RE: the Universal Probability Bound:

-given the sequence of prime numbers: “12357 ..."

According to probability theory, the first digit has a one in ten chance of matching up with the sequence of prime numbers, however the second digit has a one in 100 chance, and the third a one in 1000 chance, etc. So, how far up the pattern of prime numbers will chance take us before making a mistake? The further you go, the more likely chance processes will deviate from the specified pattern. It’s bound to happen eventually as the odds increase dramatically and quickly. But, how do we know where the cut off is?

Dembski has introduced a very “giving the benefit of the doubt to chance” type of calculation based on the age of the known universe and other known factors, and actually borrowing from Seth Lloyd’s calculations. Now, it must be noted that as long as the universe is understood to be finite (having a beginning) then there will be a probability bound. This number may increase or decrease based on future knowledge of the age of the universe. However, a UPB will exist and a scientific understanding can only be based on present knowledge.

This number, as far as I understand, when it is calculated actually allows chance to produce less than 500 bits of specific information before cutting chance off and saying that everything else that is already specified and algorithmically complex and above that bound of 500 bits is also most reasonably beyond the scope of chance operating anywhere within the universe for the duration of the universe and is thus complex specified information and the result of intelligence.

Now, let’s take a closer look at the Universal Probability Bound of 500 bits. What would it take for pure random chance to cover all possible combinations of a 500 bit sequence? Well, any given 500 bit sequence is 1 in 2^500 possible combinations; that is 1 out of more than 3.27 x 10^150 possible sequences. Now let’s look at the age of the universe. It is 15.7 billion years old; that is approx. 4.95 x 10^17 seconds old. After a few simple calculations it is easy to see that the whole universe would have to be flipping 6.61 x 10^132 sets of 500 coins every second for 15.7 billion years in order to generate 3.27 x 10^150 sequences of 500 bits.

But even after all is said and done, all possible combinations will not have been generated because there is no way to guarantee that no pattern will appear twice. Since probabilities deal with averages, it is only after many sets of 15.7 billion years that we will see, on average, an exponential appearance of all of the possible combinations being created. But of course, this assumes that there are indeed that many “sets of coins” being flipped at the above rate in the first place.

And still, there is no guarantee that even with that many random “flips of a coin” that a pattern such as “10" repeated 250 times will even be generated. In fact, it is not in the nature of pure random processes to match patterns which can be described and formulated by a system of rules. Furthermore, science always looks for the best explanation, and law and intelligence (teleological processes) are already available as better explanations than chance for the creation of specified patterns – patterns which can be described and formulated by a system of rules. The limit of 500 bits only provides a very generous Universal Probability Bound, which is based on known measurements of the universe, that places a restriction on invocation of “chance of the gaps” when other better and more reasonable explanations, based on observation, are available.

In fact, here is a little test. Take a 100 bit pattern (including spaces and ending punctuation) such as “aaaaaaaaaaaaaaaaaaaa” and randomly “spin” the letters to your hearts content for as long as you like and see if you ever get a specified pattern.

Again, as I’ve stated before, ID Theory provides a best explanation hypothesis about the nature of the cause of the ‘Big Bang’ model based upon observation and elimination of other alternatives that posit unreasonable gaps based on chance, not based on observation, which are postulated to circumvent observed cause and effect relations.

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## 9 comments:

CJYman: "-given the sequence of prime numbers: “12357 ..."

"According to probability theory, the first digit has a one in ten chance of matching up with the sequence of prime numbers, however the second digit has a one in 100 chance, and the third a one in 1000 chance, etc.

I think you left out that you are explicitly considering a random variable. In any case, the environment that biological evolution exists in is not random!

Let's try something. Start with a single-letter word, then evolve a popualtion of words by random mutation and recombination. If the resulting sequence is not a valid word, then it is instantly deselected from the population. This is what it might look like (non-random and illustrative only):

a

an

can

cam

came

...

How many mutations would it take to evolve a ten-letter word by this process? Let's say there are ten thousand ten-letter words. There are 26^10 possible letter combination. That means ten-letter words represent one in ten billionth of the sequence space. So would you predict that it would take on the order of a few billion mutations to sort through the sequence space to find a ten-letter word? Why or why not?

Zachriel:“I think you left out that you are explicitly considering a random variable. In any case, the environment that biological evolution exists in is not random!”

“The environment is not random”? Care to validate that assertion? I do agree that evolution isn’t random, and I understand how laws which make up the environment aren’t random in their operation, but a non random environment? Are you saying that our environment is somehow guided to be what it is? Interesting hypothesis. I’d like to know how you arrive at that conclusion.

Zachriel:“How many mutations would it take to evolve a ten-letter word by this process? Let's say there are ten thousand ten-letter words. There are 26^10 possible letter combination. That means ten-letter words represent one in ten billionth of the sequence space. So would you predict that it would take on the order of a few billion mutations to sort through the sequence space to find a ten-letter word? Why or why not?”

It all depends on the design of the program that is built to complete this task as well as the amount of front-loaded information.

Before we discuss probabilities, do you know anything about the NFL Theorem and do you know anything about active information? Are you aware of the type of program and information necessary for evolutionary algorithms to work? When I just stated the probabilities, that’s all I was doing – merely stating probabilities. In order for these probabilities to be overcome, even on average, active information must be present.

The purpose of the UPB is to place a probabilistic restraint on purely randomly generated specified patterns based on probabilistic resources to discourage unscientific chance of the gaps "non-explanations" since there are actually other better explanations based on information theory (NFL Theorem) and observation of cause and effect relations for specified and algorithmically complex patterns.

CJYman: "The environment is not random”? Care to validate that assertion?"It's not a controversial statement. E.g., gravity on the Earth's surface is consistently in one direction. Diurnal and seasonal cycles are other non-random patterns.

CJYman: "It all depends on the design of the program that is built to complete this task as well as the amount of front-loaded information."It doesn't depend on the design of the program any more than the result of addition depends on the type of adding machine used.

CJYman: "Before we discuss probabilities, do you know anything about the NFL Theorem.No Free Lunch is a result proven by Wolpert and Macready in 1997 and is stated as "the average performance of algorithms across all possible problems is identical". With respect to natural selection, they say "one expects the average fitness across a generation improves with time". In other words, No Free Lunch doesn't mean natural selection doesn't result in increased fitness over time, but simply that natural selection may not be the best conceivable search algorithm.

CJYman: "do you know anything about active information"I know Dembski has an unpublished draft paper on the subject. In it he states, "

Such assumptions, however, are useless when searching to find a sequence of, say, 7 letters from a 26-letter alphabet to form a word that will pass successfully through a spell checker... With no metric to determine nearness, the search landscape for such searches is binary—either success or failure. There are no sloped hills to climb."Dembski has defined the same problem I did above. He claims that without some information built into the algorithm about how words are distributed through sequence space, evolutionary algorithms will be no better than random search. Is this what Dembski is saying? And is he right?

Here

is a new blog post discussing your Evolutionary Algorithm in light of Dembski's quote.

Zachriel:"It's not a controversial statement. E.g., gravity on the Earth's surface is consistently in one direction. Diurnal and seasonal cycles are other non-random patterns."

As I stated elsewhere to you: “I do agree that evolution isn’t random, and I understand how laws which make up the environment aren’t random in their operation, but a non random environment? Are you saying that our environment is somehow guided to be what it is as opposed to some other type of environment? Interesting hypothesis. I’d like to know how you arrive at that conclusion.”

And as I asked elsewhere: “So, evolution (as the generation of algorithmically complex and specified information at consistently greater than chance probabilities) is directed by the non-random aspects of our environment such as by gravitational and electromagnetic fields? Care to explain what you mean by that and provide some evidence?

Furthermore, are the laws which craft our environment actually non-random? Are the values for the physical laws non-randomly chosen from a set of possible laws (ie: values for the strong, weak, and

nuclear force)? If not, then although law itself does not behave randomly, the set of our laws would be completely random and thus the environment itself would be random since it would be fashioned by a completely arbitrary and random set of parameters.”

If the natural laws at the base of our universe guide life, then that would show guiding, problem specific, active information is within the information which make up these laws. But, where does active information come from? Have we ever observed, or is there any rationale behind even postulating that active (problem specific, guiding) information will randomly generate itself from a random set of laws? So far, all that we have observed from scientific experiments is that in order to create algorithmically complex and specified information at consistently better than random chance (and above the UPB), active information must be front-loaded by an intelligent system (which can plan into the future) to converge upon one or more of these targets.

Zachriel:"It doesn't depend on the design of the program any more than the result of addition depends on the type of adding machine used."

Evolutionary algorithms can have many different designs for incorporating problem specific active information. These different designs use different types and amounts of front-loaded information in different ways. In fact Dembski and Marks have discussed how to measure the active information within different types of evolutionary algorithms by random mutation (such as choosing the fittest of a number of offspring or stepping stone search or partitioned search). These are three different types of evolutionary algorithms which guide the search toward the target in different ways.

I’m sure you can google many different types of evolutionary algorithms (of which one was used in research to help design a better antenna) on the web and notice many different designed programs utilizing active information in different ways. In fact, if the evolutionary algorithm isn’t designed correctly, providing and utilizing active information correctly, it won’t produce the desired results or any results at all.

RE: your EA program in light of your comment – are you trying to tell me that your EA doesn’t depend on the design of the spreadsheet software and on the way that you programmed the spreadsheet and incorporated the spell checker and non-random dictionary?

Zachriel:"No Free Lunch is a result proven by Wolpert and Macready in 1997 and is stated as "the average performance of algorithms across all possible problems is identical". With respect to natural selection, they say "one expects the average fitness across a generation improves with time". In other words, No Free Lunch doesn't mean natural selection doesn't result in increased fitness over time, but simply that natural selection may not be the best conceivable search algorithm."

And it also means that natural selection (the sorting of functional from non-functional and fit from unfit in order to provide a stepping stone to consistently provide better than chance performance) makes use of front-loaded active information. Dembski and Marks have discussed this in their recent papers as I’m sure you are aware.

Are you trying to tell me here that, in reference to your EA, a random set of laws can produce the spreadsheet software, the dictionary (along with meaning/function in order to produce anything useful), and the programming of the spreadsheet to create the EA without front loaded, guiding, problem-specific, active information. What evidence do you have for this?

CJYMan: "Are you saying that our environment is somehow guided to be what it is as opposed to some other type of environment?"You seem to think that the opposite of random is telic guidance. This is incorrect.

I have provided several examples (above). Try to grasp the basic concept. Randomness is a specific probability distribution. There are many aspects of the environment that are non-random but not guided. Gravity on the Earth's surface is not random, but highly directional.

Zachriel:"You seem to think that the opposite of random is telic guidance. This is incorrect."

Nowhere have I stated that. In fact, here I have just responded to you (my latest comment) and explained my position.

I did ask you how the guidance of physical laws of attraction and direction creates algorithmically complex and specified patterns and you still haven't answered that quesiton.

So I will ask again, for the third time:

"So, evolution (as the generation of algorithmically complex and specified information at consistently greater than chance probabilities) is directed by the non-random aspects of our environment such as by gravitational and electromagnetic fields? Care to explain what you mean by that and provide some evidence?"

CJYman: "'The environment is not random'? Care to validate that assertion?"This question indicates a gross misunderstanding of what constitutes randomness. You need to resolve this issue.

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