# Large Number Theories



## kceaster (Sep 14, 2005)

My boss and I were having a discussion at work and he mentioned a large number theory that was postulated like this:

If you took a thousand chimps and put them in a room full of typewriters for 100 years, eventually they would type any statement of your choice.

I chose, "The basketball went through the hoop."

Now, this number theory is based upon the 26 letters of the alphabet, plus spaces. And my boss is convinced that the statement would eventually appear.

I argued that the indicative statement I made requires reason and that no amount of randomness could ever produce it.

He then made an analogy that basically says if we had an infinite number of white basketballs in a bucket and one red one, we'd eventually pick the red one, if we lived long enough.

I told him that it didn't think the two were analogous. I told him that it would be analogous only if the bucket contained the materials to make a red ball. But he wasn't about to grant the premise that eventually the materials would form to make a ball. I'm pretty sure that he's not a believer of evolution.

But my argument that the chimps won't type the above statement is because the statement doesn't exist in a vacuum or without reason. In order to pull the red ball out of the bucket, it has to exist. In order to get the chimps to type any statement that makes sense, they have to have reason.

Am I wrong about this, or do I need more math?

Blessings,

KC


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## Puddleglum (Sep 14, 2005)

You've got 36 letters & spaces, if I counted correctly. 

It is a theoretically possibility to get that statement as a result of random chance. 

However, the probability is (1/27)*(1/27)*(1/27) . . . until you have 36 (1/27)'s. In other words, the probability of that statement occuring randomly is 1/(27^36). 

BTW, 27^36 is roughly equal to 3.38*10^51. 1/(27^36) is roughly equal to 2.96*10^-52. 

Basically, it's theoretically possible, but extremely improbable. If you knew how fast chimps type you should be able to work out how long you'd have to give them to come up with this random statement.


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## biblelighthouse (Sep 14, 2005)

Enough monkeys would certainly be able to type the statement, given enough time, but of course that does not mean they would be able to understand it. You don't need reason to type it, just reason to understand it. However, the odds of typing that _purely_ at random are very low.

Think of it as flipping a coin. Except instead of 2 sides, this "coin" has 27 sides: one "side" for each letter of the alphabet, plus an extra for spaces.

The odds of getting the first letter, "t", purely at random, are 1 in 27. The odds of getting the second letter immediately afterwards are also 1 in 27. So, the odds of getting the first two letters in order, purely at random, are 1 in 27*27, or 1 in 729.

The odds of getting all 36 letters and spaces in order, purely at random, are 1 in 27^36, which results in a number that is about 51 digits long. . . . i.e. it is theoretically possible, but the odds are so slight that I wouldn't wait around for it. It would take a lot of monkeys a lot of years for that particular statement to be typed.

However, how long would it take them to type _any_ sentence that you or I would recognize as having meaning? Now that is a much more interesting, though more difficult, question.

For example, even if I get some of the letters wrong, the statement still makes sense to you:
"the baskitbal wint through the hooop"

And there are numerous such "misspellings" that would make just as much sense. Thus, the underlying "meaning" is not strictly dependent on spelling. If we accept such spellings, as long as they are still understandable, the odds become much much better.

Plus, if we are only looking for _any_ meaningful sentence, then we aren't restricted to the basketball sentence. These sentences might also pop up, before the basketball sentence ever does:
--- "I like popcorn" (The odds of this one are much better: 1 in 17 sextillion)
--- "eat at joes" (odds: 1 in 5 quintillion)
--- "I am" (odd: 1 in 531,441)

Plus, there are virtually _countless_ other statements that could be typed, which you or I would consider meaningful. Add all of these possibilities together, and you would very likely have a "meaningful sentence" typed _every single day_ . . . maybe even several of them!

So, the mathematical probabilities really do depend on how you phrase the question from the beginning.

But of course, as we have already agreed, the monkeys themselves would not understand any of the sentences.

[Edited on 9-14-2005 by biblelighthouse]


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## kceaster (Sep 14, 2005)

Joseph,

How long do you think it would take a super computer to do this?

If you would do this on a computer, would you have to program it with some sort of intelligence, or just tell it to pick random letters and spaces until it eventually got the right ones?

Then, wouldn't you have to program a computer to parse the information so that it could find the correct sequence?

KC


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## Dan.... (Sep 14, 2005)

Another consideration is that just because there is a 1/(27^36) probability that they could write the sentence, does not mean that they will write the sentence within the first 27^36 time frame. 

E.g., there is a 1 in 6 chance that when I roll a dice that the number 3 will come up. That does not mean that I will necessarily roll a three within the first six rolls. I might roll 24 or more times before a 3 appears on top (which is 4 times as many rolls as the probability). So also, the monkeys might type 4*(27^36) and still not type your sentence. Probability is no guarantee.


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## JohnV (Sep 14, 2005)

Also remember that the odds do not improve by countdown. With each toss of the 27-sided dice you do not eliminate or decrease the odds. The odds remain the same after each and every toss; the odds represent the positive possibilities. It is also possible, and mostly so, that it could never happen. 

So I believe you are right, Kevin, that it is not just mathematical. The mathematical aspect, known as probability, only shows the odds. The postulation is that it will happen if the possibility is there for it to happen, or that it is likely to happen if the possibilty exists, however slight. And that is not strictly according to the odds that are mathematically possible. Even if the chimps came up, by sheer luck, with that random set of digits from the typewriters, from one of them, they still represent the exact same thing as if the digits typed were complete nonsense. In other words, a meaningful sentence would still be impossible, since it would be by random chance that the sentence was formed. It still does not address the underlying assumption that the chimp that typed it meant to express it, or that any one of the chimps was moved by it toward thinking that there was such a thing as intelligibility as an aim. For all the chimps, it would have been just fun with the keys, and no more. What you have is man-made (that is, intellligently designed) typewriters, and supposedly someone to proofread the typed results. This decreases the "large number 
theory" critically. That is, you would first need to postulate that enough chimps in a room, with enough time on their hands, would eventually put together a typewriter and figure out that the letters typed could make sense, and communicate sense. 

The probability is that there aren't enough bananas in the world to allow this to happen. 

However, what gets me is that people jump at, or are taken in by such "theories", when there is a 100% chance, (and not even by chance), that a deity, (no, a Deity with a capital "D") could create out of nothing, raise the dead, and forgive sins without spotting His purity, and yet people have a hard time with that. We live in the Pepsi generation: a generation that thinks it is watching its diet by drinking Diet Pepsi. So they'd rather believe that life can come out of non-life, that form can come out of non-form, that reason can come out of non-reason, that design-dependence can come out of randomness, and on and on ad nauseum, than the simple and straight forward, and proof-filled, revelations of God. But that is also exactly what is described to us as the Fall in the Bible, and witnessed to us in nature.


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## kceaster (Sep 14, 2005)

So is the probability of the first word of our random sentence 27^3?

If that is the case, what happens if the next character is not a space? Doesn't that mean that the random generation would have to start over? We're not trying to get them to type the word, were trying to get them to type the sentence. So doesn't that mean that it's more complicated than 1/27^36?

KC


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## kceaster (Sep 14, 2005)

New thought, what if there was no logic that said they couldn't repeat letters over and over? Wouldn't that mean that there is a lesser than 1/27 chance for them to get the first letter?

KC


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## Dan.... (Sep 14, 2005)

Kevin,

Illustration:

Let's say we are looking for a 8 letter/space phrase, "red book"

There is a 1/(27^8) chance that the first eight characters would spell "red book".

Monkey types the first eight characters.


Whatever he types is unimportant. Let's just say he misses his first chance.

The next "chance" starts at the 2nd character and ends with the 9th. The third "chance" starts with the 3rd character and ends with the 10th.

At this rate, each additionally typed character yeilds another 1/(27^8) chance of spelling "red book". No need to start over as the monkey doesn't know nor need to know what he is typing.

[Edited on 9-14-2005 by Dan....]


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## Dan.... (Sep 14, 2005)

Continuing the above: let's say the average monkey types 150 characters per minute. It would take the monkey (27^x)/150 minutes (x = number of characters in the phrase) to type 27^x characters. Hence the first (27^x)/150 minutes would yield approx. 27^x character string chances. 

Of course, how long it takes to produce 27^x character strings is *only* as relevant as the length of time it takes to roll the dice 6 times in the 1/6 odd of rolling a 3 (i.e., not very relevant, especially if it takes you 24 or more times before a 3 pops up).


[Edited on 9-14-2005 by Dan....]


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## Average Joey (Sep 14, 2005)

> _Originally posted by kceaster_
> My boss and I were having a discussion at work and he mentioned a large number theory that was postulated like this:
> 
> If you took a thousand chimps and put them in a room full of typewriters for 100 years, eventually they would type any statement of your choice.
> ...



You could always say that the chimps wouldn`t live that long.What about food and water?Why would the chimps want to type for 100 years straight anyway?


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## biblelighthouse (Sep 14, 2005)

> _Originally posted by kceaster_
> Joseph,
> 
> How long do you think it would take a super computer to do this?



You'd get many meaninful sentences all day long, every day.



> _Originally posted by kceaster_
> If you would do this on a computer, would you have to program it with some sort of intelligence, or just tell it to pick random letters and spaces until it eventually got the right ones?



No intelligence. Just pick random letters and spaces.



> _Originally posted by kceaster_
> Then, wouldn't you have to program a computer to parse the information so that it could find the correct sequence?



Here's the key to the whole thing. A monkey, and unprogrammed computer, etc., *cannot recognize* any meaningful sentence. In fact, "meaning" has no meaning without intelligence to receive it.

So yes, you would need an intelligent human to parse the data, or to write a program to parse the data.


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## bradofshaw (Sep 14, 2005)

It does seem to me that this theory supposes that the monkeys are able to type in a fassion that would produce specific leters in specific paterns. 

For instance, are monkey's fingers even coordinated enough to guarantee a single key stroke at a time? In other words, there is not an even probability of a single stroke hitting the "q" key closely followed by the "u" key. A pounding monkey is more likely to hit the "q" key along with the "w" key, due to their location on the keyboard. Doesn't this further complicate the probability? Who says monkeys are accurate? It seems to me that a computer program representative of this scenario would have to be adjusted to account for the location of the keys themselves and the likelyhood of them getting hit.

Another thing to think about, if the monkeys did pound the sentence out, this is not the same as non-intelligence giving rise to something that appears to have intelligent design. The monkeys in this scenario have obviously achieved this feat by some sort of purposeful manipulation of the event. Monkeys are animate objects (although a materialist would perhaps argue on the grounds that all intelligence is just matter in motion) and they operate by some sort of independent will. 

Not to mention that somebody probably had to train these monkeys first. The more likely scenario is 100 monkeys jumping up and down on the typewriters, and not sitting still to pound out individual keys. The more you think about this event occurring, the less it seems like random chance, but an intelligently controlled set of circumstances.

This analogy seems to me to break down completely with anything that is observable in nature. The odds assume a set, regular pattern of behavior over a period of time. There are any number of variables that would have to not happen for an event like this to occurr. It seems to me that that would only further convolute the odds.


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## Dan.... (Sep 14, 2005)

I think the "monkey" is a stumbling block to the randomness theory. Replace monkey, chimp, etc... with a device that can randomly output letter and space characters.


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## bradofshaw (Sep 14, 2005)

> _Originally posted by Dan...._
> I think the "monkey" is a stumbling block to the randomness theory. Replace monkey, chimp, etc... with a device that can randomly output letter and space characters.



That begs the question though, what is the purpose of the excercise? We are having to specifically condition the apparatus so that it is even possible for it to produce this outcome. Is it not less random the more programmed it is?

I suppose it would be helpful for illustrating the length of time it would take for such an outcome to occurr, even in a program designed to make the occurrence possible.

A better analogy for chance producing anything ordered or meaningful might be to take 1,000,000 typewriters, air drop them from planes across various points on the globe, and see if anything will ever cause them to type a meaningful sentence (meaningful to humans, which poses another question). 

I've often pondered what the probability of the dirty dishes in my sink accidentally being washed, sorted, and put away in their proper places without intelligent intervention.

[Edited on 9-14-2005 by bradofshaw]


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## Dan.... (Sep 14, 2005)

> That begs the question though, what is the purpose of the excercise? We are having to specifically condition the apparatus so that it is even possible for it to produce this outcome. Is it not less random the more programmed it is?



My guess is that the person developing this exercise was attempting to demonstrate the commonly parroted idea that vast amounts of time plus random chance can produce things as they are now (e.g. macro-evolution).

True, the idea would require something perfectly random, yet, as you point out, there are no perfectly random conditions.

Not only, but if there were perfectly random conditions, then we still could not conclude estimated amounts of time because probability doesn't gaurantee anything.


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## biblelighthouse (Sep 14, 2005)

> _Originally posted by Dan...._
> Not only, but if there were perfectly random conditions, then we still could not conclude estimated amounts of time because probability doesn't gaurantee anything.



Do you _really_ believe that, Dan? Then you'd better go to Vegas.

Play the roulette wheel. The odds are nearly 1 to 2 that you will get red. Put all your money on black every time. Sure, the odds say that the wheel could turn up red instead of black, but you don't have to worry about that, because "we still could not conclude estimated amounts of time because probability doesn't gaurantee anything."

Or, come bet some money with ME at MY house! You get to roll a pair of dice. You win 20 bucks every time you get a 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11. But I win 10,000 dollars from you, every time you roll a 12. You have to roll the dice 5,000 times.

There is only a 1 in 36 chance of you rolling a 12. But you don't have to worry about that, because "we still could not conclude estimated amounts of time because probability doesn't gaurantee anything."



[Edited on 9-14-2005 by biblelighthouse]


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## Dan.... (Sep 14, 2005)

Joseph,

You're comparing a bushel of apples to all the apples in Wisconsin.

Okay here is the bushel of apples: let's say I do take up your offer to roll some dice (but more in the line of $36 dollars on a 12, to $1 on non-12). Let's say I roll once every 10 seconds. How many seconds will it be until I roll your first lucky 12? or how much time will pass before I roll 12 five times? You can't answer either question. You can't say that I will roll a 12 within the first 36 rolls, nor within the first 72 rolls. It might take 3 rolls (30 second); it might take 50 rolls (500 seconds).


Now for all the apples in Wisconsin:
If you can't nearly predict how long it will take to roll my first 12, how can you begin to predict how long it would take with a 1/27^36 probability?


[Edited on 9-14-2005 by Dan....]


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## gwine (Sep 14, 2005)

> _Originally posted by kceaster_
> Joseph,
> 
> How long do you think it would take a super computer to do this?
> ...



This reminds me of Arthur C. Clarke's "9 Billion Names of God" scenario where the computer started writing all the different combinations.

Suddenly, one by one, the stars began to wink out of existance . . .

I wouldn't let them there monkeys mess with things they don't know anything about. :bigsmile:


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## biblelighthouse (Sep 14, 2005)

You are missing the point. I agree that I can't specifically predict the precise time at which a certain goal will be fulfilled. So what?

You have correctly pointed out that it could take twice as long as expected to get the right outcome. But it is also just as likely that it will only take half as long. You would be correct to say that it might take 10 times as long as expected per mathematical probability. But then again, it might just happen on the first try.

Winning the lottery is virtually impossible mathematically. But people still win all the time. 

You are correct that I cannot predict the specific time something will happen. But that does not make me a fool to predict that it *will* happen at some time.

A weatherman in New York cannot predict when it will snow during the winter of next year. But he CAN predict that it WILL snow there sometime next year.

Increasing or decreasing the odds of something doesn't change anything regarding what I have just pointed out. It just changes how often we should expect it to happen.


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## gwine (Sep 14, 2005)

> _Originally posted by Dan...._
> Joseph,
> 
> You're comparing a bushel of apples to all the apples in Wisconsin.
> ...



Indeed if you treat every roll as a seperate event you would never know. But I think the monkey typing question assumes that every permutation would only occur once, so you could give a worse case answer. I'll bet most of the monkeys would type

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

until the bananas run out.

And For what it's worth, the apples up here are pretty good right now.


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## Dan.... (Sep 15, 2005)

Joseph,

 we're on the same wave length.

Gerry,



> And For what it's worth, the apples up here are pretty good right now.



Speaking of which, I am going Friday to pick a few... but they'll be Illinois apples, just a couple miles south of the cheese curtain. Royal Oak Farms, near Harvard. The Senshu's are in season (world's greatest apple!!). http://royaloakfarmorchard.com/Crops.htm


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## kceaster (Sep 15, 2005)

The reason I can't believe anything to be random:

Prov 16:33 The lot is cast into the lap, But its every decision is from the LORD.

Nothing is chance. That which does not exist cannot exist because God hasn't made it to exist. That which does exist is ordered by the Lord.

I don't care how many monkeys with typewriters there are.

KC


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## gwine (Sep 15, 2005)

> _Originally posted by Dan...._
> Joseph,
> 
> we're on the same wave length.
> ...



Sound like a good place to go, and only about an hour's drive for us. We have a small orchard near us but nowhere near the variety. Maybe next Saturday . . .


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## VirginiaHuguenot (Sep 15, 2005)

> _Originally posted by gwine_
> 
> 
> > _Originally posted by Dan...._
> ...



The apple harvest season is upon us here in Virginia too. Next month our family plans to visit a wonderful orchard near Monticello which makes the _best_ apple cider doughnuts!


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## gwine (Sep 15, 2005)

> _Originally posted by VirginiaHuguenot_
> 
> 
> > _Originally posted by gwine_
> ...



That would be a little farther to drive.


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## biblelighthouse (Sep 15, 2005)

> _Originally posted by kceaster_
> The reason I can't believe anything to be random:
> 
> Prov 16:33 The lot is cast into the lap, But its every decision is from the LORD.
> ...




Amen! I love Proverbs 16:33. It proves that God is behind everything, even if apprently random.

Nevertheless, Kevin, I think it is very important to not forget that God has Sovereignly chosen to cause certain things to occur by _apparently random_ means. In other words, God chose to make certain things look random _to us_. 

If you go to the casino (I don't recommend it), the bottom line is that apparent randomness and "probabilities" are all you have to work with. Knowing that God determines everything doesn't help you pick the right number at the roulette wheel. 

Does God determine the fall of the dice? Sure. But try rolling the dice 36,000 times, and you'll roll a 12 about 1,000 of those times. God has Sovereignly decreed that it would be so.

So, studies of "probabilities" and "randomness" are very useful, even though we know God is determining everything behind the scenes. 

Just for example, there is an entire field of computer programing based off the principles of randomness and natural selection. A computer makes random changes to a computer program, to make "child" programs. Then all the "children" are compared with all the "parents". The bottom 50% "die off" while the top 50% continue being randomly modified. Most of the random modification is quite destructive. But a few of the random modifications happen to make the computer program run better, more accurately, more efficiently, etc. Over several hours of running this pseudo "selective breeding" of computer programs, you get a very useful product. Similar methods have been used in searches for physical & electrical designs of real-world products, and has sometimes led to discoveries never made by human experts. There have been a number a patents on products developed in such ways.

So, we cannot just throw the words "random" and "probability" out the window as if they are useless. Theologically, it is critical to remember the Proverbs 16:33 principle, that God determines everything. But it is also important to remember that God Himself has chosen to include _apparent randomness_ in His creation. And neither truth is dispensible.


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## gwine (Sep 15, 2005)

> Just for example, there is an entire field of computer programing based off the principles of randomness and natural selection. A computer makes random changes to a computer program, to make "child" programs. Then all the "children" are compared with all the "parents". The bottom 50% "die off" while the top 50% continue being randomly modified. Most of the random modification is quite destructive. But a few of the random modifications happen to make the computer program run better, more accurately, more efficiently, etc. Over several hours of running this pseudo "selective breeding" of computer programs, you get a very useful product. Similar methods have been used in searches for physical & electrical designs of real-world products, and has sometimes led to discoveries never made by human experts. There have been a number a patents on products developed in such ways.



Evolution by computer selection.


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## SRoper (Sep 15, 2005)

In the original scenario (assuming the monkey at a keyboard is a model for a randomly generated character) given an infinite length of time (or an infinite string of characters) the probability of generating the given sentence is 1. That is, it is guaranteed to happen.

"But my argument that the chimps won't type the above statement is because the statement doesn't exist in a vacuum or without reason. In order to pull the red ball out of the bucket, it has to exist. In order to get the chimps to type any statement that makes sense, they have to have reason.

"Am I wrong about this, or do I need more math?"

You are wrong. The chimps simply have to be able to hit each key in your sentence with a probability greater than 0 and the stamina to keep at it for an infinite length of time. In fact, to think otherwise would be to take a rather existentialist view of reality. It would be more analagous to say that you have to be able to recognize a red ball as a red ball to be able to pull a red ball out of the bin. So a blind man would never be able to pull a red ball out of the bin. This is obviously absurd.

"Nothing is chance. That which does not exist cannot exist because God hasn't made it to exist. That which does exist is ordered by the Lord.

"I don't care how many monkeys with typewriters there are."

OK, you can say that it was providence that the monkeys will eventually type your sentence, and I agree. However, that does not mean that randomness as a model is not a useful concept.

" Also remember that the odds do not improve by countdown. With each toss of the 27-sided dice you do not eliminate or decrease the odds. The odds remain the same after each and every toss; the odds represent the positive possibilities."

No, but you are more likely to be successful if you have two chances rather than one.

"Evolution by computer selection."

Yeah, they are called "genetic algorithms" because of their resemblence to the model of natural selection in biology. They have been used with great success in amplifier design.

It's been several years since I've taken EE302: Probabilistic Methods in Electrical Engineering, but I'll try to answer any question on the subject.


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## biblelighthouse (Sep 15, 2005)

Scott, you just became my "buddy" with that post! 

You exhibit very good reasoning, both theologically and mathematically!

We are definitely on the same page.


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## JohnV (Sep 16, 2005)

[q" Also remember that the odds do not improve by countdown. With each toss of the 27-sided dice you do not eliminate or decrease the odds. The odds remain the same after each and every toss; the odds represent the positive possibilities."

No, but you are more likely to be successful if you have two chances rather than one.
[/quote]
My point was that the chances are no better on the second try than on the first. Having two tries with the same chance on each try does not improve the odds. All you're doing is taking another shot at the same odds, thinking you've got two chances in 1 with some fifty odd zeros behind it, instead of one chance is 1 with fifty odd zeros behind it done twice.


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## biblelighthouse (Sep 16, 2005)

> _Originally posted by JohnV_
> [q" Also remember that the odds do not improve by countdown. With each toss of the 27-sided dice you do not eliminate or decrease the odds. The odds remain the same after each and every toss; the odds represent the positive possibilities."
> 
> No, but you are more likely to be successful if you have two chances rather than one.


My point was that the chances are no better on the second try than on the first. Having two tries with the same chance on each try does not improve the odds. All you're doing is taking another shot at the same odds, thinking you've got two chances in 1 with some fifty odd zeros behind it, instead of one chance is 1 with fifty odd zeros behind it done twice. [/quote]

John, the logic doesn't change just because it's a bigger number.

Instead of just doing it twice, do it 1000000000000000000000000000000000000000000000000000 times, and you will have a superb shot at it happening.


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## JohnV (Sep 16, 2005)

Not really. Each try still has the same odds. All you're doing is playing the same odds more times. It's just an illusion that your odds improve. You see, chance is not a person that says, "OK, he's tried it a number of times, so those odds can now be reduced, so that those results do not happen again." 

Look at it this way. You have 27 dice, and you roll them all at once. Then you do it again, and again, and again. But on one of those rolls, it turns out, you rolled exactly the same permutation that you rolled the first or second time. That was not supposed to happen, because you had already eliminated that chance, right? No, you didn't. The chance at rolling the same on the second throw that you threw on the first is the same as your chance to throw what you're aiming for. And the third throw has the same odds as the first result, or the second result, as it does the intended result. Your odds do no improve with each throw. All you're doing is accumulating a number of tries at the same odds, raising the hope that you have a better chance of hitting it if you do it more often: you're more liable to get lucky if you try your luck more often.

[Edited on 9-16-2005 by JohnV]


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## kceaster (Sep 16, 2005)

> _Originally posted by SRoper_
> In the original scenario (assuming the monkey at a keyboard is a model for a randomly generated character) given an infinite length of time (or an infinite string of characters) the probability of generating the given sentence is 1. That is, it is guaranteed to happen.
> 
> 
> ...


[/quote]

That wasn't exactly what I was aiming for. The red ball exists. The sentence doesn't exist until it is typed. I'm saying that the probabilities are not analogous.



> > Nothing is chance. That which does not exist cannot exist because God hasn't made it to exist. That which does exist is ordered by the Lord.
> >
> > "I don't care how many monkeys with typewriters there are."
> 
> ...



I don't like looking back on a scenario that is random and calling it providence. That makes it look like God has foreordained a result produced by a second cause instead of foreordaining a result and using secondary means. God is not using statistics to make things come to pass. This is our wisdom looking back on it and trying to make sense of it, systematizing what God does when something seems random.

The philosophical slant of this scenario is that given enough time, artificial intelligence can produce a reasonable statement. They're not just typing ball and hoop, but relating the two by reason - and this from a totally random set of circumstances.

But let's bring this to a whole new level. If the monkeys can type, "The baskeball went through the hoop," and this as a result of enough time and attention, what would keep them from randomly generating the words, "Jesus is the devil incarnate?" Under the scenario rules, nothing would keep them from typing this. Given, then, enough time to type random sentences, the monkeys could come up with their own bible that is the exact opposite of God's Word. Is it still "guaranteed to happen?" 

I must tell you that I didn't do well in high school physics for this very reason: I reject anything out of hand that takes away from the Godness of God. Random large numbers detract from the providence of God and make it possible given enough time, to statistically kill God.

I have to believe that God is confounding us on this point. He makes things seem in some certain way, but they are because He's says they are, not because they're statistically probable.

In Christ,

KC


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## biblelighthouse (Sep 16, 2005)

> _Originally posted by JohnV_
> Not really. Each try still has the same odds. All you're doing is playing the same odds more times. It's just an illusion that your odds improve. You see, chance is not a person that says, "OK, he's tried it a number of times, so those odds can now be reduced, so that those results do not happen again."
> 
> Look at it this way. You have 27 dice, and you roll them all at once. Then you do it again, and again, and again. But on one of those rolls, it turns out, you rolled exactly the same permutation that you rolled the first or second time. That was not supposed to happen, because you had already eliminated that chance, right? No, you didn't. The chance at rolling the same on the second throw that you threw on the first is the same as your chance to throw what you're aiming for. And the third throw has the same odds as the first result, or the second result, as it does the intended result. Your odds do no improve with each throw. All you're doing is accumulating a number of tries at the same odds, raising the hope that you have a better chance of hitting it if you do it more often: you're more liable to get lucky if you try your luck more often.



You are completely missing the point. 

It is correct that if I roll a pair of dice 27 times, it has absolutely no bearing whatsoever on what I will roll the 28th time. The 28th time I roll the dice, my chances of getting a 12 are still 1 in 36.

But what I will specifically roll on the 28th time is NOT the question!!!

Rather, the question is this: If I roll the dice 28 times, am I more likely to get a 12 _sometime_, than if I only roll the dice once? --- And the answer to that question is a definite YES! 

Rolling multiple times does not increase my odds of getting a 12 on my next try. However, rolling multiple times DOES increase my odds of getting a 12 _sometime_. I don't know _which_ roll will produce a 12, but I DO know that 28 rolls are MUCH more likely to produce a 12 than a single roll.

Thus, you should not be comparing the 28th roll to a single roll. Rather, you should be comparing the _combination of all 28 rolls_ with a single roll. The difference is HUGE.


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## biblelighthouse (Sep 16, 2005)

> _Originally posted by kceaster_
> 
> The philosophical slant of this scenario is that given enough time, artificial intelligence can produce a reasonable statement.



As has already been mentioned above, artificial intelligence _already has produced_ a number of "reasonable statements", including some impressive discoveries that have been patented. Genetic algorithms and genetic programming have brought about new discoveries which human experts did not find on their own. A computer randomly modifies an existing computer program, and over time these random changes coalesce into a computer program that solves a problem. I am not just talking about theory. I am talking about _technology that is currently in use._

Furthermore, I personally could write a computer program that would output letters in random order. Run my program for a few days, sift through the output, and you will see a number of meaningful statements. That takes away the need for monkeys and typewriters.



> _Originally posted by kceaster_
> 
> I must tell you that I didn't do well in high school physics for this very reason: I reject anything out of hand that takes away from the Godness of God. Random large numbers detract from the providence of God and make it possible given enough time, to statistically kill God.



Does the fact that genetic programming exists take away from the Godness of God? No way. God has ordained everything that comes to pass, whether the throw of the dice (Proverbs 16:33), the outcome of random typing, or the result of a genetic computer program.


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## JohnV (Sep 16, 2005)

Granted, Joseph. But we are on the topic of random chance coming up with a designed result, and that the design means something rather than just it being a random result. 

If you're looking for a twelve, and how many chances you're going to take to try for it, then you will likely stop when you get that result, and say, "Aha!" But monkeys in a room, punching keys, could conceiveably come with the desired sentence twenty times or more, and yet it means no more than the rest of the gibberish they typed. Even if there were someone in the room to proof-read all the typed papers, looking for that one sentence. If he found it, it would still be, "So what?" 

No matter how many times or chances the monkeys are given, the odds do not improve with each try. What is being postulated is that design or reason will arise, given sufficient opportunity. And to demonstrate this postulation, an example is given of chimps in a room with typewriters coming up with a random sentence that makes sense. Assuming an empirical connection has been established, how has adding years to the experiment improved the odds? 

Assuming, for the moment, that the idea was to show that primitive man, descending from apes, would eventually come up with logical sequencing of letters in order to communicate, we must deal with the fact that chimps coming, up with an intelligible sentence in a world without written code, means nothing.


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## Poimen (Sep 16, 2005)

> _Originally posted by Puddleglum_
> You've got 36 letters & spaces, if I counted correctly.
> 
> It is a theoretically possibility to get that statement as a result of random chance.
> ...



Um yeah... sure, I understand.


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## JohnV (Sep 16, 2005)

Sorry, Daniel. Would it help if we typed it in Greek? But then I would be one of the chimps.


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## SolaScriptura (Sep 16, 2005)

> _Originally posted by biblelighthouse_
> Think of it as flipping a coin. Except instead of 2 sides, this "coin" has 27 sides: one "side" for each letter of the alphabet, plus an extra for spaces.
> 
> The odds of getting the first letter, "t", purely at random, are 1 in 27. The odds of getting the second letter immediately afterwards are also 1 in 27. So, the odds of getting the first two letters in order, purely at random, are 1 in 27*27, or 1 in 729.



Actually... look down at your keyboard... there are a lot more keys than just letters and spacebar... the monkeys would have to go through all those too!


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## bradofshaw (Sep 16, 2005)

> _Originally posted by poimen_
> 
> 
> > _Originally posted by Puddleglum_
> ...




Actually, I mentioned this to a freind of mine, and he pointed out the obvious. A keyboard has more than 27 buttons. You would have to take into account the digits, symbols, return button, etc. Since the space bar and return are larger than the letters, they would probably get hit more often. You would have to add another 20 or so buttons. The numbers keep getting bigger and bigger and bigger...

Of course, we can only speak of theoretic probability in an ordered universe. Who cares about the probability in a chance universe? Something happened because it just happened to


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## Poimen (Sep 16, 2005)

> _Originally posted by JohnV_
> Sorry, Daniel. Would it help if we typed it in Greek? But then I would be one of the chimps.



I'm quite ignorant when it comes to math.


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## SRoper (Sep 17, 2005)

"Scott, you just became my 'buddy' with that post! 

"You exhibit very good reasoning, both theologically and mathematically!"

Thank you for your kind words, Joseph.

"What is being postulated is that design or reason will arise, given sufficient opportunity. "

I missed where this was postulated. I believe Joseph was only addressing the correctness of the monkey-typerwriter thought problem. I don't see anywhere where any implications from this were being affirmed one way or another.

"I don't like looking back on a scenario that is random and calling it providence."

You missed the word "model." A model is our limited way of describing reality and making predictions. It is not what actually is.

"But let's bring this to a whole new level. If the monkeys can type, 'The baskeball went through the hoop,' and this as a result of enough time and attention, what would keep them from randomly generating the words, 'Jesus is the devil incarnate?' Under the scenario rules, nothing would keep them from typing this. Given, then, enough time to type random sentences, the monkeys could come up with their own bible that is the exact opposite of God's Word. Is it still 'guaranteed to happen?'"

Yes it is guaranteed to happen. I fail to understand your point.

"Random large numbers detract from the providence of God and make it possible given enough time, to statistically kill God."

Please explain how this follows.


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## kceaster (Sep 19, 2005)

> _Originally posted by SRoper_
> 
> 
> > "I don't like looking back on a scenario that is random and calling it providence."
> ...



We describe reality by random model? Is this what you're saying? Even if it is some part of reality, I still reject it. There is nothing real that does not have the stamp of God upon it.



> > "But let's bring this to a whole new level. If the monkeys can type, 'The baskeball went through the hoop,' and this as a result of enough time and attention, what would keep them from randomly generating the words, 'Jesus is the devil incarnate?' Under the scenario rules, nothing would keep them from typing this. Given, then, enough time to type random sentences, the monkeys could come up with their own bible that is the exact opposite of God's Word. Is it still 'guaranteed to happen?'"
> 
> 
> 
> Yes it is guaranteed to happen. I fail to understand your point.



The point is that God directs monkey's fingers. Even though possible given enough time and attention, God will not allow things like this to come to pass. It doesn't matter the odds. Do you not see how the postulation makes the absolute sovereignty of God not as absolute? If God can't control random things or statistically probable things, even the most minute of things; how is He a sovereign God?

I am, of course, making the assumption that God would not allow this. It would help if it were not hypothetical. If someone actually tried to do this, it would fail miserably because experimentation with primates has shown that it would take an awfully long time to get them to pay attention to what they're doing.

But I am objecting philosophically.



> > "Random large numbers detract from the providence of God and make it possible given enough time, to statistically kill God."
> 
> 
> 
> Please explain how this follows.



It isn't the random numbers themselves, but the sinful analysis of them by sinful men. Numbers in general could be said to be neutral. But analysis of the numbers and statistics and probablility are what has given us evolution, which "statistically" kills God.

In Christ,

KC


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## biblelighthouse (Sep 19, 2005)

> _Originally posted by kceaster_
> 
> It isn't the random numbers themselves, but the sinful analysis of them by sinful men. Numbers in general could be said to be neutral. But analysis of the numbers and statistics and probablility are what has given us evolution, which "statistically" kills God.



Kevin,

Reformed Christian mathematicians like me don't want to statistically kill God any more than you do.

Please respond to some things I said to you earlier:


As has already been mentioned above, artificial intelligence already has produced a number of "reasonable statements", including some impressive discoveries that have been patented. Genetic algorithms and genetic programming have brought about new discoveries which human experts did not find on their own. A computer randomly modifies an existing computer program, and over time these random changes coalesce into a computer program that solves a problem. I am not just talking about theory. I am talking about _technology that is currently in use_.

Furthermore, I personally could write a computer program that would output letters in an unpredictable order. Run my program for a few days, sift through the output, and you will see a number of meaningful statements. That takes away the need for monkeys and typewriters.



> Quote: _Originally posted by kceaster_
> 
> I must tell you that I didn't do well in high school physics for this very reason: I reject anything out of hand that takes away from the Godness of God. Random large numbers detract from the providence of God and make it possible given enough time, to statistically kill God.



Does the fact that genetic programming exists take away from the Godness of God? No way. God has ordained everything that comes to pass, whether the throw of the dice (Proverbs 16:33), the outcome of random typing, or the result of a genetic computer program.


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## SRoper (Sep 19, 2005)

"The point is that God directs monkey's fingers. Even though possible given enough time and attention, God will not allow things like this to come to pass. It doesn't matter the odds. Do you not see how the postulation makes the absolute sovereignty of God not as absolute? If God can't control random things or statistically probable things, even the most minute of things; how is He a sovereign God?"

It seems athiests must kill God everytime they take up the pen to attack him. God directs their fingers in the same way, does he not?

"I am, of course, making the assumption that God would not allow this."

I am saying that your assumption must be wrong. You have not presented a credible case for us to consider adopting it.


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## kceaster (Sep 20, 2005)

Let me put it this way:

Say I go to Vegas and I have 10,000 50 cent pieces in a bag. I go play the .50 slot machines. Now let's say my odds are 1/1000 to get a payout of $10,000. If that is the case, I have 10 chances to double my money. Will I win?

According to the odds I will. But according to God who reigns above, I don't win, and I lose $5,000. You can say that Vegas is never random, but why are they not random? God is in control even when we're out of control. If they have rigged the machines so that I don't win, was it not God who did this? Then you could say that the odds were never 1/1000. But the lady sitting next to me, won $10,000 after putting in just 78 coins.

This happens at Vegas all the time. Some people have actually put only a few coins in and got a huge payout, while some poor saps have put in everything they came with and lost it all.

It is playing odds, whether from the winning side (casino) or the losing side (casino patrons). But the kicker is, that God is the one in control of it all. There is no randomness in any casino in the world.

Now we could collect all the data and find out the exact odds for any given slot in any given casino. But this is our analyzing the data after the fact. We make it seem as though there is a 1/1000 chance to win. But in reality, there is no chance, but providence, which is why Christians should stay away from gambling.

It is the exact same thing with the monkeys. The message will only be typed if God chooses to let it be. If He doesn't, it won't. But let's be cautious about this because we don't want to say that God doesn't care about it. He upholds all, or He upholds nothing.

If some things do occur with seeming randomness, we need to be careful how we transmit the data. Is it random? Is there a good chance it will happen again? James tells us the answer, "If the Lord wills..."

In Christ,

KC


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## JohnV (Sep 20, 2005)

Kevin:
As I understand it, the reason for the illustration is to demonstrate that randomness can conceivably cause some kind of order. The thing that I think is important is that that order means nothing if all is random. 

You don't hear of Reformed Christians (Christians of any sort, for that matter) making up these kinds of scenarios in order to prove something. In this, we take the approach that you suggest, referring always to God's providence and governance. We don't need a room full of monkeys on typewriters for any of our purposes. 

Someone pointed out that a typewriter has many more than just 26 keys and a space bar. "The basketball went through the hoop." has fewer than 26 letters, but we don't have typewriters with only those letters on it. He is correct that that the odds have to measured by the inclusion of all the keys that may be punched, rather than just the ones that are relevant to that one sentence, much less the entire alphabet. Put the chimps on a computer keyboard and things get even narrower, with even more possible permutations. 

But the over-riding thing for me is that if the sentence is typed out randomly, whether sooner or later, it still has no meaning if it is accomplished. The same thing with random programming for a computer: it only means something if there is someone to seek and find the random results for some meaning. It becomes meaning in a meaningful world: it is not outside it, and it does not produce it. 

I think that is the same point you're driving at, but from a different angle. Chimps in a room with typewriters begs the question; computers coming up with sentences or even programs out of randomness begs the question. Where did the orderliness come from that produced a random result? In the end one is still left with the question of where design came from in the first place, or even the concept of design for that matter. 

The interesting thing is that design exists where the concept is possible, and that is most intriguing to me. We cannot have the idea of design unless it already exists; and it exists because the necessity of it from possibility. There is only one answer ever given to this riddle, and that is that there is a God. And not just any God, for there is only one ever described to man as answerable to the necessaary description, namely the God the Bible declares. 

In the end of the discussion on chimps in a room with typewriters producing a random sentence, we are still just as much faced with the necessity of God's existence from our perspective, being creatures.


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## SRoper (Sep 20, 2005)

"Say I go to Vegas and I have 10,000 50 cent pieces in a bag. I go play the .50 slot machines. Now let's say my odds are 1/1000 to get a payout of $10,000. If that is the case, I have 10 chances to double my money. Will I win?"

I'm afraid you don't have the basics of probability down. "I have 10 chances to double my money" is nonsense. The expected return after playing 10,000 times would be $95,000. The probability of losing every time (your scenario) is (.999)^10000 = 4.52*10^-5 or 0.00452% or 1 in 22,000. I don't know, but I would be quite pleased if I could make most of my decisions with that kind of certainty.

Kevin, the problem is that your view isn't useful because it can't inform your decision making. For example, I check the weather report to see what the probability of rain will be for the day. This informs what activities I will plan. It seems that your view would only say, "The Lord will do what he will." That's not very helpful; in fact it seems fatalistic.

"But in reality, there is no chance, but providence, which is why Christians should stay away from gambling."

This argument also seems to disallow investing among other things. How can you assess risk without taking probability into account?


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## kceaster (Sep 20, 2005)

> _Originally posted by SRoper_
> "Say I go to Vegas and I have 10,000 50 cent pieces in a bag. I go play the .50 slot machines. Now let's say my odds are 1/1000 to get a payout of $10,000. If that is the case, I have 10 chances to double my money. Will I win?"
> 
> I'm afraid you don't have the basics of probability down. "I have 10 chances to double my money" is nonsense. The expected return after playing 10,000 times would be $95,000. The probability of losing every time (your scenario) is (.999)^10000 = 4.52*10^-5 or 0.00452% or 1 in 22,000. I don't know, but I would be quite pleased if I could make most of my decisions with that kind of certainty.
> ...



Because you do as James suggests, "Come now, you who say, 'Today or tomorrow we will go to such and such a city, spend a year there, buy and sell, and make a profit'; whereas you do not know what will happen tomorrow. For what is your life? It is even a vapor that appears for a little time and then vanishes away. Instead you ought to say, "If the Lord wills, we shall live and do this or that."

It's pretty clear to me I am dumber than you guys. I'll stay back here in the dark ages with my thinking that God is sovereign in all things. Y'all go ahead and keep planning on probabilities.

In Christ,

KC


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## biblelighthouse (Sep 20, 2005)

> _Originally posted by SRoper_
> "Say I go to Vegas and I have 10,000 50 cent pieces in a bag. I go play the .50 slot machines. Now let's say my odds are 1/1000 to get a payout of $10,000. If that is the case, I have 10 chances to double my money. Will I win?"
> 
> I'm afraid you don't have the basics of probability down. "I have 10 chances to double my money" is nonsense. The expected return after playing 10,000 times would be $95,000. The probability of losing every time (your scenario) is (.999)^10000 = 4.52*10^-5 or 0.00452% or 1 in 22,000. I don't know, but I would be quite pleased if I could make most of my decisions with that kind of certainty.
> ...




 



Well said, Scott!




[Edited on 9-21-2005 by biblelighthouse]


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## biblelighthouse (Sep 20, 2005)

> _Originally posted by kceaster_
> Because you do as James suggests, "Come now, you who say, 'Today or tomorrow we will go to such and such a city, spend a year there, buy and sell, and make a profit'; whereas you do not know what will happen tomorrow. For what is your life? It is even a vapor that appears for a little time and then vanishes away. Instead you ought to say, "If the Lord wills, we shall live and do this or that."
> 
> It's pretty clear to me I am dumber than you guys. I'll stay back here in the dark ages with my thinking that God is sovereign in all things. Y'all go ahead and keep planning on probabilities.



Kevin,

Please apologize to Scott and me for implicitly slandering the two of us. Scott and I both 100% believe that God controls every event, no matter what. God is Sovereign. Suggesting that we believe otherwise is an insult.

On the contrary, we can use the mathematics of probability to make useful predictions (such as weather predictions), *BECAUSE* God has Sovereignly ordained that we would be able to do so.

So, Kevin, are you saying that God is NOT able to ordain mathematics in such a way that probabilities would come in very handy? If that is what you are saying, then it appears that *you* are the one denying His Sovereignty, not Scott and I.





[Edited on 9-21-2005 by biblelighthouse]


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## kceaster (Sep 21, 2005)

*Joseph...*



> _Originally posted by biblelighthouse_
> 
> 
> > _Originally posted by kceaster_
> ...



I'll say I'm sorry, but I'm offended, too. I could say that you've equally slandered me because I'm not giving God credit for working out His decree with mathematical precision.

I'm not sure why you've got such a interest in science and math as it comes to God's universe. But I just don't see it the way you do. We don't agree when it comes to this sort of thing. I'm sorry I offended you. But there are two principles that I really don't think you or Scott have addressed adequately. The first was from Proverbs 16 and the second is from James 4. I think both of these clearly leave mathematical probability out of the picture when we think about God and His decretive will.

And I'm not saying we can't predict the weather with some measure of certainty. Jesus addressed the fact that we can read the signs of the winds, but not the signs of the times. When it comes to spiritual discernment about God and the way He upholds His creation, we can't use a slide rule.

This is just my opinion, don't let it bother you. I am not your judge. But as for me, I would rather err on the side of caution. I will not attribute God's actions to probability. And saying that the odds are such and such that God does this or that, or even saying that something will happen within a set of odds means that God is not absolute. It's like saying, "I knew God was going to make that happen." And I'm sorry guys, we can't say that about our next breath even though the odds are good we'll live well into our seventies.

God upholds all things by the word of His power, not by the numbers of probability.

In Christ,

KC


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## biblelighthouse (Sep 21, 2005)

> _Originally posted by kceaster_
> 
> 
> > _Originally posted by biblelighthouse_
> ...



Kevin, I apologize. I didn't mean to offend you, either. I was just irked at the moment.



> _Originally posted by kceaster_
> 
> I'm not sure why you've got such a interest in science and math as it comes to God's universe. But I just don't see it the way you do. We don't agree when it comes to this sort of thing. I'm sorry I offended you. But there are two principles that I really don't think you or Scott have addressed adequately. The first was from Proverbs 16 and the second is from James 4. I think both of these clearly leave mathematical probability out of the picture when we think about God and His decretive will.



I think these passages are quite clear. They both say that God controls everything down to the last detail. Absolutely nothing is left up to chance. You and I agree on that. (By the way, R.C. Sproul's book, "Not a Chance" is really good on this subject.)

But the Proverbs 16:33 reminds me of something else: 
Some things (such as the roll of dice) are _apparently random to us_. Let me be clear and say that these things are of course NOT truly random . . . that which God perfectly controls could hardly be called random. But that does not stop the roll of the dice from _appearing_ to be random, and it does not stop the mathematics of probability from being useful.

However, because of Proverbs 16:33 and James 4, perhaps the word "probability" is itself the problem. There is nothing wrong with the mathematics behind it which God has ordained. But the word "probability" itself is problematic, because it suggests that randomness is a real thing, and not just an appearance.



> _Originally posted by kceaster_
> 
> And I'm not saying we can't predict the weather with some measure of certainty. Jesus addressed the fact that we can read the signs of the winds, but not the signs of the times.



Kevin, please think about what you just said. How exactly is it that we can predict the weather with a fair amount of accuracy? Are you aware that the mathematics of probability are used to predict the weather? Thus, even if the word "probability" is wrong, the mathematics behind it have still proven to be very useful to us.



> _Originally posted by kceaster_
> 
> This is just my opinion, don't let it bother you. I am not your judge. But as for me, I would rather err on the side of caution. I will not attribute God's actions to probability.



Again, God determines everything. Nothing truly happens by "probability". Nevertheless, every time you roll the dice during a board game, you prove the fact that God has Sovereignly chosen to make His Sovereign decrees _appear_ random _to us_, even though we know better. 



> _Originally posted by kceaster_
> 
> And saying that the odds are such and such that God does this or that, or even saying that something will happen within a set of odds means that God is not absolute. It's like saying, "I knew God was going to make that happen."



No, not at all. The mathematics of probability never give us 100% perfect results, so we can never say "I *knew* God was going to make that happen."

Rather, it's like saying, "This is usually how God works, and God is faithful, so this is what I expect. Nevertheless, it is possible that He will choose to work differently."




> _Originally posted by kceaster_
> 
> And I'm sorry guys, we can't say that about our next breath even though the odds are good we'll live well into our seventies.



Do you really believe the "odds are good" you will live into your seventies? Or do you count it just as likely that you will die tomorrow? Of course either could happen in God's providence. But I'll bet you lean much more towards thinking you'll live for decades more, rather than just hours more. Why is that, if you have absolutely no trust whatsoever in the mathematics of probability?



> _Originally posted by kceaster_
> 
> God upholds all things by the word of His power, not by the numbers of probability.



Amen! I certainly agree with that statement.


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