Simon Powell - The Psilocybin Solution

Computations on ENIAC were supervised at Los Alamos in part by eminent mathematician John von Neumann. Although von Neumann was a mathematical wizard, his ethical stance was a little questionable. Not only was he an extremely vocal advocate for the total nuclear destruction of Russia before that country developed a nuclear capability, and not only did he feel that it was safe to carry out and closely observe nuclear test explosions (he was later to die of bone cancer, probably caused by witnessing nuclear explosions at Bikini Atoll), he even devised plans to dye the polar ice caps in order to melt them. He also helped design the nuclear bombs that were detonated over Japan.

Despite these cheery idiosyncrasies, it was von Neumann who first began to study the computational properties of cellular automata on the bulky computers at Los Alamos. Von Neumann had always been fascinated by the idea of self-replicating machines, though he believed that ultimately this was not possible using only vacuum tubes, transistors, and the like. However, by utilizing the new computers that were at hand, von Neumann was able to implement a computer program in which simulated life-forms were able to replicate themselves. The program was the original cellular automaton. That these self-replicating, computer-generated entities were not made of flesh or machine parts did not matter, as it was their logical and organizational structure that defined them. This was one of the first real insights into the simulational power of computers. They could create convincing forms of life.

Von Neumann’s work was given a whole new lease on life (literally) by Cambridge mathematician John Conway, who in 1970 invented a cellular automaton called the Game of Life. The game is deceptively simple, yet it is able to generate an endless amount of complexity and variation. It also mirrors the computational quality of biological life.

The Game of Life is referred to as a cellular automaton because it proceeds within a grid of cells (like graph paper) and because the game’s progression is entirely automatic. The game progresses according to four rules. These four rules are applied again and again to the current state of the cells in the grid. Cells are either occupied or not—which means the system holds binary values. Cells are digital, on or off, alive or dead. These are the four simple rules:

1. Any live cell with fewer than two live neighbors dies, as if caused by underpopulation.

2. Any live cell with two or three live neighbors lives on to the next generation.

3. Any live cell with more than three live neighbors dies, as if by overcrowding.

4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

An initial configuration of on/off (that is, live or dead) cells is provided as input, and then the four seemingly vacuous rules are applied. The output from this process yields a new configuration of on/off cells. The rules are applied repeatedly, hundreds or even thousands of times. The results can be striking. Not only do slightly different start configurations yield wildly different outputs, various patterns can form that endure throughout the game. If successive states of the cellular automaton are presented rapidly on a computer screen as opposed to being drawn on numerous sheets of graph paper, a Life movie can be watched as it progresses. Patterns emerge, move around, collide, mutate, oscillate, and some even seem able to replicate themselves.

Conway’s Game of Life grabbed media attention in the early 1970s through coverage in Scientific American . The various Life objects began to acquire names. Shuttles, beehives, and flotillas were born. Ships, boats, barges, and blocks were readily observed and documented as they meandered about the two-dimensional Life plain. (Animated examples of the Game of Life along with relevant freeware can still be found on the Internet—indeed nowadays certain interesting configurations can be iterated billions of times in just seconds.)

The genelike pattern with the capacity to replicate that sometimes emerged in the primordial Life soup was named the glider. Gliders were observed to collide with one another, resulting in the formation of a glider gun that shot out further gliders as though they were its offspring. It was even discovered that glider guns could be set up in such a way as to constitute a virtual computer. Conway proved that processions of gliders were able to code binary numbers, and that logic gates could be formed by making glider streams collide with one another in a specific way. The result is startling. The Life computer can itself embody yet another computer, and so on ad infinitum. A digital information process within a process within a process (this, of course, is reminiscent of patterns within patterns within patterns).

The fascinating feature of the lifelike patterns that evolved in the Game of Life was their origin. From initial simplicity, complexity was born. Furthermore, cellular automata were clearly computational, whether they were played out on a computer, a chessboard, or on graph paper. Through state transitions, information was being processed throughout the game. There was an unavoidable implication that life itself might represent a similar information-processing system. If so, then the Universe could most definitely be understood in computational terms.

We have now arrived back at the Universe-as-a-computation scenario. An ongoing computational system, the Game of Life vividly demonstrates how initial conditions and some basic state transition rules can give rise to organized complexity and the emergent phenomenon of self-replication. The real computational game of life in which we have been born similarly depends upon a well-defined initial state at some distant moment in the past and a set of rules. In this case the rules are the laws of physics and the constants of Nature (like the particular strengths of the various forces of Nature). This implies that we are inside the Universal Computation, much as gliders are inside of cellular automata.

The case is still not watertight. Cellular automata, and indeed all computations proceeding within a computer, move in discrete steps. If the Universe is an ongoing computation, then, strictly speaking, it ought to proceed in discrete state transitions, frame by frame as it were. The late mathematician Martin Gardner, who originally introduced the Game of Life to readers of Scientific American, was one of the first to speculate about this. He wrote: “There is even the possibility that space-time itself is granular, composed of discrete units, and that the universe… is a cellular automaton run by an enormous computer.” {39} 39 4. Gardner, Wheels, Life and Other Mathematical Amusements, 240.

In other words, if the Universe is indeed a kind of computation, there is likely to be a smallest unit of time (time is granular) that cannot be broken down further. Such a hypothetical smallest unit of time is known as a chronon. A chronon is an absolute moment, or quantum of time, in which the Universe is in a particular state. This state will then proceed by a discrete “jump” to form the next chronon according to whatever laws are operating on that state, much like the movement of electrons, which are supposed to discretely jump from one orbit to another. There are believed to be no intermediary states between successive “jumps.”

If time does indeed move in discrete jumps, one might well ask why we experience time as flowing. There is no surprise here, for to talk of discrete time is like talking of the successive frames of a movie. If the frames are presented quickly enough, the illusion of continuity becomes apparent. An illusion of continuity is also manifest in the Game of Life. The state transitions of Life automata can be processed by a computer so quickly as to give rise to patterns, which, on the computer monitor, appear to flow across the two-dimensional playing field. In fact, all computer displays move in discrete stages, even in the most advanced programs. Popular computer games and cell phone apps might look as if they are flowing smoothly, yet in actuality they are proceeding in rapid state transitional jumps (hence a still frame, or “RAM slice,” can be observed if a computer game is paused).