Touching The Limits Of Knowledge

Cosmology and our View of the World


Is Information an Irreducible Entity in the World?
Austin Purves


Summary by Alex Miklos

Information: Definitions, Understanding, and Implications

At this point in the semester we have covered topics ranging from what constitutes life to what constitutes consciousness to what constitutes the “dark” 96% of the universe, yet underlying each and every discussion and each and every presentation is an entity so fundamental, so basic, that it is easily neglected. It is an entity ignored so often in common discourse either because it is taken for granted or because the concept itself rests on the most massive of scales. Austin Purves accepted the challenge of creating a presentation to help identify, examine, and explain the most essential and omnipresent unit of the universe, the entity of information.

How does one begin to define information? Three approaches are utilized in order to grasp a basic idea of what to look for in defining it. The three approaches are:

Reductionist Non-Reductionist Antireductionist

This approach believes that information can be reduced into a single concept from which all else is derived.

The problem with reductionism is that it tends to place restrictions on what can or can not be defined as information since there is only one central concept. This is problematic when considering the severe differences between distinct entities in the universe (e.g. tree rings and poetry).

This approach leans towards the idea that information consists of multiple central notions rather than just one.

A non-reductionist approach is the plausible when dealing with the task of defining information in acceptably flexible terms.

This approach holds that there is no central binding concept of information and that information has many different natures and can neither be reduced nor connected in any way.

Just as with the reductionist problem of restricting the definition of information, antireductionism also limits our understanding of information since it basically states that the search for a definition of information is ultimately futile.


Floridi, author the article “Information,” favors a non-reductionist approach in order to define what information actually is. His goal is to define one specific concept, namely semantic information, in hopes that it will turn out to be one of the central concepts characteristic of the diagram depicting non-reductionism. The term semantic can be understood to mean that which pertains to language or words and therefore must be attributed to a conscious observer, for what are words without an intelligent interpretation of some sort? But before delving into the definition of semantic information, Austin offers us the Cambridge Dictionary of Philosophy definition of information. It defines information as an objective entity that can be carried by or generated by messages or cognizers but exists without any such media. This ambiguous definition leaves much to the imagination and helps very little in actually defining anything, as Professor DeVries pointed out. Floridi tries to clarify this definition by suggesting two forms of information via Edgar Alan Poe’s The Raven and Ray Bradbury’s Fahrenheit 451. Decidedly, there are differences between the information associated with The Raven and information associated with tree rings or claps of thunder, all of which points back to the plausibility of non-reductionism as a means of understanding information. [Side note: The reductionist approach is currently in effect for physicists who are researching ways in which to formulate a coherent theory of unification of all the forces of the universe.]

Floridi proposes a general definition of information (GDI):

Strictly concerning a datum (singular data), it can be understood as a lack of uniformity of symbols, therefore defining scribbles into the realm of information.

Next, several types of neutrality should be examined in order to conceive of a better formulation of what the GDI accepts as information. Neutrality here should be taken to mean the vastly encompassing nature of the GDI as a definition of information. The following types of neutrality show just how broad the GDI is.

Typological Neutrality sets out to divide data into four separate types:

  1. Primary data: A simple sequence of ones and zeros without any uniformity or coherence other than the fact that there is something.
  2. Metadata: “About” data, meaning the format or language through which one can understand a sequence of primary data. Unicode is an example of metadata since it makes strings of binary digits intelligible as alphabetic letters.
  3. Operational data: Can be understood as the usage and storage of data, e.g. an operating system or types of RAM.
  4. Derivative data: Data extracted from any of the, or combination of the, first three types of data.

To make heads and tails of this notion, Professor Davis offers a biological illustration of the four data types. He purports that primary data can be seen as the strand of DNA itself. The fact the nitrogen bases of the DNA nucleotide are A, C, T, G can be considered the metadata since it makes something out of the constituents of the DNA strand. The operational data can be seen as the genetic code, that is, the encoding of different codons and anticondons to amass a string of amino acids. It is the utilization of the DNA strand and the way it is organized to synthesize proteins. Finally, the derivative data is the actual synthesis of proteins from long strands of amino acids. It is the meaning behind a thread of nitrogen bases. What this all shows in terms of the GDI is that a general definition of information does not prefer a particular type of data since all of the universe necessarily consists of data of the four types. [Side note: All single letters of the alphabet are data, but to be considered well-formed there must be associated with it an element of operational data, i.e. the letter I is a datum and in some uses is itself well-formed since some meaning is built into the letter, information specific to a concept in the English language.]

Taxonomic Neutrality is the next type of data distinction. The term taxonomic refers to classification. It shows that a datum can be reduced to a lack of uniformity between two variables [depicted as d = (x ∫ y)]. This means that datum is expressed in terms of a relationship between two things. For example, a black dot on a white page is devoid of meaning aside from the fact that it contrasts with the white of the paper. What this means in terms of the GDI is that a general definition of information is neutral to the class of relations used to specify a certain datum.

Ontological Neutrality sets out to separate the possibility of the existence of information without first the existence of some sort or type of data. Ontological refers to the essence or nature of being. This does not imply that information must necessarily be something of a material nature, nor does it even imply that the data in question must be of a material nature. It simply states that the existence of information owes itself to the fact that prior to its own existence there necessarily must have existed some sort or type of data, be it non-extended or be it material. This again shows the GDI to be a definition that seeks to include as much as possible into the definition of information. [Side note: Other interpretations of the essence of information may hold that data can exist in thought or consciousness, with no need for matter at all, a la Berkeley.]

Genetic Neutrality is the property of the general definition of information that data can have semantic meaning independent of an informee. For example, the Egyptian hieroglyphs would therefore have semantic meaning, to a non-Ancient Egyptian, before they were discovered in modern times. This begs the question: How can there be something with semantic meaning if there is not one who can ever interpret it as more than primary data? (Remember, primary data does not necessarily have semantic meaning.) GDI would say that information without an interpreter still has semantic content no matter who can or can not interpret it, since GDI is a flexible standard for defining information. Another brain teaser involving genetic neutrality is: If a tree falls in the woods and no one will ever hear it, is there really data and meaning in the sound waves produced? The answer, of course, is yes there is information in any and all sound waves, but this may be a little bit off the track of an appropriate context for semantic information. Professor DeVries clarifies this notion by adding that a personless universe which still consists of causal interactions still has information, although not semantic. Professor Davis then adds that genetic information (DNA nitrogen bases and genetic the genetic code) seems to be semantic, since A’s T’s C’s and G’s are alphabetic pictorials and can even be made into GATTACA can provoke thoughts of Uma Thurman and Ethan Hawke. Professor DeVries ties it together by recognizing that the genetic code is prospective, or forward looking since proteins will be synthesized which shows that it is analogous to semantic meaning in that semantic information is necessarily prone to misuse just as protein are sometimes made incorrectly.

To recap the GDI:

Shannon’s Theory is an attempt to quantify an amount of information. He uses the equation

I = log2 (1/p)

where p is the probability of a certain state being chosen at random and I is the amount of information constituted by that state. This means that a highly unlikely state, i.e. lower case p, will constitute a large amount of information, I. The amount of information that can be represented by a system with only one state (p = 1) is zero. The amount of information that can be stored by a single letter in the English alphabet is ideally (p = 1/26) about 4.7.

Shannon’s equation bears a striking resemblance to thermodynamic entropy. The second law of thermodynamics states that the entropy of a closed system is irreducible and can only increase. Just as this is practical in physics, are there practical consequences for information too? Could some similar law be discovered in the case of info? Could it be irreducible?

It is important now to touch on ways of destroying information since that will lead to answers to questions dealing with its reducibility. Would destroying the medium or physical implementation of the information destroy it? No, because if you smash a floppy disk the encoded information is still written on the tiny pieces of plastic, even though it is unreadable now. But what if you threw your floppy disk into a black hole? Would recovery be impossible?

Hawking radiation says that yes, information lost in a black hole can eventually be recovered! Hawking radiation is the slow dissipation of the contents and structure of a black hole. However, it is still unclear how information is stored in a black hole.

Some final questions left for us to ponder:

Can we find a unified theory of information based on a single concept?
Could there be an irreducible or conservation law regarding information?