leonardo da vinci

People point out that Leonardo Da Vinci was about experience, and not just "a man of letters."  What they mean by "not a man of letters" is that he wasn't formally educated. Leonardo himself says this many times(see Walter Isaacson's "Leonardo Da Vinci" which is the book I draw from for much of this.  I read his Einstein like a decade ago or so, and so, when I saw that he wrote about Leonardo Da Vinci, I had to read that book.  There's many books out lately about Leonardo; but, I knew Walter Isaacson; so, I knew this had to be the one of the better books to read about Leonardo Da Vinci)

When people think of the Renaissance, they think of Greek science and philosophy rediscovered. And, that's correct. But, the point here is that Leonardo, being "the" Renaissance figure, was actually not formally educated, was self taught, and preached a hundred years before Galileo to learn on your own, to go the source, the data.

Leonardo Da Vinci lived during the time of the discoveries of the Americas.  In fact, he knew and was friends with AmerigoVespucci.  Another famous character he knew and seemed to be on good terms with is Machiavelli.

Another major scientific/technological event during Leonardo's life was the Gutenberg printing press.  He learned of Euclid's Elements amongst so much else in his later years when the printing press made these things much more available. Leonardo was also born poor, and out in a country farmland, not some inner city.

"I am fully aware that my not being a man of letters may cause certain presumptuous people to think that they  may with reason  blame me, alleging that I am a man without learning. Foolish folk! . . . They strut about puffed up and pompous, decked out and adorned not with their own labors, but by those of others . . . . They will say that because I have no book learning I cannot properly express what I describe- but they do not know that my subjects require experience rather than the words of others." - Leonardo Da Vinci

But, the printing press actually allowed him to read books that he wanted to read and not what others wanted to him to read.  The printing press era later allowed him to read some of that standard stuff.  The important point perhaps here is that Leonardo learned not to be dogma or follow dogma.

Leonardo describes an early discovery and adventure of his childhood. "Bending back and forth, I tried to see whether I could discovery anything inside, but the darkness within prevented that. Suddenly there arose in me two contrary emotions, fear and desire- fear of the threatening dark cave, desire to see whether there was any marvelous thing within."  Leonardo then describes that he found fossils.

Leonardo studied anatomy and geology to make better paintings.  He painted both for fun and profit. But, he was also into making all kinds of mechanisms for the elaborate plays of the day.

He drew birds and studied them to learn how to make manned flight. He tried to conceive of a perpetual motion machine.  To his credit he figured out that such a machine was impossible for friction reasons. Leonardo appears to be the first to understand this - not Galileo.

He not only studied perspective geometry to make his paintings more realistic, but he studied human emotions to make emotional paintings and sculpture.

Leonardo may have been influenced by Roger Bacon.  Leonardo drew submarines, water powered cannon's, stealth black ships. . . . Leonardo observed that the sum of the branches equals the trunk of a fractal . . .  the vitruveus man is obviously inspired by a Vitruvius to picture the proportions of mankind . . .

Birds inspired Leonardo Da Vinci to think of human flight. He noticed Bernouli's principle intuitively.

Leonardo came up with the spiral metal arm to keep clocks ticking at a consistent rate. This was one of the mechanical things James Burke shows.

James Burke points out the history of clocks in episode/chapter 5 of his Connections. He mentions a sundial, and a water clock, and how these technologies have limitations of cloudy day, water freezing. James then points out a verge and foliat system

It's a gearing system that goes tick/tock.  There's a weight, and a gearing system that engages to slow the weight down. This is brilliant, but large and unweildy.  Leonardo Da Vinci came up with his spiral gear system that led to what's called the Nuremberg Egg,

As James Burke exclaims, these Nuremberg Eggs were the high technology of the day.

Machines use energy to do things. Leonardo analysed the Human body as a machine and determined how much weight each muscle can lift.  He did this analyses to design a flying machine.  But, he then went on to make such an analyses for many machines - saw mills,  wool-cleaning machines, paper mills, hammers for forgers, flour mills, knife grinding, burnishing arms, manufacture of gunpowder, silk spinners, ribbon weaving, shaping vases.

Leonardos study of machines led to try to make a perpetual motion machine. He intuitively figured out friction saps the energy - Perpetual motion is impossible  This led to Galileo noting that motion continues in a vacuum, but not where  there's friction.

In designing machines to study friction, he created machines that wouldn't be built till the 1800s - a Tribometer and ball bearings.  Leonardo seems to be the first to record a mix of metals that would reduce friction.  These anti-friction alloys wouldn't be rediscovered till 1839 by a Isaac Babbitt.

Another curious contemporary of Leonardo was Michelangelo.  The contrast of characters is striking. Leonardo is the Albert Einstein curiosity character. He did not believe in superstitions, alchemy and astrology.  He sought cause and affect.  Michelangelo was haunted by inner mystic demons.

Michelangelo, as Vasari reported, displayed "a very great disdain" toward Leonardo."  Walter Isaacson further mentions a story of Leonardo walking with friends in Florence.  They were talking about a Dante passage, when Michelangelo walked by and snickered that Leonardo ordered a hugh bronze horse to be made, but did not finish it. Michelangelo is quotes as saying "My delight is in melancholy."

My favorite Leonardo Da Vinci inventions are his musical instruments. Like the way the nineteen eighties used synthesizers to do on one instrument what was normally done on another - for instance a hand held keyboard used as a guitar, or a keyboard synthesizer to play guitar, drums, you name it, Leonardo mixed and matched different instruments to get different capabilities. He mixed a lyre  and  fiddle. It had seven strings - five were meant to be played with a bow, and two were to be plucked.  This instrument was pictured by Raphael after Leonardo's life. Lira da braccio

"Leonardo knew how to play the lyre "with rare distinction" according to the Anonimo" - Walter Isaacson.  Leonardo played music from Petrarch, and his own compositions. A Paolo Giovio mentions "He was a connoisseur and marvelous inventor of all beautiful things, especially in the field of stage performances, and sang masterfully to his own accompaniment on the lyre."

Leonardo turned a bell into a keyboard.  He had two hammers striking at different places of the bell, and four dampers to strike it differently

He created drums with different tensions to create different sounds.  He created drums with holes to be played like a flute. He even created a kind of drum keyboard.

Then, there was the viola organista, a cross between a violin and an organ. He created a looped bow that allowed the sound to be sustained unlike a regular violin.

Leonardo Da Vinci's mathematics was mostly drawing illustrations for Luca Pacioli's "On the Divine Proportion."  Geometric proportion was Leonardo's main interest in mathematics.  He tried to think of squaring the circle in terms of proportions.

The above is Leonardo Da Vinci's almost topological effort to square the circle.

Leonardo duplicated the cube, one of the three Greek classical delian problems not solved by them by a three dimensional version of the Pythagorean theorem,

Recently, it has come to light that Leonardo thought of a mechanical calculator.  But, there's no indication he ever actually built it.

- I can't help finishing this writeup of Leonardo Da Vinci by noting that he seems to have influenced a Gerolamo Cardano.  Leonardo Da Vinci was good friends with a Fazio Cardano.

Most people today have seen the quadratic formula. If you can either memorize the quadratic formula, or, if you know how to derive it, you can solve any second degree equation just by plugging in values.  The Greeks solved this geometrically. Through a long evolution of mathematics going from one culture to another, this became symbolized algebraically.  Archimedes did solve a special case of the third degree equation - by intersection of conics.  But, in one of the most Renaissance like stories, the third degree equation was finally solved as a closed form solution like the quadratic formula. Cardano got the formula from a Tartaglia.  But, Cardano figured he got it from someone else.  He eventually found the true discoverer of the general third degree formula - Scipione del Ferro

Cardano had a Ferrari colleague.  This Ferrari solved the general fourth degree equation.  I've done the general third degree, but have only taken stabs at the general fourth. Well, Gerolamo did invent complex numbers and used them effectively with solutions to the general third degree equation.  Gerolamo also was the first to introduce the binomial formula.  He did probability theory from his gambling days.  But, it's his mechanical inventions(and that he's the son of a former friend of Leonardo) that makes me want to point out Gerolamo Cardano here.

Gerolamo invented a gyroscope, a combination lock, shaft with universal joints which allows transmission of forces at different angles; this is still used in vehicles today.  And, he used hypocycloids to make for faster printing presses.