# Hoyle's Calculation of the Odds of Life

This web page addresses probably one of the most quoted statements about evolution -- that the odds of life arising by chance are 1 in 1040,000. Hoping to find the basis of this computation, I decided to track down the reference. Unfortunately, what I found was not a series of probabalistic equations, but rather an account of Hoyle saying that he computed this number. As far as I can tell, there is no publicly available documentation supporting this figure. (I haven't checked out his books yet. It may be in there.)

Here is the argument, as posed by Kyle Dillon (spiffy@summitsoft.com):

Abiogenesis is a mathematical impossibility. Sir Fred Hoyle, a British astronomer and mathematician, calculated the odds of one simple bacterium arising from a primordial soup. He assumed that the 20 amino acids were present in the soup (contrary to the results of the Miller-Urey experiment, which yielded only seven of the simplest amino acids). A simple bacterium is comprised of 2,000 different functioning proteins. In turn, each protein consists of a chain of about 300 amino acids. There are 20 distinct amino acids, so the odds of one proteinated amino acid occurring in the correct sequence is one in 20. The odds of 300 occurring in the correct sequence is one in 30020. Hoyle realized that there can be some variation in the exact sequence, so the odds would be reduced to one in 1020. But because there must be 2,000 different functioning proteins, the odds of the spontaneous generation of a cell is one in 10(20)(2,000) = 1040,000. Even ignoring the problems beyond the math (such as the counter-productive effects that individual essential chemical components have upon each other, and the inability to create all 20 amino acids under simulated conditions), abiogenesis is impossible.
It should be stated that biological evolution has very little to do with abiogenesis. The former describes the gradual change in the gene pool of a species, while the latter addresses the creation of life from non-living matter.

That said, there are several problems with this analysis:

• Further, Hoyle's calculations, as described by many Christians, assume that the combinations are independent events, which is not generally the case with molecular interactions. Lastly, it is not valid to apply probability to an event that has already occurred -- it's like saying that the odds of winning the lottery are 1 in 23 million, so no one could have won it.
• The analysis assumes independence of variables (proteins, molecules, etc.) This is obviously false, as we know that proteins strongly interact. This means that certain combinations will not occur because the interactions disallow them. If one takes dependence into account, the numbers will be lower.
• The analysis assumes independence of trials. That is, it assumes that one combination is created, evaluated, then destroyed. In fact, the combinations interact strongly with each other---groups of proteins interact with other groups of proteins. As a result, the analysis is flawed.
• Even if we believe the independence argument, we have no data on how many trials there have been. In the lottery, we know that someone will win because we know that even though the odds are astronomical of winning, there are many tickets sold. When it comes to life, we have no idea how many "losing tickets" there are. So any number is meaningless unless we have the context for interpreting it.
Below is the article that appeared in the November 12, 1981 issue of Nature, page 105 (volume 294, number 5837). It is a text box in the "News" section of the journal.

Hoyle on Evolution

The serious part of the Kellogg symposium provided Sir Fred Hoyle with an opportunity for a moderate (and self-critical) statement of his case for disbelieving conventional views about the evolution of the Universe, the "big bang" among them. Hoyle has been associated with the Kellogg laboratory since his collaboration in the mid-195Os with W.A. Fowler and the two Burbidges (Margaret and Geoffrey), now known as the gang of four, on the problem of nucleogenesis.

Hoyle said last week that, although content in the mid-1960s to give the supposed connection between the microwave background radiation and the big bang a "good run for its money", he had now lost patience with this approach. Two of his reasons involve the origin of life -- the calculated time since the origin of the Universe of 10,000 million years or so is not enough to account for the evolution of living forms, while adiabatic expansion of the Universe would have been inimical to the evolution of highly ordered forms. But Hoyle also said that new evidence in support of the big-bang hypothesis was emerging only slowly. Yet "when people are on the right track, I new facts emerge quickly". Hoyle said he would change his view if it turned out that neutrinos have a mass of between 20 and 30 electron volts.

The essence of his argument last week was that the information content of the higher forms of life is represented by the number 1040,000 -- representing the specificity with which some 2,000 genes, each of which might be chosen from 1020 nucleotide sequences of the appropriate length, might be defined. Evolutionary processes would, Hoyle said, require several Hubble times to yield such a result. The chance that higher life forms might have emerged in this way is comparable with the chance that "a tornado sweeping through a junk-yard might assemble a Boeing 747 from the materials therein".

Hoyle acknowledged that steady-state theories of cosmologies, of which he was one of the chief exponents in the 1950s, are not now tenable because of the evidence for evolutionary galactic and stellar processes. But the big-bang view is similarly not tenable because of the way in which it implies the degradation of information. Of adherents of biological evolution, Hoyle said he was at a loss to understand "biologists' widespread compulsion to deny what seems to me to be obvious".

Back to Thoughts on Christianity and God.