In this article, it is argued that it makes sense to define and distinguish three levels of human intelligence: intelligence as genotypical potential, intelligence as actualised in environmental interaction, and intelligence as measured by tests (IQ). This raises the questions of what is meant by the term "intelligence as potential", and how and in what sense does a child's cognitive potential express the parents' potential and genetics? The larger the number of genes involved in a certain trait, the more possibilities emerge for the formation of new combinations for that trait. The degree of similarity between a child and their parents depends on the "unique" combination of innate genes in each newborn child. The more genes are connected with a human trait or ability, the more refined or intricate the structure of the distribution for that trait in a population will be. The question of how a parents' genes relate to their children's genes has been studied, among other things, in 'twin studies'. Another relevant, but complicated question concerns the relation between genetics (nature) and environment (nurture). Nature appears to be at work in nurture, while nurture influences processes of nature. In psychological research, some DNA differences can be used to predict psychological differences, called polygenic scores. In this context, it is argued that individual cognitive growth comes about by all kinds of influences; psychologists call such influences 'bidirectional' influences. It is also argued that, ultimately, it is the individual human explorative "activity" that is responsible and a strong catalyst for the development and mastery of human traits and for the cognitive qualifications of all newborn children.