On a crisp, blue-skyed sunny morning, do you ever stand under a tree and wonder at all the ways the sunlight brightens the leaves as it shines through them? An amazing painter-inventor, Leonardo da Vinci, 500 years ago in Renaissance Italy, loved to study leaves, too.
He wrote that each leaf's hue changed according to ``shadow, lightness, luminous highlight, and transparency.''
And that ``a leaf of concave surface seen in reverse from underneath sometimes is seen half shaded and half transparent.''
Leonardo-the-painter studied the leaves because he believed that art and science were essential to each other and that skillful artists could record knowledge, which is the original meaning of the word science, more accurately than writers could.
With these ideas Leonardo was able to paint pictures that seem even more beautiful than nature, but never unnatural!
Leonardo-the-painter worked most of his life as an engineer, hired to solve princes' military, city-planning, architectural, and theatrical problems with clever mechanical inventions. Here he combined science, knowledge, and art.
Twenty-two years ago in Madrid, Spain, Leonardo's long-lost manuscript (a handwritten book) on ``mechanics,'' the science and art of these mechanical inventions, was found.
This manuscript shows Leonardo-the-engineer's interest in how and why machines, ``engines,'' worked (in his day before electricity and fossil fuels).
In observing nature - birds flying, water swirling - Leonardo-the-scientist-artist wrote that every natural form had been perfectly designed to fulfill its function with nothing extra or lacking. This rule described how ``engines'' should act, too.
As in Leonardo's other unpublished writings on painting, architecture, and anatomy, his 1490s Madrid manuscript on mechanics includes many, many drawings.
Twenty years ago when modern restorers in Milan lifted a sheet that had been glued onto another for safekeeping, they were extremely surprised to find the drawing pictured on this page.
A two-wheeler bike in a Renaissance manuscript! But two-wheelers were invented for all the world to enjoy only 100 years ago, in the 1880s!
Leonardo's idea for a bike does not have inflatable rubber tires like yours. The long pedals turn a cogged wheel with squared wooden cogs.
On bikes a chain transfers the motion of the cogged wheel turned by the pedals to a smaller cogged wheel in the center of the back wheel, which turns that wheel.
Doesn't Leonardo's drawing explain how this part of a machine could be made?
Leonardo constantly taught himself by asking questions about how all sorts of things work, by observing, by drawing, and by making notes. Do you think that Leonardo-the-scientist-artist-engineer was describing himself in this funny note?
``A clock is used by those who grudge the wasting of time. And this is how it works: when as much water has been poured through the funnel into the receiver as there is in the opposite balance, this balance rises and pours its water into the first receiver; and this being doubled in weight jerks violently upwards the feet of the sleeper, who is thus awakened and goes to his work.''
Now you have discovered a few more of Leonardo's ideas on the mechanics of the universe: The beauty of nature's workings in leaves, flying birds, and flowing water is irresistible; the bike looks good. But aren't you glad that Leonardo's alarm clock doesn't get you up in the morning]