Maynard Smith’s point can also be expressed in another way: embryonic development is a process that increases the complexity of a living system, but we do not know how to build machines that increase their own complexity, and we cannot therefore understand the logic of development.
We can also leave aside the physical construction of machines and concern ourselves only with their planning. If we could prove with a mathematical model that it is possible to increase the complexity of a system, we would already have taken a major step forward. The search for the logic of development begins therefore with the search of a mathematical model for systems which are capable of increasing their own complexity.
At this point, however, a formal distinction between two very different cases is called for. An increase in complexity took place even during the history of life, but in this case new structures arose by chance mutations, and the increase was therefore a divergent process. In embryonic development, on the contrary, new structures are never formed by chance, and we are dealing with a convergent increase of complexity. This is the great difference between evolution and ontogenesis, and such a dichotomy does require two very different types of mathematical models.
In the case of evolution, we already have algorithms that simulate the effects of natural selection, and we do therefore understand how a divergent increase of complexity can take place. But we do not have algorithms that describe a convergent increase, and it is for this reason that the embryo’s logic still eludes us. The real key to embryonic development is the logic of systems which are capable of increasing their complexity in a convergent way, and in order to understand this we need, if not a machine, at least a model that is functioning according to that logic. This chapter is devoted to the description of a new class of algorithms which have precisely that property.

Reconstructions from incomplete projections

The starting point for a new model of embryonic development was the reconstruction of structures from their projections, a problem which arises in many fields such as computerized tomography and electron microscopy.