I’m reading a book about Leonardo da Vinci by Walter Isaacson that is quite interesting.  Da Vinci was obsessed and investigated the geometries of perspective, the optics of light, the effect on the human mind, the shading of lines, and colors and so much more.  Vast curiosity, imagination, and a drive to learn through experimentation and hyper-keen observation were his hallmark traits.  It’s rare that such traits combine with that of a creative and ambitious genius, and at a time in which discovery and learning was so valued by humanity.  There are so many life lessons to be understood.  But the ones that I’d like to draw on (note the pun) are his work on perspective, a favorite topic of mine, as well as shading.

First shading.  Mathematically a line has no width, and hence no volume.  In nature, in everything we can see we cannot see a line.  We see a geometry, a volume, and hence in representing lines in our mind we really see shading.  Leonardo experimented and worked to understand optics, light, and the volume and effect of shading.  And we learn too.  We are taught to think of the world as good and bad, right and wrong, and paths that are clearly defined.  When like in art and math, there are not lines without shades, that paths are not as clearly delineated as our framing would like.  It takes time and experience to understand that our greatest challenges and life-learning is when we are pushing boundaries of hard drawn lines and it is there that we find the shading.

Perspective too, has a way of being fuzzy.  As we look into the distance, items twice as far away are half the size, and so too we find that features blur, color is muted and faded.  It is necessary to journey there to see clearly the features.  It is necessary to keep in mind that as we look into our futures, that those futures are never as clear as you may try to play them in your mind.  They too have a lot of shading and blurring of features.  It is wise to use perspective in life and planning, to see broad directions on where to go and why, but also to know that there are many things that cannot be seen clearly until you are there, and even then we find shading.  Perspective gives us a point of view, that used wisely, is invaluable. While shading reminds us of the complexity of life, keeping the world interesting, and challenging us always…