The simple model of conflict-prone situations called Prisoner’s Dilemma is discussed. Whereas the best strategy for the model is to defect, in the case of its iterated version (Iterated Prisoner’s Dilemma—IPD) it is possible and more profitable to cooperate with the opponent.The simple strategy called Tit for Tat (TFT) which is easy to recognize, never defects first, punishes every defection but is also forgiving is presented. The TFT strategy is very successful being able to establish the cooperation with its opponents. The possible outcome of the competition between the TFT strategy and non-cooperative strategies is considered. It turns out that even small number of TFT strategies can overcome the greater number of more “egoistic” strategies.The described model can give the better understanding of some psychological, sociological and biological processes as well as help to propagate the altruistic attitudes in the society.

1. Living organisms are characterized by complexity and uniqueness of structure, as well as by specific pattern of changes during ontogenesis programmed in their own genome.2. Although general mechanisms of gene expression and regulation are well understood, our knowledge of spatial morphogenesis is rather limited and patchy despite discovery of homeotic genes.3. Developmental biology is able to explain principles of formation of neuronal network in the brain, whereas neurophysiology provides detailed information on the role of various neurotransmitters, but we still do not understand the essence of consciousness, and even more self-consciousness of the man.4. Some philosophical theories trying to explain the nature of self-consciousness, such as parallelism and interactionism, are briefly discussed.

Differences between macro and microphysics. How do we come to know the world? Theories—can they be beautiful? Cloakroom principle. Microparticles are identical—conssquences. Platonian beings.

Problems connected with the questions of: being-nonbeing, existence, modes of existence and alike, belong to the basic and most important in metaphysics. The article discusses some answers to the aforementioned issues, as proposed by the ancient philosophers, St Thomas Aquinas, R. Ingarden and A.N. Whitehead. In the Appendix some remarks are made on Aristotle’s and S. Thomas’ theory of act and potency.

It is a story presenting various hiking trips “with Karol Wojtyła”. During these trips a lot of philosophical and scientific problems were discussed. That produced a basis for seminars including those which were held in Castel Gandolfo in 1980–2003.