Galileo Math Quotes

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

. . . we come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and other latter-day cabalists will have numbers to tell them the truth or they will have nothing. . . . We must remember that Galileo merely said that the language of nature is written in mathematics. He did not say that everything is. And even the truth about nature need not be expressed in mathematics. For most of human history, the language of nature has been the language of myth and ritual. These forms, one might add, had the virtues of leaving nature unthreatened and of encouraging the belief that human beings are part of it. It hardly befits a people who stand ready to blow up the planet to praise themselves too vigorously for having found the true way to talk about nature.

A feeling rose inside him, making him queasy, as though an elaborate formula he’d thought was perfect was now giving false results because of an unpredictable variable.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics.

It is through Galileo that the connection between math and the physical world became solidified.

Isaac Newton was hardly the person people would pick to be the cultural guru of his age. Everyone recognized that this son of a clergyman from northwestern England (born the same year Galileo died, in 1642) was an incredible math prodigy.

There is no event in Nature,” Galileo wrote, “such that it will be completely understood by theorists.”36 God’s perfection was to be found in the numbers, not in the shapes or objects. Yet without real objects, the math can become an exercise in pure speculation or even hallucination, as Giordano Bruno’s life revealed.

As William Bouwsma pointed out, the late medieval and early Renaissance crises of representation did not stall out at their skepticism of the old systems but rather progressed to an even more urgent defense of objective boundaries and quantifiable truths.27 In “The Secularization of Language in the Seventeenth Century,” Margreta de Grazia has shown how this pursuit of certainty led to a skepticism about language itself that dissociated words from God and deverbalized God’s message, prompting thinkers from Thomas Sprat of the Royal Society to Hobbes, Robert Hooke, Galileo, and Newton to seek cer- tainty in mathematical knowledge; quantifiable, identifiable substances; and trial, experiment, and experience.28 As Puritan propagandist Vavasor Powell put it in the middle of the seventeenth century, “Experience is like 42 Rituals of Spontaneity steel to an edged tool, or like salt to fresh meat, it seasons brain- knowledge, and settles a shaking unsetled soule.” Paralleling more sec- ular quests for certainty, the Puritan quest for grounding religious knowledge in a literalist reading of Scripture focused ever more intensely on manifest, genuine experience confirming salvation and the personal application of scriptural truth. The spontaneous “pouring out of the heart” in prayer was just such an evidentiary experience.

The first helpful notion is that it is usually best to simplify problems by deciding big no-brainer questions first. The second helpful notion mimics Galileo’s50 conclusion that scientific reality is often revealed only by math as if math was the language of God.

The second helpful notion mimics Galileo’s50 conclusion that scientific reality is often revealed only by math as if math was the language of God. Galileo’s attitude also works well in messy, practical life. Without numerical fluency, in the part of life most of us inhabit, you are like a one-legged man in an ass-kicking contest.