Quantum Soul

In the beginning ...

We want to construct a toy to play with and explore - one that will surprise us with its behavior.

So, we begin by considering the simple automaton, perhaps the simplest interesting example of which is the game of "Life" as developed by John Conway (mathematician, see the "Rules of the Game of Life" box). If you play with this game for a while you learn that you can make things move, for example, the glider

Even more complex conditions (a "glider factory" that shoots out glider after glider ...) show that you can get growth. By adding additional ways to label cells ({"dead" or "alive"} is so limiting) and by adding more complex rules (movement, inertia, attraction (gravity) repulsion (electrical charge)) we can get very complex behavior indeed. So complex that we might call it chaotic.

Rules of the Game of Life

"Life" is a game best played on a computer. It uses a grid of square cells (like a chessboard but bigger, often infinite). Each cell is either alive (1) or dead (0). Every cell has eight neighbors .
Each generation, the status of every cell changes according to three simple rules:

  1. Birth a dead (empty) cell with exactly three live neighbors will become live.
  2. Survival a live cell with two (2) or three (3) live neighbors will continue to live.
  3. Death all other cases a cell dies or remains dead
    • Loneliness Live cell with one or zero neighbors dies
    • Overcrowding Live cell with four or more neighbors dies

Generations upon generations Each new generation, every cell must live or die by these rules based on its neighbors in the current generation.

Background Life was developed by John Conway (a mathematician) in 1970. It was introduced to the lay world in a series of articles by Martin Gardner in the magazine Scientific American. A Google™ search for "conway life glider" returns several interesting sites including some that let you create your own "Conway Life" universes.

Chaos Theory While the toy we have to this point can be very complex, it is quite predictable in its behavior, after all, a simple computer program can be written to predict its future, since it is entirely deterministic. However, a more complex toy can be written using continuous equations. We can describe complex systems as a set of equations that describe the behavior of the system. These equations can sometimes be solved exactly, in which case we can predict the future exactly from the starting state, which seems to put us back to the starting gate on getting interesting behavior, no better off than we were with the original game of life. For example, the equations for a spring show that (absent friction) if we pull down on the spring and let it bounce up and down, the weight will travel through a well defined mathematical function with a nice closed form (meaning exact) solution. We will be able to predict where the weight will be exactly at any time in the future.

Unfortunately, if we add gravity, air currents and vibrations to our model, we can no longer compute position exactly, and must compute position in tiny steps using approximations. The position of the weight becomes chaotic and seemingly unpredictable.

Further, if we change the starting condition ever so slightly, the path the weight follows becomes completely different. This so astonished researchers (who should have known better) that they dubbed it the "butterfly effect", noting that if their model was attempting to predict weather in Chicago, a butterfly's wing flap in China would change the outcome.

But, if we feed the computer exactly the same starting conditions, we get the same outcome every time. Thus, chaos becomes little more than unpredictability, and we are back to the same situation we had with the game of life, theoretically predictable, though very messy behavior.

A physician, a secretary and a politician were arguing about whose profession was the oldest.
    "God created Eve from Adam's rib, clearly a medical procedure.", said the physician.

    "He first created order out of chaos, surely that is a secretarial task.", said the secretary.

    "Yes, ", hissed the politician sibilantly, "but whom do you think created the chaos?".

"We will be able to predict where the weight will be exactly at any time in the future."

"The position of the weight becomes chaotic and seemingly unpredictable."

"if we change the starting condition ever so slightly, the path the weight follows becomes completely different."

"if we feed the computer exactly the same starting conditions, we get the same outcome every time."

So, at the end of the day, we know where the game will end up because we know where it started. It gets boring. Fortunately, there is an easy solution. We will add randomness -- and not just any randomness. We will add quantum uncertainty - uncertainty at the most fundamental level. At this level, a particle does not even "know" its own exact state (position, velocity), and we can only measure it as a probability density. We can show this density as a hill, though its actual shape may be more complex. This randomness must permeate our toy space, and to avoid the chaos trap, we must tie each random event to some quantum mechanical random process - a process that is truly random in that not only do we not know the next outcome, even god does not know it. Further, we must elect the granularity at which to apply this randomness.

A Fractal View We need another tool, we need the concept of a fractal. Fractals, like chaos, are tools that allow us to generate huge amounts of variability from minimal descriptors. In a fractal, a simple rule is applied recursively to a function until the limits of the space are reached. The simple examples of these are similar to the snowflake, a visual presentation that is immediately recognized as the application of the rule "put a triangle in the middle of each segment".

If we apply another set of rules we construct the Mandlebrot set, which is a much more refined fractal shape that, like the snowflake, is a recursive application of a simple function.

"a particle does not even 'know' its own exact state"

"put a triangle in the middle of each segment"

"the Mandlebrot set"

So what can we call the finished quantum function? Let's call it free will, since only it "knows" where it will go next. And if we look at it closely, I imagine it will appear to be a fractal, made up of the many sentient beings in the universe, including me.

"free will"


Quantum Soul, Bruce W. Morlan, (C)2004, SimCash, LLC, Northfield, Minnesota, USA.