The notion of “a single tree of life” is a fractal

It isn’t easy to understand our tool conceptualization, but it is fairly easy to understand that the notion of “a single true tree of life” is an impossibility as being a conceptual contradiction.

The notion of “a single true tree of life” requires that there is a single true classification of “life”, because “a single true tree of life” can only be a classification. But, what is a “true” classification? What is an “untrue” classification?  Which objective facts do we have to compare a classification with? Since we have no objective facts to compare it with, the only thing a “true” classification can be is a “consistent” classification.

However, the notion that there is a single consistent classification among all possible classifications would mean that all other classifications should be inconsistent, which is contradicted by the fact that there are different classifications per se, because it should mean that there is one infinite class that is finite, which, apart from being impossible already theoretically, should contradict the entities it consists of. If such class was possible, then infinity should thus equal finity, and it should thus contradict its entities.

This class is actually the class “clade”. This class is thus a fractal (see figure below).

About fractals Wikipedia says: A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers.

Fractals are typically self-similar patterns, where self-similar means they are “the same from near as from far”. Fractals may be exactly the same at every scale, or, as illustrated in the figures to the right, they may be nearly the same at different scales.The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself .

As mathematical equations, fractals are usually nowhere differentiable, which means that they cannot be measured in traditional ways. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.

The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century. The term “fractal” was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning “broken” or “fractured”, and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.

There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art, and law.

For more about fractals, see Wikipedia.

The the notion of “a single true tree of life” is thus a fractal. This is also what Darwin must have meant with his statement that “without an explicit notion of species, the discussion [of evolution] risks an indefinitive continuation in a vain search to define the indefinable”, although he didn’t understand that the insoluble problem is ”an explicit notion of species” itself.

These facts does not mean that “life” does not have a common origin, but just  that if so, then this origin can’t be described unambiguously.  Willi Hennig’s claim that it can is thus simply wrong, instead leading into a fractal. It can’t. On the contrary, Hennig’s approach (ie, what traditionally is called realism) leads into a fractal, ie, infinite recursion.

Another contribution to understanding of conceptualization http://menvall.wordpress.com/