John Horton Conway |

**is a cellular automaton devised by John Conway. Let's see how it works, in a little more detail:**

*The Game of Life*
This
cellular automaton acts on a potentially infinite two-dimensional space,
divided into square cells. In each cell there is a simple automaton, or if you
want, a program with two states that we can call

**and***alive***, or 1 and 0. The program in each cell takes as input its own state and the states of its eight neighbors. If it is alive (i.e. in state 1) and two or three of its neighbors are alive, in the next instant it will still be alive. If it is dead (in state 0) and exactly three of its neighbors are alive, in the next instant it will become alive. In any other case, it will become dead. Let's look at a figure to make it clearer:***dead*
The program
in the center box is in state 1. As two of its eight neighbors are in state 1,
the next instant it will continue to be in state 1 (i.e.

**).***alive*
It
is usual to represent those squares whose associated program is alive (in state
1) by filling the square in black and leaving white the squares in the dead
state (0), or vice versa: using black for dead squares and white for those alive.

It
seems quite simple, but these rules give rise to very complex behaviors. Let’s
see, for example, a disposition called a

**, because it moves over time, keeping its structure constant.***glider*
It
can be seen in the figure (where the dead squares are empty) that, after four
steps, the combination of zeros and ones that make up the

**has moved diagonally one position down and to the right, recovering its initial shape. If it does not find on its way other alive cells that could modify its behavior, the diagonal movement would continue indefinitely (remember that the grid is potentially infinite).***glider*
Another
interesting combination is the one shown on the left, which is called the

**. After a certain number of steps, the initial arrangement repeats itself, but a glider has come off it and thereafter moves away indefinitely. After another identical set of steps, a new glider appears, following the steps of the first.***glider gun*
By
combining two glider guns in various ways, an OR gate can be built (a device
that, when impacted by one or two gliders at the same time, generates one
output glider if any one of its two input gliders is present); or an AND gate (gliders
come out only if both input gliders are present); or a NOT gate (a glider comes
out if, and only if the arriving glider is not present). We know that with
these three logic gates (OR, AND, NOT) one can build a computer. Therefore, in the
grid of the game of life, it is potentially possible (although hardly feasible)
to build a computer, capable of solving the same problems as the computer on your
table.

This
is just a sample of the amazingly complex structures that can be assembled with

**.***The Game of Life*
How
did Soler and I prove that

**?***Tegmark's multiverse doesn't solve the fine-tuning problem*
The Swedish-American
mathematician Max Tegmark invented the

**, which is based on the claim that***mathematical multiverse***. In other words, there are an infinite number of universes, as the number of coherent mathematical structures is infinite. Tegmark argues that in this multiverse there would be no fine-tuning problem: as there are infinite universes, some of them must be compatible with our existence and that’s where we are. Then he adds an additional condition that makes it possible to test his theory:***every mathematically coherent structure must exists physically in some universe***.***the universe where we are must be the most probable among all those compatible with our existence, for otherwise the fine-tuning problem would arise again*
To
prove that Tegmark’s multiverse does not solve the fine-tuning problem, Soler
and I put forward the following argumentation:

- The Game of Life is a coherent
mathematical structure. Then, according to Tegmark,
.*somewhere there is a universe that implements the Game of Life* - The Game of Life
at the same level as ordinary computers. According to Tegmark’s condition, and for a hypothetical intelligent observer located in the Game of Life universe,*allows complex structures to exist*.*the fine-tuning problem would not arise if that universe were the most probable among all those compatible with the existence of this type of complex structures* - Analyzing the cellular automata of the
Game of Life type, we have found four different versions of the rules
compatible with the existence of complex structures. In addition, an
infinite number of versions, also compatible with this existence, must be
added, which are built assuming that
. Then*the rules for state change are not constant, but oscillate over time between the four compatible rules, in all possible ways*, chosen at random among all the possible universes,*the probability that a universe capable of supporting complex structures*, like the Game of Life,*is based on fixed rules that do not vary with time*(4 divided by infinity). Therefore, in the universe of the Game of Life, the fine tuning problem would arise.*is zero* - Our universe seems to be specially
designed to make life possible (
), as*fine-tuning*(but not absolutely critical)*the universal constants have fairly critical*. If these universal constants were not constant, but*values*, the universe would still be compatible with our life.*varied over time without leaving their respective critical zones* - The number of universes with parameters
that vary over time would be infinite. Therefore
, for*our universe is not the most probable among all those compatible with our existence*. Therefore, the condition established by Tegmark himself is not met. Therefore*the probability that we find ourselves in a universe with constant parameters is vanishingly small*.*Tegmark’s multiverse doesn't solve the fine-tuning problem*

Note
that, unlike other multiverses, Tegmark's multiverse lets us experiment with
other universes (

**is one of them). Therefore, it is possible to reach reasonable conclusions, such as that***The Game of Life***.***this multiverse does not solve the problem of fine tuning*
For
further details, see our paper

*Fine tuning explained? Multiverses and cellular automata**.*F.J. Soler Gil, M. Alfonseca. Journal for General Philosophy of Science, Springer, March 2013. DOI: 10.1007/s10838-013-9215-7.**The same post in Spanish**

**Thematic Thread on Multiverse and Fine Tuning: Previous Next**

**Thematic Thread on Synthetic**

**and Artificial**

**Life**

**: Previous Next**

**Manuel Alfonseca**

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