### The Probability of Information

I recently searched youtube.com using the search words "evolution probability" and found a number of atheist apologists making variations of the same stupid argument that the guy in this video is making. In this blog entry I explain why this guy and blogger Lord Runolfr get it wrong.

Consider the following paragraph:

Mathematics is the language of science. To succeed in science, one must use mathematics. Thus high quality science depends on high quality mathematics.

This paragraph contains 151 characters. It contains information which can be understood by those who can read English. If we consider the space of characters to consist of all upper and lower case characters, space, comma and period there are 55 characters in all. The probability that this paragraph could be generated randomly is 1 in 55 to the 151st power. If I punch that into my calculator I get 6.23E+262 which is a huge number. On the other hand, consider the random sequence of characters below

jqloHdfnecUmfnpwlkiayfnsklufnmB,sloodmsioi dkmeijdp.jdsewydnsj. kYsdflklgagdkjqlknc lgjha lkjdjhbadkghlkjfajdlkjalkgddopauneo aoij Lkdn ienonismdngsdfg

This sequence of characters also has 151 characters and has the same probability of being generated as the well formed paragraph above. So what’s the big deal about the first sequence? Well if you are asking which of the two sequences is more probable you are asking the wrong question. That's where blogger Lord Runolfr and the dude staring in the YouTube video above get it wrong. The first sequence of characters has three properties that the second sequence does not.

1) It consists of properly spelled English words.

2) It is grammatically correct,

3) It makes sense.

So to illustrate the last property consider the grammatically correct sentence: Mathematics is the job of refrigerators. This sentence is grammatically correct but it doesn't make sense. If you have any doubts about the grammar type the sentence into Microsoft Word and see if its grammar checker flags any problems. So the question we should be asking is this: What is the probability that a random character generator world produce a grammatically correct sequence of characters that makes sense? The answer is too hard to calculate but it is still infinitesimal. Even computing the probability of satisfying (1) is difficult and beyond the scope of this blog. However, we can compute the probability of something similar to (1) which can serve as an upper bound.

Let’s approximate the probability that a sequence of about 150 characters will satisfy property (1) above. To make the approximation let’s make the following assumptions:

1) The average word has a length of seven characters

2) There are 100,000 seven character sequences that represent words.

Now there are 26 to the 7th power possible seven character sequences; that is more than 8 billion. If only 100,000 of those sequences are words the odds that a seven character sequence is a word is 1 out of 80,000. Given that the average word length is seven characters, and words are followed by a space, there are an average of 18.75=150/(7+1) words in a 150 character sequence. So you could say that the odds that a 150 character sequence is made up of entirely properly spelled words are less than one in 80,000 to the 18.75 power. Plug this into your calculator and you will find the odds to be less than 1 in 8.5E+90. Remember, we are only trying to compute the probability of a simplified model of property (1). The probability of satisfying properties (1), (2) and (3), would actually be much less.

Someone will point out that I haven’t actually said anything about biology or evolution yet and that I am arguing by analogy. And I get that. What I am talking about here is the nature of information, whether it is written language, a computer program or a genome. Each information type has its own set of properties that make it essentially impossible to be generated randomly.

ADDENDUM

This is funny. Even Kenneth Miller, a biology professor at Brown University gets it wrong.

ADDENDUM 2013

The above video has been withdrawn from YouTube. I wonder why.