We conclude with a more mathematical, or at least pre-mathematical, account of what has been described above (cf. [2]). The generative mechanisms mediate transformations on existing behaviour, and these transformations lead to the emergence of new features. There is selection in favour of particular features, the totality being end-directed: in other words, the features selected for must be such that a chain of transformations can lead to the desired end result. This account is however a gross oversimplification, in that a relevant feature such as `capacity to understand a language' is not a simple Boolean variable but some kind of distribution of competence.
One may also see the transformations as opening up windows into spaces of possibilities. The spaces must be large enough to include the domains that are of value, but there must also be restrictions that ensure that the period of development is a period of time that is effectively spent. In this the individual's culture plays an important role, since a culture, with its collective experience of many individuals over many generations, can know about what is useful to know in a way an individual of that culture cannot.