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Probability Mistakes Darwinists Make

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Several years ago I delivered a lecture at the University of Maine, showing how advances in science increasingly point to an intelligent mind behind biological life. During the question period a professor in the audience conceded that the probability of evolution “discovering” an average globular protein is vanishingly small. Nonetheless, he insisted we are surrounded by endless examples of highly improbable events. For example, the exact combination of names and birthdates of the hundred or so people in the audience was also amazingly improbable. In the ensuing conversation, it became obvious that there was something about probabilities that he had not considered.

It only takes a few minutes of searching YouTube to discover that there are numerous Darwinists who commit the same mistake. In one example, a fellow randomly fills in a grid of 10 columns and 10 rows with 100 symbols. Then, he states that the probability of getting that exact combination is 1 chance in 10^157. In another clip, a man shuffles a deck of cards, spreads them out on a table, then repeats this two more times. He states the probability of getting that exact triple combination of cards is roughly 1 chance in 10^204. Both scenarios are supposed to show that we are surrounded by extremely improbable events all the time, so we should not be surprised in the least if evolution has accomplished the fantastically improbable. Ironically, these examples demonstrate a profound ignorance of this problem.

In clearing up misconceptions that Darwinists promote, the first step is to clarify what scientists speak of when they discuss the infinitesimal probability of evolution “discovering” a sequence for a novel protein. That probability is found embedded within an equation published by Hazen et al.1:

I(Ex) = -log2 [M(Ex)/N]


I(Ex) = the information required to code for a functional sequence within protein family, and

M(Ex) = the total number of sequences that are functional, and

N = the total number of possible sequences, functional and non-functional.

Hazen’s equation has two unknowns for protein families: I(Ex) and M(Ex). However, I have published a method2 to solve for a minimum value of I(Ex) using actual data from the Protein Family database (Pfam)3, and have made this software publicly available. We can then solve for M(Ex).

Now, back to the question of what type of probability scientists are interested in. The answer is M(Ex)/N. This ratio gives us the probability of finding a functional sequence from a pool of N possibilities in a single trial. To clarify, we are not interested in the probability of getting a specific sequence; any functional sequence will do just fine. Armed with this information, let us see what M(Ex)/N is for the Darwinist/YouTube examples given above.

In the first video, the total number of possibilities is N = 10^157, but what is M(Ex)? In this case, any sequence of symbols would have served as an example. Therefore, M(Ex) = N. The probability M(Ex)/N of obtaining a sequence that serves the purpose is therefore 1. Using Hazen’s equation, the functional information required to randomly place the 100 symbols in the grid is 0 bits.

In the second example, the narrator shuffles 52 cards three successive times, then claims the total number of possibilities is N = 10^204. The real question is, What is M(Ex)? How many other sequences of shuffled cards would have served this function? Not surprisingly, any sequence would have sufficed — again, M(Ex) = N. The probability M(Ex)/N of obtaining three series of card sequences that serves this purpose is exactly 1.

For my lecture at the University of Maine, any combination of people would have been fine so, again, M(Ex) = N and M(Ex)/N = 1.

Now let us do the same thing for a protein, using data from the Pfam database.

I downloaded 16,267 sequences from Pfam for the AA permease protein family. After stripping out the duplicates, 11,056 unique sequences for AA Permease remained. After running the resulting multiple sequence alignment through the software I mentioned earlier, the results showed that a minimum of 466 bits of functional information are required to code for AA permease. Using Hazen’s equation to solve for M(Ex), we find that M(Ex)/N < 10^-140 where N = 20^433. The extreme upper limit for the total number of functional sequences for AA permease is M(Ex) = 10^97 functional sequences. The actual value for M(Ex) is certain to be numerous orders of magnitude smaller, due to site interdependencies as explained in my paper2.

So what do we see? In a single trial, the probability of obtaining a functional sequence by randomly sequencing codons is pretty much 0. Conversely, the probability of evolution producing a non-functional protein is very close to 1. Therefore, we can predict that evolution will readily produce de novo genes that fail to give functional, stable 3D structures. Clearly, the Darwinists on YouTube ignore this problem in protein science. If you estimate the extreme upper limit for the total number of mutation events in the entire history of life, using 10^30 life forms, a fast mutation rate, large genome size, and fast replication rate, it is less than 10^43 . Not surprisingly, this is pathetically underpowered for locating proteins where only 1 in 10^140 sequences is functional. However, it gets far worse, for evolution must “find” thousands of them.

Nonetheless, scientific literature reveals an unshakable belief that evolution can do the wildest, most improbable things tens of thousands of times over. Consequently, I believe Darwinism has become a religion, specifically a modern form of pantheism, where nature performs thousands of miracles — none of which can be reproduced in a lab. On the other hand, if we apply a scientific method to detect intelligent design discussed here, we see that 433 bits of information is a strong marker of an intelligent origin. This test for intelligent design reveals the most rational position to take is that the genomes of life contain digital information from an intelligent source.

In a future post, I plan to examine the Darwinists’ assumption that if the sequence is assembled step by step, it is much more probable.


(1) Hazen et al., “Functional information and the emergence of biocomplexity,” PNAS, 2007 May 15: 104:. suppl 1.

(2) Durston et al., “Measuring the functional sequence complexity of proteins,” Theor Biol Med Model, 2007 Dec. 6;4:47.

(3) The Pfam protein families database: towards a more sustainable future: R.D. Finn, P. Coggill, R.Y. Eberhardt, S.R. Eddy, J. Mistry, A.L. Mitchell, S.C. Potter, M. Punta, M. Qureshi, A. Sangrador-Vegas, G.A. Salazar, J. Tate, A. BatemanNucleic Acids Research (2016) Database Issue 44:D279-D285.

Image credit: Kirk Durston.

Cross-posted at SQyBLu/Contemplations.