My first Google search was “Tu as de beaux yeux tu sais”, the famed line from Quai des brumes, with Michèle Morgan and Jean Gabin. The first Google result was right, I never came back to AltaVista, Google’s algorithms were better.

This finding power is amazing, both in terms of speed and width, and we can be temped to compare it to the human brain, if we do then we must take into account the whole Google system, many thousands of computers collectively weighing tons and using a lot of energy, thousands of human brains writing code to sustain it, millions of human brains writing web pages to feed it. But when I see a picture of Rick’s Café, I know it is from the movie Casablanca, and I do not have tons of hardware to find it, and we are better than the best of computers to read and understand images, our algorithms are better, and we only have one billion neurons with a few thousands connections each in a very small volume, compared to the Google’s data centers with petabytes of memory. The algorithms of search engines have evolved on a few decades; programming languages knew four paradigm shifts; the low-level algorithms of our brain may have a billion years of evolution. Our brain is very good at processing and storing images. When I store a picture in my computer it uses compression algorithms, the brain certainly has its own compression algorithms; otherwise it would be impossible to store so much information in such a small volume, a volume that is also self sustaining, self organizing, self-programming, and requires a very small amount of chemical energy to work, not only a volume devoted to processing and memory, but to life and consciousness.

Well known and studied compression algorithms are found in languages, which use symbols and grammars to structure the representation of meaning. The various languages have common attributes, because the various language evolution paths are submitted to the same constraints: to communicate easily and to build compressed and shared representations of the world. These common attributes are mainly found in grammars, so evolution brought us from many paths to the same conceptual structures: verb, subject … recursion. We know many universal conceptual structures, the five platonic solids, for example, the texture of prime numbers… There are so many conceptual and universal objects that I postulate, for the purpose of this speculation, the existence of a conceptual space.

The physical space has four or twenty or so dimensions whether you see it from a Newtonian or quantum perspective. The conceptual space has many dimensions, is this number of dimensions infinite? Is it possible to build a mathematical model describing the conceptual space while being part of it? Maybe with a recursive description. Is this space created by human thinking or discovered? I guess we are discovering rather than creating it because even if we would like to add a sixth Platonic solid, nobody could. So the conceptual space has a predefined structure, and the mankind’s various languages common set of grammar objects could be the result of organic compression algorithms progressively adapting to the structure of the conceptual space. Languages can be seen as an ongoing effort to adapt physical means of communication and information storage to existing structures of the conceptual space, in a biological effort of efficiency, another aspect of natural selection.

When I eat a food based on sugar and fat, I feel a form of satisfaction related to the detection by my body of a rich food able to give me a lot of energy. Pleasure is related to energy efficiency. Is beauty, whom it is said that it lies in the eye of the beholder, related to the same efficiency? Could it be a signal of an efficient compression algorithm? When I look at a beautiful woman, I feel a pleasure probably related to the conformity of the person to an archetype of physical and psychological characteristics favorable to efficient reproduction, this archetype being hardwired in my brain or implanted by cultural conditioning. The conformity to an archetype is a form of data compression, my brain only has to record the differences with the archetype because the archetype is already recorded, the fewer differences, the less storage space used to record the description of the person, the more beautiful feelings associated with this person.

It is actually impossible to decipher compression algorithms at the molecular level in the brain. Even if we could build and implant nanosensors recording and transmitting electrochemical activity in the brain, we could be in front of another type of the Uncertainty principle, and more if memory and compression processes were related to quantum mechanics activity, involving energies far different than electrochemical, then it would be many orders of magnitude more difficult to observe data compression in a human being. I suppose that quantum processes are implied in memory and brain activity, not only electrochemical processes, because it seems to me impossible that such a small volume contains as much information, even with powerful compression algorithms, if this information is based on molecular differences. We already have a good example of electrochemical memory, the DNA code that survives to the person, but this type of data storage, even using all the brain mass, would not be enough I think to encode all the memory we have between our two ears.

How is beauty related to communications and memory?
Rhyme and rhythm in poetry, invented by oral cultures in antiquity, and felt like beauty/pleasure by the brain, are a type of conformity to temporal and acoustic patterns, and are algorithms of error detections in the transmission of a text. If you replace a word in a poem by another word and still have a coherent meaning, it may lose the rhythmic pattern, the number of syllables may be different, and the acoustic pattern, the rhyme, may fail, so we have here a technique similar to the checksum, a control bit in a binary word that detects transmission errors by comparing the bit to the result of a simple operation on the word. Beauty in texts is often perceived when very few words are used to describe a complex concept, we feel pleasure when ideas are expressed with elegant and sober prose, again a principle of economy is at play, less data storage, great conformity with conceptual structures. Beauty can also be related to style, style being arbitrary algorithms created and shared in a particular culture, but this adds a layer of complexity.

Beauty in music is a very special case, first because there is no need to use a shared dictionary to be felt (to feel the beauty of a text you need to know the meanings of its words), and second because it is apparently opposed to the principle of economy. Dissonant chords have a shorter periodicity than harmonious chords when you analyze it from their mathematical representations; apparently, it takes more memory space to record a representation of a harmonious chord in the brain than of a dissonant chord. So there are other factors to consider in analyzing acoustic beauty. If we suppose that memory, in its earlier forms, was probably the recording of events by unicellular organisms, then temporal sequences were the first kind of data to be compressed, maybe by recursive algorithms. Temporal and not spatial because space perception requires sophisticated sensory organs, contrary to time perception. Temporal data of apparent complexity, the long periodicity of harmonic chords, could be conforming to recursive temporal compression algorithms. Is our brain built on top of compression algorithms used since a billion years by unicellular organisms? Is it possible to validate this hypothesis by building sounds using recursive algorithms rather than by adding sinusoidal curves, and using perceived beauty as a measure of conformity between sound generative algorithms and compression algorithms at the neural, and probably quantum, level?
Music is more than acoustics, music is formally a structure of algorithms and patterns; the first programming language was probably music notation, written to be performed by human processors, monks in a choir, for example; at this level, music algorithm analysis is complexified by cultural factors and probably improper to study low-level brain activity.

Beauty analysis in images is more complex than in music because there are many types of images, a continuum of types defined by few axes.
Images can be representations of objects, build by optical processes, like photography, or pseudo-optical processes like computer photorealistic rendering, or by gestural manipulation of pictorial matter, like painting or drawing with pigments or pixels. In all theses types of images, beauty is in part related to conformity between the real object and its representation. The representation can be realistic, with all the details and colors, or schematic, leaving aside many details to concentrate on essential parts of the objects, in both cases there is an economy associated with beauty: in a realistic painting there is conformity between the image and the object, so the brain simply records the differences, and in a schematic image the compression is already done, beauty is the result of efficient data compression when the more is expressed with the fewer strokes. Styles, artist’s personal styles or specific culture styles, add another level of complexity to the analysis of images beauty, and again representation of objects are probably improper to study low-level brain activity.
Abstract works can be built with optical or gestural means, their beauty or meaning may be the result of low-level brain activity, conformity to emotional structures, or the result of highly sophisticated relations established between the work and its context, again, this is not an easy study.
Abstract images can also be built with algorithms, algorithms can be studied, synthetic images can be beautiful, and a direct correlation can be made between beauty and their algorithms.

There are five platonic solids, how many types of graphic algorithms? What in graphic generative grammars creates beauty? Is it possible to collect and structure these to understand the way our brain can store so much data in such a small place, in the same way that X-ray diffraction patterns lead to the discovery of the DNA structure? Could this intricate mix of images and underlying programming languages let us explore undiscovered parts of the conceptual space?