Do Highly Improbable Events Ever Happen?

Do Highly Improbable Events Ever Happen?

Arthur S. Lodge

Fifty years ago, Wald (1) and Fisher (2) made similar improbable events claims. How do they look today?

Attributing the origin of life to spontaneous generation, Wald stated: "However improbable we regard this event, ¼ it will almost certainly happen at least once…. The time ¼ is of the order of two billion years¼ Given so much time, the `impossible' becomes possible, the possible probable, and the probable virtually certain". Morowitz (3) subsequently assessed probabilities for the chance re-assembly (when equilibrium is attained after dissociation followed by re-association) of the bonds in a single bacterium to be of the order of 1 in 10^(100,000,000,000), so 2 billion years

[< 10^(26) nanoseconds] is much too short a time to support Wald's claim.

Morowitz supposed that a chance-driven mechanism could produce a single cell from inanimate matter. So, also, does macro-evolutionary Neo-Darwinian Theory (NDT), which, however, includes other mechanisms (such as natural selection) which are alleged to increase probability. It is, therefore, reasonable to suppose that Morowitz' probability represents a provisional value for NDT macro-evolutionary processes until calculation shows that the additional mechanisms do, indeed, increase probability above the Morowitz value. To the best of my knowledge, there is still no published plausible estimate showing that the claimed probability increases could have been large enough for the NDT to provide a feasible explanation of macro-evolution. [Although some NDT features are well known, I cannot find any complete, generally agreed, NDT formulation in the literature. This is consistent with the opinions of two authorities: "There is no simple definition of the `evolutionary synthesis'"(4); "Darwinism is not a simple theory to be proved right or wrong" (5).]

"Natural selection exists, to be sure, but no one has evidence that it can accomplish anything remotely resembling the creative acts that Darwinists attribute to it" (6). In his 4-page review (7) of the book containing this statement, Gould would surely have shown it to be incorrect, if he could have done so. He didn't; therefore, he couldn't.

In a fallacious argument, unchallenged for fifty years, Fisher (2) sought to make plausible, by analogy, his claim that natural selection increases probability: "Darwin¼ brought to light a process by which contingencies a priori improbable are given, in the process of time, an increasing probability, until it is their non-occurrence rather than their occurrence which becomes highly improbable". For an example in which the probability of a man having at least one son is 5/8, Fisher considered "the prior probability that a hundred generations of his ancestry in the direct male line should each have at least one son. The odds against such a contingency as it would have appeared to his ancestor¼ require for their expression forty-four figures of the decimal notation; yet this improbable event has certainly happened¼ natural selection¼ constantly modifies the probability of all the types of organism that might appear¼ The rate at which the probability is modified will not be as great as that illustrated by the continuance of the male line".

Huxley (8) used this argument to dismiss "hoary" improbability objections to Darwinian theories.

Each 1st-generation man either is an ancestor of some 100thgeneration man (and so may be placed in a set "A", say) or isn't (set "B"). Let P denote the probability that a 1stgeneration man will have an unbroken 100generation male succession. Each 100thgeneration man necessarily had an unbroken male ancestral line to generation 1; therefore, his ancestor there must have had an unbroken male succession for 100 generations and hence, for him (an Aman), and, similarly, for all Amen, P = 1. (Clearly, P = 0 for all Bmen). For a man chosen at random from the 1st generation (an "R" man), P = e, where

0 < e << 1. To get the event that "certainly happened" (P = 1), Fisher correctly chose an Aman. To get his "improbable event" (P = e), Fisher should have chosen an Rman but, instead, mistakenly chose an Aman and consequently concluded (wrongly) that an "improbable event has certainly happened". In fact, Fisher demonstrated neither that an improbable event happened nor that a probability increased.

Considering Morowitz' estimate, Shapiro (9) wrote: "One escape hatch yet exists for spontaneous generation. Why need the event have been probable? ¼ improbable events occur all the time." The only support that he offered for this claim was to consider a lottery in which the odds against winning were 10^(7) to 1: "¼we would have to buy a ticket every day for about 30,000 years to make a win a probable event. Yet every so often we note¼ that there is a winner. That person was not 30,000 years old, and usually has bought just one or two tickets. He was merely lucky". In the set of all ticket holders for such a lottery, the probabilities (1) that there will be, and (2) that a person chosen at random will be, a lottery winner are 1 and 10^(-7), respectively. Shapiro confused these two probabilities; he did not show that an improbable event happened.

Half-century Improbable Events Scoreboard: Events: 0. Errors: 3.

References

1. G. Wald, Scientific American 191, 46 (August, 1954).

2. R. A. Fisher, in Evolution as a Process, J. Huxley, A. C. Hardy, E. B. Ford, Eds. (Allen & Unwin, London, 1954), pp. 91, 92.

3. H. J. Morowitz, Energy Flow in Biology (Academic Press, New York & London, 1968), p.317.

4. W. B. Provine, private communication, 2001.

5. E. Mayr, Toward a New Philosophy of Biology (Belknap Press of Harvard University Press, Cambridge, Massachusetts, 1988), p. 535.

6. P. Johnson, Darwin on Trial (Intervarsity Press, Downers Grove, Illinois, 1991), p. 115.

7. S. J. Gould, Scientific American, 267(1), 118 (July, 1992).

8. J. Huxley, in Evolution as a Process, J. Huxley, A. C. Hardy, E. B. Ford, Eds. (Allen & Unwin, London, 1954), p.2.

9. R. Shapiro, Origins: A Skeptic's Guide to the Origin of Life on Earth (Summit Books, New York, 1986), p.128.

In January, 2004, this article was submitted to and rejected by Science magazine on the grounds that the article is too specialized.	Arthur S. Lodge \| home Darwin's Eye: Bait and Switch \| Fisher's Fallacies \| Shapiro's Shenanigans \| Huxley's "Hoary Objection" Howler \| Richard Dawkins: Designer! \| Dembski's Disaster \| Do Highly Improbable Events Ever Happen? \| Miller's Mistake \| Wald's Wand \| The Typing Monkeys Fallacy "Unlikely Events" Fallacies: \| Evolution \| Darwinism's Debit Sheet: 23 items \| The Neo-Darwinian Theory: Version 2004 \|Criticisms of "Finding Darwin's God"
	Do Highly Improbable Events Ever Happen? Arthur S. Lodge Fifty years ago, Wald (1) and Fisher (2) made similar improbable events claims. How do they look today? Attributing the origin of life to spontaneous generation, Wald stated: "However improbable we regard this event, ¼ it will almost certainly happen at least once…. The time ¼ is of the order of two billion years¼ Given so much time, the `impossible' becomes possible, the possible probable, and the probable virtually certain". Morowitz (3) subsequently assessed probabilities for the chance re-assembly (when equilibrium is attained after dissociation followed by re-association) of the bonds in a single bacterium to be of the order of 1 in 10^(100,000,000,000), so 2 billion years [< 10^(26) nanoseconds] is much too short a time to support Wald's claim. Morowitz supposed that a chance-driven mechanism could produce a single cell from inanimate matter. So, also, does macro-evolutionary Neo-Darwinian Theory (NDT), which, however, includes other mechanisms (such as natural selection) which are alleged to increase probability. It is, therefore, reasonable to suppose that Morowitz' probability represents a provisional value for NDT macro-evolutionary processes until calculation shows that the additional mechanisms do, indeed, increase probability above the Morowitz value. To the best of my knowledge, there is still no published plausible estimate showing that the claimed probability increases could have been large enough for the NDT to provide a feasible explanation of macro-evolution. [Although some NDT features are well known, I cannot find any complete, generally agreed, NDT formulation in the literature. This is consistent with the opinions of two authorities: "There is no simple definition of the `evolutionary synthesis'"(4); "Darwinism is not a simple theory to be proved right or wrong" (5).] "Natural selection exists, to be sure, but no one has evidence that it can accomplish anything remotely resembling the creative acts that Darwinists attribute to it" (6). In his 4-page review (7) of the book containing this statement, Gould would surely have shown it to be incorrect, if he could have done so. He didn't; therefore, he couldn't. In a fallacious argument, unchallenged for fifty years, Fisher (2) sought to make plausible, by analogy, his claim that natural selection increases probability: "Darwin¼ brought to light a process by which contingencies a priori improbable are given, in the process of time, an increasing probability, until it is their non-occurrence rather than their occurrence which becomes highly improbable". For an example in which the probability of a man having at least one son is 5/8, Fisher considered "the prior probability that a hundred generations of his ancestry in the direct male line should each have at least one son. The odds against such a contingency as it would have appeared to his ancestor¼ require for their expression forty-four figures of the decimal notation; yet this improbable event has certainly happened¼ natural selection¼ constantly modifies the probability of all the types of organism that might appear¼ The rate at which the probability is modified will not be as great as that illustrated by the continuance of the male line". Huxley (8) used this argument to dismiss "hoary" improbability objections to Darwinian theories. Each 1st-generation man either is an ancestor of some 100thgeneration man (and so may be placed in a set "A", say) or isn't (set "B"). Let P denote the probability that a 1stgeneration man will have an unbroken 100generation male succession. Each 100thgeneration man necessarily had an unbroken male ancestral line to generation 1; therefore, his ancestor there must have had an unbroken male succession for 100 generations and hence, for him (an Aman), and, similarly, for all Amen, P = 1. (Clearly, P = 0 for all Bmen). For a man chosen at random from the 1st generation (an "R" man), P = e, where 0 < e << 1. To get the event that "certainly happened" (P = 1), Fisher correctly chose an Aman. To get his "improbable event" (P = e), Fisher should have chosen an Rman but, instead, mistakenly chose an Aman and consequently concluded (wrongly) that an "improbable event has certainly happened". In fact, Fisher demonstrated neither that an improbable event happened nor that a probability increased. Considering Morowitz' estimate, Shapiro (9) wrote: "One escape hatch yet exists for spontaneous generation. Why need the event have been probable? ¼ improbable events occur all the time." The only support that he offered for this claim was to consider a lottery in which the odds against winning were 10^(7) to 1: "¼we would have to buy a ticket every day for about 30,000 years to make a win a probable event. Yet every so often we note¼ that there is a winner. That person was not 30,000 years old, and usually has bought just one or two tickets. He was merely lucky". In the set of all ticket holders for such a lottery, the probabilities (1) that there will be, and (2) that a person chosen at random will be, a lottery winner are 1 and 10^(-7), respectively. Shapiro confused these two probabilities; he did not show that an improbable event happened. Half-century Improbable Events Scoreboard: Events: 0. Errors: 3. References 1. G. Wald, Scientific American 191, 46 (August, 1954). 2. R. A. Fisher, in Evolution as a Process, J. Huxley, A. C. Hardy, E. B. Ford, Eds. (Allen & Unwin, London, 1954), pp. 91, 92. 3. H. J. Morowitz, Energy Flow in Biology (Academic Press, New York & London, 1968), p.317. 4. W. B. Provine, private communication, 2001. 5. E. Mayr, Toward a New Philosophy of Biology (Belknap Press of Harvard University Press, Cambridge, Massachusetts, 1988), p. 535. 6. P. Johnson, Darwin on Trial (Intervarsity Press, Downers Grove, Illinois, 1991), p. 115. 7. S. J. Gould, Scientific American, 267(1), 118 (July, 1992). 8. J. Huxley, in Evolution as a Process, J. Huxley, A. C. Hardy, E. B. Ford, Eds. (Allen & Unwin, London, 1954), p.2. 9. R. Shapiro, Origins: A Skeptic's Guide to the Origin of Life on Earth (Summit Books, New York, 1986), p.128.