Structures and Structural Information
Mark Burgin
University of California, Los Angeles, 520 Portila Plaza, Los Angeles, CA 90095, USA
Rainer Feistel
Leibniz Institute for Baltic Sea Research, Warnemünde, D-18119, Germany
Everything has a structure and this structure makes things such as they are. This was declared by Aristotle for material things and demonstrated in the general theory of structures developed in (Burgin, 2012; 2016) for the whole generality of existing and possible objects. This is the core reason of importance of structural information, which provides and/or changes knowledge about structures.
As Brinkley writes, “implicit in the word "structure" is not only the concept of elementary units or parts, but also the interdependence and relationships of those parts to form a whole and it can thus be argued that modern science has adopted a structural approach to understanding the natural world, in which parts are defined and the interactions among them are explored” (Brinkley, 1991; 1999).
Structural information is the core of structuralism, the heart of structural realism and the basic essence of structural informatics.
The goal of this work is to study structural information based on the general theory of information (Burgin, 2003; 2004; 2010; 2011), research of Feistel and Ebeling (Feistel and Ebeling, 2011; 2016; Ebeling and Feistel, 2015; Feistel, 2016) and works of other authors in this area. The goal is developing more comprehensive and advanced knowledge about structural information.
It is possible to comprehend structural information in different ways. For instance, Bates (2005) treats structural information as “the pattern of organization of matter and energy,” while Reading (2006) defines it as “the way the various particles, atoms, molecules, and objects in the universe are organized and arranged.”
At first, we consider the approach developed in the general theory of information. The general theory of information discerns information in the broad sense (Ontological Principle O2) and information in the strict sense (Ontological Principle O2a).
Structural information is information in the strict sense being defined as a capacity to change the subsystem of knowledge in an intelligent system.
This definition allows getting key properties of structural information. Let us consider some of them.
- Structural information can be more correct or less correct.
Correctness of structural information about a system depends on correctness of knowledge produced by this information (Burgin, 2016). As we know, some knowledge can be more correct, better representing the essence of the system, while other knowledge is less correct, providing a worse representation of the fundamental nature of the system.
Here are two examples.
Example 1. For a long time, people believed that the Earth was flat, i.e., had the structure of a plane.
Then scientists found that the Earth had the structure of a ball.
Then scientists assume that the Earth had the structure of a geoid.
Example 2. For a long time, people believed that in the structure of the Solar system, the Sun rotated around the Earth.
Then scientists found that the Earth rotated around the Sun and the orbit had the structure of a circle.
Then scientists assume that the Earth rotates around the Sun and the orbit had the structure of an ellipse.
2. As a rule, structural information about a system is not unique.
Many researchers believe that each (at least, a natural) system has a unique structure. At the same time, according to the general theory of structures (Burgin, 2012), any system has several structures. For instance, the structure of a table on the level of its parts is essentially different from the structure of this table on the level of molecules as well as from the structure of this table on the level of its parts such as legs. In essence, material systems, which people can see with their eyes and touch with their hands, have structural information on different levels.
3. Structural information about a system is inherent to this system.
Indeed, as it is stated above, structure makes things such as they are. Naturally, structural information reflects this identity of things although structural information about different systems and objects can be similar.
4. Processes in a system can change structural information about this system.
Indeed, the evolution (development) of a system can produce an essentially new structure when the system is changed, even becoming another system. For instance, butterflies have the four-stage life cycle. In it, winged adults lay eggs, which later become caterpillars, which later pupate in a chrysalis, while at the end of the metamorphosis, the pupal skin splits and a butterfly flies off.
5. Structural information about a system describes this system to a definite extent of precision, i.e., structural information can be more precise and less precise.
For instance, the Copernican model (structure) of the Solar System is more precise than the Ptolemaic model (structure) of the Solar System. Another example comes from mathematics where mathematicians are striving to find the decimal structure of the number p with higher and higher precision.
6. For complex systems, it is possible to consider structural information on different levels and various scales.
For instance, it is possible to treat the structure of a human being on the level of visible parts, on the level of its functional systems, on the level of inner organs, on the level of cells, on the level of chemical compounds or on the level of molecules.
7. Structural information about a subsystem of a system is not always a part of the structural information about this system.
For instance, when we consider an organism as a system of its visible parts, the structure of its nervous system is not a part of this structure.
8. The process of conversion of structural information about a system into knowledge about this system is, in essence, structuration of this system.
Note that the general theory of information provides other possibilities for defining structural information. For instance, it can be information that changes the system of beliefs of an intelligent system.
At the same time, Feistel and Ebeling suggest the vision of structural information, in which structural information may no longer be restricted to changing just “knowledge in an intelligent system”, and may more generally be defined as the capacity of a physical system, the “carrier of structural information”, to cause changes in a second physical system, the “receiver of structural information” (Feistel and Ebeling, 2011; 2016; Ebeling and Feistel, 2015; Feistel, 2016).
Indeed, people get information about different objects in the form of raw data. Only after reception of this information, the brain converts these data into knowledge and this knowledge is often about the structure of studied objects.
If in particular, the receiver is the same system as the carrier but at some later point of time, reversible microscopic dynamics described by the Liouville equation is universally understood as “conserving [microscopic] [structural] information” (Hawking, 2001; Zhang et al., 2013). In contrast to this, irreversible macroscopic dynamics is commonly associated with a loss of [macroscopic] [structural] information, directly related to the growth of thermodynamic entropy (Feistel and Ebeling, 2011; 2016; Ebeling and Feistel, 2015; Feistel, 2016). In the sense of Planck (1966) who wrote that “a macroscopic state always comprises a large number of microscopic states that combine to an average value”, macroscopic structural information represents a portion of the microscopic structural information of a given system.
Structural information available from a carrier depends on the receiver determining what portion of this information is actually received. If, for example, the receiver is a thermometer and the carrier is liquid, then all information received is the temperature of the liquid. Structural information can be extracted from a given system by “measurement” when e.g. a sensor is used as a receiver. Structural information can be quantified if it is comparable to the structural information of a reference system, such as the length scale of a mercury thermometer.
A numerical value being the result of a comparison between the same kinds of structural information available from two different systems, such as by counting their parts, is a “measurement result”. Numbers represent information in the symbolic form, or as “symbolic information”. The meaning of symbolic information is subject to convention (such as what “reference” system is used) and is no longer a portion of the structural information of the carrier, such as printed symbols on a sheet of paper. Very different structural information carriers can carry the same symbolic information. Symbolic information is restricted to the realm of life (Feistel and Ebeling, 2011; 2016; Ebeling and Feistel, 2015), such as in the form of genetic DNA molecules or human knowledge, and emerged from structural information in the course of evolution by a transition process regarded as ritualisation.
References
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