” If I have seen further than others, it is by standing upon the shoulders of giants.” Isaac Newton in a letter to Robert Hooke, 1676

Introduction

From “Rav-Bariach” web page (in Hebrew) I copied the following paragraph:

“In 1972 an upset customer came into the locks shop where Abraham Bachri used to work and requested to install four locks on her door to provide her lost sense of security following a burglary she experienced. This innocent request sparked the imagination of Abraham, who along with his friend Moshe Dolev, developed a multi-lock that was installed in the center of the door, first a wooden door and later with steel core.”

I have no reason to suspect that either man knew the “four bolt” lock designed by al-Jazari, but the lovely similarity made me think about inventions and “reinventions.” The question of who invented the telephone or the light bulb, to name famous cases, generally has legal and economic implications. I am more interested in the human spirit, and this will be the topic of this post.

Drawing of the locking mechanism of the four bolts, Topkapi manuscript, 1206

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in bolts or locking mechanism can skip those bits. There are four bolts made from wood or iron, on the back of a door, in all four directions. One closes to the right, one to the left, another upwards and another downwards. Each bolt is notched with “, triangular teeth “sawtooth”  facing the locking mechanism, in the center, with a key lock:

Drawing of the notched bolt, Topkapi manuscript, 1206.

The locking wheel has teeth match to the bolts, but it only rotates when the key is inserted into the lock, then each bolt locks the door on one of the sides (top, bottom, left and right). The following image compares the original lock “Rav Bariach ” and the reconstruction of the lock of al-Jazari from the Museum of The History of Science and Technology in Islam in Istanbul:

You can see two locks with four bolts on four sides with a central locking system and a single key. This is a short video of the reconstruction of al-Jazari lock

A little bit of trigonometry

During my military service, I met a guy, from a religious Kibbutz, called Yakir Katz. (It was almost 40 years, and I could be confused with the details) He told me, bursting with laughter, that his father, who worked in the Kibbutz workshop, came home full of excitement and said he discovered a relation between the two legs of a right angle triangle depends only on the angle. Yakir explained to his father that this is the tangent (marked as tan or tg), and  it is a basic trigonometric function that every high school student learns:

tan(alpha)=a/b

I remember us arguing vigorously because I thought that the “rediscovery” of the Tangent is not ridiculous at all but really a reason for astonishment and even admiration to a man whose life circumstances allowed him who only limited education (I think eight years) and he had to go to work at a young age.

Trigonometry (from Greek τρίγωνον “triangle” + μέτρον “measurement”) is the study of triangles and the relationships involving lengths and angles of triangles.These relationships are expressed using the trigonometric functions, of which the most used are the Sine, Cosine and the Tangent already mentioned. Hipparchus of Nicaea, astronomer, geographer and Hellenistic mathematician is known as “the father of trigonometry,” was the first to create trigonometry tables. For young people who never saw a trigonometry table this is how we used to find Tangent or Sine values before calculator become available:

Sine values from the trigonometry tables

His other famous achievements in Astronomy include setting the length of the solar year with an error of about 6 min per year, inventing a system of coordinates to position stars and ranked stars according to their brightness further developed by Ptolemy. That system by Ptolemy is effectively still in use today.

Shoulders of giants

The metaphor of dwarfs standing on the shoulders of giants (Latin: Nanos gigantum humeris insidente) is attributed to Bernard of Chartres, a twelve-century French scholar. The metaphor meaning is that science and technology advance based on previous knowledge. Its most familiar expression is by Isaac Newton (the motto of this post) “If I have seen further it is by standing on the shoulders of Giants.”

Newton’s quote appears in a letter to Robert Hooke one of the greatest experimental scientists of the 17th century, a polymath, architect, astronomer, philosopher, and the author of Micrographia the first scientific best-seller. Some people believe that this comment was an insult to Hooke, who was a hunchbacked due to a severe Kyphosis, following the criticism of Hooke on the Newtonian optics and the bitter feud between the two men who accompanied them until the death of Hooke in 1703. But the original letter is three years early to the conflict and Newton write with high esteem to Hooke. From the letter, it seems that the famous quote reflects the genuine perception of Newton of his achievements and science in general. It is interesting to note, in this context, that in various places al-Jazari indicates his debt to giants from the past.

Obviously, I don’t recommend anyone to “reinvent” something, and it is far superior to lean on “the shoulders of giants.” But is there a significant difference between the human achievement of Yakir’s father and Hipparchus of Nicaea? As far as both are concerned trigonometry as a mathematical tool didn’t exist, and both developed what was necessary from scratch.

It’s not really connected, but I couldn’t resist. The picture of dwarfs standing on the shoulders of giants reminded me the story of Orion, son of Poseidon. He was enormous in stature and the most handsome of the earthborn. He courted Merope, daughter of Oenopion. Oenopion was unhappy with the giant lover, gave him wine to drink and stabbed out Orion’s eyes. Orion stumbled to the workshop of Hephaestus. Hephaestus told his servant, Cedalion, to guide Orion to the uttermost East where Helios, the Sun, healed him.

Greek mythology: A manuscript from the 15 century. The blind giant Orion is carrying the boy Cedalion on his shoulders to act as the giant’s eyes.