From Monochrome to Noise – Aesthetics, Information Theory, and Creativity

Think of a monochrome picture, let’s say a white one. It can be completely described with a very small amount of information. You may say: 512 x 512 pixels of white (or any other color that can be described with a few numbers of any color coding system).

That you can describe such a picture with a few words means that it contains very little information. If you think of it as a file in your computer’s file system, it may be compressed into a very small file. Its information content is small. In the mathematical theory called “information theory”, this information content is called “entropy”. It is a measure for the amount of information needed to describe the data or a measure for the amount of disorder in it.

In the following picture, there are rounded edges and a white frame and this adds to the amount of information necessary to describe it completely, but the file could still be compressed a lot.

File:Untitled blue monochrome2.png

(Picture from http://commons.wikimedia.org/wiki/File:Untitled_blue_monochrome2.png)

This picture is very repetitive, it has a high degree of order and thus a small entropy. On the other hand, its repetitiveness, called redundancy in information theory, is high. (In case you are interested in the mathematical detail, search the web for “information theory”.)

On the other hand, if you fill the pixels with random “noise” (as it is called in information theory), i.e. you determine each pixels color value using some random process, you get something like this:

Picture from (http://commons.wikimedia.org/wiki/File:White.noise.col.png)

Try to compress such a file and there will be hardly any compression at all. This means that it contains a very large amount of information. Not necessarily useful information about something, but you need a lot of storage space to store it because the pixels in it are not correlated. Having no correlation, no structure, means that you cannot compress the picture. You have to tell for each single point which color it has. If you look at the details, you may find some trace of a structure here and there but any such structure disappears if you look at larger areas. If you would increase the number of pixels, you would not be able to find any structure at all. Being random means that the color of the pixels are not correlated. There is no regularity.

If you look at a monochrome picture, you will notice it is very boring. If you look at the noise picture on the other hand, if you try to view it as a pattern of pixels you will not be able to discover much structure in it. It would be frustrating. You may also view it as just evenly covered with a noise pattern. Then it would look as boring as the monochrome picture.

Both kinds of pictures, the monochrome and the noise, are uninteresting. Between these two extremes are the interesting and the beautiful pictures.

Imagine a picture that is white but contains some black straight lines. The amount of information in such a picture is larger than in the monochrome picture. You would have to describe the position of the end points of the lines, maybe also how thick they are. But still the amount of information needed for a complete description is quite small. If you describe the picture in a pixel by pixel fashion, you would need the same amount of information as in the noise picture, but by discovering the lines, you can compress that information into a small amount. As the example shows, the discovery of structure may be seen as a process of information compression. Some scientists have described the process of perception as a process of information compression.

Think of a picture with parallel lines in regular distances. Here to describe the picture, it would be sufficient to describe one line and then to describe the others as parallels, just giving their distance. So if there is a regularity in the picture (or more generally: in the data) discovering this regularity may enable you to compress the file. In human perception, discovering a regularity means you can reduce the amount of information you have to process or memorize, and it becomes easier to spot the non-regular rest.

If the data is very regular, we can just compress it right away using a known procedure, something we may model as an algorithm. There is no challenge. The perceptual task is boring.

If there is too much complexity, we will not be able to compress the information. We will be confused or frustrated, or we will switch to ignoring the detail and thus perceiving the complex data as smooth noise. This in turn will be boring.

If there is some structure of a medium complexity, we will manage to discover regularities. We will manage to compress the information, but not by just applying a preexisting algorithm but by creatively constructing new knowledge on the spot. Succeeding in this task will generate a positive experience of success. My hypothesis is that this is the emotion we perceive as beauty. It is the reward for integrating novel information.

If the data contains a rich and varied structure so that whenever we manage to assimilate part of it, some will remain and our perceptive system remains engaged for an extended time, we will be rewarded with a prolonged experience of beauty. This requires structures of a medium amount of information content. There must be a lot of information so that it does not become boring but not too much so we are not overwhelmed by it. Unlike the monochrome picture, such a picture will resist compression into a very small file, but it will be compressible to some extent because it contains some regularity or order (redundancy).

Pictures with such a medium degree of order look less boring than a monochrome picture and more interesting or even than the confusing or boring noise picture. You might like them. Look at this, for example:

(Pictue from http://commons.wikimedia.org/wiki/File:Abstract_oil_on_paper_w._smolarek_436.JPG?uselang=de)

This picture has a middle amount of regularity and irregularity. There might be better pictures than this one (I choose it because it is open domain, but also because I don’t find it bad) but you will notice that it is less boring than the other two. It is somewhere in the middle and it gives our visual system some work to do over an extended time.

The connection between beauty and medium information (or entropy) content has been noted before, e.g. by the philosopher Max Bense. There is actually quite some scientific literature on this topic. However, I suspect here a link to creativity. Following the works of Kurt Ammon, I view creativity as the ability to break out of any given formal system or algorithm. In perception, that means to extend the preexisting knowledge to assimilate novel information. The reason that medium-information structures are beautiful is that they lead to repeated extensions of the analytical spaces our perceptive system consists of.

Composers learn to create auditory structures that have this property. This is what we call music. Photographers learn to find such structures and snap them. Artists, e.g. painters, learn to create such structures using canvas and paint.

If I am right, the possibility of art, especially pre-conceptual (or “abstract”) art in which novel beautiful structures are created by the artist, is a side effect of the way our perceptive system works, and that is the permanent extension and growth or our perceptive knowledge.

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13 comments

  1. Reblogged this on The Asifoscope and commented:

    An article about the connection of aesthetics, information theory, and creative systems, on my philosophy blog.

  2. I have forwarded this to a more technical-minded loved one who has some knowledge of entropy and algorithms. Very interesting! I find the Asifoscope blog a bit easier to read. (gulp) I do admire your complexity of thought!

    1. That is why I created this extra blog. I am planning some more scientific articles here, about the work of my friend Kurt Ammon (there is one article here about one of his articles, and I will try to provide an in-depth analysis of that his article since it is hard to read if you don’t have a background in mathematics or theoretical computer science). Since this will tend to be hard stuff for many people (I have a degree in computer science and I am studying philosophy. Kurt Ammon is a mathematician) and I don’t want to drive my average followers away, I decided to start this extra blog for such things. I will normally re-blog or put references on my other blog for anything I post here.
      Basically, Kurt developed a theory of what creativity is. He developed it in the context of mathematics (which requires creativity to do it, as can be proven mathematically). His approach has interesting consequences in several areas of philosophy and I want to try to translate it into something more easily understandable. However, since I do not have much time at the moment, this has to wait a bit.
      The things I want to publish here are connected to what I do on the Asifoscope and I will try to point out the connections.
      Maybe I should start each article here with some kind of abstract or summary targeted at the general audience.

      1. Your work sounds fascinating and very complex. I have an interest in mathematics, creativity, and philosophy and yet not anywhere near this depth of understanding. Any efforts to translate into ‘general audience’ language will be most appreciated. Kurt’s work sounds interesting especially as it has consequences in areas of philosophy. Do you find it frustrating knowing things that are hard to communicate? I have a similar problem in a different field, and feel that making an interactive movie might be the best way to approach it!

        1. An interactive movie sounds like an interesting idea. I have to think about it. It would probably take a lot of time to do it well but it could make it much easier to convey the ideas.
          My father was a teacher. From his work I know that didactics is hard work. It can take a lot of time.
          My grandfather was a graphics artist and my father could visualize things well but I never learnt that. I will start with text and then try to find good graphical representations. It will be a process.

      2. I am not so keen on didactics. Open learning and experiential learning hold more appeal for me. Not sure how to incorporate this into an interactive movie. It would need programming/technical skills that would be rather a large challenge for me. Sometimes I imagine a kind of ‘game of life’ challenge for the movie ‘audience.’ Where they have options to choose from, and it affects what they see next on the movie. Not sure how that would fit with the mathematics and philosophy. I am probably digressing off topic. Apologies.

  3. Honestly, from my perspective, the first image is a color.
    The second image is a representation of a texture.
    The third image is entertaining, delightful and much more.

    1. Exactly, you are right. The point in the article is, the single colour can be completely described by a short bit of information (all pixels have the colour Nr. …). The Noise picture may be seen as a texture, but unlike other textures, there is no correlation between the points. So the amount of data needed to describe it is very large. To describe it exactly, you have to describe the color of each single point. In more ordered textures, there is some pattern so you can say “Patter xyz is repeated in this or that way”. The third image is in the middle, some structure and order some disorder, so you would need a medium amount of data to describe it completely, and that medium area is where the interesting pictures are.

      1. A happy medium! Oh, and thanks for reminding me about prime numbers they other day! 🙂

  4. […] certain scale, there is a maximum of beauty where order and disorder are at the right balance (see FROM MONOCHROME TO NOISE – AESTHETICS, INFORMATION THEORY,  CREATIVITY and THE AESTHETICS OF DECOMPOSITION: “THAT “BEAUTY ZONE” WHERE THERE IS AN […]

  5. […] (FROM MONOCHROME TO NOISE – AESTHETICS, INFORMATION THEORY, AND CREATIVITY) as well as some of the articles on this subject in […]

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