7. Finite Information Agency

From a historical perspective, this chapter is a substantial extension of our first contribution (Schuster 2014) in the area of finite information spaces.

It is not a trivial affair to define, exactly, what we mean by the expression ‘the world around us’. In this chapter, it is helpful to envisage the world around us as the everyday world of our experiences or, likewise, as the world that covers everything that physically exists. This does not necessarily imply that this chapter neglects or excludes, de facto, the world of the mind (Feser 2006). Actually, the chapter considers this possibility with great interest. It only means that from the position of this work, the term ‘the world around us’ provides a somewhat more solid grounding for our arguments than the world of the mind does.

Information capacity may be envisaged as the size of a computer memory (e.g., 300 TB [terabyte]), or as the number of unique words in a work of literature (e.g., with 4024 lines, Hamlet is the longest play by Shakespeare Dunton-Downer and Riding 2004, pp. 324–335).

Although it is possible to consider infinite information capacities for agents, sources, environments, and universes, this work avoids such considerations. Instead, this work considers the familiar world of our everyday life experiences where biological agents and sources (e.g., humans, or the genetic code of a human being), as well as artificial agents and sources (e.g., a robot, or a database this robot may access) exist. One argument for assuming finite information capacities for all these entities could be the following. When we think about information existing in a human body then we may assume that this information will cease to exist when this human life ends (Krauss and Starkman 2000; Marois and Ivanoff 2005). Likewise, as long as there are no computers or data stores with infinite memory (capacity), it is reasonable to consider the information capacity of a robot or that of a database to be finite too (Frank 2002; Hilbert and López 2011). In short, this chapter considers the information capacity of all agents, sources, environments, and universes as limited (finite) in space and time.

An environment may be envisaged as a mathematical set containing one or more agents and sources. Note that, depending on the context, it is possible for one information environment to include several other information environments.

A universe may be envisaged as a kind of superset containing all agents, sources, and environments existing in this universe. Depending on the context, it is possible for one information universe to include several other information universes.

Data and information are not the same thing. In this chapter, we adopt the widely shared view that data constitutes information. Data needs to have (or acquire) a particular syntax in order to generate (meaningful) information (Floridi 2010, 2011).

Of course, the memories of the agents in Scenario 1 (two numbers) and Scenario 2 (one number and one reference) could be different. It could be n numbers in Scenario 1, and m numbers and k references in Scenario 2 (\(k,m,n \in \mathbb{N}\)). Likewise, it does not really matter in a scenario, whether the memory size is the same for every agent involved. In Scenario 2, it is no problem to imagine one agent with a capacity \(c_{a_{i}}\) and another agent with capacity \(c_{a_{j}}\), such that \(c_{a_{i}}\neq c_{a_{j}}\) (\(i,j \in \mathbb{N},i\neq j\)). Essentially, what really matters is that the information capacity of any agent is finite.

ACM A.M. Turing Award. http://​amturing.​acm.​org/​. Accessed: 2016-11-28. This award is an annual prize given by the Association for Computing Machinery (ACM). It is the highest recognition awarded in the field of computer science and often referred to as the Nobel Prize of computing.

Here, we would like to, briefly, refer back to Case-1 and Case-2 again. Case-1 may have generated an impression of the Internet as an altogether passive environment. Actually, this is not entirely correct. There are already various active elements on the Internet (search engines or so-called web crawlers, for instance). Arguably, the degree of intelligence or autonomy these agents demonstrate is still a bit limited. It is not too difficult, however, to imagine the Internet as a platform where virtual reality worlds get enriched by AI, deep learning networks empower ‘big data’, and humanoid robotics, autonomous cars, and other technologies merge into a multidimensional ‘Internet of Things’ (e.g., see Silver et al. 2016; Kajita et al. 2016; Anderson et al. 2014; Zanella et al. 2014). Contemplating such a development, we could say that the current Internet is passive at large, while the Internet of the future strives to be more active (autonomous). Or, in the language of our work, the current Internet has an autonomy index around A _I = −1, while the Internet of the future may have an autonomy index around A _I = 0. In such a case, we may wonder about the similarity between humans and the Internet. If the autonomy index for both is around zero, then what does that mean? Are humans and machines essentially the same type of information space?

Information society. https://​en.​wikipedia.​org/​wiki/​Information_​society. Accessed: 2016-11-20. Please note that we are aware about the issues involved when using information from sources such as Wikipedia, or, for that matter, any other source that is freely available on the new media environment today. In this particular case, we refer to Wikipedia to indicate its standing as a powerful tool in the modern-day information environment. For a broader exploration on the concept of an information society, we refer the reader to the more academic works of Press and Williams (2010), or Han (2015), who investigate various aspects of this large field of study.

Please note that unless a clear distinction is required, from now on, we use the term Internet synonymously for both expressions.

Note that it is outside the scope of this text to provide a detailed understanding about these machines. For readers interested in these topics, we would like to mention that Schuster (2007) provides a general investigation to the topic of computing, while the work by Cohen (1996) provides a solid introduction to the formal underpinnings of the classical theory of computing.

For instance, in physics one goal is to find a so-called ‘theory of everything’ from which the behavior of all matter and energy in the universe could be derived. In order to be meaningful, this endeavor must rely on the idea that there is some structure, pattern, or order in the world around us.

At this point, it might be interesting to diverge into the work of the philosopher Edmund Gustav Albrecht Husserl (1859–1938). In his phenomenology, Husserl introduces terms such as: ‘innerer Horizont’ (inner horizon), ‘äußerer Horizont’ (outer horizon), ‘Regionen menschlicher Erkenntnis’ (regions of human cognition), or ‘Intentionalität’ (space of potentiality) (Lutz 1999, pp. 208–215). From the point of view of these terms, the square in Fig. 7.5, which we used to demonstrate an agent’s finite information capacity, could be an agent’s inner horizon (something similar to a snapshot taken by the agent, expressing the agent’s state of affairs in environment e). This gives the environment e the character of a (potential) region of cognition. There is a potentiality for the agent a to explore this region of cognition. Everything the agent may be able to experience (sense, understand, comprehend), could be equivalent to an agent’s outer horizon. Whether it is possible for an agent to experience (sense, understand, etc.) everything that exists in environment e is an open question. From our work, however, we understand that finiteness, is intrinsically linked to this question.