Update onSelf-Reproducing Automata

Robert C. Newman

(April, 1989)

 

Since IBRI Research Report #36 was printed in 1987, its contents were published (in a slightlyedited form) in Perspectives on Science and Christian Faith 40, 1 (March 1988): 24-31.

 

In the March, 1989 issue of the same journal, Dr. John Byl,of the Department of Mathematical Sciences at Trinity Western University,Langley, British Columbia, took up the challenge offered in my conclusion anddesigned a much simpler self-reproducing automaton than that of Langton.  See his letter, PSCFI 41, 1 (March 89): 26-29 for details.

 

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

With an array of only 12 cells, with 36 special transitionrules and 7 default rules, Byl uses my estimates for the probability of thisautomaton arising by chance in the known universe to get a timespan forformation of only 5 x 10-45 seconds as against my value of 3 x 10139years for the Langton automaton. This would seem to make the random production of a self-reproducingautomaton quite likely somewhere in the history of our vast universe.  Byl has made an important step forwardin the search for the simplest possible self-reproducing automaton, but hisconclusion regarding the ease of its formation does not follow.

 

Realizing that the Langton automaton was quite unlikely, Imade a number of very generous concessions in the probability calculation inorder to simplify it and to avoid haggling.  In the interests of realism (though not wishing to appearstingy) I must take some of these back.

 

1. It was assumed that all relevant atoms in the universewere already in 276-link chains (or for the Byl automaton, these would be55-link chains).  This is certainlynot the case.  The actual number of55 (or larger) atom molecules is an astronomically small fraction of the atomsinvolved.  As yet I do not know howto calculate this fraction.

 

2. It was assumed that these chains were trading atoms insuch a way as only to make newcombinations.  This will probablynot make more than an order of magnitude difference in the result.

 

3. It was assumed that these traded atoms were moving at aspeed appropriate for a temperature of 300 degrees Kelvin (about 80oF).  But few of the atoms in theuniverse are in such a temperature regime.  Those in much colder regions will be moving around much moreslowly, so that fewer combinations will be formed.  In any case, life would not survive in such areas even if itcould form, and it is not likely there would be much transport form suchregions to warmer regions, as the mass movement is nearly all in the oppositedirection (outward from stars).  Onthe other hand, those atoms in much hotter regions will have much faster atomicmotions, but that very motion will disrupt any long-chain molecules.

 

It seems best to restrict our calculations to that fractionof matter in Òlife zonesÓ around stars. Taking our solar system as an average, this fraction amounts to theratio:

 

F = Mearth/Msun= 3 x 10-6.

 

Thus the fraction of atoms making such combinations isreduced by a third of a million.

 

Here on earth, it is only the material near the surface thatis in a temperature/pressure regime for life to function .  This fraction of the total earthÕs massis something like that of a think shell at the earthÕs surface (say 1 to 6miles thick), which gives us a further reductio of 10-3 to 2 x 10-4.

 

4. It appears that an error was made in calculating thecomplexity of the Langton automaton which was also carried over to the Bylmodel.  The transition rules wererepresented as one digit per rule (the result), but in fact a label isnecessary for each rule to identify it. In BylÕs automaton, each of the seven default rules needs one digit (thecurrent value of the cell) to distinguish among them.  The non-default transition rules depend upon the currentvalues of the founr neighboring cells, which thus require a four-digit label foreach.  Adding in this complexityraises the number of combinations from BylÕs value of 6 x 1042 (page28 of his article) to 2 x 10173.  Without even taking back the concessions discussed in items1-3, above, this gives a formation time of 3 x 1079 years again, andrandom formation appears to be out of the question.

 

I would appreciate correspondence from readers on possibleimprovements to this model calculation, as I believe the determination ofminimum complexity for any reasonable analogs to life is desirable in workingthrough the basic questio of lifeÕs origin.