Living, intelligent patterns in Conway’s Life

Conway’s Game of Life, a cellular automaton devised by the British mathematician John Horton Conway in 1970, is a rich mental laboratory to think about our own universe.

I have used Conway’s Life (from now on just “Life” with capital L) to analyze the Problem of Evil. See “My MTA 2013 talk: Life and The Computational Problem of Evil” and the previous “The physics of miracles and the problem of evil.” I am studying Life again to refine my argument, to be detailed in a forthcoming essay.

The computational universe of Life shares important properties with our universe, including emergent complexity, computational irreducibility, and Turing-completeness. The main difference is that Life is fully deterministic, which seems not to be the case of our universe. Another important difference is that, though Life can contain phenomena as complex as anything in our universe, the fundamental physics of Life (the cellular automata evolution rules) is fully known (we put it there) and very simple.

The Recursive Universe” (by William Poundstone) is a classic treatise on Life (the universe, and everything), written in 1985, with an encyclopaedic coverage of Life (as known in 1985) and intriguing parallels with physics, thermodynamics, computation, and life in our universe. Poundstone’s Afterword to the 2013 edition briefly covers important developments in Life since 1985, such as Turing machines and replicators.

Life Universal Turing Machine (UTM), initial configuration. Note the input stream of gliders.

Life UTM after 50,000 steps. Note that the tape is longer.

Top image: Life UTM after 50,000 steps, zoom.

The chapter “Self-Reproducing Life Patterns” details Conway’s analysis of true, lifelike self-reproduction in the Life universe. Poundstone – and Conway – think that life and consciousness would eventually emerge in a sufficiently large (actually, unthinkably huge) Life field, initially in a random state.

An important condition is that the random initial Life field should be sparse (with a very low density of on cells) to give enough time to self-reproducing patterns to propagate, evolve and learn new tricks without being untimely destroyed by random gliders and debris.

Besides huge size and vanishingly small density, no conditions are imposed to the initial random configuration – Poundstone and Conway believe that the laws of Life physics are “stronger” than any specific initial conditions and similar outcomes will eventually emerge from different initial random fields (this may well be a property of our own universe as well).

Excerpts from the chapter:

“Conway concluded: ‘There are Life patterns which behave like self-replicating animals… It’s probable, given a large enough Life space, initially in a random state, that after a long time, intelligent self-replicating animals will emerge and populate some parts of the space.”

“Eventually, self-reproducing patterns must tend to fill the Life plane. The most common, most natural large objects in a thin random Life field might—ultimately—be self-reproducing patterns. The fate of any typical region of the plane could be to become populated with self-reproducing patterns, all the offspring of an accidental creation that probably took place in a distant part of the infinite plane.”

“A self-replicating Life pattern that moves might benefit from sensory and nervous systems to deal with new environments. Double side-tracking can send a glider out and bring it back. Gliders that fail to return would indicate an obstacle ahead. Thus a pattern could have ‘eyes’ or ‘antennae’ of sorts.”

“Presumably, the long-term evolution of an infinite Life field would proceed somewhat like biologists imagine the evolution of life on the early earth proceeded.
First the Life plane would become populated with colonies of first-generation self-replicating patterns. Each colony would derive from a single seed pattern that arose purely by chance. The odds against a pattern arising by chance grow even steeper for more complex patterns, so practically all of the first-generation patterns would possess only the minimum level of organization necessary to reproduce. They would be the Life version of Von Neumann’s machine—a mindless self-replicator.
From time to time, mutations would occur. A pattern might be constructed in a site containing other Life objects. A stray glider might wander into a pattern’s works. Most such mutations would be harmful. But rare cases would produce patterns better able to survive than their neighbors. Natural selection would favor the mutated patterns. The species of self-reproducing patterns in a given region would gradually change through mutation, extinction, and migration from distant regions.
The existence of universal computers in Life implies that the nervous systems of self-reproducing patterns can be arbitrarily complex. Eventually, ‘intelligent’ species might evolve from the same sort of selective pressures that operated on earth.”

Of course, there is no reason to stop at human-level intelligence. We are starting to boost our evolution by developing superintelligent technology, and the same could happen in a Life universe.

Poundstone ponders how big are Life self-reproducing patterns, and how big are the smallest Life random fields that spontaneously form self-reproducing patterns, and arrives at unthinkably huge sizes. My own analysis below is based on typical scales in Life and in our physical universe, and also arrives at hyper astronomical numbers.

Let’s consider one nanometer (10-9 meter) as the size of the smallest forms of life in our universe (the smallest known forms of life are bigger than that, but let’s leave some room for new findings). Let’s consider the Planck length (10-35 meters) as the fundamental scale (the smallest meaningful size) in our universe.

In the framework of this rough analogy, on a display where one Life cell is 1 cm across, the size of the smallest life form would be 1024 meters. How big is that? One light year is 1016 meters, so that the smallest life form in Life is 108 (100 millions) light years across (that is the space occupied by thousands of galaxies).

Of course, that is not big enough, because life doesn’t exist in isolation but needs a whole ecology to support it. Considering the size of a small planet (1000 kilometers) as a typical size for a whole ecology, we must multiply the size of the smallest life form in Life times the size of the planet expressed in nanometers (1015). The result is 1023 light years. The size of the observable universe is 100 billions (1011) light years. In conclusion, the smallest Life board that supports life is a trillion (1012) times bigger than the universe.

Based on these numbers, we are not likely to build a Life computation with sentient and intelligent inhabitants anytime soon. But perhaps one may be built in the (far) future, and/or alien super-civilizations out there create intelligent Life computations based on some kind of weird quantum technology. Also, perhaps all consistent realities exist in some sense, and Life is certainly consistent. If so, mathematical universes populated by superintelligent forms of life (aka Gods) exist elsewhere, and in principle we know of a very short recipe to build at least one: take a random Life field with size X and density Y, and let it evolve until it develops life, intelligence, and superintelligence.