Galileo’s “Discorsi” of 1638: The First Physics “Textbook”

There are many milestone books in the history of science. True to the definition of “milestone,” these works mark pivotal achievements in mankind’s effort to understand natural law and the world in which we live. Among the very top tier of milestone science books is the Discorsi, published in 1638 by Galileo Galilei. It is his last and most significant contribution to science and is often referred to as the first physics “textbook.”

The Discorsi derives its fame as the published repository of Galileo’s life-long efforts to decipher the concept of motion and the “law of fall,” the mathematical characterization of free-falling bodies under the influence of gravity. Attempts to determine the velocity and distance profiles of falling bodies as a function of elapsed time of fall had yielded only conjecture over the centuries since Aristotle himself pondered the question. As Aristotle observed over two thousand years ago, “In order to know the natural world, one must first understand motion,” and, until Galileo and Isaac Newton came along, what we “knew” about motion was indeed largely conjecture – much of it erroneous!
It was clear that the force of gravity was the prime-mover causing bodies of mass to fall toward the earth’s center, but until Isaac Newton in 1687 established how gravity worked, no one really understood the mathematical details of gravitational attraction between any two bodies of mass. When we weigh ourselves on a scale, we are, in fact, measuring the force of gravitational attraction between the earth as one mass and our bodies as the other. One’s weight on the moon is less than that on earth because of the moon’s smaller mass. In empty space, we are weightless. Here, then, is the great question posed by the elusive “law of fall” whose answer had eluded man for centuries – until Galileo solved the riddle:

What is the velocity attained by a free-falling body as a function of the elapsed time of fall? We know the velocity at the onset of fall: It is clearly zero at the instant of release. But what is its precise instantaneous velocity at each second of elapsed time thereafter? Furthermore, what is the distance of fall covered from the release point at each elapsed second of time?

A falling body precisely one second into free-fall is already traveling with an instantaneous velocity of 32.2 feet per second. Making such measurements without modern instrumentation and high-speed strobe photography would be virtually impossible. In the early seventeenth century when photography was unimaginable and there certainly were no stopwatches or even accurate clocks, Galileo had to find a way to slow down the motion of a free-falling body. He “diluted” the effect of gravity by repeatedly rolling a small ball from a standing start down a long grooved, inclined plane. He then measured the distances covered by the slowly accelerating ball over successive constant-time intervals of an arbitrary “musical beat.” It is said that he used for a “timing clock” the steady cadence of a hummed Italian march for his equal timing intervals. Using multiple trials and noting the precise position of the rolling ball along the track on successive numbers of downbeats of the steady cadence, he was able to deduce the “law of fall.” Here is a figure illustrating the essence of Galileo’s brilliant inclined plane experiment. The figure is from chapter four of my book on motion, The Elusive Notion of Motion: The Genius of Kepler, Galileo, Newton, and Einstein.

Here is the critical essence of what Galileo determined:

A body free-falling under gravity exhibits a constant acceleration value (near the earth’s surface). It remained for Galileo’s successors to determine the exact numerical value of that acceleration. Near the earth’s surface, a body of mass in free-fall attains an additional velocity of 32.2 feet per second for each additional second of elapsed time. Galileo’s determination that acceleration is constant in free-fall dictates two major conclusions:

-The velocity attained is proportional to the elapsed time of fall. Twice the elapsed time, twice the velocity, for example.

-The distance traveled is proportional to the square of the elapsed time of fall. Twice the elapsed time, four times the distance traveled.

This is the celebrated “law of fall.” There might be a tendency for the casual reader to shrug-off Galileo’s achievement as no big deal in light of modern scientific achievements, but it was a VERY big deal for the progress of physics. Galileo, along with Johannes Kepler and Kepler’s experimentally formulated three laws of planetary motion, paved the way for the truly great reformation in mathematical physics initiated by Isaac Newton in his masterwork book of 1687, the Principia, universally acclaimed as the greatest scientific book ever published.

Image: Pierre Barge & Associates Auctions

First-state presentation copy of Galileo’s Discorsi to the French Ambassador, Count Francois de Noailles who smuggled the manuscript from Florence, Italy, to Leiden, Holland, for publication in 1638. Auctioned in Paris for over $790,000 in April, 2017 by Pierre Barge & Associates, the book itself is dedicated to de Noailles.

Here is perhaps the finest copy extant of Galileo’s Discorsi E Dimostrazioni Matematiche intorno a due nuoue scienze, otherwise known as Discourses on Two New Sciences. This one-of-a-kind presentation copy from 1638 was given to a friend of Galileo’s who smuggled the final portion of Galileo’s manuscript out of Florence, Italy, into Leiden, Holland for publication by the famed Elzevir Press. Galileo was being held in virtual house arrest within his villa outside of Florence by mandate from the Catholic Church and its Inquisition. Galileo had been accused of suspicion of heresy by the Church for his previous 1632 book, the Dialogo, which the Church felt promoted the Copernican “world system” which featured a sun-centered solar system. This went against established scripture which suggested that the earth was at the center of everything, according to the Church. Galileo famously maintained that religion’s role on earth should be to show the way to heaven; it should be the role of science, not the Church, to explain the clockwork of the heavens. The Church did not agree.

As for the “two new sciences” introduced by Galileo’s Discorsi: The first treatise in the book deals with what would today be called “Strength of Materials” and “Reliability Engineering.” This constituted a pioneering effort by Galileo in a new field of endeavor. The second treatise in the book involves those categories of physics known as “Mechanics,” and “Kinematics.” The centerpiece of the book is, of course, Galileo’s findings on motion and the long-delayed, finally published documentation of the “law of fall.” Most of the work presented in that section was done by Galileo as early as 1604. Galileo was in poor health and almost blind from glaucoma in 1638; accordingly, publication of this, his most important scientific work was, for him, a very high priority made complicated by the censorship of the Church. Galileo died in 1642, the year Isaac Newton came into this world. The torch had been passed.

The Key to Physical Attraction…It’s Called “Gravity” (and “Love”)

As unlikely as it may seem, the language of science has expressions in common with the language of love. The notion of  “physical attraction”  has roots in both. We humans are selectively attracted to others during our lifetimes, yet we are constantly attracted, in reality, to everyone and every thing in the universe as revealed by Isaac Newton in his masterwork of science, the Principia. Two marbles, one inch apart on a smooth table, exert an attractive force on one another which would tend to draw them together, except that the force is too small to overcome the rolling friction on the table. Yet, on the larger scale of the sun and planets, the forces of attraction between such massive bodies are immense.

 “Falling” in love may happen but rarely in our personal lives, yet we are, in fact, constantly falling – even though we are not conscious of the reality. All earth-bound denizens fall constantly… toward the sun as the earth orbits our nearest star. That motion, due to gravity, of continually “falling toward the sun” works in concert with a component of planetary motion tangential to the orbit to define the path of our earth around the sun. That tangential component of motion represents the inertial path the earth would take if the gravitational attraction to the sun suddenly ceased. The concept of  “gravity” has historically been one of mankind’s greatest comprehension challenges – one of nature’s great mysteries.

 

Early man’s curiosity as to why things apparently fall toward the center of the earth was at least temporarily assuaged (for hundreds of years) by Aristotle’s assertion some two thousand years ago that the earth’s center was the “natural center of the universe,” hence the logical place for objects to congregate (prior to Copernicus in 1543, the sun and planets were assumed to revolve around the earth). The great mathematician/scientist, Johannes Kepler, in the early seventeenth century was an early disciple of Copernicus’s sun-centered solar system and one of the first to seriously contemplate what kind of natural, physical mechanism was at play to keep the planets moving around the sun as they do. He conjectured that perhaps some form of solar, “magnetic” winds or vortices swept the planets along in their almost-circular paths. It was generally believed, prior to Newton, that whatever phenomena, or “force,” that caused apples to fall to earth was distinct and different from the celestial forces that held the heavens together. For a long time, celestial motions beyond the moon were even attributed to divine influence and motivation.

It took the genius of Isaac Newton to declare, in his 1687 milestone book on science and mathematics, that earthly gravity and heavenly forces are one and the same – hence, universal. Indeed, Newton claimed that all objects of mass in the universe attract all other objects to greater or lesser degrees via the force of universal gravitation. He stated that the nature of gravity and the equation which describes how it works is applicable everywhere and at all times – a truly “universal” law of nature! Although Newton explained the scientific version of “physical attraction,” he wisely made no attempt to explain the underpinnings of the version expressed in the language of love. Nor will we! That remains as captivating and mysterious as ever and seemingly beyond the ability of science and mathematics to explain.

But Newton really did not explain what gravity is or why it acts the way it does; he admitted so in the 1713 second edition of the Principia stating: “Non fingo hypotheses,” which, translated from Latin declares, “I feign no hypotheses!” He was criticized by his peers for his advocacy of this mysterious force-at-a-distance; they asked, “How can a body like the sun transmit, through empty space, the tremendous forces necessary to steer the planets?” His contemporary critics should have called to mind that other mysterious force which travels through space – magnetism, in the form of the magnetic field – which also has the power to attract objects. Newton was sage enough and courageous enough to stick by his contentions even though he could not explain them all. Although his famous equation does not hint at why gravity works the way it does, it describes precisely how it works – well enough to be used by NASA for its precise orbital computer computations. Despite the tremendous success of his theory of gravity and his numerical analysis of it, Newton did not – could not at that time – grasp the true essence of gravity. This is a remarkable situation which aptly reflects the reality that science will continue to inexorably peel-back, layer by layer, the deepest mysteries of our existence. Sometimes, genius like Newton’s transcends the state-of-the-art and “the possible”…for a while.

 Albert Einstein Peels Back Another “Layer” of Gravity

It took Albert Einstein’s 1916 general theory of relativity to go Newton “one better” and unmask the true face of gravity. Planets including the earth go around the sun in almost-perfect circles (ellipses) and not off into distant space not due to an explicit force of attraction between themselves and the sun as Newton proposed; Einstein showed that they are merely following a “natural path” determined by the curvature of four-dimensional space-time around the sun. That curvature is caused by the presence of the sun’s mass. All bodies of mass curve space-time in their vicinity. Einstein advanced physics immeasurably by contributing this radically unique physical interpretation of all gravitational effects. The complexity of Einstein’s mathematics in the general theory of relativity required to demonstrate this conclusively dwarfs Newton’s simple equation for an attractive force as presented in the first illustration of this post. Nonetheless, Newton’s achievement regarding gravity remains one of the greatest milestones in the history of science.

The Makers of  Universes!

George Bernard Shaw’s famous toast to Albert Einstein who was sitting near him at a tribute dinner held in 1930 at the Savoy Hotel in London, is well-known and oft-referred to. After extolling the virtues of mathematicians and scientists who, through the ages, have built “universes” instead of merely fractious empires like Napoleon and others, Shaw concluded by saying, “Ptolemy [the early astronomer/philosopher] made a universe which lasted 1400 years; Euclid [the great mathematician and founder of modern geometry] also made a universe which has lasted for 300 years; Einstein has made a universe, and I can’t tell you how long that will last!” Einstein is shown in the grainy black and white film footage clearly letting-go a big belly-laugh. Science does move relentlessly forward – always with a great assist from mathematics. Look at where we are today. Love and science do go together: To love studying the history of science and its impact on humanity is to experience what I call the “joy of science.”

Despite the phenomenal track record science has compiled while continually advancing the state of our knowledge and well-being, the greatest of all mysteries may prove to be beyond the comprehension of science: Who is the ultimate maker of universes and what can we truly know about that?

One of Einstein’s famous quotations says it beautifully: “The most beautiful emotion we can experience is the mysterious. It is the fundamental emotion that stands at the cradle of all true art and science. He to whom this emotion is a stranger, who can no longer stand rapt in awe, is as good as dead, a snuffed-out candle. To sense that behind anything that can be experienced there is something that our minds cannot grasp, whose beauty and sublimity reaches us only indirectly: this is religiousness. In this sense, and in this sense only, I am a devoutly religious man.”