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What are fractals? They are geometric shapes that are part of a larger shape. Each geometric shape is a smaller version of the whole, larger shape. That is, the smaller shape is a reproduction of the larger one, but on a tinier scale, (almost) ad infinitum.

This is called ‘self-similarity’. Mathematically, a self-similar object is a similar part of itself. Thus, a fractal is an example of self-similarity. Mostly, this property is seen at a very small level. Another characteristic of this is scale invariance, where the smaller reproduction is an exact form of the larger object. The ‘Koch snowflake’ is an example, where no matter how much you magnify the snowflake each part always has the same shape, a microcosm of the whole.

What does this mean? Let us look at something we take for granted – a length of smooth, planed wood. You measure it and it comes to, say, exactly 3 feet long. But, that is only a ‘normal’ measurement. In reality, that piece of wood measures to infinity! Perhaps you are now thinking I am disturbed in mind? No, I am telling you the truth.

If you place the edge of that wood under a magnifier, you will see that even though it appears to be smooth and planed, it begins to look far from smooth. In fact, it even looks rough. If you magnified it even more, you will see that the wood edge is not even at all, but consists of a continuously spiked or uneven surface. Keep on magnifying and you will find the edge is fractal – with each magnification the edge actually looks the same as the larger magnification. Think of a simple triangle shape. Magnify it and the smaller section will look just like the larger one – a triangle. Keep going and magnify that smaller section, say to ten times, and you will see exactly the same shape!

What this means is that if you measure the piece of wood according to what is presented to the naked eye, it will be just three feet long. But, if you apply continuous magnification to it, you will never reach the end! You just find more and more bits that go in and out… and if you measure each small section, it will be almost impossible to measure, because each smaller section can be magnified into even smaller sections, to infinity (or close to it). The real measurement for the edge of that piece of wood is then shown to be possibly millions of miles long!

Sign of a Good Idea

You are probably scratching your head and wondering what on earth this has to do with theology. Well, when I was a teacher and lecturer, I knew that the sign of a good idea is that anything arising from the basic idea will ‘flow’ fairly easily, from one step to the next. If you have to halt and keep finding reasons to accept it, then it is probably not a good idea, or, you have not begun with a suitable model. The same happens when writing a story or an article… if the initial subject and approach is right, the writing will flow and the next step will almost automatically lead to another step, and so on. But, bad ideas or themes will show as difficult, being very hard to decipher and operate. Many bad theologies come into this category.

The same occurs in artwork. If the artist finds it hard to paint, for example, and keeps stopping and trying his best, then it means he has no ‘feel’ for the subject or the way he is doing it. It is best to scrap it and start again.

Take the concept or idea again, in the matter of writing or science. A sound argument will flow from the initial idea and develop naturally into a larger and more complex treatise. You can keep going, constantly adding more and more detail. Not only that, but if you work backwards from the ‘final’ presentation, you will find that the steps are logical. You can work backwards to the beginning, and even work beyond that. In other words, you can divide the whole thesis into sub-themes, and those sub-themes can be divided into parts, and each part can be divided into even smaller parts, each one perfectly aligned and interlinked. This is the sign of a solid and sound argument, where no matter what sub-part you look at, it always contains elements of the whole. If it did not, then it is artificial and will not work properly.

Good Theology

Now, apply that to theology, and the same thing occurs. Which is why I say good theology is fractal. Look at, say, the work of 19th century Higher Criticism that has brought much harm to theology and the churches. None of the Higher Critical theories can ‘hold water’ – each part collapses because it cannot sustain itself. It cannot work, because it is full of further-fragmented parts unlinked to the other parts. This is because Higher Criticism does not begin with a sound idea, but with an human construct, an invented system. It therefore has no ‘flow’ and dealing in its phases is arduous and broken. It is not, then, fractal.

Theology is an in-depth examination of what scripture says. It goes beyond the immediate context of interpretation, by providing extra information, and is a valid exercise in Biblical thinking. If the theology is correct, it will ‘flow’ from point to point, starting with the initial Bible statement, verse, or doctrinal teaching. It does not start with an external theory, but begins with scripture.

Because scripture is always perfect and correct, it means that any ideas and later formulations based on it, must also be correct. It may even extend to thousands of pages of theology, one element leading to another, without strain or human intervention. If human intervention is found, it can be removed, without harming the whole. And so the ‘idea’ can be constantly worked, to produce more and more detail, without entering into error. This is sound theology.

Bad theology does not arrive at sound conclusions. Good theology is usually capable of constant progress, and each smaller section of that theology will reflect and contain elements of the original scriptural text or teaching. It will not matter how ‘small’ or detailed you become, the original will always be strongly present because the detail is merely a microcosm of the whole… it is fractal.

© December 2009

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Bible Theology Ministries - PO Box 415, Swansea, SA5 8YH
United Kingdom