We may be bots in a reality-wide simulation, and perhaps the player(s) from above can violate our simulated physics when they want. In a more popular formulation of the same concept, called Religion, the player(s), called God(s), created our reality and can perform miracles. The two formulations are equivalent for all practical purposes. Many religions assume that Gods are omnipotent and benevolent, but then we have the problem of evil: how can omnipotent and benevolent Gods permit evil and suffering?
If omnipotent and benevolent Gods permit evil and suffering, then they are either not omnipotent, or not benevolent, or neither, or perhaps they don’t exist at all. In fact, the problem of evil is one of the main reasons why former believers become atheists. I argued that the problem of evil has a simple solution when examined with a rigorous approach based on the physics of computation.
I will write down the full argument after going back to Europe today. Here are some notes on the Life analogy. I find Life totally fascinating, and every year or so I scan the net to learn of new developments. I wrote these notes in preparation of the talk:
Universal Turing Machines in Life
Paul Rendell has implemented a Universal Turing Machine (UTM) in Conway’s Game of Life.
A Turing Machine (TM) consists of a Finite State Machine (FSM) with a (theoretically infinite) long tape on which symbols can be written and read back via a moving read/write head. The FSM is the program which determines from the symbol read and an internal ‘state’ what the symbol to write should be and which way to move the read/write head. It can also change its internal state, or halt.
A Universal Turing Machine is a TM which simulates the actions of another TM. It takes as its input a description of a specific TM.
The program in the Finite State Machine below (the square pattern) is a Universal Turing Machine program. The description a specific TM is provided as an input stream of gliders. Rendell developed first a specific Life TM, then a first UTM with the description of a specific TM on the tape, then this more general UTM.
Life UTM, initial configuration. Note the input stream of gliders.
Life UTM after 50,000 steps. Note that the tape is longer.
Life UTM after 50,000 steps, zoom.
Conscious life patterns?
The existence of a Universal Turing Machine in Life forces us to consider whether consciousness can arise in Life. This is difficult to imagine, but if you think of it it is even more difficult to see why not. Actually, IF the brain/mind system is a TM, THEN consciousness can arise in Life (a UTM can emulate any TM).
Games, Life and the Game of Life, by Rachel Thomas | “I believe that if you have a large enough configuration you will see evolution in the plane,” says Conway. “What would happen is every now and then there would be a creature capable of reproducing itself and then they would start to populate the plane. Except the plane is still filled with random junk which might kill some of them. So some of them will be better equipped to survive than others and every now and then they will run into something that hurts and might start a change. Most of these changes will probably be for the worse but every now and then one of these might be for the better and then you know the story. You will probably get evolution happening and you would get creatures that really deserve the name living.” He can even imagine that if Life was left to play for a very long time, these creatures might eventually achieve consciousness.
Conway’s Game of Life, by Stephan Kinsella | “As Conway said, ‘It is no doubt true that on a large enough scale LIFE would generate living configurations. Genuinely living. Evolving, reproducing, squabbling over territory. Writing Ph.D. theses. On a large enough board there’s no doubt in my mind this sort of thing would happen.’ A situation could arise in which a simulation of a LIFE plane had progressed so far that conscious life has actually arisen.”
Of course Conway’s “large enough” means _really very, very, very large_, way larger than the UTM example. I guess if a Life cell is one centimeter, the smallest pattern that can be considered alive would be larger than the Earth, and the smallest pattern that can be considered conscious in the usual sense would be many orders of magnitude larger. But the Life plane is infinite in all directions…
Life of a glider
Perhaps conscious, thinking and feeling patterns can exist in Life, but of course a glider is too simple to think or feel. At the same time, gliders can be considered “alive” in some sense, just like a molecule may be considered alive. In Being a Glider in the Game of Life, by Markus Echterhoff, and Autopoiesis and Cognition in the Game of Life, by Randall D. Beer, the authors describe the life of a glider. A glider can move in one or four directions, and be in one of four phases, shown in the diagram below. These possible glider states and their transformations into other glider states according to the cellular automata laws of Life physics constitute “gliderness” and can be thought of as simple “mental states” in the life of a glider.
Being a Glider in the Game of Life, by Markus Echterhoff
Stephen Wolfram terms the inability to shortcut a program (e.g., a system), or otherwise describe its behavior in a simple way, “computational irreducibility.” It is impossible to predict what computationally irreducible systems will do before essentially running them. The idea demonstrates that there are occurrences where theory’s predictions are effectively not possible.
“There are some cellular automata whose behaviour can never be reduced to a formula,” says “Explorations in the Cellular Microworld‘ (interview with Wolfram). “The only way to find out what they do is to simulate them step by step. No simpler computation provides a significant short cut. This property is known as computational irreducibility. Universal computers such as general Turing machines are among the systems which possess it. At least two cellular automata [including Life] are known to be universal computers. They can be programmed to solve any computer-soluble problem, by setting up an appropriate initial configuration of cells.”
Life within Life
A Life simulation can be build within Life by using the unit cell (picture below). The state of the unit cell after 5760 steps is the presence/absence of a glider at the center of the red box. So a Life computer 5760 times slower than Life itself can be built within Life.