Fractal geometry swept through popular culture notably around the turn of the millennium. Many have a sense of fractals as the most visual aspect of chaos theory, coined by mathematician, Benoit Mandelbrot. On some level fractals and other aspects of chaos theory seem difficult if not impossible to exactly pin down, even by many scientists, yet intuitively the essence is easily grasped.
Almost any kid in a high chair notices that broccoli looks like little trees. It also resembles the structure of bronchi in our lungs, and, if you break off a smaller shoot of broccoli from a larger one, it seems like a variation of the larger piece. An example of fractal geometry; irregular but similar forms in nature that repeat to inform the structure of a given thing. Another example would be longer, narrower tree branches. The tree is split and split and split into smaller versions of the same nonlinear pattern, not unlike our own blood vessels.
There is a concept in fractal versus the more familiar and linear and simplistic Euclidean geometry involving a length of beach. Approximate the distance between two points on a beach and it might be three miles long. Close in to look at the actual details of jagged terrain where water meets earth, and smaller and smaller jagged fractal twists and turns are revealed. Measure and add every nook and cranny on the beach on smaller and more precise scales, and our three mile stretch might be seen as infinite in length.
There was a time when I saw the ultimate questions of science and spirituality in terms that closer resembled the three mile approximation. On one end of that conceptual beach was reason and evolution, and on the other end was Biblical Creationism. I, like many I expect, knew which end of that beach I was on, and it had nothing to do with God creating the heavens and the earth.
I still am not a Christian, let alone a fundamentalist, but my length of intellectual beach in this regard is now much more like the fractal than the simple Euclidean. I am no longer anti-Christ, and once certainly was. I still believe in reason and evolution, but I now see the possibilities between these two polarities as my own infinite stretch of three mile long real estate. Giving at least some nod to beliefs other than Judeo-Christian on the one hand, (Such as those of the ancient Greeks and the ancient Egyptians.), or Darwinian on the other, the possibilities of a perhaps loosely intentional universe that results in life through evolution are infinite in my perception.
So where I once defended an angry outpost at one end of the beach and still am not interested in crowding myself into the opposite end, I now enjoy strolling past the breakers with an open mind.

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Comment by Michel-san on February 11, 2010 at 8:25pm
Fractal geometry is a great subject, I remember spending a lot of time studying it, in particular Hausdorff dimension.

Intuitively you measure the length of a line, the area of a carpet, the volume of a liquid. You don't mix and match and measure the area of a liquid, or the volume of a line - it doesn't make sense. Hausdorff dimension expresses the dimension in which it makes sense to talk about a measurement. The coastline of Great Britain has a Hausdorff dimension of 1.25. The more accurately you measure it the longer it gets, the length tends to infinity yet it doesn't have an area.

For science & religion. I think religion asks "what can we know without investigation?" and science asks "what can we know with investigation?". Certainly with effort you can keep the two confined to separate domains, but is it worth the effort and is there reason to do so?
Comment by Mike Donohoe on February 11, 2010 at 9:54pm
Interesting comment, Michael. I think that as long as one is not trying to subvert fact in order to support personal beliefs, spirituality can be a positive and valid thing. I feel that science and--I hate the connotations associated with the word!--religion, are a bit like apples and oranges. They inevitably cross paths, yet need to be distinguished, too.

As far as investigation in the case of spirituality, a lot of it is internal experience. Not so easy to demonstrate in a laboratory, yet valid for an individual.

Sometimes I have to hammer these things into my head but I will need to look into the Hausdorff dimension.

Comment by Mike Donohoe on March 2, 2010 at 9:53am
Nicely put, Michel. I appreciate that you don't seem to pretend that a Deity question is ultimately knowable, although you know where you stand on the issue. I think there are probably more Mikes in the world than any other name. =)


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