I believe some of the strongest arguments in favor of a creation based interpretation of the data of history are from observations of design. Of course evolutionists debate this point and claim we only observe the “appearance” of design. One way creationists talk about design is from Borel’s law which states “events whose probability is sufficiently small never occur”.^{1} Borel further states the numerical value of “sufficiently small” depends upon the scale, for example, on the earth vs. in the universe. Creationists have used Borel’s value for the scale of phenomena in the universe of 1×10^{-50} and applied it to the terrestrial scale. For example, the probability of a sequence of amino acids randomly assembling in the correct order to form a single protein of *cytochrome a* is 1×10^{-60}.^{2} In most cases the probabilities are so low for forming just one protein that creationists rationally conclude random chance events can not lead to the formation of a living cell which requires at least 382 proteins.^{3}

I recently found a critique of how creationists use Borel’s Law, but the calculations presented there were seriously flawed.^{4} Briefly, they claimed the probability to see light from the Andromeda galaxy by the human eye was less than the 1×10^{-50} number used by creationists. But a human can see the Andromeda galaxy with the naked eye. The event was predicted by Borel’s Law to be impossible, but yet we see it. Thus, the creationist use of Borel’s law is falsified.

However, this calculation misses two points which have a huge impact on the final result. First, implicit in their calculation is a single emission of photons from the galaxy. In reality a star is emitting on the order of 10^{43} photons per second. Second, the human eye has about 100 million rods to detect these photons from a distant star or galaxy. So, when these factors are taken into account the human eye is estimated to be detecting approximately 25 photons per second of light from the Andromeda galaxy. As that famous French detective Inspector Clouseau has said, “case sol ved.”

Yes, there are questions about the specific cut-off probability for an event to be labeled as statistically impossible. However, the general principle in Borel’s Law is well-founded and not maliciously misapplied by creationists.

*Written by Dr. Al Gotch*

FOOTNOTES

1. Borel, Emil; *Probability and Life*, Dover, New York, 1962. (translated from the original, Les Probabilite et la Vie, 1943, Presses Universitaire de France)

2. For example http://www.parentcompany.com/creation_essays/essay44.htm (accessed 2013.02.23)

3. Glass, John; Nacyra Assad-Garcia, Nina Alperovich, Shibu Yooseph, Matthew R. Lewis, Mahir Maruf, Clyde A. Hutchison III, Hamilton O. Smith *, and J. Craig Venter. “Essential genes of a minimal bacterium”. *PNAS* 2005, **103**, 425–430. http://www.pnas.org/content/103/2/425

4. http://rationalwiki.org/wiki/Borel%27s_Law (accessed 2013.02.23)

I’ve written a response to this.

It’s more than I could say in a comment here, but what I’ll say here is that’s not how evolution works, and your use of Borel’s law doesn’t apply because there wasn’t just one chemical reaction to generate a molecule that self-replicates but many over billions of years causing the probability for it to happen to approach 1.

There is more background to this argument. A primary issue is whether a probability is so low that we can say with great certainty the event would never happen. For example, a box filled with a gas, lets say Argon, is sitting on your desk. There is a small probability that all the molecules could strike the top of the inside of the box at the same time and the box jumps off the table. A probability of this nature would be at a minimum in the range of 1×10^-25. We never observe this happening. Again, is there a probability that is so small that we can say we do not expect to observe it? Borel actually had different numbers he used for a cut-off depending on the scale of the system. By scale of the system I mean on planet earth vs. our galaxy vs. the entire universe. In the entire universe it is estimated there are 1×10^80 electrons. If you filled the empty space with electrons the estimate is 1×10^130. So, a number in the range of 1×10^100 represents, very roughly, all the possible parts of matter that are present in the entire universe. If a probability is this small (1×10^-100), by extension people will say it is never expected to occur in the entire universe. Technically you are correct, no matter how small a probability, there is still a chance it could occur, therefore we should not say it is impossible. However, on a practical basis, we don’t see boxes flying off tables and would say it never happens. And note this probability is much, much higher than the limit first proposed by Borel.

Hello dr,

I’m hopeing you can give me a little more information.

Borel’s law isn’t a mathematical law or a law of physics correct? If it were it would be contradictory! To say that if something has a probability of 1×10^-50 an then to say that it will never happen sounds wrong. If we took a die with 1×10^50 sides and rolled it, the probability that the number 7 would come up would be very low, but it could still happen.

Wondering if I’m seein this incorrectly.

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