On the web forum Theology web, a gentleman asked how theistic evolutionists thought God worked in evolution. I wrote this to answer that question.

To answer the question I must explain some systems I have studied. During one period of my life I put in a lot of study of nonlinear iterative systems, systems with chaos and systems without. One of the systems which interested me most is called Sierpinski's Gasket.

If you take a dot on a computer screen and randomly move it around the screen, no pattern will arise. It will be chaos. But if you add some rules to the random motion, you can create some interesting mathematical objects. In the case of Sierpinski's gasket, one starts with 3 fixed points and one movable point. The moveable point can be placed anywhere on the plane, it really doesn't matter where. The 3 fixed points are placed at the vertices of an equilateral triangle. Label them A, B, and C. Then take a die and roll it. If you roll a 1 or a 2, move the movable point half the distance from where it is to point A; if you roll a 3, or a 4 move half the distance to point B, and for a 5 or 6 half the distance to point C. Mark each point that the moveable point lands on. do this for 30-40,000 times and you will end up with Sierpinski's gasket:



The thing that fascinates me about Sierpinski's gasket is that regardless of the random directions I move the moveable point (in other words regardless of the sequence of die rolls, I will deterministically end up with the same picture. This feature unites chance and determinism into one mathematical object.

The big fear that the Christian anti-evolutionists have of evolution concerns chance. They think God can't control chance. Chance is controlled by the rules.

Then one day at lunch when I was bored, I decided to program the gasket in from memory. I messed up the program and got some really strange shape. I saved the program meaning to bring in a copy of the program from home to see what I had done wrong. But I forgot the next day, so I tried again to program it from memory and I screwed up again but got a different shape. When I finally compared the 3 programs, I realized that I had stumbled onto a mathematical system of programs which can be mutated and create new shapes as they are mutated. When I formalized this, I found that the system actually mimicked punctuated equilibrium. some mutations brought minor changes, but then suddenly after 5 or 6 with only minor changes, a mutation would occur which made a major change to the computer object. This can be seen in the following picture:



That is the first panel in a sequence. Starting with a dot shape, mutation gradually changes it to very different 2d shapes. The next picture is the next set of 40 mutations:



One can see the punc-eq in the pictures.

What I believe is that God set up the evolutionary system. And far from being due to chance, the rules of mutation would inevitably lead to us as happens when chance is united with rules and deterministically produces Sierpinski's gasket. Thus, I have no problem with chance and no problem with God being able to predetermine the outcome. I predetermine the outcome every time I run Sierpinski's gasket. I can't predict the exact set of die rolls, but I can predict that the gasket will appear at the end of the process.


I even can mimic the Cambrian explosion. In the following pics, each box represents a lineage which is mutated independently of all other boxes. I start with all 'organisms' as a clone. This looks like:



All animals are mutated, but each is mutated in its own way and after 1 generation of mutation, the screen 'organisms' look like:



Mutation 7:



Mutation 12:




One clearly sees diversification in shape. The first two boxed pics follow a single lineage. The last 4 follow 40 different lineages.

Because of this type of outcome of iterative, mutational systems in mathematics I see no reason why this can't happen when the shapes are 3 dimensional rather than 2 dimensional.

So to answer the  question, I believe God designed a system which would irrevocably lead to us. This view is not that much different from the outlook Simon Conway Morris holds. He believes that if you re-ran the tape of life that you would get essentially the same thing. Why? because over and over life has solved the same problems in the very same way. This is clearly a different view from Gould, who thought you would get an entirely different end result. Before going blindly with Gould, who was a very smart individual, one really should see Conway Morris' presentation on this issue.

I also believe this solves the YEC fear of chance in biological systems.