume within the Level
I universe. The only constraints that are imposed at Level I are the
values we see for the fundamental constants. Level I assumes that the
universe is isotropic in that regard. Since we live in a
demonstration of an adequate state, it was inevitable. That may be
what the "strong" anthropic principle requires, I don't remember.

As I read Tegmark, there is no need at all for anthropic selection
since, one way or another, all possible states are "explored"
(redundantly) even at Level I. Selection implies a narrowing,
inflation implies the opposite.

BTW, thanks again for that link.

For example, simple 'triangle universes' would not be complex enough to
give rise to intelligence.

Whooosh again. :-)

If Tegmark is correct, then there are an infinite number of versions of
this universe, and it starts to look a bit like the Many Worlds
Interpretation (but is apparently unrelated).

FFF
Dirk

http://www.onetribe.me.uk/ - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM

[Randy Yates]

Dirk Bruere at NeoPax writes:

Randy Yates wrote:
Dirk Bruere at NeoPax writes:
[...]
Pi ... is infinite in extent ...
Not in base pi. In base pi, pi = 1.

Then 1 is infinite in extent.

cake, eat.
--
% Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven.
%% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and
%%% 919-577-9882 % Verdi's always creepin' from her room."
%%%% % "Rockaria", *A New World Record*, ELO
http://home.earthlink.net/~yatescr

[[email protected]]

Randy Yates wrote:
Dirk Bruere at NeoPax writes:
[...]
Pi ... is infinite in extent ...

Not in base pi. In base pi, pi = 1.

Which is a VERY good point. It demonstrates that pi
itself is NOT 'infinite in extent," it's merely that the
REPRESENTATION of pi that result through our choice
of a particular symbol-based system is incoveniently
large. We universally chose a represntation, or a
"modeling" system, if you will, based on a power-of-ten
hierarchy which can represent many values exactly, but
which can only represent some approximately. That's
not a property of those few values, per se, but a property
of the symbol system we chose to represent it. Randy
quite validly points to a symbol system which can, with
great compactness, represnet pi precisely, but one that
fails to represent, say, integers with perfect accuracy.

In a similar vein, it is not possible to represent fractional
values in binary notations if they are not based on appropriate
powers of 2. The decimal value of 1/10 cannot be represent
accurately by a finite string of binary digits, while 10 can.
10, for example, is imply the sum of 2^3 + 2^1 (8+2), but
try doing the same for 1/10: It's smaller than 1/8, bigger
that 1/16, so it must be a sum of 1/16 and smaller
fractions. Unfortunately, it takes an infinite series of
reciprocal power-of-two fractions to precisely equal
1/10.

1/16 + 1/32 = 3/32 = 0.09375, 6% low,

1/16 + 1/32 + 1/64 = 7/64 = 0.109375, 9% high

1/16 + 1/32 + 1/128 = 13/128 = .1015625, 1% high

1/16 + 1/32 +1/256 = 25/256 = 0.09765625, 2.3% low

1/16 + 1/32 + 1/256 + 1/512 = 51/512 = 0.99609735, .04%low

and so on. The series converges but never terminates

Why is that? Is 1/10 magic like pi? Nope, it's just
because binary is simply not a convenient symbol
system to represent value like 1/10.

And, by the way, pi is the value it is ONLY in flat Euclidian
space. In one sufficently positive curved space, pi is
EXACTLY equal to 3, and in another sufficiently
negatively curved space, pi is EXACTLY equaly to 4
(all this is normal base 10 representation).

In that sense, any wish one might have that the digits of
pi have some mystical message, the answer is, uh, no.
The digits we calculate for pi are an artifact of the symbol
system we chose.

[Bob Cain]

Dirk Bruere at NeoPax wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:
Bob Cain wrote:
Dirk Bruere at NeoPax wrote:

I rather like the AUH.
IMO it makes a lot more sense to ask 'why just this' rather than 'why
this'.
How does AUH address the former rather than the latter?
Well, one of the constraints that must be imposed on the selection of
all possible universes is conditions for intelligent life to perceive
them. So there is obviously an anthropic selection effect for starters.

I was remaining within what Tegmark calls Level I. He says that with
inflation (which requires infinite extent as it is formulated) and
quantum fluctuation there are bound to be instances and repeats of
this or any possible quantum state of a Hubble volume within the Level
I universe. The only constraints that are imposed at Level I are the
values we see for the fundamental constants. Level I assumes that the
universe is isotropic in that regard. Since we live in a
demonstration of an adequate state, it was inevitable. That may be
what the "strong" anthropic principle requires, I don't remember.

As I read Tegmark, there is no need at all for anthropic selection
since, one way or another, all possible states are "explored"
(redundantly) even at Level I. Selection implies a narrowing,
inflation implies the opposite.

BTW, thanks again for that link.

For example, simple 'triangle universes' would not be complex enough to
give rise to intelligence.

Whooosh again. :-)

If Tegmark is correct, then there are an infinite number of versions of
this universe, and it starts to look a bit like the Many Worlds
Interpretation (but is apparently unrelated).

Indeed. He describes four levels of infinities, each of a different
nature and containing all of the levels below. At each level there
are an infinite number of branches containing exact copies of our
Hubble volume. MW is level III.

We're a side effect.


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein