Automata and the Origin of Life: Once Again

Robert C. Newman
Biblical Theological Seminary
200 N. Main Street
Hatfield, PA 19440

From : PSCF 42 (June 1990): 113-114.

I have appreciated the unusual amount of feedback from my article on Langton's self-reproducing automaton published in this journal.¹ Besides several letters to me personally, Mark Ludwig wrote a program which simulates the operation of the automaton on computers compatible with the IBM PC,² and John Byl has devised a significantly simpler automaton in response to my challenge.³ As Byl's paper might be misunderstood to suggest that such a self-reproducing automaton could easily form in a universe the size and age of ours, I submit the following comments.

Briefly, Byl has designed a cellular automaton with simplified structure and transition rules which reproduces in only 25 time-steps. The initial configuration looks like this:

22
2632
2642
25

With an array of only 12 cells, with 36 special transition rules and 7 default rules, Byl uses my estimates for the probability of this automaton arising by chance in the known universe to get a timespan for formation of only 5 x10^-45 sec as against my value of 3 x 10 ¹³⁹ years for the Langton automa ton. This would seem to make the random production of a self-reproducing automaton quite likely somewhere in the history of our vast universe. While Byl has made an important step forward in the search for the simplest possible self-reproducing automaton, his conclusion regarding the ease of its formation does not follow. The fault, however, is mine rather than his for this‚impression.

Realizing that the Langton automaton was quite unlikely, I made a number of quite generous concessions in the probability calculation to simplify it and to avoid haggling. In the interests of realism (and at the risk of appearing stingy) I must take some of these back.

1.  It was assumed that all relevant atoms in the universe were already in 276-link chains (or for the Byl automaton, 55-link chains). This is certainly not the case. The actual number of 55-atom (or larger) molecules is surely much smaller. I am not sure how to calculate the actual proportion of 55-atom polymers, but perhaps a rough estimate can be made from a simple-minded application of the mass-action law.⁴

Assume a polymer Pn consisting of n atoms, formed by the reaction of a atoms of element X, b atoms of Y, c atoms of Z, and so on, such that

aX + bY  + cZ + ... -> XaYbZc... (i.e., Pn)
where a + b + c +... = n

Then the concentration of Pn is given by the formula

                                        [Pn] = K [X]^a[Y]^b[Z]^c _...

Assume K to be of order unity. Since we are seeking some sort of organic molecule, perhaps 1/3 of the atoms in the polymer will be carbon, which makes up only some 320 parts per million of the earth's crust⁵ and even less of the ocean.⁶ Taking the concentration of the other elements to be of order unity:

                                         [Pn ] = O(320 x 10^-6)¹⁸

                                         [Pn] = O(10^-63)

So 55-atom polymers will only make up an astronomically small fraction of the total atoms. We have assumed a site on earth (or an earth-like planet) for reasons cited in #3 below.

2.  It was assumed that these chains were trading atoms in such a way as only to make new combinations. This will probably not make more than an order of magnitude difference in the result.

3.  It was assumed that these traded atoms were moving at a speed appropriate for a temperature of 300deg. Kelvin (about 80deg. F). But few of the atoms in the universe are in such a temperature regime. Those in much colder regions will be moving around far more slowly, so that fewer combinations will be formed. In any
case, life would not survive in such areas even if it could form, and it is not likely there would be much transport from such regions to warmer regions, as the mass movement is nearly all in the opposite direction (outward from stars). On the other hand, those atoms in much hotter regions will have much faster atomic motions, but these very motions will disrupt any long-chain molecules.

It seems best to restrict our calculations to that fraction of matter in "life zones" around stars. Taking our solar system as an average,⁷ this fraction amounts to the ratio:

                                    f = Mearth  / Msun = 3 x 10^-6

Thus, the fraction of atoms making such combinations is further reduced by a third of a million.

Here on earth, it is only the material near the surface that is in a temperature/pressure regime for life to function. This fraction of the total earth's mass is like a thin shell at the earth's surface (say 1 to 6 miles thick), which gives us a further reduction of 10^-3 to 2 x 10^-4

4.  I believe I made an error in calculating the complexity of the Langton automaton which was carried over to the Byl model. The transition rules were represented as one digit per rule (the result), but in fact a label is necessary for each rule to identify it. In Byl's automaton, each of the seven default rules needs one digit (the current value of the cell) to distinguish among them. The non-default transition rules depend upon the current values of the four neighboring cells, which thus require a four-digit label for each. Adding in this complexity raises the number of combinations from Byl's value of 6 x 10⁴² (page 28 of his article) to 2 x 10²⁷³. Without even taking back the concessions discussed in items 1-3, above, this gives a formation time of 3 x
10⁷⁹ years again, and random formation appears to be out of the question.

Byl is undoubtedly right in suggesting that some of the complexity of the automaton will translate into physical characteristics of the component atoms for the molecule(s) involved in self-reproduction, and that these characteristics are already given rather than generated by a random process. However, the structure of the
automaton and its transition rules do not exhaust its complexity, as no small amount of organization is supplied by the computer used to run the program. I would suggest that we let the computer's complexity stand for the structure of the individual atoms, leaving both automaton structure and transition rules as the minimal complexity which random combination must supply to begin self-reproduction in a hypothetical universe without a designer.

I would appreciate correspondence from readers on possible improvements to this calculation, as I believe the determination of minimum complexity for any reasonable analogs to life is most desirable in thinking through the basic question of life's origin.

©1990

NOTES

¹Robert C. Newman, "Self-Reproducing Automata and the Origin of Life," Perspectives on Science and Christian Faith, 40:24-31 (1988).
²"A Program Evolves-By Design," ASA/CSCA Newsletter, 30(4):5-6 (Aug/Sept 1988).
³John Byl, "On Cellular Automata and the Origin of Life," Perspectives on Science and Christian Faith, 41:26-29 (1989); "Self-Reproduction in Small Cellular Automata," Physica, D 34:295-299 (1989).
⁴e.g., Donald H. Menzel, Fundamental Formulas of Physics (New York: Dover, 1960), 2:641.
⁵ Handbook of Chemistry and Physics (55thed.), F-188.
⁶Ibid., F-190.
⁷This is still a generous concession. See Michael Hart, "Habitable Zones about Main Sequence Stars," Icarus, 37:351-357 (1979).