Borel's Law

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Named after mathematician Émile Borel, who would probably be horrified, Borel's law states:

Phenomena with very low probabilities do not occur.

The corrupted creationist version is:

Any odds beyond 1 in 1050 have a zero probability of ever happening.
—Karl Crawford (ksjj)[1][2]

Original meaning[edit]

It was intended as a rule of thumb for specific scenarios before they happen. Borel introduced it in a book written for non-scientists, as an example of the kind of logic that any scientist might use to generate estimates of the minimum probability below which events of a particular type are considered negligible.[2] It was created for specific physical examples, not as a universal law. It certainly does not mean that any probability below 1 in 1050 is automatically zero, which is contradictory.

So, of course, this rule is often cited by creationists as evidence against evolution and abiogenesis when they are misunderstanding that improbable things happen. They appear to be the only people to give it the status of a "law." This is a staggering misrepresentation of what Borel said and one can only feel sympathy for him for having such a misguided "law" named after him.


The probability of an event with odds of 1 in 1050 is 10−50. Small, yes. Negligible, yes — but not zero. You can observe such events happening to you every night. Although the probability of a photon emitted in the Andromeda Galaxy, 2.6 million light years from Earth, reaching your eye is only 8.1 · 10−51, the galaxy is clearly visible in the night sky.[3] If you roll a fair ten-sided die 51 times, the probability of rolling this particular sequence is 10−51. These observations are impossible according to the proponents of universal application of "Borel's law."

Borel's actual law[edit]

Borel also has a real law named after him, usually known as "Borel's law of large numbers". It can be expressed in many ways, but in its simplest form, if an event E occurs X_n times in n trials, than the probability p of E occurring is:


Another Borel theorem[edit]

A very powerful theorem Borel did prove is given to show his eminence[4]: Taylor SeriesWikipedia's W.svg can be problematic, but Borel proved that every Power SeriesWikipedia's W.svg is the Taylor Series of some function. Very powerful indeed.

Just browsing Wikipedia turns up a number of Borel's theorems and that can at least be used as an indicator of how important a mathematician he was[5].

In remembrance of USENET[edit]

Borel's "law" was often invoked in discussions in, alt.atheism and other groups which seemed to attract more preachers than atheists or biologists. One answer to a Young-Earth Creationist claiming evolution to be impossible — said creationist did not distinguish between a priori and a posterori, which can hardly be a problem for the gentle readers of RationalWiki — is worth paraphrasing: In order for you to exist, your parents had to have sex exactly at a given time. One particular sperm cell had to fertilize one particular egg. Taking this back only a few generations we quickly reach the limit of Borel's "law". You, Sir, are therefore impossible.


  2. 2.0 2.1 Borel's
  3. This number can be obtained by dividing the surface area of the pupil (roughly 63 mm2) by the surface area of a sphere with a radius of 2.6 million light years. It is assumed that photons are, on average, emitted uniformly in all directions.
  4. Mathematicians have been heard mentioning this with awe.
  5. Anyone who has some of the most important things in Measure TheoryWikipedia's W.svg named after him is a grandmaster of abstract thinking, as generations of puzzled students will tell you.