The subject of this article is the specificity of socio-cultural situation in which the individual professionally engaging in natural sciences and mathematics does act in politary society (ancient Egypt, ancient India and China, medieval Arab-Muslim world, etc.). It focuses on the complex and contentious relationship between scientists seeking to acquire increasingly precise and adequate knowledge of the structure and development of the material world, and on methods of acquiring such knowledge, and bureaucratic apparatus, whose tip led by an autocratic Monarch (labeled as “Caesar”, or “politarch”) is interested in the maximum control of the process and the results of any serious theoretical and empirical studies. Intense conflicts between these cognitive trends affect the general nature and characteristics of the deployment of epistemic discourse in politary societies. As concepts, through which this conflict is interpreted, are elected category of “regularity” (as characteristic of any variety of politary management) and “spontaneity” (as an attribute of free, creative and administrative unregulated scientific search).