It is clear that strong antibodies exist against the idea of a mathematical model of epigenesis, but there simply is no alternative. If we want to understand the Cambrian explosion, we must understand not only the genetic but also the epigenetic side of development, and in order to grasp epigenesis we must have a model that explains how a convergent increase of complexity can be achieved. This is the critical point, and we will try therefore to approach the Cambrian explosion with the assistance of the one and only mathematical model of epigenesis that does exist in the literature.

The reconstruction model

In order to build a mathematical model of embryonic develoment, it is necessary to ignore a multitude of secondary features and to concentrate all attention on its fundamental property, i.e. on epigenesis. Even this, however, is not enough. As soon as we specify that epigenesis is a convergent increase of complexity, we seem unable to go any further, apparently because there is no satisfactory definition of complexity. We realize in this way that naming the essential feature of development does not help us: we also need to translate the problem into an algorithm, if we are to have a working model.
Luckily, a solution does exist: we can start from a different formulation of the problem, and say that embryonic develoment is a reconstruction from incomplete information. This is equivalent to saying that new structures appear in stages during development, and is therefore another way of expressing the basic idea of epigenesis. With the new formulation, however, we do not have to provide a precise definition of complexity in order to build a model. We are facing instead a reconstruction problem, and this we know how to deal with.
Tomography, for example, is a reconstruction of structures from radiographic projections and gives us a precious guideline, because there are mathematical theorems which tells us exactly how many projections are required to make a complete reconstruction (Chapter 3).