Fractals as an illustration in the argument for Free Will

I spend some of my spare time in discussions with a very interesting group of people who like to discuss philosophy, science, and all kinds of other things.  It’s fun for me.

One of the favourite topics in this group is the concept of free will.  It seems that many of the most vocal people in the group favour the idea that there isn’t any.  I am not one of them!  I have made my arguments for free will to them, but these arguments fall on deaf ears, most of the time.  I have, for some time now, thought my experience zooming in to the deepest parts of fractals was somehow illustrative of the (in my opinion) flawed logic that is often used as “evidence” that we have no free will.  I was wondering how I could bring this visually to the group and make them see the idea I was trying to convey.

Last night I realized I already have this illustration fairly handy.  It’s the Key, from my series entitled “The Ball Went Over the Fence”.  Some of you may remember this one from several years ago.  The Key shows what part of the large fractal image I zoomed in on to make the next smaller fractal image.

Zoom Key, The Ball Went Over the Fence series

Wikipedia defines Free Will in the following way:  “Free will is the ability to choose between different possible courses of action unimpeded.” The argument many in the group make, against the existence of free will, is that everything is caused by what went before it. Wikipedia also states that “Some conceive free will to be the capacity to make choices in which the outcome has not been determined by past events.”

My main problem with this is that while it is usually easy, from the standpoint of the outcome, to see what came before, and possibly follow a chain of causality, there is no reason to assume that means a choice made is the only choice that could have been made, given all previous conditions.  We can see into the past just fine.  The future, however, is indeterminate.

So, looking at the Key, shown here, you can see a white outlined square in each square image of the key (click on the image to make it bigger, if that helps).  From each outlined square, you can follow the white angled lines to the image found at that location if you were able to zoom in while in the fractal software.  If we start at the smallest square image (the final outcome), we can see where it came from (it’s very close to the top of the next larger image).  Likewise, if we follow to the next one, we see that it came from a very tiny place in the top middle third.  And if we keep going, we can see that the third image came from a recognizable portion of the second largest image.  And that image came from a very tiny spot in the largest image.

This is the chain of causality – it goes from the outcome back to the origin.  It would, however, be impossible to go from the largest image to the smallest one without the Key in place to guide you.  There is no chain in that direction, because it looks into the future.  The outcome would never ever be the same twice.  There is absolutely no logical reason why that particular tiny spot was the one chosen on the first image to zoom in on and make the second one.  In a fractal, while constrained by the mathematics of that fractal, the possibilities at each level of zoom are for all practical and human purposes, infinite.  I’ll grant you that maybe I would have zoomed in on an area near it, or any one of the areas where you can see the little greenish greyish balls.  Just because those areas look interesting to me.  But they all look interesting, and certainly from the perspective of the large image, equally so.  If we look at the second largest image and are choosing where to zoom in for the third… even if you make the argument that I will almost definitely choose a square featuring a ball… that square is never going to be the same exact square.  And now we get to the third image, and you can see no reason why I would have chosen to zoom in as much as I did, and in the area that I chose.

It was my free will in action, plainly and simply.  I chose, unimpeded.  The outcome was never a given.