Idea Fractals

A fractal is described by Wikipedia as “A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.”

I have in a prior blog used the term Idea Fractal to describe a unity of ideas resulting in a larger idea. This unity of ideas forming a larger idea has an isomorphic relationship to the geometrical fractal which I will talk about in this blog. I do however suspect that many people will not understand my use of the term “isomorphism” in this context, I will therefor start by explaining it.

The term is explained in the book GEB (Gödel, Escher, Bach – An Eternal Golden Braid). An isomorphic relation is in this context a relation of similarity between two subjects on a very abstract level. A car does for example have an isomorphic relation to a bicycle in the sense that both objects are meant to bring a person from point a to point b in a way faster than the person would be capable of by him/her self. The fact that both objects have wheels or that they both have steering capabilities are other examples of isomorphic relationships.

It’s very easy to see the isomorphism between the different patterns emerging from a fractal like the Mandelbrot Fractal as it’s based on visual data, we can easily identify the different patterns to be based on the same theme. An Idea Fractal is purely based on thought which is a bit more tricky to imagine, but it might help to explore the Mandelbrot Fractal to better understand my explanation of an Idea Fractal.

Notice how the bigger spirals consists of smaller spirals which them selves consists of even smaller spirals and so on.

I was exploring a method the brain is using to form ideas by finding synergies between other ideas in a prior blog. I described larger ideas as being formed by connecting smaller ideas, similarly a huge idea could be formed by finding synergies among the larger ideas. This process was described as starting out from small ideas and growing into bigger and bigger ideas as the mind find more and more synergies between the existing ideas.

I would like to invert this process, let’s start by looking at a huge idea and the ideas which was used to form it. We would most certainly find isomorphism between the huge idea and the ideas being the basis for the huge idea, we would similarly find isomorphisms between those ideas and the smaller ideas being used to form them. The smaller ideas have isomorphic relations to the bigger whole in a larger idea in the same sense that the emerging patterns form the Mandelbrot Fractal have an isomorphic similarity to the pattern they emerge from.

Example 1
Going back to the example of a car, let’s compare the car as a whole to some basic components of the car. The idea behind the car is that it’s supposed to roll forward, the same idea applies to a wheel, thus there is an isomorphism between the car and it’s wheels. The ball bearing inside the wells has isomorphic relationships to the wheel in the sense that they’re round and build to spin.

Example 2
Writing this blog I’m trying to define Idea Fractal which is how ideas are based on each others isomorphic relationship to form a bigger whole. The idea behind this concept and blog came from writing the blogs Encouraging the formation of new ideas and The importance of visualization which both explores the idea that more significant ideas are formed when the mind is finding new synergies between older and less significant ideas.

The isomorphism here is pretty clear as both the idea behind the concept Idea Fractal and the ideas behind those other two blogs are exploring the connection between thoughts within the human mind. But from where did I get the idea to write those other two blogs?

Seeing the connection between thoughts has isomorphic relations to the act of pondering about how thoughts are formed by connecting to each other, as my realization was about just that. Isomorphism in it self also has an isomorphic relationship to my realization as well as the idea behind the formation of thoughts, because all this is about networking nodes. Connection of thoughts is a network, isomorphic relations between subjects is also a network.

I’ve just used the idea behind this blog as an example of an Idea Fractal, the idea of doing so is the result of my idea to write a blog defining the concept Idea Fractal, thus it is while writing this at the top level of my Idea Fractal. This example also has an isomorphic relation to the blog containing it as both the blog and this example are describing the concept Idea Fractal.

So an Idea Fractal is mean to describe the isomorphism of a mathematical fractal like the Mandelbrot Fractal to the network of isomorphic relations between ideas within the mind.

And yes this is the most far-out-blog I’ve written so far.

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  1. Far-out but well written and really assessable.

    The car example was specific yet easy to comprehend.

  2. Tobias Wallin (Mentation Away)
    Aug 4, 2010


  3. Charles
    Aug 9, 2010


    Very nice blog. I’m flattered by your linking to my site; of course I returned the favor. I also posted a response to the comment you left, though I’m not sure if you were notified–I’m not used to people reading my boring blog. I look forward to reading more from you.

    All the best,

  4. Tobias Wallin (Mentation Away)
    Aug 10, 2010

    I’ve read some stuff on your blog and I find it quite interesting, not boring at all! I’m looking forward to reading some of your more advanced blogs when I’m in the right mind set. Thanks for linking to my blog!


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