Natural systems are categorized according to their structural and dynamical similarities. A two-dimensional schema is proposed as a kind of "periodic table" of natural systems. Six of eight levels in this schema serve as sources of analogies, two levels are the targets of analogical reasoning.
The source domains are the atomic, molecular, macromolecular, micro-organismic, organismic and socio-cultural systems and processes.
One of the target domains discussed in the article is the level of subatomic particles. The other target domain, not discussed in the article, could be the level of future supra-national systems.
Three types of processes are identified occurring in natural systems: conservation, modification and transformation. Modifications allow a reversible adaptation of a system to environmental influences by changing its internal state. The entirety of all internal states defines the "state space" of the system. Similarities of state spaces between systems of six levels are investigated. A dual-space picture of natural systems can be defined on six levels, the source domains of analogical reasoning.
On the subatomic level, space-time is identified as part of the state space of subatomic particles. However, space-time needs a completion by an additional state space in order to obtain a dual-space picture also for subatomic particles. A "basic space" is proposed, so that subatomic particles exist simultaneously in space-time and in basic space. The basic space is assumed to be a circular space, where masses and charges circulate force-free and generate the spin and the magnetic moment of particles.
A presumption about the existence of hypothetical matter not detectable in space-time is derived. Such primitive forms of matter could exist in basic space only and represent the dark matter.