自然之美Natural Beauty
从飞机舷窗往外看，哪些结构是天然的、哪些是人为的，一目了然。天然结构弯弯曲曲，混沌无序，却自有递归之妙。它们把极其复杂的模式以一种非常简洁的方式呈现在我们眼前。人为结构恰恰相反——它们以简单的底层形状（方块、直线、完美的圆形）为起点，却以杂乱、不可预测、难以编码的方式组合在一起。看着它们，就像在看一堆有序元素胡乱拼凑而成的混沌体。
顺便说一句，这也是数学家所说的"优雅"解——一个简单的公式，底下却编码着大量的复杂性与变化。
当然，美是相对的，因为我们各自储存着不同的模式可供比对。因此，一个在深谙中东艺术的人看来优雅简洁的模式，在惯于欣赏西方艺术的人眼里，可能就显得过于复杂、毫无递归性。
大脑喜欢补全模式。我们无时无刻不在这么做，为的是生存——用来预判周围的环境。但大脑也会为了玩乐而补全模式（我怀疑我们根本关不掉这项能力）。轻松自在地补全一个模式，其中自有一种美感。这也是我们爱听音乐的原因——在下一个音符响起之前，我们就能预判到它，而那音符听起来恰到好处。一旦我们把一首歌听得太熟，补全带来的兴奋感消失，音乐就变得"乏味"，我们只好另寻新曲。一些最好的音乐在多个层面都具有递归性，模式由此在时间、振幅/音量、不同乐器、不同乐章之间延展。调动多种感官会强化这种体验——对懂得踩着节拍跳舞的人来说，他们的大脑能同时在听觉与身体感官上补全模式。而对我们这些不会跳舞的人而言，某个无法补全的模式带来的挫败感，会盖过其他模式带来的愉悦。
不过，我对很多现代艺术依然欣赏不来。似乎自摄影发明之后，绘画失去了客观的衡量标准（写实主义），退化成了艺术家代际之间近亲繁殖般的对话和接连不断的回应（正如哲学几百年来所做的那样）。
Looking out of an airplane window, it’s quite obvious what structures are natural and what structures are manmade. The natural structures are curvy, chaotic, yet recursive. They take very, very complex patterns and project them to us in a very simple way. The man-made structures are the opposite – they take simple underlying shapes (squares, straight lines, perfect circles) and combine them in haphazard, unpredictable, and hard-to-encode ways. Looking at them is to look at a chaotic jumble of ordered elements.
By the way, this is also what mathematicians mean by an “elegant” solution – a simple formula that encodes much complexity and variance underneath.
Of course, beauty is relative because we have different patterns stored that we can match against. Therefore it’s possible for a pattern that seems elegant and simple to one versed in Middle-Eastern art to appear overly complex and non-recursive to one who is mostly used to Western Art.
The brain loves to complete patterns. We do it for survival value all the time to predict the environment around us. But it also completes patterns for play (I suspect that we can’t turn this ability off). There is something aesthetic in completing a pattern in a casual, easy way. That’s why we enjoy listening to music – we can predict the next note, which seems just right, before it occurs. Once we know the song too well and the thrill of completion goes away, the music is “stale,” and we have to move on. Some of the best music is recursive on many levels, so that the patterns extend in time, amplitude / volume, across instruments, across sections, etc.. Engaging multiple senses heightens the experience – for people who know how to dance to a given beat, their brain can complete the patterns across the aural and corporal senses simultaneously. For those of us who can’t dance, the frustration of one pattern which cannot be completed overwhelms the joy from the other.
I still don’t get a lot of modern art though. It seems that after the invention of photography, painting lost its objective measure (realism) and devolved into inbred conversations between generations of artists and successive responses (as philosophy has been doing for centuries).