[RL] Scientific thoughts on art

(How might this be relevant to SL? Well, all art presented in SL has been digitized and sampled at a relatively low resolution -- 1024x1024 for visual art, 44kHz 128kbps MP3 for music; this begs the question: how much can one reduce the resolution before human art becomes indistinguishable from computer-generated art? What is it that makes some textures worth more than others, some sounds more than others? Can one really say that there is "feeling" contained within an MP3 consisting of a few tens of millions of 1's and 0's?)

Dimensionality:

As far as a listener is concerned, a piece of music can be represented by a scalar function of time. (Well, actually, two functions of time -- one for the right ear and one for the left -- and perhaps a few auxiliary functions representing other sensory input such as changes in perceived sound due to turning of the head and resonances of the whole body to low-pitched sounds.) Written poetry is a discrete function in two-dimensional space (its "atoms" are individual letters); spoken poetry is a continuous function in one-dimensional time. Still visual art is a three-dimensional function (with red, green, and blue components -- or hue, saturation, and value) of two-dimensional space. Sculptures are 3D. Motion pictures are 2+1D.

This method of representation is not very useful for humans; we perceive things differently from a computer or measuring instrument. We have structures in our ears that resonate at different frequencies; we perceive sound not as a waveform, but more as a sequence of wavelets; we cannot pinpoint exact details of waveforms, but we can "feel" subtle "correlation" effects that a computer would be unable to identify. Perhaps MIDI is a more meaningful description of music than 24-bit PCM. From this viewpoint, music is not merely a one-dimensional function of time; there may be many parts playing simultaneously, and each of these can have intricate changes of pitch (including vibrato), volume, tempo, timbre (attack, decay, harmonic content), note duration (articulation), and so on. Each of these aspects is like a new dimension. So, one can sacrifice the fine-grained time resolution (44kHz) of the one-dimensional description, and gain a picture of multiple parts moving through multi-dimensional space in a carefully orchestrated, highly correlated manner. Similarly for other art forms.

Correlations:

One can define correlation functions (of a PCM representation or of a MIDI representation) relating signals at two or more times. If the correlation in a piece of art decays exponentially, with a correlation length (for visual art) or correlation time (for music) that is less than the extent of the picture or the duration of the piece, then the work essentially consists of two or more unrelated sections -- one might argue that it should really be split up. My guess is that for good art there must be at least one correlation function that maintains a reasonable value throughout the work (i.e., the "system" has "long-range order" or at least "quasi-long-range order") ... This is about the principle of coherence/unity/continuity in art.... e.g., even in long symphonies lasting an hour, there is coherence -- it is the same instruments that are being used, the starting and ending keys are the same, etc. Of course, one should remember that anticorrelation is a form of correlation (the correlation function goes negative) -- so a poem could contain a section describing "whiteness" and another section describing "blackness" and it would still be strongly correlated by my definition.

Surprisingly, the information content (Shannon entropy?) of a correlated pattern is LESS than that of an uncorrelated one. That seems to say that we make something more artistic by reducing its information content. On the other hand, a completely random pattern (e.g., spam) has maximal information content, and it is not art. Hence there must be a certain optimal information content. Speculation: correlation functions must not decay to zero immediately [completely disordered phase], nor should they be too close to unity over the whole work [strongly ordered phase]; maybe quasi-long-range order is desirable, i.e., correlation functions decaying as power laws of space and time. ... like at a critical point, a phase transition? ... which occurs near an instability? ... Does it take a mind "at a critical point" to produce such work? There has been research showing that the neural networks in our brains are very near criticality, so that a single input (stimulus) will trigger an avalanche of events corresponding to useful computation; epilepsy occurs when something tips the balance (of the "chain reaction") from slightly subcritical to supercritical.