| Topic: |
Religions > Atheism |
| User: |
"AcesLucky" |
| Date: |
15 Oct 2006 08:16:40 AM |
| Object: |
Question to Atheists |
This is an honest question to which an honest reply would be interesting
(to me).
What would be your best argument in "support" of a god?
(As an aside, Marilyn vos Savant [who claims not to answer publicly on
questions of religion or god but did venture this one] answered by
stating, "because so many people believe in one.")
Without being dishonest, what would be your best argument in support of
a god?
AcesLucky
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| User: "Al Klein" |
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| Title: Re: Question to Atheists |
18 Oct 2006 01:28:17 PM |
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On Wed, 18 Oct 2006 00:15:14 -0700, AcesLucky <acesLucky@netscape.net>
wrote:
Al Klein wrote:
On Tue, 17 Oct 2006 11:38:56 -0700, AcesLucky <acesLucky@netscape.net>
wrote:
Al Klein wrote:
On Mon, 16 Oct 2006 13:29:53 -0700, AcesLucky <acesLucky@netscape.net>
wrote:
Any life that can claim and demonstrate immortality suddenly makes room
for a consciousness worthy of the /possibility/ of a god, where none
existed with any seriousness before.
It also immediately precludes change, because it limits the number of
beings possible. At some point the species stagnates. Death is
necessary for life.
Theistic arguments seldom look past the first move.
I didn't follow. Please give more detail.
The flood. Nice story. When you start peeling off the layers, you
find difficulties.
The Exodus. Same thing. It looks good on the surface, but the
logistics of keeping about 4 million people moving as a body?
Immortality. Nice idea, but the galaxy can support a certain maximum
number of beings that require X amount of energy each. (Asimov worked
out for this planet and it came to about 12 billion.) What happens
once the galaxy is filled?
It's the same as any engineering problem. Once marketing hands it off
to engineering, the details can kill the idea. As in "sure we can
make it but you can't possibly sell it for more than it costs to build
it".
Got it.
Prey tell; doesn't that assume that all resources in existence are
ultimately finite?
The resources in any given volume of space are not only limited but
fixed.
What if the expansion of our big bang was merely an atom of another
universe?
There was no matter at the big bang.
What if there were truly no limit to the size of existence?
There probably isn't.
(That the consumption of one form of energy was the potential of another.)
We can't 'consume' energy, we can only convert it from one form to
another - and eventually to heat.
--
rukbat at optonline dot net
"If anyone comes to me, and does not hate his father, mother, wife, brothers, and sisters and even himself, he cannot be my disciple."
Luke 14:26
(random sig, produced by SigChanger)
This signature was made by SigChanger.
You can find SigChanger at: http://www.phranc.nl/
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| User: "Al Klein" |
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| Title: Re: Question to Atheists |
16 Oct 2006 10:46:43 PM |
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On 15 Oct 2006 19:13:55 -0700, "MemePilot" <memepilot@cox.net> wrote:
What would be your best argument "against" the existence of a god?
If you define a god to be omnipresent, the conditions needed to prove
that the god doesn't exist preclude the proof, making the question
meaningless.
--
rukbat at optonline dot net
"Speculating on the possible reaction to evidence is no excuse for
failing to produce the evidence."
- Wayne M. Delia+
(random sig, produced by SigChanger)
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
17 Oct 2006 01:42:36 PM |
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Al Klein wrote:
On 15 Oct 2006 19:13:55 -0700, "MemePilot" <memepilot@cox.net> wrote:
What would be your best argument "against" the existence of a god?
If you define a god to be omnipresent, the conditions needed to prove
that the god doesn't exist preclude the proof, making the question
meaningless.
Clever. To prove it, you'd need any area "absent" its presence, which by
definition cannot already exist.
My brain feels funny.
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| User: "James Burns" |
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| Title: Re: Question to Atheists |
17 Oct 2006 06:24:49 PM |
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AcesLucky wrote:
Al Klein wrote:
On 15 Oct 2006 19:13:55 -0700, "MemePilot" <memepilot@cox.net> wrote:
What would be your best argument "against" the existence of a god?
If you define a god to be omnipresent, the conditions needed to prove
that the god doesn't exist preclude the proof, making the question
meaningless.
Clever. To prove it, you'd need any area "absent" its presence, which by
definition cannot already exist.
My brain feels funny.
Here's another one (maybe a repeat):
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
18 Oct 2006 02:29:58 AM |
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James Burns wrote:
AcesLucky wrote:
Al Klein wrote:
On 15 Oct 2006 19:13:55 -0700, "MemePilot" <memepilot@cox.net> wrote:
What would be your best argument "against" the existence of a god?
If you define a god to be omnipresent, the conditions needed to prove
that the god doesn't exist preclude the proof, making the question
meaningless.
Clever. To prove it, you'd need any area "absent" its presence, which
by definition cannot already exist.
My brain feels funny.
Here's another one (maybe a repeat):
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be true.
This argument is circular in advance (before you get to the steps) if
the definition of "S then G" is defined as S. It in essence says "S = G"
before you ever get out of the blocks.
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "James Burns" |
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| Title: Re: Question to Atheists |
18 Oct 2006 08:44:37 AM |
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AcesLucky wrote:
James Burns wrote:
[...]
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be
true. This argument is circular in advance (before you get to the
steps) if the definition of "S then G" is defined as S. It in
essence says "S = G" before you ever get out of the blocks.
I don't assume that S is true. Neither do I assume that S is false.
The only thing that the definition of S assumes is that S means
"If S is true, then G".
Obviously, the definition of S is circular (or self-referential),
but the argument below is not circular -- that is, the truth of
the proposition to be proven is not assumed.
No, I don't think it is a valid argument, but I do think it
is an interesting question as to why it is invalid. It is not
so obvious a fallacy as making a circular argument.
Jim Burns
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
18 Oct 2006 12:38:43 PM |
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James Burns wrote:
AcesLucky wrote:
James Burns wrote:
[...]
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be
true. This argument is circular in advance (before you get to the
steps) if the definition of "S then G" is defined as S. It in
essence says "S = G" before you ever get out of the blocks.
I don't assume that S is true. Neither do I assume that S is false.
The only thing that the definition of S assumes is that S means
"If S is true, then G".
Ohhhhhh, yes you do! You are assuming outright that S is true, in your
definition! For example, allow me to state in english what ...
Define S = S -> G, or "If S is true, then G (ie, God exists)."
....means. Feel free to correct me if I'm wrong (but this is my
understanding):
You are saying:
S means ... if S is true, then god exists. (So far, so good?)
It does NOT carry on to say that if S is not true then god does not
exist, which leaves open the possibility that god could exists even if S
is not true.
So, the ONLY way step 2 can work is if S "is" true. Step 2 just
replaces step 1 with what the identity means. At that point it can only
mean S = G. But that was how your definition limited it in the first place!
(Care to hit this?)
Obviously, the definition of S is circular (or self-referential),
but the argument below is not circular -- that is, the truth of
the proposition to be proven is not assumed.
No, I don't think it is a valid argument, but I do think it
is an interesting question as to why it is invalid. It is not
so obvious a fallacy as making a circular argument.
Jim Burns
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "James Burns" |
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| Title: Re: Question to Atheists |
18 Oct 2006 07:21:50 PM |
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AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
[...]
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be
true. This argument is circular in advance (before you get to the
steps) if the definition of "S then G" is defined as S. It in
essence says "S = G" before you ever get out of the blocks.
I don't assume that S is true. Neither do I assume that S is false.
The only thing that the definition of S assumes is that S means
"If S is true, then G".
Ohhhhhh, yes you do! You are assuming outright that S is true,
in your definition!
OK, this is a little confusing for me, because (1) typically, a
properly made logical/mathematical definition does /not/ assert
the truth of anything, but (2) in /this one case/, S is proven
true with no assumptions beyond the rules of logic (or, as you
may be putting it, from just the definition).
I hope you are allowing me to distinguish between defining S
and asserting S.
For example, allow me to state in english what ...
Define S = S -> G, or "If S is true, then G (ie, God exists)."
...means. Feel free to correct me if I'm wrong (but this is my
understanding):
You are saying:
S means ... if S is true, then god exists. (So far, so good?)
It does NOT carry on to say that if S is not true then god does
not exist, which leaves open the possibility that god could
exists even if S is not true.
S does not carry on to say some other thing that maybe would not
give rise to a paradox, but how can that resolve the paradox?
S exists. (Or maybe it doesn't? That might be one way out.)
Remember, I am not asserting S; I am just pointing to it.
By the way, the alternate to S (call it T) that you seem to
prefer also leads to a similar paradox.
Define T as "The sentence T is true if and only if God exists."
Either T is true or it's false.
If T is true, then "God exists" has the same truth value as T,
that is, true.
If T is false, then "God exists" has the opposite truth value as T,
that is, not false or true again.
Heads I win; tails you lose.
So, the ONLY way step 2 can work is if S "is" true. Step 2 just
replaces step 1 with what the identity means.
Step 2 is allowed because S -> G is what S means. I don't see
how it could not be allowed. I don't understand what you mean
by "... if S 'is' true."
At that point it can only mean S = G.
But that was how your definition limited it in the first place!
You lost me on that last curve. I don't see where we get to
S = G. Also, even if my definition did set things up so that
it follows that S = G (it's not at all clear to me that's true),
it did it while I was only assuming true things like S -> S
or G -> G. Surely, you don't object to those?
(Care to hit this?)
I applaud your spirit, but I think this is going to take dissecting
the meaning of Truth, Meaning, Reference and all that. There are
a family of these, and they seem to be uniformly nasty. In the
same vein, Russell's set of all sets not containing themselves
(which does and does not contain itself) forced the re-evaluation
of a fair-sized chunk of mathematics in order to get rid of it.
Jim Burns
Obviously, the definition of S is circular (or self-referential),
but the argument below is not circular -- that is, the truth of
the proposition to be proven is not assumed.
No, I don't think it is a valid argument, but I do think it
is an interesting question as to why it is invalid. It is not
so obvious a fallacy as making a circular argument.
Jim Burns
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
18 Oct 2006 09:46:01 PM |
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James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
[...]
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be
true. This argument is circular in advance (before you get to the
steps) if the definition of "S then G" is defined as S. It in
essence says "S = G" before you ever get out of the blocks.
I don't assume that S is true. Neither do I assume that S is false.
The only thing that the definition of S assumes is that S means
"If S is true, then G".
Ohhhhhh, yes you do! You are assuming outright that S is true,
in your definition!
OK, this is a little confusing for me, because (1) typically, a
properly made logical/mathematical definition does /not/ assert
the truth of anything, but (2) in /this one case/, S is proven
true with no assumptions beyond the rules of logic (or, as you
may be putting it, from just the definition).
I hope you are allowing me to distinguish between defining S
and asserting S.
For example, allow me to state in english what ...
Define S = S -> G, or "If S is true, then G (ie, God exists)."
...means. Feel free to correct me if I'm wrong (but this is my
understanding):
You are saying:
S means ... if S is true, then god exists. (So far, so good?)
It does NOT carry on to say that if S is not true then god does
not exist, which leaves open the possibility that god could
exists even if S is not true.
S does not carry on to say some other thing that maybe would not
give rise to a paradox, but how can that resolve the paradox?
S exists. (Or maybe it doesn't? That might be one way out.)
Remember, I am not asserting S; I am just pointing to it.
By the way, the alternate to S (call it T) that you seem to
prefer also leads to a similar paradox.
Define T as "The sentence T is true if and only if God exists."
Either T is true or it's false.
If T is true, then "God exists" has the same truth value as T,
that is, true.
If T is false, then "God exists" has the opposite truth value as T,
that is, not false or true again.
Heads I win; tails you lose.
So, the ONLY way step 2 can work is if S "is" true. Step 2 just
replaces step 1 with what the identity means.
Step 2 is allowed because S -> G is what S means. I don't see
how it could not be allowed. I don't understand what you mean
by "... if S 'is' true."
At that point it can only mean S = G.
But that was how your definition limited it in the first place!
You lost me on that last curve. I don't see where we get to
S = G. Also, even if my definition did set things up so that
it follows that S = G (it's not at all clear to me that's true),
it did it while I was only assuming true things like S -> S
or G -> G. Surely, you don't object to those?
(Care to hit this?)
I applaud your spirit, but I think this is going to take dissecting
the meaning of Truth, Meaning, Reference and all that. There are
a family of these, and they seem to be uniformly nasty. In the
same vein, Russell's set of all sets not containing themselves
(which does and does not contain itself) forced the re-evaluation
of a fair-sized chunk of mathematics in order to get rid of it.
Jim Burns
Yeah; we could probably torture this for years. I'll egress by trying to
answer the part where I lost you "on that last curve".
Think of S as the set "any quantity that equals 4"; think of G as the
quantity 4. So "S" can be 2+2, or 1+3, or any set of circumstances that
equal the quantity 4. "G" on the other hand "is" the quantity 4.
So..., S -> G, or "If S is true, then G.
Can you see how S is inherently ALREADY G, by definition?
"If S is true, then G" establishes the /requirements/ for S in advance.
----
Now, here's what I think you're trying to say by symbolizing S as an
independent element that lends truthfulness to establishing G.
(Again, correct me if I'm wrong.)
You're trying to assert that S can be /any/ object that can MAKE the
definition of G (which means, god exists); like so...
In the previous example I used 2+2 to establish 4, but here I think you
want to symbolize S as ANY "S" such that (and for example):
The argument: if {-1 + 2 + 3} is true, then 4; where "S" is defined as(
-1 ). Because S as used here is an element that when true establishes G,
so it's fair game.
..
It, however, fails at step 2 because you now have:
if (-1) is true, then (if -1 is true, then 4) *my interpretation of step
2 when written*
---
(if -1 is true, then 4), then the first part "(if (-1) is true)" can
only work if (-1) is 5. This contradicts the argument where S is defined
as -1.
---
My point is that the ONLY way step 2 can work is if S "is" already
true. (That is any quantity whose set already equals 4). "If S is true,
then G" establishes the /requirements/ for S in advance. Because of
this, I think you can eliminate steps 1 and 2 altogether. If you start
with step 3, you're still right at the definition of S that's required
to be whatever makes G true!
I don't see it as a paradox, I see it as a circle.. or I don't
understand the problem.
Obviously, the definition of S is circular (or self-referential),
but the argument below is not circular -- that is, the truth of
the proposition to be proven is not assumed.
No, I don't think it is a valid argument, but I do think it
is an interesting question as to why it is invalid. It is not
so obvious a fallacy as making a circular argument.
Jim Burns
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
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| User: "James Burns" |
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| Title: Re: Question to Atheists |
19 Oct 2006 06:38:33 PM |
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AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
"If S is true, then G" is a presupposition which may or may not be
true. This argument is circular in advance (before you get to the
steps) if the definition of "S then G" is defined as S. It in
essence says "S = G" before you ever get out of the blocks.
I don't assume that S is true. Neither do I assume that S is false.
The only thing that the definition of S assumes is that S means
"If S is true, then G".
Ohhhhhh, yes you do! You are assuming outright that S is true,
in your definition!
OK, this is a little confusing for me, because (1) typically, a
properly made logical/mathematical definition does /not/ assert
the truth of anything, but (2) in /this one case/, S is proven
true with no assumptions beyond the rules of logic (or, as you
may be putting it, from just the definition).
I hope you are allowing me to distinguish between defining S
and asserting S.
For example, allow me to state in english what ...
Define S = S -> G, or "If S is true, then G (ie, God exists)."
...means. Feel free to correct me if I'm wrong (but this is my
understanding):
You are saying:
S means ... if S is true, then god exists. (So far, so good?)
It does NOT carry on to say that if S is not true then god does
not exist, which leaves open the possibility that god could
exists even if S is not true.
S does not carry on to say some other thing that maybe would not
give rise to a paradox, but how can that resolve the paradox?
S exists. (Or maybe it doesn't? That might be one way out.)
Remember, I am not asserting S; I am just pointing to it.
By the way, the alternate to S (call it T) that you seem to
prefer also leads to a similar paradox.
Define T as "The sentence T is true if and only if God exists."
Either T is true or it's false.
If T is true, then "God exists" has the same truth value as T,
that is, true.
If T is false, then "God exists" has the opposite truth value as T,
that is, not false or true again.
Heads I win; tails you lose.
So, the ONLY way step 2 can work is if S "is" true. Step 2 just
replaces step 1 with what the identity means.
Step 2 is allowed because S -> G is what S means. I don't see
how it could not be allowed. I don't understand what you mean
by "... if S 'is' true."
At that point it can only mean S = G.
But that was how your definition limited it in the first place!
You lost me on that last curve. I don't see where we get to
S = G. Also, even if my definition did set things up so that
it follows that S = G (it's not at all clear to me that's true),
it did it while I was only assuming true things like S -> S
or G -> G. Surely, you don't object to those?
(Care to hit this?)
I applaud your spirit, but I think this is going to take dissecting
the meaning of Truth, Meaning, Reference and all that. There are
a family of these, and they seem to be uniformly nasty. In the
same vein, Russell's set of all sets not containing themselves
(which does and does not contain itself) forced the re-evaluation
of a fair-sized chunk of mathematics in order to get rid of it.
Yeah; we could probably torture this for years. I'll egress by
trying to answer the part where I lost you "on that last curve".
Think of S as the set "any quantity that equals 4"; think of G
as the quantity 4. So "S" can be 2+2, or 1+3, or any set of
circumstances that equal the quantity 4. "G" on the other hand
"is" the quantity 4.
So..., S -> G, or "If S is true, then G.
Can you see how S is inherently ALREADY G, by definition?
"If S is true, then G" establishes the /requirements/ for S in
advance.
I think I would say "any expression that equals 4".
I would change your analogy a little (making it closer). It's not
that S /equals/ G, but that S /is larger than/ G.
I could agree with this analogy (though it doesn't look circular
to me). I can imagine having a series of propositions and knowing
that each implies the next proposition: X -> Y, Y -> Z, Z -> W,
If I know X, then all the others fall like dominoes. Similarly,
if I have a series of inequalities, x > y, y > z, z > w, then
I know that if I have x bricks, I also know I have y, z and w
bricks (assuming they are appropriate values of brickness).
But I don't know that I have x bricks; I don't know X;
and I don't know S.
I think your point is that, /if I assert S/, then G follows.
That's true (and it may be part of where the paradox comes form):
1. S assumed
2. S -> G def of S
3. G modus ponens
However, I do not assert S below (at least, not without supporting
it logically):
-- I assert that S -> S.
-- I assert that S -> G can be substituted for S.
-- I assert that S -> G is equivalent to S -> (S -> G).
-- I assert that S can be substituted for S -> G.
-- I assert that modus ponens is valid in this particular case.
That's it.
----
Now, here's what I think you're trying to say by symbolizing S as an
independent element that lends truthfulness to establishing G.
(Again, correct me if I'm wrong.)
You're trying to assert that S can be /any/ object that can MAKE the
definition of G (which means, god exists); like so...
In the previous example I used 2+2 to establish 4, but here I think you
want to symbolize S as ANY "S" such that (and for example):
The argument: if {-1 + 2 + 3} is true, then 4; where "S" is defined as(
-1 ). Because S as used here is an element that when true establishes G,
so it's fair game.
.
It, however, fails at step 2 because you now have:
if (-1) is true, then (if -1 is true, then 4) *my interpretation of step
2 when written*
---
(if -1 is true, then 4), then the first part "(if (-1) is true)" can
only work if (-1) is 5. This contradicts the argument where S is defined
as -1.
---
My point is that the ONLY way step 2 can work is if S "is" already
true. (That is any quantity whose set already equals 4). "If S is true,
then G" establishes the /requirements/ for S in advance. Because of
this, I think you can eliminate steps 1 and 2 altogether. If you start
with step 3, you're still right at the definition of S that's required
to be whatever makes G true!
It may be that S (or S -> G) establishes the requirements for G.
But I'm not given S (or S -> G); I have to earn it. I can't just
jump over steps 1 and 2. That's how I earn the right to assert S.
I think you are saying that I'm hiding my conclusion somehow
in my assumptions, perhaps transforming them to look unfamiliar.
What can I say except that I'm not doing that? You can look
at the argument yourself. S may assert this or that, but I
don't assert S until I establish the argument for it.
I don't see it as a paradox, I see it as a circle.. or I don't
understand the problem.
I think what you're doing is looking at the outcome of the
argument, G, with apparently nothing as the input, and saying
"Obviously, G is being assumed somewhere inside this argument,
thus it's circular". Can you point to a step that is not
justified? There are only five. If you can't, then maybe you're
working backwards from "It's obviously circular." to
"Something's wierd about this step; it must be wrong."
About step 2, S -> (S -> G) : Let me point out that
X -> (Y -> Z) is equivalent to (X & Y) -> Z. Then step 3
just says that S -> G follows from (S & S) -> G.
The paradox is that there should be a circle in order to get
something from nothing like the argument does, but there
isn't.
Obviously, the definition of S is circular (or self-referential),
but the argument below is not circular -- that is, the truth of
the proposition to be proven is not assumed.
No, I don't think it is a valid argument, but I do think it
is an interesting question as to why it is invalid. It is not
so obvious a fallacy as making a circular argument.
Jim Burns
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
.
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| User: "James Burns" |
|
| Title: Re: Question to Atheists |
20 Oct 2006 08:20:29 AM |
|
|
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the impression
that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not depend
on special revelation, that could not be "written" (in the
digits of /pi/?) by any conceivable means. Yeah, I might buy that.
Jim Burns
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
[big snip]
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
.
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| User: "AcesLucky" |
|
| Title: Re: Question to Atheists |
20 Oct 2006 03:56:10 PM |
|
|
James Burns wrote:
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the impression
that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not depend
on special revelation, that could not be "written" (in the
digits of /pi/?) by any conceivable means. Yeah, I might buy that.
Jim Burns
You're going to think I'm just being argumentative, but I disagree.
Remember the old story about setting a hundred monkeys in front of
typewriters, letting them peck away indefinitely, and eventually getting
the complete works of Shakespeare? This is merely a probability problem.
Let's say they do, on the one hand, and let's they never do on the other.
Neither concludes a god, any more than an appearance of ones and zeros
in an expansion of pi. The expansion yields what it yields independently
of our ability for any special affinity for circles.
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
AcesLucky wrote:
James Burns wrote:
Theorem: God exists.
Proof:
Define G = "God exists."
Define S = S -> G, or "If S is true, then G (ie, God exists)."
[big snip]
1. S -> S
identity
2. S -> (S -> G)
substitution into (1), by definition of S
3. S -> G
from (2) by contraction
4. S
substitution into (3), by definition of S
5. G (ie, God exists)
modus ponens, from (3) and (4)
QED
http://en.wikipedia.org/wiki/Curry%27s_paradox
Jim Burns
.
|
|
|
| User: "Jim Burns" |
|
| Title: Re: Question to Atheists |
22 Oct 2006 02:36:32 PM |
|
|
AcesLucky wrote:
James Burns wrote:
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the
impression that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not
depend on special revelation, that could not be "written"
(in the digits of /pi/?) by any conceivable means. Yeah,
I might buy that.
Jim Burns
You're going to think I'm just being argumentative, but I
disagree.
I would be the wrong person to object to someone else being
argumentative.
Remember the old story about setting a hundred monkeys in
front of typewriters, letting them peck away indefinitely,
and eventually getting the complete works of Shakespeare?
This is merely a probability problem. Let's say they do,
on the one hand, and let's they never do on the other.
It might be interesting to see just how long "indefinitely"
needs to be for the monkeys to produce Shakespeare.
Let's assume that a volume of the Compleat Workes of
Wm. Shakespeare has 1000 pages with 1000 characters on each
page, so that typing it correctly means hitting one specified
sequence of 1,000,000 characters. Looking at my keyboard,
I see I have about 100 characters available. The chance of
a given monkey hitting the first key of 1,000,000 correct keys
in a row is about a one in 100^1,000,000 chance (or 1 in
10^2,000,000).
Whoa, that is such a mind-numbingly small chance, that I'm
going to loosen things up a bit. We're still going to end up
with mind-numbingly small chances, though.
Assume that, instead of Shakespeare, it could be any book in
the Library of (U.S.) Congress. Picking numbers out of the air,
assume that there are a trillion, 10^12, such volumes, that
they all have 1000 pages of 1000 characters each, and that
success is redefined to be any 10 continuous pages (10,000
characters) out of any of these books. If we let the 10 pages
start on any character, each 1000 page book holds within it
990,000 target 10 page sequences. This raises the number of our
targets to (9.9*10^5)(10^12), or about 10^17.99.
With the shorter sequence now required, the chance of a
particular sequence starting on a particular key stroke
is "only" one in 10^20,000 now. The chance of any of the
acceptable sequences starting at a given keystroke is
one in 10^(20,000 - 17.99) which also the expected number
of keystrokes required before our monkeys hit one of our
targets: 10^(20,000 - 17.99), plus or minus the square root
of that, 10^(10,000 - 8.99).
Instead of 100 monkeys, we'll use a monkey for each particle
in the universe, 10^87. Each monkey will make a keystroke
every Planck time, 1.35*10^-43 sec (where our notions
of space and time start to breakdown), so there are 10^87*10^42.87
opportunities for a success every second. That means
we will need 10^(20,000 - 17.99 - 129.87) seconds for success
(plus or minus 10^(10,000 - 8.99 - 129.87) seconds).
To put it in more convenient units, define one AotU as
13.6 billion years, the current estimate of the age of the
universe, which is 10^10.13 seconds. We'll need
10^(20,000 - 17.99 - 129.87 - 10.13), or 10^19,842 AotU
for our universe of monkeys typing away at space-time warping
speeds to give us any ten pages out of our trillion volumes.
That's not thousands of lifetimes of the universe.
That's [a one followed by thousands of zeroes] lifetimes
of the universe.
Neither concludes a god, any more than an appearance of ones
and zeros in an expansion of pi. The expansion yields what
it yields independently of our ability for any special
affinity for circles.
Sure, I didn't mean that the circle was some sort of
mathematical proof-of-god. Just that the appearance of some
kind of message in the digits of /pi/ in any humanly
accessible time (or even any super-humanly accessible time)
would be very, very, ..., very unlikely.
The argument would be that the appearance of a message would
be either a really, truly super-colossal coincidence or
it was put there somehow.
A little irony: I don't think it's been proven yet, but
mathematicians believe that the digits of /pi/ are normal,
that is, every n-digit sequence is just as likely as every other
n-digit sequence. That would mean that the circle, the works
of Shakespeare and every other book in the Library of Congress
are somewhere in the infinite expansion of /pi/, an infinite
number of times, actually. Of course, the question is where
in the expansion they are.
A question I would have for Dr. Sagan is how a hypothetical
Creator would determine which mathematical constants to
put a message in. Even if you assume intelligent creatures
will have some sort of affinity for circles, should they
look in the ratio of circumference to diameter, that is,
pi, or the ration of diameter to circumference, 1/pi, or
the square root of pi (the "squared circle" of classical
Greece), or something else?
Jim Burns
.
|
|
|
| User: "AcesLucky" |
|
| Title: Re: Question to Atheists |
22 Oct 2006 04:00:50 PM |
|
|
Jim Burns wrote:
AcesLucky wrote:
James Burns wrote:
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the
impression that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not
depend on special revelation, that could not be "written"
(in the digits of /pi/?) by any conceivable means. Yeah,
I might buy that.
Jim Burns
You're going to think I'm just being argumentative, but I
disagree.
I would be the wrong person to object to someone else being
argumentative.
Remember the old story about setting a hundred monkeys in
front of typewriters, letting them peck away indefinitely,
and eventually getting the complete works of Shakespeare?
This is merely a probability problem. Let's say they do,
on the one hand, and let's they never do on the other.
It might be interesting to see just how long "indefinitely"
needs to be for the monkeys to produce Shakespeare.
Let's assume that a volume of the Compleat Workes of
Wm. Shakespeare has 1000 pages with 1000 characters on each
page, so that typing it correctly means hitting one specified
sequence of 1,000,000 characters. Looking at my keyboard,
I see I have about 100 characters available. The chance of
a given monkey hitting the first key of 1,000,000 correct keys
in a row is about a one in 100^1,000,000 chance (or 1 in
10^2,000,000).
Whoa, that is such a mind-numbingly small chance, that I'm
going to loosen things up a bit. We're still going to end up
with mind-numbingly small chances, though.
Assume that, instead of Shakespeare, it could be any book in
the Library of (U.S.) Congress. Picking numbers out of the air,
assume that there are a trillion, 10^12, such volumes, that
they all have 1000 pages of 1000 characters each, and that
success is redefined to be any 10 continuous pages (10,000
characters) out of any of these books. If we let the 10 pages
start on any character, each 1000 page book holds within it
990,000 target 10 page sequences. This raises the number of our
targets to (9.9*10^5)(10^12), or about 10^17.99.
With the shorter sequence now required, the chance of a
particular sequence starting on a particular key stroke
is "only" one in 10^20,000 now. The chance of any of the
acceptable sequences starting at a given keystroke is
one in 10^(20,000 - 17.99) which also the expected number
of keystrokes required before our monkeys hit one of our
targets: 10^(20,000 - 17.99), plus or minus the square root
of that, 10^(10,000 - 8.99).
Instead of 100 monkeys, we'll use a monkey for each particle
in the universe, 10^87. Each monkey will make a keystroke
every Planck time, 1.35*10^-43 sec (where our notions
of space and time start to breakdown), so there are 10^87*10^42.87
opportunities for a success every second. That means
we will need 10^(20,000 - 17.99 - 129.87) seconds for success
(plus or minus 10^(10,000 - 8.99 - 129.87) seconds).
To put it in more convenient units, define one AotU as
13.6 billion years, the current estimate of the age of the
universe, which is 10^10.13 seconds. We'll need
10^(20,000 - 17.99 - 129.87 - 10.13), or 10^19,842 AotU
for our universe of monkeys typing away at space-time warping
speeds to give us any ten pages out of our trillion volumes.
That's not thousands of lifetimes of the universe.
That's [a one followed by thousands of zeroes] lifetimes
of the universe.
Neither concludes a god, any more than an appearance of ones
and zeros in an expansion of pi. The expansion yields what
it yields independently of our ability for any special
affinity for circles.
Sure, I didn't mean that the circle was some sort of
mathematical proof-of-god. Just that the appearance of some
kind of message in the digits of /pi/ in any humanly
accessible time (or even any super-humanly accessible time)
would be very, very, ..., very unlikely.
The argument would be that the appearance of a message would
be either a really, truly super-colossal coincidence or
it was put there somehow.
A little irony: I don't think it's been proven yet, but
mathematicians believe that the digits of /pi/ are normal,
that is, every n-digit sequence is just as likely as every other
n-digit sequence. That would mean that the circle, the works
of Shakespeare and every other book in the Library of Congress
are somewhere in the infinite expansion of /pi/, an infinite
number of times, actually. Of course, the question is where
in the expansion they are.
A question I would have for Dr. Sagan is how a hypothetical
Creator would determine which mathematical constants to
put a message in. Even if you assume intelligent creatures
will have some sort of affinity for circles, should they
look in the ratio of circumference to diameter, that is,
pi, or the ration of diameter to circumference, 1/pi, or
the square root of pi (the "squared circle" of classical
Greece), or something else?
Jim Burns
I understood your point the first time. But since you went through all
that math, let's suppose it's correct. And let's suppose the final
probability is represented by 1:X, where X is your maximum number of tries.
It does not imply that X tries will have to be carried out before the 1
success is reached, any more than a 1 in 6 chance means as 6 must appear
on 6th try. A 6 could appear on the 1st try. And of course, it may not
appear after six tries.
But say that it appears on the 6th try, and then in another creation
scenario it appears on the 1st. Both fit within your limit of
possibility without the requirement for a god. The validity of your
calculations actually proves that!
Another way of looking at it is the hat with a bunch of letters in it.
Let's say that when the letters are mixed in the hat and the hat turned
over and dumped on the ground, they spell a complete sentence of
something. The point is that that sentence, given all probable outcomes,
is not only probable but (virtually) necessary as an outcome given more
opportunities for a turn of the hat than possible outcomes. (The fact
that it spells something means nothing to the letters any more than we
can pick stuff out of a hot bowl of alphabet soup.)
What, for example, is the probability of the sentence spelling
1,2,3,4,5,6 given six one-sided dice in a hat? (Now dump the hat several
times MORE than that, and the 1-6 sequence is inevitable.) What is the
probability for the sentence to spell 1,2, given a one and a two being
mixed and turned 70 or 80 times? As you can see the chances will have to
appear (the sentence will have to appear) just given the turns and
tosses outweighing the total possibilities.
The monkey problem is no different. If it happened on the very first
try, it would /still/ fit within your total limit of possible tries!
For you to prove god through probability (and I'd be immediately suspect
of that method), you'd have to prove that an outcome unequivocally
CANNOT happen, and then show that it does on the impulse of a confirmed
communication from such a god.
A close second might be, let's say that we announce to the world that
all cancer will be eradicated as promised from some god, on a specific
date and time. And then it happens! Such a being, from our present
knowledge, would appear to us to be god-like. It still doesn't prove its
a god, but may serve as a practical purpose to see it that way, relative
to us.
.
|
|
|
| User: "James Burns" |
|
| Title: Re: Question to Atheists |
24 Oct 2006 07:34:11 PM |
|
|
AcesLucky wrote:
Jim Burns wrote:
AcesLucky wrote:
James Burns wrote:
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the
impression that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not
depend on special revelation, that could not be "written"
(in the digits of /pi/?) by any conceivable means. Yeah,
I might buy that.
Jim Burns
You're going to think I'm just being argumentative, but I
disagree.
I would be the wrong person to object to someone else being
argumentative.
Remember the old story about setting a hundred monkeys in
front of typewriters, letting them peck away indefinitely,
and eventually getting the complete works of Shakespeare?
This is merely a probability problem. Let's say they do,
on the one hand, and let's they never do on the other.
It might be interesting to see just how long "indefinitely"
needs to be for the monkeys to produce Shakespeare.
Let's assume that a volume of the Compleat Workes of
Wm. Shakespeare has 1000 pages with 1000 characters on each
page, so that typing it correctly means hitting one specified
sequence of 1,000,000 characters. Looking at my keyboard,
I see I have about 100 characters available. The chance of
a given monkey hitting the first key of 1,000,000 correct keys
in a row is about a one in 100^1,000,000 chance (or 1 in
10^2,000,000).
Whoa, that is such a mind-numbingly small chance, that I'm
going to loosen things up a bit. We're still going to end up
with mind-numbingly small chances, though.
Assume that, instead of Shakespeare, it could be any book in
the Library of (U.S.) Congress. Picking numbers out of the air,
assume that there are a trillion, 10^12, such volumes, that
they all have 1000 pages of 1000 characters each, and that
success is redefined to be any 10 continuous pages (10,000
characters) out of any of these books. If we let the 10 pages
start on any character, each 1000 page book holds within it
990,000 target 10 page sequences. This raises the number of our
targets to (9.9*10^5)(10^12), or about 10^17.99.
With the shorter sequence now required, the chance of a
particular sequence starting on a particular key stroke
is "only" one in 10^20,000 now. The chance of any of the
acceptable sequences starting at a given keystroke is
one in 10^(20,000 - 17.99) which also the expected number
of keystrokes required before our monkeys hit one of our
targets: 10^(20,000 - 17.99), plus or minus the square root
of that, 10^(10,000 - 8.99).
Instead of 100 monkeys, we'll use a monkey for each particle
in the universe, 10^87. Each monkey will make a keystroke
every Planck time, 1.35*10^-43 sec (where our notions
of space and time start to breakdown), so there are 10^87*10^42.87
opportunities for a success every second. That means
we will need 10^(20,000 - 17.99 - 129.87) seconds for success
(plus or minus 10^(10,000 - 8.99 - 129.87) seconds).
To put it in more convenient units, define one AotU as
13.6 billion years, the current estimate of the age of the
universe, which is 10^10.13 seconds. We'll need
10^(20,000 - 17.99 - 129.87 - 10.13), or 10^19,842 AotU
for our universe of monkeys typing away at space-time warping
speeds to give us any ten pages out of our trillion volumes.
That's not thousands of lifetimes of the universe.
That's [a one followed by thousands of zeroes] lifetimes
of the universe.
Neither concludes a god, any more than an appearance of ones
and zeros in an expansion of pi. The expansion yields what
it yields independently of our ability for any special
affinity for circles.
Sure, I didn't mean that the circle was some sort of
mathematical proof-of-god. Just that the appearance of some
kind of message in the digits of /pi/ in any humanly
accessible time (or even any super-humanly accessible time)
would be very, very, ..., very unlikely.
The argument would be that the appearance of a message would
be either a really, truly super-colossal coincidence or
it was put there somehow.
A little irony: I don't think it's been proven yet, but
mathematicians believe that the digits of /pi/ are normal,
that is, every n-digit sequence is just as likely as every other
n-digit sequence. That would mean that the circle, the works
of Shakespeare and every other book in the Library of Congress
are somewhere in the infinite expansion of /pi/, an infinite
number of times, actually. Of course, the question is where
in the expansion they are.
A question I would have for Dr. Sagan is how a hypothetical
Creator would determine which mathematical constants to
put a message in. Even if you assume intelligent creatures
will have some sort of affinity for circles, should they
look in the ratio of circumference to diameter, that is,
pi, or the ration of diameter to circumference, 1/pi, or
the square root of pi (the "squared circle" of classical
Greece), or something else?
Jim Burns
I understood your point the first time. But since you went through all
that math, let's suppose it's correct. And let's suppose the final
probability is represented by 1:X, where X is your maximum number of tries.
Nothing I've done involves a maximum number of tries. The last very
large number I reported, 10^19,842 AotU, is the expected wait.
If the universe of full monkeys is set up over and over, sometimes
it will be shorter than that, sometimes longer, but the average
wait will quickly approximate that number.
It does not imply that X tries will have to be carried out before the 1
success is reached, any more than a 1 in 6 chance means as 6 must appear
on 6th try. A 6 could appear on the 1st try. And of course, it may not
appear after six tries.
My argument is that a message appearing would be so inconceivably
unlikely that we would be wise to look for explanations other
than random chance. Rolling a die and having it come up 6 is not
a good analogy to this, since it is not inconceivably likely.
A better analogy would be rolling a die and having it turn
into a potted plant.
Here are some more numbers:
A six on the first try: 1 in six.
A six on seven or more tries: 1 in three.
A six on 27 or more tries: 1 in 100
A six on 77 or more tries: 1 in a million.
A six on 153 or more tries: 1 in a trillion.
Suppose you rolled an apparently fair die 153 times and
it never came up six. Would you say, "Oh, that's
unusual. Still, it's not impossible. Yawn." or
would you look for another explanation?
Suppose we have a universe of monkeys typing away as above.
On average, they will succeed after 10^19842 AotU.
What are the chances they will succeed...
Before 10^19842 AotU? 2 in 3 (63%).
Before 10^19841 AotU? One in 10.
Before 10^19840 AotU? One in 100.
Before 10^19742 AotU? One in 10^100.
Before 10^100 AotU? One in 10^19742.
If something happened that had only a one in 10^19742
chance of happening randomly, wouldn't you look for a non-random
explanation for it happening? Don't think of winning the
Lottery. Think of winning the Lottery every time you play;
and the horse you bet on always winning; and always
drawing a straight flush when you play poker. And that
/still/ wouldn't use up the luck expressed above. Wouldn't
you think there might be something beyond mere luck involved?
In /Contact/, the message was not discovered by a universe
full of monkeys or some other fantastical assemblage of
processors. It was found using near-present computer
technology available here on panet Earth. It could only
have been found if it were much, much closer to the beginning
of pi than we would expect from a random ditribution.
The question analogous to the above would be:
What are the chances they'll succeed
Before 0.00000...0001 AotU? Damn small.
But say that it appears on the 6th try, and then in another creation
scenario it appears on the 1st. Both fit within your limit of
possibility without the requirement for a god. The validity of your
calculations actually proves that!
Another way of looking at it is the hat with a bunch of letters in it.
Let's say that when the letters are mixed in the hat and the hat turned
over and dumped on the ground, they spell a complete sentence of
something. The point is that that sentence, given all probable outcomes,
is not only probable but (virtually) necessary as an outcome given more
opportunities for a turn of the hat than possible outcomes. (The fact
that it spells something means nothing to the letters any more than we
can pick stuff out of a hot bowl of alphabet soup.)
What, for example, is the probability of the sentence spelling
1,2,3,4,5,6 given six one-sided dice in a hat? (Now dump the hat several
times MORE than that, and the 1-6 sequence is inevitable.) What is the
probability for the sentence to spell 1,2, given a one and a two being
mixed and turned 70 or 80 times? As you can see the chances will have to
appear (the sentence will have to appear) just given the turns and
tosses outweighing the total possibilities.
The monkey problem is no different. If it happened on the very first
try, it would /still/ fit within your total limit of possible tries!
For you to prove god through probability (and I'd be immediately suspect
of that method), you'd have to prove that an outcome unequivocally
CANNOT happen, and then show that it does on the impulse of a confirmed
communication from such a god.
A close second might be, let's say that we announce to the world that
all cancer will be eradicated as promised from some god, on a specific
date and time. And then it happens! Such a being, from our present
knowledge, would appear to us to be god-like. It still doesn't prove its
a god, but may serve as a practical purpose to see it that way, relative
to us.
I'm guessing that you're letting me know here what you personally
would or would not find convincing. To each their own.
Personally, though, I don't like to be so dogmatic about the
non-existence of God. I mean, it's not like real evidence is
at all likely to turn up. I would guesstimate the chance of
any such evidence being found as somewhere around the chance
of the circles randomly turning up in pi.
Besides, as a bonus, by holding that possibility open, I get to exude
scientific righteousness. And maybe the horse will sing.
Jim Burns
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
26 Oct 2006 10:12:17 AM |
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James Burns wrote:
AcesLucky wrote:
Jim Burns wrote:
AcesLucky wrote:
James Burns wrote:
It just occurred to me that the existence odd little "proofs"
like the one below could be taken as evidence of a god, not
the Hairy Thunderer but the Trickster.
I think Carl Sagan would have agreed with me. In the final
pages of his novel /Contact/, he has a SETI computer program
churning out the digits of /pi/ and looking for some kind
of message in them. A circle composed of 1's and 0's appears
in the base 10 expansion. Then in the base 11 expansion. Then
in the base 13 expansion. He closes the book with the
impression that more detailed instructions will soon follow...
That would be evidence that can't be faked, that does not
depend on special revelation, that could not be "written"
(in the digits of /pi/?) by any conceivable means. Yeah,
I might buy that.
Jim Burns
You're going to think I'm just being argumentative, but I
disagree.
I would be the wrong person to object to someone else being
argumentative.
Remember the old story about setting a hundred monkeys in
front of typewriters, letting them peck away indefinitely,
and eventually getting the complete works of Shakespeare?
This is merely a probability problem. Let's say they do,
on the one hand, and let's they never do on the other.
It might be interesting to see just how long "indefinitely"
needs to be for the monkeys to produce Shakespeare.
Let's assume that a volume of the Compleat Workes of
Wm. Shakespeare has 1000 pages with 1000 characters on each
page, so that typing it correctly means hitting one specified
sequence of 1,000,000 characters. Looking at my keyboard,
I see I have about 100 characters available. The chance of
a given monkey hitting the first key of 1,000,000 correct keys
in a row is about a one in 100^1,000,000 chance (or 1 in
10^2,000,000).
Whoa, that is such a mind-numbingly small chance, that I'm
going to loosen things up a bit. We're still going to end up
with mind-numbingly small chances, though.
Assume that, instead of Shakespeare, it could be any book in
the Library of (U.S.) Congress. Picking numbers out of the air,
assume that there are a trillion, 10^12, such volumes, that
they all have 1000 pages of 1000 characters each, and that
success is redefined to be any 10 continuous pages (10,000
characters) out of any of these books. If we let the 10 pages
start on any character, each 1000 page book holds within it
990,000 target 10 page sequences. This raises the number of our
targets to (9.9*10^5)(10^12), or about 10^17.99.
With the shorter sequence now required, the chance of a
particular sequence starting on a particular key stroke
is "only" one in 10^20,000 now. The chance of any of the
acceptable sequences starting at a given keystroke is
one in 10^(20,000 - 17.99) which also the expected number
of keystrokes required before our monkeys hit one of our
targets: 10^(20,000 - 17.99), plus or minus the square root
of that, 10^(10,000 - 8.99).
Instead of 100 monkeys, we'll use a monkey for each particle
in the universe, 10^87. Each monkey will make a keystroke
every Planck time, 1.35*10^-43 sec (where our notions
of space and time start to breakdown), so there are 10^87*10^42.87
opportunities for a success every second. That means
we will need 10^(20,000 - 17.99 - 129.87) seconds for success
(plus or minus 10^(10,000 - 8.99 - 129.87) seconds).
To put it in more convenient units, define one AotU as
13.6 billion years, the current estimate of the age of the
universe, which is 10^10.13 seconds. We'll need
10^(20,000 - 17.99 - 129.87 - 10.13), or 10^19,842 AotU
for our universe of monkeys typing away at space-time warping
speeds to give us any ten pages out of our trillion volumes.
That's not thousands of lifetimes of the universe.
That's [a one followed by thousands of zeroes] lifetimes
of the universe.
Neither concludes a god, any more than an appearance of ones
and zeros in an expansion of pi. The expansion yields what
it yields independently of our ability for any special
affinity for circles.
Sure, I didn't mean that the circle was some sort of
mathematical proof-of-god. Just that the appearance of some
kind of message in the digits of /pi/ in any humanly
accessible time (or even any super-humanly accessible time)
would be very, very, ..., very unlikely.
The argument would be that the appearance of a message would
be either a really, truly super-colossal coincidence or
it was put there somehow.
A little irony: I don't think it's been proven yet, but
mathematicians believe that the digits of /pi/ are normal,
that is, every n-digit sequence is just as likely as every other
n-digit sequence. That would mean that the circle, the works
of Shakespeare and every other book in the Library of Congress
are somewhere in the infinite expansion of /pi/, an infinite
number of times, actually. Of course, the question is where
in the expansion they are.
A question I would have for Dr. Sagan is how a hypothetical
Creator would determine which mathematical constants to
put a message in. Even if you assume intelligent creatures
will have some sort of affinity for circles, should they
look in the ratio of circumference to diameter, that is,
pi, or the ration of diameter to circumference, 1/pi, or
the square root of pi (the "squared circle" of classical
Greece), or something else?
Jim Burns
I understood your point the first time. But since you went through all
that math, let's suppose it's correct. And let's suppose the final
probability is represented by 1:X, where X is your maximum number of
tries.
Nothing I've done involves a maximum number of tries. The last very
large number I reported, 10^19,842 AotU, is the expected wait.
If the universe of full monkeys is set up over and over, sometimes
it will be shorter than that, sometimes longer, but the average
wait will quickly approximate that number.
What precludes the event happening "before" that number?
It does not imply that X tries will have to be carried out before the
1 success is reached, any more than a 1 in 6 chance means as 6 must
appear on 6th try. A 6 could appear on the 1st try. And of course, it
may not appear after six tries.
My argument is that a message appearing would be so inconceivably
unlikely that we would be wise to look for explanations other
than random chance.
Then your math would have to be incorrect by default. If
your math states it should take an average of X amount of
time (or tries), why would you assert right behind it that
it takes too long?
Rolling a die and having it come up 6 is not
a good analogy to this, since it is not inconceivably likely.
A better analogy would be rolling a die and having it turn
into a potted plant.
No. One "can" happen and the other cannot.
Here are some more numbers:
A six on the first try: 1 in six.
A six on seven or more tries: 1 in three.
A six on 27 or more tries: 1 in 100
A six on 77 or more tries: 1 in a million.
A six on 153 or more tries: 1 in a trillion.
Suppose you rolled an apparently fair die 153 times and
it never came up six. Would you say, "Oh, that's
unusual. Still, it's not impossible. Yawn." or
would you look for another explanation?
We both would look for another explanation.
But would we look for another explanation if we found 153
earth-like planets orbiting suns in an outer space area of
roughly a trillion stars?
Every week, somebody does the highly improbable. They win a
lottery. You're looking at it from the one-person-winning
point of view. Look through the other end, and ask: out of a
trillion tosses of the die, approximately how many times
should a 6 appear in a row?
Suppose we have a universe of monkeys typing away as above.
On average, they will succeed after 10^19842 AotU.
What are the chances they will succeed...
Before 10^19842 AotU? 2 in 3 (63%).
Before 10^19841 AotU? One in 10.
Before 10^19840 AotU? One in 100.
Before 10^19742 AotU? One in 10^100.
Before 10^100 AotU? One in 10^19742.
If something happened that had only a one in 10^19742
chance of happening randomly, wouldn't you look for a non-random
explanation for it happening? Don't think of winning the
Lottery. Think of winning the Lottery every time you play;
and the horse you bet on always winning; and always
drawing a straight flush when you play poker. And that
/still/ wouldn't use up the luck expressed above. Wouldn't
you think there might be something beyond mere luck involved?
In /Contact/, the message was not discovered by a universe
full of monkeys or some other fantastical assemblage of
processors. It was found using near-present computer
technology available here on panet Earth. It could only
have been found if it were much, much closer to the beginning
of pi than we would expect from a random ditribution.
The question analogous to the above would be:
What are the chances they'll succeed
Before 0.00000...0001 AotU? Damn small.
But say that it appears on the 6th try, and then in another creation
scenario it appears on the 1st. Both fit within your limit of
possibility without the requirement for a god. The validity of your
calculations actually proves that!
Another way of looking at it is the hat with a bunch of letters in it.
Let's say that when the letters are mixed in the hat and the hat
turned over and dumped on the ground, they spell a complete sentence
of something. The point is that that sentence, given all probable
outcomes, is not only probable but (virtually) necessary as an outcome
given more opportunities for a turn of the hat than possible outcomes.
(The fact that it spells something means nothing to the letters any
more than we can pick stuff out of a hot bowl of alphabet soup.)
What, for example, is the probability of the sentence spelling
1,2,3,4,5,6 given six one-sided dice in a hat? (Now dump the hat
several times MORE than that, and the 1-6 sequence is inevitable.)
What is the probability for the sentence to spell 1,2, given a one and
a two being mixed and turned 70 or 80 times? As you can see the
chances will have to appear (the sentence will have to appear) just
given the turns and tosses outweighing the total possibilities.
The monkey problem is no different. If it happened on the very first
try, it would /still/ fit within your total limit of possible tries!
For you to prove god through probability (and I'd be immediately
suspect of that method), you'd have to prove that an outcome
unequivocally CANNOT happen, and then show that it does on the
impulse of a confirmed communication from such a god.
A close second might be, let's say that we announce to the world that
all cancer will be eradicated as promised from some god, on a specific
date and time. And then it happens! Such a being, from our present
knowledge, would appear to us to be god-like. It still doesn't prove
its a god, but may serve as a practical purpose to see it that way,
relative to us.
I'm guessing that you're letting me know here what you personally
would or would not find convincing. To each their own.
Personally, though, I don't like to be so dogmatic about the
non-existence of God. I mean, it's not like real evidence is
at all likely to turn up. I would guesstimate the chance of
any such evidence being found as somewhere around the chance
of the circles randomly turning up in pi.
All I'm saying, Jim, is that if a highly unlikely situation
can presuppose god, then why not any other less likely
situation as well? I mean, what's the connection between one
probability and another automatically defaulting to god?
The lottery winner says "I've been blessed by god because
the probability of ME (specifically) winning is so unlikely
I must have been chosen. But he completely ignores the other
several million that DIDN'T win.
Why, therefore, would any probability default to god? In
other words, if there was no god, would the laws of
probability change?
Besides, as a bonus, by holding that possibility open, I get to exude
scientific righteousness. And maybe the horse will sing.
Jim Burns
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| User: "Jim Burns" |
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| Title: Re: Question to Atheists |
29 Oct 2006 08:30:03 PM |
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AcesLucky wrote:
James Burns wrote:
[...]
Nothing I've done involves a maximum number of tries. The
last very large number I reported, 10^19,842 AotU, is the
expected wait. If the universe of full monkeys is set up
over and over, sometimes it will be shorter than that,
sometimes longer, but the average wait will quickly
approximate that number.
What precludes the event happening "before" that number?
What do you mean by "preclude"? How I understand the word,
I just got finished stating the exact opposite of what your
question implies.
If your question can be stated, "What /prevents/ the event
happening "before" that number?" I just said, in that paragraph
right before your question, "sometimes it will be shorter
than that". So the answer to that question would be "It's
not prevented from doing so; it's just extremely unlikely."
If you're asking, "What's special about 10^19,842 AotU
away from now that it should happen then and not now?",
then there's nothing special about then as opposed to
now that makes it more likely or now less likely. That's
not why now is so unlikely.
If I were to predict that California would have a major
earthquake sometime in the next century, that would be
fairly uncontroversial, I think. However, if I were to
predict a major earthquake in California starting at
1:23:45 AM PST to the seocnd, I would not be believed
(beforehand) and I would have to show how I made my prediction
if I were somehow right (afterwards). The second prediction
is much less likely than the first because it is so much
more specific than the first.
Set the monkeys typing away eon after eon. It's about 1/10
as likely that one of the 10-page targets will be created in
the first 13.6 billion years (1 AotU) as that one will be
created in the first 136 billion years (10 AotU). This is not
because there's anything special about the first AotU, but
because it's the shorter period.
Suppose we count as successful the universe full of monkeys
typing one of their targets sometime in the next 100 billion
(100,000,000,000) years. (This is a grotesquely unfair comparison
to the message in pi, because that message was found by a
single computer in a handful of years, but never mind.)
That seems like an enormous length of time from the human
perspective, but it's just a tiny blip compared to the length
of time you're dealing with in this monkey-Shakespeare deal.
My prediction is that there's a 63% that the monkeys will be
successful over the next 100,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
... < insert 415 more rows of zeroes > ...
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000, years. The chance that
they'll be successful in any specific 100,000,000,000 year
period (for example, the first such period) is calculable,
but it's not significant in any way I can think of.
[...]
My argument is that a message appearing would be so
inconceivably unlikely that we would be wise to look for
explanations other than random chance.
Then your math would have to be incorrect by default. If
your math states it should take an average of X amount of
time (or tries), why would you assert right behind it that
it takes too long?
I don't understand where you think I said something will
take too long. Could you quote the offending phrase, please?
Rolling a die and having it come up 6 is not
a good analogy to this, since it is not inconceivably likely.
A better analogy would be rolling a die and having it turn
into a potted plant.
No. One "can" happen and the other cannot.
Why do you think one can happen and the other cannot?
Because you've seen one happen and the other not? No, that
can't be it, because, while you have seen dice come up
six, you haven't seen monkeys turn out pages of Shakespeare
or circles appear in the digits of pi or dice turn into
potted plants.
We have no explanation for why a die would turn into a
potted plant, but we also don't have an explanation for why
Shakespeare or circles would just happen to show up in
that one tiny blip of time that we could devote to looking
for them, the 100,000,000,000 years we find ourselves living in.
Are there laws of physics that prevent dice from turning
into potted plants? If you think so, you should say what
they are. I don't think so. I do think there are calculations
that could be made (in principle) that would show it's
extremely unlikely for a die to turn into a potted plant,
but that's where my analogy comes from.
(In quantum mechanics, if you calculate the overlap of
the wave functions of two states, you get the probability
that the system will jump from one state to the other
(assuming all the conservation laws are followed). If
you had the exact wave function for a die (the being-a-die
state) and the exact wave function for a flower pot (the
being-a-flower-pot state) and calculated their overlap,
it would very likely be extremely small but not zero.
It would be even more unlikely for the overlap of the
two states to be precisely zero, because that would
indicate that the die and the flower pot are closely
related in an important way ("orthogonal"). And why
would they be related? I'd rather talk about typewriting
monkeys.)
Here are some more numbers:
A six on the first try: 1 in six.
A six on seven or more tries: 1 in three.
A six on 27 or more tries: 1 in 100
A six on 77 or more tries: 1 in a million.
A six on 153 or more tries: 1 in a trillion.
Suppose you rolled an apparently fair die 153 times and
it never came up six. Would you say, "Oh, that's
unusual. Still, it's not impossible. Yawn." or
would you look for another explanation?
We both would look for another explanation.
Here you are agreeing with my exact point. We should look
for another explanation for a message showing up in the
digits of pi because it would be such an unlikely thing
to happen.
Here are all the possible explanations I can think of:
(1) random chance (not off the table, but I'll have to see
that the other options are even more unlikely if I'm going
to take it seriously--see David Hume's "On Miracles"),
(2) fraud (my preferred candidate, but because this is a
calculation, double-, triple- and n-tuple-checking would
make it a different miracle if it weren't found out), and
(3) the message was put there. How the message was put there
would be an interesting question. Even if we assume some
superbeing made the universe, I don't see how it could put a
message in pi. On the other hand, I am about as certain as I
could be that anything remotely human could not.
But would we look for another explanation if we found 153
earth-like planets orbiting suns in an outer space area of
roughly a trillion stars?
Tell me what the odds are for that happening. Show your work.
I'm especially interested in what you know about the formation
of earth-like worlds.
If we thought we understood the process of formation of
earth-like planets well enough and our understanding predicted
a wildly lower or a wildly higher number, then we absolutely
would look for another explanation. The wrong number would be
an indication that we weren't as smart as we thought we were.
This is how science is done.
Every week, somebody does the highly improbable. They win a
lottery. You're looking at it from the one-person-winning
point of view. Look through the other end, and ask: out of a
trillion tosses of the die, approximately how many times
should a 6 appear in a row?
I deny that I'm looking at it from the one-person-winning
point of view.
If I play the lottery once and win, there's a one in 7 million
chance of that happening (assuming pick 6 out of 44). If
millions of people play day after day, the chance of someone
in those millions winning every day or so will be much higher,
enough so that no one is surprised when that happens.
My example is way beyond millions of people playing
the lottery day after day. Not just one winning lottery
combination, I use 10^18, that is, 1,000,000,000,000,000,000
winning ten page sequences of characters. Not played every day,
but 10^43 times every second, 10,000,000,000,000,000,000,000,
000,000,000,000,000,000,000 "tickets" every second. Not
millions of monkeys playing, but 10^87, that is, 1,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000 monkeys.
With all that help for the monkeys, the probability of any
one of them succeeding once is still so remarkably low
because it was even lower, incredibly lower, to start with.
I don't understand what your question about sixes
in a row has to do with anything.
[...]
Personally, though, I don't like to be so dogmatic about the
non-existence of God. I mean, it's not like real evidence is
at all likely to turn up. I would guesstimate the chance of
any such evidence being found as somewhere around the chance
of the circles randomly turning up in pi.
All I'm saying, Jim, is that if a highly unlikely situation
can presuppose god, then why not any other less likely
situation as well? I mean, what's the connection between one
probability and another automatically defaulting to god?
The reason the god explanation would come up is because
I can't think of any other explanations. (See above.)
You're welcome to try.
The lottery winner says "I've been blessed by god because
the probability of ME (specifically) winning is so unlikely
I must have been chosen. But he completely ignores the other
several million that DIDN'T win.
Except I haven't ignored the several million who didn't win.
(See above.)
Why, therefore, would any probability default to god? In
other words, if there was no god, would the laws of
probability change?
I've explained why the laws of probability are not a good
explanation in this case. I've also mentioned that they
could still turn out to be the best of a bad lot.
But tell me, what explanation do you have besides
random chance, fraud and god?
Jim Burns
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| User: "AcesLucky" |
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| Title: Re: Question to Atheists |
01 Nov 2006 10:43:16 PM |
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Jim Burns wrote:
AcesLucky wrote:
James Burns wrote:
[...]
Nothing I've done involves a maximum number of tries. The
last very large number I reported, 10^19,842 AotU, is the
expected wait. If the universe of full monkeys is set up
over and over, sometimes it will be shorter than that,
sometimes longer, but the average wait will quickly
approximate that number.
What precludes the event happening "before" that number?
What do you mean by "preclude"? How I understand the word,
I just got finished stating the exact opposite of what your
question implies.
If your question can be stated, "What /prevents/ the event
happening "before" that number?" I just said, in that paragraph
right before your question, "sometimes it will be shorter
than that". So the answer to that question would be "It's
not prevented from doing so; it's just extremely unlikely."
If you're asking, "What's special about 10^19,842 AotU
away from now that it should happen then and not now?",
then there's nothing special about then as opposed to
now that makes it more likely or now less likely. That's
not why now is so unlikely.
Yes and yes. I'm asking what automatically prevents the
event from happening at any time "within" that range from
zero (now) to 10^19,842 AotU?
I see [10^19,842 AotU] as the number of faces on a
[10^19,842 AotU] sided die.
So the chances of the event happening at any point (today or
tomorrow, or 100 eons from now) is equal; or 1 to [10^19,842
AotU].
This is why I also said that (assuming your math is correct)
the event (within that time span) will actually LIKELY
happen...once!
How, then, can the event happening (at all) imply god, when
(given that amount of time) the event will happen anyway?
If I were to predict that California would have a major
earthquake sometime in the next century, that would be
fairly uncontroversial, I think. However, if I were to
predict a major earthquake in California starting at
1:23:45 AM PST to the seocnd, I would not be believed
(beforehand) and I would have to show how I made my prediction
if I were somehow right (afterwards). The second prediction
is much less likely than the first because it is so much
more specific than the first.
Set the monkeys typing away eon after eon. It's about 1/10
as likely that one of the 10-page targets will be created in
the first 13.6 billion years (1 AotU) as that one will be
created in the first 136 billion years (10 AotU). This is not
because there's anything special about the first AotU, but
because it's the shorter period.
Suppose we count as successful the universe full of monkeys
typing one of their targets sometime in the next 100 billion
(100,000,000,000) years. (This is a grotesquely unfair comparison
to the message in pi, because that message was found by a
single computer in a handful of years, but never mind.)
That seems like an enormous length of time from the human
perspective, but it's just a tiny blip compared to the length
of time you're dealing with in this monkey-Shakespeare deal.
My prediction is that there's a 63% that the monkeys will be
successful over the next 100,000,000,000,000,000,000,000,000
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000, | | | | | | | | | | | | | | | | | |
