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Author Topic:   Proving God Statistically
Rei
Member (Idle past 7013 days)
Posts: 1546
From: Iowa City, IA
Joined: 09-03-2003


Message 16 of 96 (66770)
11-16-2003 12:06 AM
Reply to: Message 15 by DNAunion
11-15-2003 9:00 PM


In a system where we are talking about something that is truly random, you are correct. In a system such as the creation of life on earth, that is not an apt description, because we are not looking at a completely random system.
------------------
"Illuminant light,
illuminate me."

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compmage
Member (Idle past 5153 days)
Posts: 601
From: South Africa
Joined: 08-04-2005


Message 17 of 96 (66810)
11-16-2003 9:53 AM
Reply to: Message 13 by DNAunion
11-15-2003 6:28 PM


DNAunion writes:
Therefore, while we should not be surprised to hear that "Frank" hit upon your sequence by chance in a single shot, we should be surprised to hear that "Frank" hit upon the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 by chance in a single shot (in fact, we should probably reject "Frank"'s claim).
Why?
As I said, ANY sequence has EXACTLY the same chance as any other. Just because you find that sequence "special" means nothing. All you have done is argued for the fact that a recognizable sequence is "special". That some people will assign more meaning to certain combinations is not disputed. It does however have no bearing on the likelyhood of getting that combination.
------------------
He hoped and prayed that there wasn't an afterlife. Then he realized there was a contradiction involved here and merely hoped that there wasn't an afterlife.
- Douglas Adams, The Hitch Hiker's Guide to the Galaxy

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 18 of 96 (66825)
11-16-2003 11:06 AM
Reply to: Message 17 by compmage
11-16-2003 9:53 AM


I think in this case the coins were deliberately numbered to pick *in advance* the sequence 1,2 ... 10. This makes it "special". As you say any sequence has the same odds against. Calling it amazing after it has occured sounds pretty silly. However, calling it in advance and then pulling it is something else altogether.

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Replies to this message:
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DNAunion
Inactive Member


Message 19 of 96 (66932)
11-16-2003 7:39 PM
Reply to: Message 18 by NosyNed
11-16-2003 11:06 AM


quote:
I think in this case the coins were deliberately numbered to pick *in advance* the sequence 1,2 ... 10. This makes it "special". As you say any sequence has the same odds against. Calling it amazing after it has occured sounds pretty silly. However, calling it in advance and then pulling it is something else altogether.
It can be done afterwards, but it is not always as clear cut as it is when a specific prediction is made ahead of time. Since letter sequences demonstrate this better than numbers, I'll switch to using them.
Take 27 identical tiles and paint a unique letter of the English alphabet on each, and on the remaining one an underscore to represent a space, then place them all into an urn. For this thought experiment the number of letters we will select one at a time from the urn will be represented by the variable n. Draw a linear and contiguous series of n boxes from left to right, each of which will hold a single letter that is drawn from the urn. The letters will be written sequentially, each in the leftmost empty box at the time it is drawn.
Now perform the following steps n times:
(1) thoroughly shake the urn to randomize the tiles
(2) randomly select a single tile from the urn
(3) write down the letter on the tile in the appropriate box
(4) replace the tile
Now any single n-letter outcome is just as unlikely as any other single outcome. I am not disputing that. My argument is based on an aggregate view, which involves partitioning the possible outcomes into two sets: success and failure. With that in mind...
Would you be surprised if someone claimed to have followed the above method and ended up with, in a single trial, the following?
P_AOZIUHV_EU_KS__IPBODQKVO_IYTCR
Probably not: there’s nothing readily noticeable in that result that immediately raises suspicion of cheating.
But, what if the person claimed to have obtained any of the following in a single run through:
FOR_SCORE_AND_SEVEN_YEARS_AGO___
or
ME_THINKS_IT_IS_LIKE_A_WEASEL___
or
ONTOGENY_RECAPITULATES_PHYLOGENY
You should seriously doubt the claim that chance alone produced those results. But why? After all, each one of these particular sequences has the same exact probability as the other single sequence...so why should we be surprised to see any of these results, but NOT be surprised to see the first one?
Because the second outcomes match patterns specified independently of the event: they're a line from Lincoln's Gettysburg Address, a line from one of Shakespeare's works, and a summarization of Haeckel's position of recapitulation.
Note that no one had to proclaim ahead of time, "Hey, I predict this guy is going to select ME THINKS IT IS LIKE A WEASEL" or either of the other two. The MATCHING of the outcome to an independent pattern that eliminates chance from being the best explanation occurred AFTER the event, not before.
Now we can go the extra step to show that the pattern itself can be specified after the event.
Suppose n is 66 and a person claims to follow the method spelled out above and to have hit upon the following in a single shot:
I_WAS_PULLING_TILES_OUT_OF_AN_URN_AND_THIS_IS_WHAT_I_ENDED_UP_WITH
Clearly such a recognizable English sentence doesn't have to be specified PRIOR to the event in order to be used as a non-ad hoc pattern capable of eliminating chance.
We simply don’t accept that someone is going to pull chips from an urn using a truly random process and end up with a long and meaningful English statement: sufficiently complex and specified outcomes do not occur by chance alone. It is important to keep in mind that there are two requirements for eliminating chance: sufficient complexity (sufficiently low probability) and specification (a non-ad hoc pattern that the outcome matches).
[This message has been edited by DNAunion, 11-16-2003]

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Replies to this message:
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crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 20 of 96 (66939)
11-16-2003 8:38 PM
Reply to: Message 19 by DNAunion
11-16-2003 7:39 PM


You should seriously doubt the claim that chance alone produced those results.
Should I? It depends of course on how many trials it took before they got that result.
We simply don’t accept that someone is going to pull chips from an urn using a truly random process and end up with a long and meaningful English statement:
See, you had it right at the first part; partitioning all possible strings into two different sets. The set of significant strings is considerably smaller than the set of insignificant strings, yes.
So, the odds of acheiving a significant string is the number of such strings divided by the number of all possible strings. If it's your position that this number is astronomicall small, you would be correct. But, when you say things like this:
sufficiently complex and specified outcomes do not occur by chance alone.
You seem to be implying that there's zero chance. There's a considerable difference. In fact it's the difference between something and nothing. Could you explain your mathematics here? Especially how you get 0 from p divided by q, where p and q are both non-zero integers.
[This message has been edited by crashfrog, 11-16-2003]

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 21 of 96 (66951)
11-16-2003 10:00 PM
Reply to: Message 20 by crashfrog
11-16-2003 8:38 PM


The real point is that you know the number of all possible results and you can define the number of "acceptable" results to calculate the odds.
Even in this case there is some prior selection being done. We speak English, in fact we are really interested in the odds of something coming out in any language.
If we were to compare this to the patterns in DNA we would have to accept all possible languages as well. I'm not sure we can even calculate the odds in the case of letters talk about anything else.

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Replies to this message:
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crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 22 of 96 (66956)
11-16-2003 10:26 PM


What's the point of this thread? Precisely which thing are we saying couldn't have happened by "chance"? (How about chance + selection?)

  
DNAunion
Inactive Member


Message 23 of 96 (66961)
11-16-2003 11:04 PM
Reply to: Message 20 by crashfrog
11-16-2003 8:38 PM


quote:
You should seriously doubt the claim that chance alone produced those results.
quote:
Should I?
Yes, you should...
quote:
It depends of course on how many trials it took before they got that result.
Which was stated in my post: 1 attempt.
*************************
quote:
See, you had it right at the first part; partitioning all possible strings into two different sets. The set of significant strings is considerably smaller than the set of insignificant strings, yes.
So, the odds of acheiving a significant string is the number of such strings divided by the number of all possible strings. If it's your position that this number is astronomicall small, you would be correct. But, when you say things like this:
*****************************
sufficiently complex and specified outcomes do not occur by chance alone.
*****************************
You seem to be implying that there's zero chance. There's a considerable difference.
Which is why I intentionally refrained from saying what you think I said.
I purposely avoided saying that such things CANNOT occur by chance alone; I said they DO NOT. There is a difference.
(Well, let me head off attempts to show that there is not difference. To do that, one would have to demonstrate that literally everything that is not impossible actually does occur. Of course there is the highly speculative MWI: it's hardly able to be demonstrated. How about sticking to things that are testable. Let's see...I'm sitting here typing on my keyboard and it is not literally impossible for my hard drive to fail before I finish typing this sentence. Well, it wasn't impossible and it didn't happen.)
quote:
Could you explain your mathematics here? Especially how you get 0 from p divided by q, where p and q are both non-zero integers.
No, because I didn't end up with 0. Here’s what I actually said.
quote:
... sufficiently complex and specified outcomes do not occur by chance alone. It is important to keep in mind that there are two requirements for eliminating chance: sufficient complexity (sufficiently low probability) and specification (a non-ad hoc pattern that the outcome matches).
I said sufficiently low probability, not 0 probability.

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Replies to this message:
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 Message 54 by Peter, posted 11-19-2003 2:24 AM DNAunion has replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 24 of 96 (66963)
11-16-2003 11:18 PM
Reply to: Message 23 by DNAunion
11-16-2003 11:04 PM


Which was stated in my post: 1 attempt.
But say, if we were talking about a trillion trials a second, perhaps, for a billion years, you wouldn't find anything odd about arriving at those sequences?
I said sufficiently low probability, not 0 probability.
And how low is that? Is there a specific threshold? Or are we just supposed to "know"? And then of course the problem is showing that the specific chemical reactions that lead to life (if that is indeed where this thread is going) fall under that threshold.
[This message has been edited by crashfrog, 11-16-2003]

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Replies to this message:
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DNAunion
Inactive Member


Message 25 of 96 (66964)
11-16-2003 11:29 PM
Reply to: Message 21 by NosyNed
11-16-2003 10:00 PM


quote:
Even in this case there is some prior selection being done. We speak English, in fact we are really interested in the odds of something coming out in any language.
Yes, we are interested in any language. I believe French uses the same set of symbols for their language, so if a meaningful French sentence appeared I would miss it, but a French speaking person would not. Is that a problem? Not as far as eliminating chance is concerned. Here's why.
ME: I see no recognizable pattern so I don't eliminate chance.
HENRI: I see a meaningful French statement so I eliminate chance.
The point is that chance was not eliminated when it shouldn't have been. Thus, the method is still a reliable method of eliminating chance.
quote:
If we were to compare this to the patterns in DNA we would have to accept all possible languages as well. I'm not sure we can even calculate the odds in the case of letters talk about anything else.
Actually, that has basically been done by Dembski (please, let's stick to probability and not try to apply it to evolution!).
I'm a bit rusty on this, but...
What he was looking for was the maximum number of specifications (non-ad hoc patterns) that could have been produced since the origin of the Universe. To arrive at this number he took the estimated number of elementary particles in the universe (10^80), multiplied it by the number of seconds the Universe has existed (based on 15 billion years, I think), and then multiplied that by the number of reactions that can occur per particle per second, based on Planck time (I think 10^43 or something like that). When all was done, he calculated that since the origin of the Universe a maximum of 10^150 specifications could have been made.
At this point I am losing track of his argument: how exactly one gets from here to the final conclusion (I told you I was rusty).
Anyway, his position is that any event that did occur and (1) was sufficiently complex (had a probability smaller than 10^-150), and (2) was specified (matches an independently created, no-ad hoc pattern), should not be attributed to chance.
The 10^-150 is his "universal probability bound". For events that we don't have to look at the whole universe - for example, Mr X winning the state lottery 5 times in a row - we can use a local probability bound.
[This message has been edited by DNAunion, 11-16-2003]

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 Message 21 by NosyNed, posted 11-16-2003 10:00 PM NosyNed has replied

Replies to this message:
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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 26 of 96 (66965)
11-16-2003 11:31 PM
Reply to: Message 24 by crashfrog
11-16-2003 11:18 PM


Yes, Crash there is a threshold but it isn't very specific. It would vary depending on the importance of making a decision one way or the other.
In fact, picking a threshold would have to involve some of what you are suggesting. How many trials can be performed? If a lot then a very low probability is still over the "threshold".

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Replies to this message:
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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 27 of 96 (66966)
11-16-2003 11:38 PM
Reply to: Message 25 by DNAunion
11-16-2003 11:29 PM


Well, the problem is that still only eliminates chance for things which are independant random events.
With letters drawn from a hat we can be careful that it is random (but have to work at it a little). With chemistry we know that many reactions are not random so the whole calculation goes out the window.
Of course, in addition, we have to know how to calculate the "success" probability. In our letters example, as you noted, we have to know for all possible languages. And we can not know all possible languages.
[This message has been edited by NosyNed, 11-16-2003]

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 Message 25 by DNAunion, posted 11-16-2003 11:29 PM DNAunion has replied

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DNAunion
Inactive Member


Message 28 of 96 (66968)
11-16-2003 11:49 PM
Reply to: Message 26 by NosyNed
11-16-2003 11:31 PM


quote:
Yes, Crash there is a threshold but it isn't very specific. It would vary depending on the importance of making a decision one way or the other.
In fact, picking a threshold would have to involve some of what you are suggesting. How many trials can be performed? If a lot then a very low probability is still over the "threshold".
Which Dembski takes into account. He speaks of taking all probabilitist resources into consideration to arrive at a saturated probability. For example, the probability of tossing a 20 heads in a row with a fair die in a single attempt is 1 in 1,048,576. This is indeed small and we should not expect to do it in a single attempt. But taking all of the coin tosses every made into account, which would easily be greater than one million, we should not be surprised to learn that someone somewhere has achieved 20 consecutive heads by chance alone.
But what about 500 heads in a row by chance? We should reject that no matter how many people performed how many tosses...the probability is simply too low for this specified event to occur by chance alone, even taking all humans that ever lived into consideration.
This may not be the ultimate quote on this, but it does show the general idea.
quote:
"In sum, probabilistic resources comprise the relevant ways an event can occur (replicational resources) and be specified (specificationsl resources) withing a given context. The important question therefore is not What is the probability of the event in question? but rather What does its probability become after all relevant probabilitist resources have been factored in? Probabilities can never be considered in isolation, but must always be referred to a relevant class of probabilitist resources. A seemingly improbable event can become quite probable when referred to the relevant probabilitist resources." (William Dembski, The Design Inference: Eliminating Chance Through Small Probabilities, Cambridge University Press, 1998, p181-182)

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DNAunion
Inactive Member


Message 29 of 96 (66971)
11-17-2003 12:00 AM
Reply to: Message 27 by NosyNed
11-16-2003 11:38 PM


quote:
Well, the problem is that still only eliminates chance for things which are independant random events.
With letters drawn from a hat we can be careful that it is random (but have to work at it a little). With chemistry we know that many reactions are not random so the whole calculation goes out the window.
To a greater extent, once evolution comes into play, I don't see how Dembski's method can be applied. I think Dembski's EF works accurately to eliminate chance in general probabilistic events (tossing coins, choosing letters, and many other everday things) but not for biological processes.
quote:
Of course, in addition, we have to know how to calculate the "success" probability. In our letters example, as you noted, we have to know for all possible languages. And we can not know all possible languages.
But the purpose of the method is to be able to eliminate chance: that is, when we eliminate chance using the method chance has been correctly eliminated. This doesn't depend upon our being able to recognize French, for example: in such cases where we miss meaningful French statements we would fail to eliminate chance, leaving chance as a possible explanation. That is not a problem because of the purpose of the method (it is not to detect chance, but to eliminate it).

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 Message 27 by NosyNed, posted 11-16-2003 11:38 PM NosyNed has not replied

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 30 of 96 (66972)
11-17-2003 12:04 AM
Reply to: Message 28 by DNAunion
11-16-2003 11:49 PM


But the probability of any number of head and tails in 500 trails is just as low. We do have to specify it as you say. All heads isn't "special" unless it is specified to be in someway.
The problem with our letters drawn from a hat example is we don't know the limits of the specificity. If we are using it as an analogy for things like different physcial laws in universes or different bases patterns in DNA (or some other possible life like chemical ) then we have to know not just all EXISTING languages but all possible languages that would "work". We don't know that.
Also if we did prespecify heads as being "special" then we would be surprised by 500 in a row. And what would our first guess be about what is going on? A fixed coin! In other words the chances are not random. We know in chemistry that things aren't random. We don't have a clue about universal physical laws one way or the other. (not yet anyway).
On that basis the whole chance calculation comes to pieces.
Additionally, if we are talking about the origin of life we still don't know how complex the simplest form of a self replicator can be. So we don't know how many "heads" we have to through.

This message is a reply to:
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