What is information? 

If we stick to its definition, which can be found in dictionaries, we can see that it always refers to a set of data and often adds the fact that these are sorted and processed. But we are going to see that these definitions are imprecise and even erroneous in assimilating it to the concept of knowledge.

One of the things that information theory has taught us is that any object (news, profile, image, etc.) can be expressed precisely by a set of bits. Therefore, the formal definition of information is the ordered set of symbols that represent the object and that in their basic form constitute an ordered set of bits. However, information theory itself surprisingly reveals that information has no meaning, which is technically known as “information without meaning”.

This seems to be totally contradictory, especially if we take into account the conventional idea of what is considered as information. However, this is easy to understand. Let us imagine that we find a book in which symbols appear written that are totally unknown to us. We will immediately assume that it is a text written in a language unknown to us, since, in our culture, book-shaped objects are what they usually contain. Thus, we begin to investigate and conclude that it is an unknown language without reference or Rosetta stone with any known language. Therefore, we have information but we do not know its message and as a result, the knowledge contained in the text. We can even classify the symbols that appear in the text and assign them a binary code, as we do in the digitization processes, converting the text into an ordered set of bits.

However, to know the content of the message we must analyze the information through a process that must include the keys that allow extracting the content of the message. It is exactly the same as if the message were encrypted, so the message will remain hidden if the decryption key is not available, as shown by the one-time pad encryption technique.

Ray Solomonoff, co-founder of Algorithmic Information Theory together with Andrey Kolmogorov. 

What is knowledge?

This clearly shows the difference between information and knowledge. In such a way that information is the set of data (bits) that describe an object and knowledge is the result of a process applied to this information and that is materialized in reality. In fact, reality is always subject to this scheme.

For example, suppose we are told a certain story. From the sound pressure applied to our eardrums we will end up extracting the content of the news and also we will be able to experience subjective sensations, such as pleasure or sadness. There is no doubt that the original stimulus can be represented as a set of bits, considering that audio information can be a digital content, e.g. MP3.

But for knowledge to emerge, information needs to be processed. In fact, in the previous case it is necessary to involve several different processes, among which we must highlight:

• Biological processes responsible for the transduction of information into nerve stimuli.
• Extraction processes of linguistic information, established by the rules of language in our brain by learning.
• Extraction processes of subjective information, established by cultural rules in our brain by learning.

In short, knowledge is established by means of information processing. And here the debate may arise as a consequence of the diversity of processes, of their structuring, but above all because of the nature of the ultimate source from which they emerge. Countless examples can be given. But, since doubts can surely arise that this is the way reality emerges, we can try to look for a single counterexample!

A fundamental question is: Can we measure knowledge? The answer is yes and is provided by the algorithmic information theory (AIT) which, based on information theory and computer theory, allows us to establish the complexity of an object, by means of the Kolmogorov complexity K(x), which is defined as follows:

For a finite object x, K(x) is defined as the length of the shortest effective binary description of x.

Without going into complex theoretical details, it is important to mention that K(x) is an intrinsic property of the object and not a property of the evaluation process. But don’t panic! Since, in practice, we are familiar with this idea.

Let’s imagine audio, video, or general bitstream content. We know that these can be compressed, which significantly reduces their size. This means that the complexity of these objects is not determined by the number of bits of the original sequence, but by the result of the compression since through an inverse decompression process we can recover the original content. But be careful! The effective description of the object must include the result of the compression process and the description of the decompression process, needed to retrieve the message.

Complexity of digital content, equivalent to a compression process

A similar scenario is the modeling of reality, where physical processes stand out. Thus, a model is a compact definition of a reality. For example, Newton’s universal gravitation model is the most compact definition of the behavior of a gravitational system in a non-relativistic context. In this way, the model, together with the rules of calculus and the information that defines the physical scenario, will be the most compact description of the system and constitutes what we call algorithm. It is interesting to note that this is the formal definition of algorithm and that until these mathematical concepts were developed in the first half of the 20th century by Klein, Chruch and Turing, this concept was not fully established.

Alan Turing, one of the fathers of computing

It must be considered that the physical machine that supports the process is also part of the description of the object, providing the basic functions. These are axiomatically defined and in the case of the Turing machine correspond to an extremely small number of axiomatic rules.

Structure of the models, equivalent to a decompression process

In summary, we can say that knowledge is the result of information processing. Therefore, information processing is the source of reality. But this raises the question: Since there are non-computable problems, to what depth is it possible to explore reality?