**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 P**n** 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)

wherea+b+c+... =n

Then the concentration of P**n** is given by the formula

[P**n**] = 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 crust^{5}
and
even less of the
ocean.^{6} Taking the concentration of the other
elements to be of
order unity:

[P**n **] = O(320 x 10^{-6})^{18}

[P**n**] = 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 10^{42} (page
28 of his
article) to 2 x 10^{273}. Without even taking back
the concessions
discussed in items 1-3, above, this gives a formation time of 3 x

10^{79} 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**

^{1}Robert 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).

^{3}John 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).

^{4}e.g., Donald H. Menzel, *Fundamental
Formulas of
Physics* (New York: Dover, 1960), 2:641.

^{5 }*Handbook of Chemistry and Physics* (55thed.),
F-188.^{
6}*Ibid*., F-190.

^{7}This is still a generous concession. See Michael
Hart, "Habitable Zones about Main Sequence Stars," *Icarus*,
37:351-357
(1979).