Although the term "information" is discussed in a lot of publications since decades, a generally accepted definition of information does not exist. The prevailing discourse focuses on semantic and technical definitions, but with the rising vision of quantum computing also physicists are more interested in understanding information. But still today semantic definitions seem to be stronger than physical concepts. The reason might be the experience, that information pervades all scales, from the quantum level to a railway signal. This fact can be addressed easier semantically, than by a physical entity. In a similar case like the entity "energy" it took nearly two centuries to receive a fundamental and finally accepted definition.
Derived from that experience with the term "energy", the present approach is looking for a definition of the smallest part of information. Based on such a simple entity, formalisms are needed to describe more complex information structures within higher scales. Finally such a definition has to be compatible to semantic definitions of information. The quest for the smallest information starts with an analogy to the pixel.
Today’s ubiquitous concept of a pixel is based on its technical use to characterize visual media technologies like scanners, displays and printers by their capability to represent information. The definition of a pixel addresses it’s to key features: (1) It is defined as smallest addressable piece of information in that specific context of technology. (2) As additional requirement by the visual application a pixel has to be specified as small as it remains indistinguishable by the human eye. For the eye the single pixel does not exist, but an observer will be able to recognize structures of multiple pixels. And a wide variety of different structures with different functions may arise out of these individually invisible pixels. For this artificial and fully controllable, but real system of pixels we can discuss basic features of emergence. Focus of these considerations is not the semantic understanding of pattern generation, but the characterization of the process. The example of pixels offers an opportunity for an abstract formulation of emergence and its relation to information.
The observations of the interdependencies at this macroscopic emergent situation can be used for the further argumentation by reducing the size of the pixel. Scaling down though different levels of so called “mega evolution”, we finally can look out for candidates for the smallest information.
The current debate among physicists offers quantum dots, the Minkowski space-time cell and black holes as smallest physical entities. Also if keeping the Bremermann limit and Landauer's principle in mind, a kind of an ontological gap remains if these smallest physical phenomena are taken as physical pixels, representing something like pure "information".
One hypothesis to bridge this ontological gap will be presented. Based on the emergent understanding of information it is assumed that there must be a smaller informational entity below the physical limit. The ontological, or better mathematical argument for this assumption is discussed. In an admittedly hypothetical manner we can define in this sub-physical approach the smallest form of information –the initial pixel– and an elementary emergent process. A modern understanding in mathematics inspirits the idea for this approach, as it can be found in the Homology Type Theory (HoTT). There mathematics is not a fixed, steady logical structure, only explore able by a human brain. Mathematics itself might be an infinite process, independently from human understanding. And information has to be identified as a concept, which has to be a constitutive element of mathematics.
This paper is not able to proof this hypothesis by physical arguments; this will be a task for further investigations. But it offers a feasible explanation for the semantic part of information and a linkage from the very basic but simple definition of information towards complex appearances.
The idea of this paper is not to offer a final solution but to trigger a discussion about further needs to receive a clarification of the obstacles.