Euclid's Window Quotes

“In Leipzig [in the 14th century], the university found it necessary to promulgate a rule against throwing stones at the professors. As late as 1495, a German statute explicitly forbade anyone associated with the university from drenching freshmen with urine.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“One morning during Lent in 415, Hypatia climbed into her chariot, some say outside her residence, some say on a street intending to ride home. Several hundred of Cyril's stooges, Christian monks from a desert monastery, swooped upon her, beat her, and dragged her to a church. Inside the church they stripped her naked and peeled away her flesh with either sharpened tiles or broken bits of pottery.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“Today we know that there are other solar systems only tens of light years away. Had the Golden Age continued unabated, we might by now have sent probes exploring them. We might have landed on the moon in the year 969 instead of 1969. We might have an understanding of space and life that is unimaginable to us today. Instead, events occurred that would delay the progress begun by the Greeks by a millennium.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“But in philosophy, he was closer to his contemporary Siddhartha Gautama Buddha (c. 560 – 480 B.C.). Both believed in reincarnation, possibly as an animal, so even an animal could be inhabited by what was once a human soul. Thus, both placed a high value on all life, opposing the common practice of animal sacrifice and preaching strict vegetarianism.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“It is hard to believe that the myths told about Pythagoras did not influence the creation of some of the later stories about Christ. Pythagoras, for instance, was believed by many to be the son of God, in this case, Apollo. His mother was called Parthenis, which means “virgin.” Before traveling to Egypt, Pythagoras lived the life of a hermit on Mount Carmel, like Christ's solitary vigil on the mountain. A Jewish sect, the Essenes, appropriated this myth and is said to have later had a connection to John the Baptist. There is also a myth that Pythagoras returned from the dead, although, according to the story, Pythagoras faked this by hiding in a secret underground chamber.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“Pythagoras was a charismatic figure and a genius, but he was also a good self-promoter. In Egypt, he not only learned Egyptian geometry but became the first Greek to learn Egyptian hieroglyphics, and eventually became an Egyptian priest, or the equivalent, initiated into their sacred rites. This gave him access to all their mysteries, even to the secret rooms in their temples.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“What can you prove about space? How do you know where you are? Can space be curved? How many dimensions are there? How does geometry explain the natural order and unity of the cosmos? These are the questions behind the five geometric revolutions of world history. It started with a little scheme hatched by Pythagoras: to employ mathematics as the abstract system of rules that can model the physical universe.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“Twenty-four centuries ago, a Greek man stood at the sea’s edge watching ships disappear in the distance. Aristotle must have passed much time there, quietly observing many vessels, for eventually he was struck by a peculiar thought. All ships seemed to vanish hull first, then masts and sails. He wondered, how could that be? On a flat earth, ships should dwindle evenly until they disappear as a tiny featureless dot. That the masts and sails vanish first, Aristotle saw in a flash of genius, is a sign that the earth is curved. To observe the large-scale structure of our planet, Aristotle had looked through the window of geometry.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

“The Babylonians did not write equations. All their calculations were expressed as word problems. For instance, one tablet contained the spellbinder, “four is the length and five is the diagonal. What is the breadth? Its size is not known. Four times four is sixteen. Five times five is twenty-five. You take sixteen from twenty-five and there remains nine. What times what shall I take in order to get nine? Three times three is nine. Three is the breadth.” Today, we would write “x2 = 52 – 42.” The disadvantage of the rhetorical statement of problems isn’t as much the obvious one—its lack of compactness—but that the prose cannot be manipulated as an equation can, and rules of algebra, for instance, are not easily applied. It took thousands of years before this particular shortcoming was remedied: the oldest known use of the plus sign for addition occurs in a German manuscript written in 1481.”
― Leonard Mlodinow, Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace