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.

Sir Isaac Newton: “I Can Calculate the Motions of the Planets, but I Cannot Calculate the Madness of Men”

Isaac Newton, the most incisive mind in the history of science, reportedly uttered that sentiment about human nature. Why would he infer such negativity about his fellow humans? Newton’s scientific greatness stemmed from his ability to see well beyond human horizons. His brilliance was amply demonstrated in his great book, Philosophiae Naturalis Principia Mathematica in which he logically constructed his “system of the world,” using mathematics. The book’s title translates from Latin as Mathematical Principles of Natural Philosophy, often shortened to “the Principia” for convenience.

The Principia is the greatest scientific book ever published. Its enduring fame reflects Newton’s ground-breaking application of mathematics, including aspects of his then-fledgling calculus, to the seemingly insurmountable difficulties of explaining motion physics. An overwhelming challenge for the best mathematicians and “natural philosophers” (scientists) in the year 1684 was to demonstrate mathematically that the planets in our solar system should revolve around the sun in elliptically shaped orbits as opposed to circles or some other geometric path. The fact that they do move in elliptical paths was carefully observed by Johann Kepler and noted in his 1609 masterwork, Astronomia Nova.

In 1687, Newton’s Principia was published after three intense years of effort by the young, relatively unknown Cambridge professor of mathematics. Using mathematics and his revolutionary new concept of universal gravitation, Newton provided precise justification of Kepler’s laws of planetary motion in the Principia. In the process, he revolutionized motion physics and our understanding of how and why bodies of mass, big and small (planets, cannonballs, etc.), move the way they do. Newton did, indeed, as he stated, show us in the Principia how to calculate the motion of heavenly bodies.

In his personal relationships, Newton found dealing with people and human nature to be even more challenging than the formidable problems of motion physics. As one might suspect, Newton did not easily tolerate fools and pretenders in the fields of science and mathematics – “little smatterers in mathematicks,” he called them. Nor did he tolerate much of basic human nature and its shortcomings.

 In the Year 1720, Newton Came Face-to-Face with
His Own Human Vulnerability… in the “Stock Market!”

 In 1720, Newton’s own human fallibility was clearly laid bare as he invested foolishly and lost a small fortune in one of investing’s all-time market collapses. Within our own recent history, we have had suffered through the stock market crash of 1929 and the housing market bubble of 2008/2009. In these more recent “adventures,” society and government had allowed human nature and its greed propensity to over-inflate Wall Street to a ridiculous extent, so much so that a collapse was quite inevitable to any sensible person…and still it continued.

Have you ever heard of the great South Sea Bubble in England? Investing in the South Sea Trading Company – a government sponsored banking endeavor out of London – became a favorite past-time of influential Londoners in the early eighteenth century. Can you guess who found himself caught-up in the glitter of potential investment returns only to end up losing a very large sum? Yes, Isaac Newton was that individual along with thousands of others.

It was this experience that occasioned the remark about his own inability to calculate the madness of men (including himself)!

Indeed, he should have known better than to re-enter the government sponsored South Sea enterprise after initially making a tidy profit from an earlier investment in the stock. As can be seen from the graph below, Newton re-invested (with a lot!) in the South Sea offering for the second time as the bubble neared its peak and just prior to its complete collapse. Newton lost 20,000 English pounds (three million dollars in today’s valuations) when the bubble suddenly burst.

Clearly, Newton’s comment, which is the theme of this post, reflects his view that human nature is vulnerable to fits of emotion (like greed, envy, ambition) which in turn provoke foolish, illogical behaviors. When Newton looked in the mirror after his ill-advised financial misadventure, he saw staring back at him the very madness of men which he then proceeded to rail against! Knowing Newton through the many accounts of his life that I have studied, I can well imagine that his financial fiasco must have been a very tough pill for him to swallow. Many are the times in his life that Newton “railed” to vent his anger against something or someone; his comment concerning the “madness of men” is typical of his outbursts. Certainly, he could disapprove of his fellow man for fueling such an obvious investment bubble. In the end, and most painful for him, was his realization that he paid a stiff price for foolishly ignoring the bloody obvious. For anyone who has risked and lost on the market of Wall Street, the mix of feelings is well understood. Even the great Newton had his human vulnerabilities – in spades, and greed was one of them. One might suspect that Newton, the absorbed scientist, was merely naïve when it came to money matters.

That would be a very erroneous assumption. Sir Isaac Newton held the top-level government position of Master of the Mint in England, during those later years of his scientific retirement – in charge of the entire coinage of the realm!

 

For more on Isaac Newton and the birth of the Principia click on the link: https://reasonandreflection.wordpress.com/2013/10/27/the-most-important-scientific-book-ever-written-conceived-in-a-london-coffee-house/

Jet Engines and Michelangelo’s “Moses”

What do these two “finished products” have in common?

The “reason” side of us acting alone would likely prompt the quick response, “Not much!” After some careful thought, our “reflective” side could provide some convincing arguments to support the contention that these two seemingly diverse objects, one from the world of technology, one from the art world, actually have much in common. Here is the way I see it.

The famous “Moses” at Rome, sculpted in hard marble by Michelangelo, represents the epitome of man’s ability to represent life and human nature using artistic mediums. In Moses, the inherent artistic genius of Michelangelo is brought to full bloom by the countless hours of diligent study and practice he devoted to mastering the techniques of working with marble. One man’s extreme dedication to his artistic cause has given us such priceless art as Moses, the Pieta, and the Sistine Chapel just to name a few.

As with Michelangelo’s Moses, the modern turbojet engine used in today’s airliners is the epitome of a product which demanded extreme dedication to a cause – only, here, the dedication extends over decades, indeed centuries, as armies of thinkers, scientists, and engineers fought to understand nature and natural forces.

Michelangelo’s Moses began as nothing more than a rudimentary “chunk” of marble; correspondingly, man’s knowledge of the various technologies inherent in modern turbojet engine designs ranged from rudimentary to non-existent as recently as four hundred years ago – well after Moses emerged from his marble prison. Michelangelo at least had his toolbox of fairly refined chisels and sculpting tools with which to work. The early “natural philosophers,” as early scientists and technologists were called, had little with which to work. They initially faced a confusing scramble of nature’s puzzle-pieces requiring painstaking assembly into a larger picture before true technology was possible.

Even allowing for whatever handed-down knowledge the artist might have received from mentors and colleagues, I see Moses more as the ultimate tribute to a single man’s talent and determination. I see the modern turbojet engine (and virtually all other technological wonders) as the ultimate tribute to mankind as a whole – the cumulative outcome of generations who worked to build our technology hierarchies. The iPhone, the modern automobile, the internet – these and all such technology triumphs are a tribute to the human spirit and its desire to “know.”

Highly-Polished Works of Art!

Michelangelo sculpted Moses cut-by-cut, chip-by-chip. And when Moses’ rough form finally emerged from the block of marble, he polished the innumerable rough spots – over and over again until the rippling muscles in Moses’ forearms fairly glistened of sweat. Like Moses, the modern turbojet engine is a highly-polished work…of the technological art, but with a much-extended gestation period and many fathers!

We recently returned from a two-week trip to New England, made possible by the marvels of modern aviation…and, specifically, the turbojet engine. Whenever I travel, I am cognizant of this monument to man’s ingenuity and dedication. Today, these engines are called upon to power countless tons of aircraft, passengers, baggage and cargo into the sky, hour after hour, trip after trip, week after week, without hesitation and without the need for frequent maintenance. Today, jet engine performance and reliability are so highly refined that travelers rarely think twice about flying over the rugged, isolated regions of polar routes in a large aircraft with only two engines.

A Bit of Historical Perspective

Jet engines were not so reliable in early aircraft. As a young boy, I recall numerous accounts of early jet fighter planes going down due to “flameouts” where the continuous fiery combustion and expelling of combustion materials out the back ceases and all thrust is lost. That problem and other major issues have long been solved. Today’s engineering efforts are focused on fuel efficiency and performance/cost factors along with quieter operation.

I also recall the public interest and excitement when the first U.S. commercial jet airliner service began – in 1959. My family lived not too far from San Francisco International Airport at the time. We could see the earliest American Airlines Boeing 707 jetliners off in the distance on final approach to the airport. It is interesting, today, to recall the fascination and excitement attendant to the advent of the commercial jet age, especially in light of today’s tendency to take it all for granted – which is a shame. I am a firm believer that when society loses its sense of wonder and perspective, it has lost something vital and precious.

The fundamental principle of physics which explains rocket and jet propulsion was first formally identified by Isaac Newton in his scientific masterpiece of 1687 – his book known as the “Principia” (See my post of Oct. 27, 2013, “The Most Important Scientific Book Ever Written: “Conceived” in a London Coffee House).

The third of Newton’s foundational “three laws of motion” states:

For every action, there exists an equal and opposite reaction

Despite this revelation and other fundamental physical principles so expertly articulated by Mr. Newton in 1687, much more physics and many new technologies were required for the first baby-steps on the long journey necessary to produce “engines” capable of powering our human desire to travel. The critical mass of required knowledge had not materialized until the nineteen-thirties when Frank Whittle, an English engineer, built the first laboratory version of a jet engine; it was operating by 1937.

 An early Whittle engine

As with so many technologies, potential military applications provided great momentum to the product development cycle of the jet engine. The first airplane to fly powered solely by a turbojet was the German Heinkel 178, in 1939. In the 1944/45 time frame of World War 2, German engineering produced the Messerschmitt 262, the first jet-powered operational aircraft.

 Messerschmitt 262

While much faster than the propeller-driven aircraft of the Allies, the planes were too few, too late, and plagued with reliability issues (including its pioneering jet engines) for it to be a decisive weapon in the war.

The die was cast by the end of the war, however; the jet engine’s rapid maturation and future domination was inevitable. One of the technologies which quickly matured out of necessity was the science of materials which dealt with the  “strength of materials” and their physical properties. The multiple internal turbine-fans spinning at very high speeds are populated with hundreds of turbine “blades.” The metallurgy to insure that these relatively small blades withstand the extreme forces and temperatures they experience requires a sophisticated metallurgical knowledge.

An interesting aside: One of the very first “textbooks” on the strength of materials was written by Galileo Galilei in 1638. The first half of Discourses on Two New Sciences is Galileo’s pioneering analysis of material strength and reliability – one of the “two new sciences.” The second half consists of his milestone revelations on the developing science of motion physics. The latter work qualifies this book as one of the most important science books ever published, one tier below Newton’s Principia of 1687 – like all other books except Darwin’s On the Origin of Species.

      

The next time you are at an airport, you might make it a point to observe jet aircraft which pull into a gate, power down, and sit there awaiting the next flight. The engine turbine fans can be seen still spinning 45 minutes after power-down, thanks to the superb, ultra low-friction ball-bearing designs which support the rotor shafts. You might notice also a “curly-cue” spiral painted on the front of the fan assembly just inside the engine cowl. They are there to provide easy visual indication that an engine is powered-up and turning at very high RPM. The tremendous appetite of these engines for air creates enough suction at the front-end to actually ingest ground crew members who get too close. This has, in fact, happened many times over the decades. Like the whirling propellers on older aircraft, jet engine intakes pose a deadly hazard to the folks who work around them.

Engine manufacturers such as General Electric and the U.K.’s  Rolls-Royce have learned enough of nature’s secrets to manufacture this product with an almost inconceivable reliability and performance capability. There is one aspect of nature which has proven stubborn to control and deal with, however.

Modern Jet Engines are NOT for the Birds!

The greatest enemy of the jet engine appears to be …birds! Our science and engineering capabilities have not figured out how to prevent the ingestion of our fine feathered friends into the compressor blades of these engines; it happens all too often. Do you recall Captain “Sully” Sullenberger and his short trip into the Hudson River minutes after takeoff from LaGuardia in New York? No engine is tough enough to digest a large bird and spin merrily along as if nothing happened. Oh well, even Moses has always been susceptible to “chipping” if not handled carefully.

One final comment about the similarities drawn between Michelangelo’s Moses and the highly developed modern jet engine: I am certain that jet engine technology will continue to evolve and that the end-product will improve even beyond today’s high standard. I am not sure there will be anyone coming along anytime soon who will improve upon Michelangelo’s “design!”

 

 

 

 

Addicted to Books

For some, alcohol is the indispensable commodity. For others, it is drugs. For a number of us, books prove to be irresistible and foremost among those things in life that we cannot do without. It is fascinating to reflect on why that should be the case for millions of booklovers all over the world. The answers to such musings are many and varied, I suspect. The feelings of attachment can be very strong.

 “The Bookworm” by Carl Spitzweg

When she was ill and dying, Jacqueline Kennedy reportedly asked to have some of her favorite books moved into her room. Presumably, she was not embarking on a final reading binge; she apparently wanted them near so she could spend just a bit more time with old and dear friends before the end came. I can completely understand that impulse, for a true bookworm becomes very attached to books.

 The Allure of Books

What is it about books? Where to start? For fiction fans, there is the pure entertainment factor and the escape from life’s hum-drum. The ability of a well-written story to whisk the reader away from today’s here-and-now troubles, even for a little while, is a powerful draw. The literary voyage can transport one anywhere, from the exotic capitals of civilized Europe, to the darkest jungles of Africa – even to the contradiction of Antarctica’s desolate yet serenely beautiful landscape of white. Time is equally capricious; the story can take place hundreds of years in the past, or, just as plausibly,at some time in the far distant future – as in science fiction. And what adventures await the reader/voyager along the way and at the final destination? Anything a creative writer can imagine is possible! Espionage and intrigue, great battles fought long ago, a journey to newly discovered planets – the list is endless.

The most effective fiction books, as with screenplays, are those that weave their spell using superb character development and portrayal. Human nature and societal behavior, as vividly displayed in text, is seemingly among the most inexhaustible of captivating themes. The great novelists all had superb skills in that regard; Charles Dickens always comes to mind for me.

Fiction allows the reader to live vicariously through the main characters – like Walter Mitty. Readers enjoy tagging along with characters who, perhaps unlike themselves, dare to live life to the fullest while dismissing danger, forsaking the conventional, and ignoring social taboos.

There is a large divide between fans of fiction and readers of strictly non-fiction books. Sure, there is often much overlap in interests, but I find that people tend to reside in one camp or the other. Followers of this blog have surely deciphered how I spend most of my reading hours. Although I am aware of missing out on something very good, I do not read much fiction. Why is that? I am in the vexing position of the kid in the candy store when it comes to reading – too many wonderful choices, both fiction and non-fiction. “Too many books, too little time” constitutes the short version of my plight. I have on my shelves, a small selection of excellent fiction; these are books I have obtained mainly because of their universal appeal as great literature and because of the fact that I know I would enjoy them. I really want to read The Great Gatsby, The Adventures of Huckleberry Finn, The Last of the Mohicans, etc. It is the fault of those not-yet read non-fiction books on my shelves that I have not gotten very far into my carefully selected fiction shelf. I will read them in due time, God willing.

 Fact Is Stranger than Fiction

At first that may seem a trite expression, but I find its declaration to be quite true. I gravitate toward true stories for two reasons: First, because they are true – they really happened to real people; second, because, often, “you just can’t make this stuff up” as the saying goes. Why read fictionalized history when the real thing is every bit as intriguing and the real-life protagonists are just as remarkable as any character imaginable? Well, that’s just my take!

The name of this blog is Reason and Reflection: Reason as in science, mathematics, and logical thought – knowledge; Reflection as in a fascination with the human side of life – wisdom. The name reflects my eclectic interests in pretty much everything – from science and mathematics to the nature of the human condition.

Books as Repositories of Knowledge and Wisdom:
This, for Me, Is the Ultimate Attraction

This concept, this view of books as precious repositories of mankind’s accumulated knowledge and wisdom, is the glue which forms such strong bonds to many booklovers. The ideas and discoveries which have changed the nature of human existence have virtually all surfaced, or at least survived, on pages nestled between the covers of books – books which silently preside over the years, the decades, the centuries, on library shelves….somewhere. After 1454 and the emergence of Gutenberg’s printing press, the holy-grail of such printed repositories has been the first editions which initially made the breakthroughs of great thinkers readily available to their fellow man. In rare cases, the “earliest available versions” of books are ancient, one-of-a-kind, hand-written texts which have managed to survive. The printed book is clearly the workhorse of this early “information age,” however. And many of the thoughts and discoveries disseminated in books have fundamentally changed man’s view of himself and his place in the cosmos. See my earlier post on Isaac Newton’s Principia (in the archives) from October 27, 2013, The Most Important Scientific Book Ever Published: Conceived in a London Coffee House.

 The Great Books: A Once-in-a-Lifetime Experience at Stanford University

Several years ago, Stanford University offered a course on “The History of the Book” through its continuing education program. I fortunately heard about it through my younger daughter, another great fan of books and reading. The several-week course convened on campus in the rare book library. Led by one of the university’s rare book librarians, the classes were structured as two hours of lecture and one hour of “show-and-tell.” The lectures were fascinating, and covered all aspects of “the book” from early forms of books and their construction to printing and collation (organization and page-numbering), bindings, and historical importance. Many of history’s greatest books were covered, from science to philosophy.

During the lecture phase, the instructor would produce, from his ever-present cart, a book to illustrate his point. The books he chose were often first editions of the most important books that exist. I cannot accurately recall them all, but a typical lot would reflect authors like Pliny, Copernicus, Vesalius, Galileo, Kepler, Hobbs, Newton, Adam Smith, Darwin, Freud, Einstein, Fitzgerald, Hemmingway, and so-on. After each lecture, the books on the cart were wheeled over to join others open for perusal on the long library tables. The class of approximately twenty adults was invited to roam about and personally examine, even “thumb-through,” some of the greatest books ever written – many of them present in their rare, first editions. The instructor was available to answer any and all questions, and there were many.

Often, when the class was over and we had filtered out of the rare book library and into the dark, pleasant coolness of the spring evening, my head was spinning as I contemplated what I had seen…and touched. We students had the privilege of holding, in our own two hands, the well-springs which revealed much of humanity’s accumulated knowledge and wisdom – centuries-worth, many in their original, first edition formats. The total value of such books on the rare book market, today, is very high; their true value: Priceless.

A Reference Library – Steps Away

I have, over many years, accumulated a reference library on science and the history of science. These are books that, while very affordable, are valuable resources on scientific milestones and biography. Since I enjoy writing on matters scientific, it is handy to have these books nearby.

 

Above, you can see what happens when there are too many books and not enough bookshelves!

My wife loves books, too, and she has her own collection. She is a fan of the author/illustrator, Tasha Tudor, and this is one of her favorite items. Long live books!